tag:blogger.com,1999:blog-78672649951211086492024-03-06T01:43:46.355+00:00WCMBlograndom walks in a biological worldLinus Schumacherhttp://www.blogger.com/profile/09580921538587285737noreply@blogger.comBlogger32125tag:blogger.com,1999:blog-7867264995121108649.post-88732359662089118482015-08-11T18:33:00.000+01:002015-08-11T18:33:29.108+01:00Video: Squirrels, Cancers, and other Invaders<div class="separator" style="clear: both; text-align: left;">
Recently, at the <a href="http://www.newton.ac.uk/event/cgpw01" target="_blank">Isaac Newton Institute's program on Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation</a>, our very own Professor Philip Maini, FRS, gave another one of his classic talks, featuring (almost) everything from squirrels to cancer, including the admission of crying and how to cope with it (<a href="http://sd.keepcalm-o-matic.co.uk/i/keep-calm-and-just-drink-now.png" target="_blank">spoiler</a>). The talk was cleverly titled: "<strike>Case studies in modelling pattern formation</strike> Some other stuff"</div>
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Watch the video <a href="http://www.newton.ac.uk/seminar/20150720090010151" target="_blank">here</a>, or check out the <a href="http://www.newton.ac.uk/event/cgpw01/timetable" target="_blank">other videos from the workshop</a> and <a href="http://www.newton.ac.uk/science/programmes/future" target="_blank">future events</a> at the Newton Institute. And remember: "The devil is in the mesoscale!"</div>
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<tr><td style="text-align: center;"><a href="http://www.newton.ac.uk/files/covers/968265.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://www.newton.ac.uk/files/covers/968265.jpg" height="195" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Can you spot the devil? (image from the <a href="http://www.newton.ac.uk/event/cgp" target="_blank">program website</a>)</td></tr>
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Linus Schumacherhttp://www.blogger.com/profile/09580921538587285737noreply@blogger.com30tag:blogger.com,1999:blog-7867264995121108649.post-89847795647291919162014-11-24T15:14:00.002+00:002014-11-24T15:15:37.877+00:00Ebola Crisis Hackathon<div class="separator" style="clear: both; text-align: center;">
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNqXsAadsXVR98_c_bnfAylwW6Izf2LeAD5mRr1yIwhdsWK9VHI-feecN2hsL_qQa4wAXKLsWZU_sRLqs5PASBw0spAQPTyI4WOu4APBW1gcn8WX1PgInlaPmb-jziWQ0Bhzagyjx-mJYL/s1600/Ebola_virus_virion.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNqXsAadsXVR98_c_bnfAylwW6Izf2LeAD5mRr1yIwhdsWK9VHI-feecN2hsL_qQa4wAXKLsWZU_sRLqs5PASBw0spAQPTyI4WOu4APBW1gcn8WX1PgInlaPmb-jziWQ0Bhzagyjx-mJYL/s1600/Ebola_virus_virion.jpg" height="147" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The Ebola Virus has killed almost 6000 people in West Africa since Dec 2013</td></tr>
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Ebola has infected over 15000 people in West Africa since the start of the current outbreak in December 2013. The disease has an estimated case fatality rate of about 71%, and efforts to control the outbreak have been hampered by the political and economic situations in the countries affected (so far almost all cases have occurred in Liberia, Sierra Leone and Guinea). Problems have included, but are certainly not limited to, the extreme poverty in the region (including very limited infrastructure), a lack of trust in government officials, traditional death customs (e.g. physical contact with the dead) and the propensity of health workers to become infected with Ebola.<br />
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It was with these obstacles in mind that the Said Business School's <a href="http://www.sbs.ox.ac.uk/community/school-university/collaborations/oxford-launchpad">Oxford Launchpad</a> (which aims to support entrepreneurial endeavour in Oxford) organised and hosted the Ebola Crisis Hackathon, which aimed to "explore and solve 'pinch-points' in the response, care and management of the global response against Ebola". The hackathon (an exciting name for a workshop or study group, which has the consequence of labelling its participants as hackers, in this case making me sound much cooler and edgier than I am) was held on the weekend of the 8th-9th of November and brought together life-scientists, MBAs, software developers, physicians and charity workers.<br />
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Participants were encouraged to gather ideas over the week or so before the workshop and the event started on the Friday evening with brainstorming sessions. We worked in groups to generate and evaluate different ideas for solutions. The most popular ideas were then pitched to all participants, with groups forming around a few ideas.<br />
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While researching the problems around the diagnosis and treatment of Ebola, before the hackathon, I read about the <a href="http://www.bbc.com/future/story/20141017-the-ebola-detector-in-your-pocket">potential for Ebola to be diagnosed using mobile apps</a>. However I soon discovered that internet access was severely limited in West Africa (1.5% in Guinea, 1.3% in Sierra Leone and 3.8% in Liberia) which reduced the scope for using apps. However, mobile phone use is reasonably high (47% in Guinea, 52% in Liberia and 48% in Sierra Leone), and this encouraged me to think about developing similar systems using SMS text messages. I found that an open-source Django based package for writing SMS based systems had been developed and had been deployed in similar medical applications around Africa (<a href="https://www.rapidsms.org/">RapidSMS</a>).<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZxxNvCE0i3jiWCJVZKK8pLSpkLPl-McOnfrsomFOHkf20gqHa80185ZQiMkdyyMg_6lr8EG_tRXGFJB9IxaxFPVFNoXSOnh_I9AGryzNUoha-2qO-b5kMtKyD0c3eM4IRa2Afzw0qD71U/s1600/253px-Nokia_3310_blue.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZxxNvCE0i3jiWCJVZKK8pLSpkLPl-McOnfrsomFOHkf20gqHa80185ZQiMkdyyMg_6lr8EG_tRXGFJB9IxaxFPVFNoXSOnh_I9AGryzNUoha-2qO-b5kMtKyD0c3eM4IRa2Afzw0qD71U/s1600/253px-Nokia_3310_blue.jpg" height="320" width="135" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Mobile phones are a primary communication method in West Africa</td></tr>
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At the Hackathon, I teamed up with others who had had similar ideas. Given the severe lack of health workers in the affected region, we decided that a risk assessment tool would be particularly useful. Concerned individuals would text a number, and would receive a series of five questions on their symptoms and recent travel history. They would then be categorised into several risk categories and would be given automated advice by the system and, in some cases, have their details passed onto agencies who would be able to help. We worked in three subgroups: one looking at the risk assessment questions, another looking at the obstacles to deployment and one implementing the system in RapidSMS. <br />
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We called our product SymptomSMS and were mentioned in an <a href="http://www.newscientist.com/article/mg22429963.100-hackathon-develops-tech-tools-to-fight-ebola-epidemic.html#.VHM8MYWxucE">article</a> on the Hackathon in last week's New Scientist.Unknownnoreply@blogger.com7tag:blogger.com,1999:blog-7867264995121108649.post-23381566621995411622014-09-02T16:43:00.000+01:002014-09-02T16:43:09.146+01:00Maths in the city<div style="text-align: justify;">
<i>Outreach is an incredibly important part of a researcher's job. Many mathematicians are funded through research councils that rely on tax payer money, so we really should be able to justify the work that we do. One project set up to do just that is <a href="http://www.mathsinthecity.com/">Maths in the City</a>. WCMB members, <a href="http://people.maths.ox.ac.uk/~woolley/">Dr Thomas Woolley</a> and <a href="http://www.dtc.ox.ac.uk/people/12/ptaylor/">Paul Taylor</a>, were recently filmed demonstrating the tour. Here, Paul recounts the experience.</i></div>
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The close proximity of London is one of the perks of living in Oxford.
Residents trek to the capital for a wide range of reasons, but it's
probably safe to say that Thomas and I were the only people making the
journey on Thursday 21st August to run a mathematical
walking tour.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJHl6i5SxXeQNkBD6XrSRzCPRxjZJUkLJlTFwDquYsZaGhElZWGsc_IKjHi2HFyz74aqaullAUhK45ds7BrPDlyYdn2PCDddhXyDH5M8xbBUwtZBca2lj7YOks2Y0IMv7U2tzy2nuXIiY/s1600/logo.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJHl6i5SxXeQNkBD6XrSRzCPRxjZJUkLJlTFwDquYsZaGhElZWGsc_IKjHi2HFyz74aqaullAUhK45ds7BrPDlyYdn2PCDddhXyDH5M8xbBUwtZBca2lj7YOks2Y0IMv7U2tzy2nuXIiY/s1600/logo.png" /></a>Maths in the City tours are just one of the activities run by the
<a href="https://www.maths.ox.ac.uk/notices/mathemagicians">Mathemagicians</a>, an outreach group based in Oxford and championed by
Professor Marcus du Sautoy, the Simonyi Professor for the Public
Understanding of Science. They can be especially fun to run
because the tour groups are so varied. For example, we have had the privilege of meeting and guiding many national and international school groups, undergraduates, companies as well as the general public. Essentially, anyone who wants a glimpse of London from a mathematician's
perspective is welcome on our tours.
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The project caught the attention of <a href="http://www.londonlive.co.uk/">London Live</a>, who
asked if they could film a tour. The edited footage was broadcast as a
segment of "<a href="http://www.londonlive.co.uk/programmes/not-the-one-show">Not the One Show</a>", and can still be seen online.<br />
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For anyone curious about the snippets of activities shown in the video,
the opening shot is a live-action demonstration of the famous Bridges of
Koenigsberg problem. The slinky, and the swinging weights, are being
used to explain why the Millennium Bridge swayed
so alarmingly when first constructed. The full tour includes much more,
such as the topology of the Tube, and the shapes of the domes of St
Paul's Cathedral (yes, 'domes': there are actually three, but one is
hidden...) Full details of all the activities are
available on the <a href="http://www.mathsinthecity.com/tours/maths-city-london?full=1">Maths in the City website</a>.</div>
Thomas Woolleyhttp://www.blogger.com/profile/07895826981003298350noreply@blogger.com1tag:blogger.com,1999:blog-7867264995121108649.post-91627987114100104402014-06-25T16:50:00.000+01:002014-06-25T16:54:08.578+01:00On tweetcasting<i>After a travel- and conference-induced</i> <i>silence over the past months, we're back from the ECMTB in Gothenburg with some fresh thoughts for new posts. To start, Alex Fletcher, Linus Schumacher and Jacob Scott discuss a newly fashionable conference activity: tweetcasting.</i><br />
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<a name='more'></a>An increasing number of academics are <a href="http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001535">using twitter professionally</a>. One popular usage is tweetcasting presentations at conferences. This can range from advertising your own or your peer's research to live commenting - essentially taking notes publicly on twitter.<br />
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For a recent example of tweetcasting from the <a href="http://ecmtb2014.org/" target="_blank">ECMTB 2014</a> see the <a href="https://storify.com/" target="_blank">Storify</a> by <a href="http://cancerconnector.blogspot.co.uk/" target="_blank">Dr Jacob Scott</a> <a href="http://cancerconnector.blogspot.co.uk/2014/06/ecmtb-2014-in-goteborg-sweden.html" target="_blank">on his blog</a>.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://pbs.twimg.com/media/BqZmUlVCQAAtnGE.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="240" src="https://pbs.twimg.com/media/BqZmUlVCQAAtnGE.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">A packed audience <a href="https://twitter.com/ECMTB2014" target="_blank">@ECMTB2014</a>. Can you spot the tweetcasters?</td></tr>
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Tweetcasting can be incredibly useful to someone stuck in a different parallel session or not even attending the conference or seminar in question, especially when tweets are archived as a Storify or blog post afterwards.<br />
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However, the high frequency of tweets from often multiple people simultaneously can dominate one's feed and drown it in duplicated tweets and re-tweets of content irrelevant to you. Worse, it can take statements out of context. Worse still, a picture of a slide of unpublished work can expose it to greater danger of being scooped.<br />
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Some best practices to consider are:<br />
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1 - make sure that your tweets could be of value to people not involved in the session/conference by including links to speakers websites, papers being presented or informational pages<br />
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2 - ensure you are using the same hashtag (keep it saved to your clipboard, or use an app) to increase speed and to enable aggregation with an app like <a href="http://www.storify.com/">storify</a><br />
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3 - try not to take quotes out of context<br />
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4 - if you are giving a talk, and DON'T want your info tweeted, just ask at the beginning of the session, or better yet, if you are chairing a session, ask all of the presenters and then announce at the beginning a policy for the session<br />
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What do you think? Is tweetcasting a useful form of science communication or should tweetcasters chirping away better spend their time offline? Share your thoughts in the comments below.<br />
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*WCMB members on twitter: <a href="https://twitter.com/ruth_baker" target="_blank">Ruth Baker</a>, <a href="https://twitter.com/FergusCooper" target="_blank">Fergus Cooper</a>, <a href="https://twitter.com/AlexGFletcher" target="_blank">Alex Fletcher</a>, <a href="https://twitter.com/haharrington" target="_blank">Heather Harrington</a>, <a href="https://twitter.com/omaclaren" target="_blank">Oliver MacLaren</a>, <a href="https://twitter.com/ParkerAndrew91" target="_blank">Andrew Parker</a>, <a href="https://twitter.com/LinusSchumacher" target="_blank">Linus Schumacher</a>, <a href="https://twitter.com/CancerConnector" target="_blank">Jacob Scott</a>, <a href="https://twitter.com/ThomasEWoolley" target="_blank">Thomas Woolley</a>, <a href="https://twitter.com/Kit_Yates_Maths" target="_blank">Kit Yates</a>Linus Schumacherhttp://www.blogger.com/profile/09580921538587285737noreply@blogger.com2tag:blogger.com,1999:blog-7867264995121108649.post-7741430418387584422014-04-06T11:30:00.000+01:002014-04-06T11:30:00.572+01:00James D Murray, Reflections of a life in Academia, in conversation with Phillip MainiFounder of the WCMB, <a href="https://en.wikipedia.org/wiki/James_D._Murray" target="_blank">James Murray</a>, visited Oxford last month to give the inaugural <a href="https://en.wikipedia.org/wiki/Robert_Hooke#" target="_blank">Hooke</a> lecture, <a href="http://podcasts.ox.ac.uk/why-there-are-no-three-headed-monsters-resolving-some-problems-brain-tumours-divorce" target="_blank">"Why there are no three-headed monsters, resolving some problems with brain tumours, divorce prediction and how to save marriages"</a>. While he was here, he was interviewed by his former student and our current director <a href="https://people.maths.ox.ac.uk/maini/" target="_blank">Prof. Philip Maini</a>, featuring questions from various members of the WCMB. You can watch the interview <a href="http://podcasts.ox.ac.uk/james-d-murray-reflections-life-academia-conversation-phillip-maini">here</a> as part of the podcast series <a href="http://podcasts.ox.ac.uk/series/secrets-mathematics" target="_blank">The Secrets of Mathematics</a>.Linus Schumacherhttp://www.blogger.com/profile/09580921538587285737noreply@blogger.com8tag:blogger.com,1999:blog-7867264995121108649.post-70369549803759468462014-03-31T10:53:00.002+01:002014-03-31T21:39:34.819+01:00Discrete and continuous models for tissue growth and shrinkage<div style="text-align: justify;">
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<![endif]--><span style="font-family: inherit;"><i><span style="line-height: 115%;">In
this post </span></i><span style="line-height: 115%;"><a href="http://people.maths.ox.ac.uk/yatesc/" target="_blank"><i>Dr. Christian Yates</i></a></span><i><span style="line-height: 115%;"> summarises his recent paper “</span></i><span style="line-height: 115%;"><a href="http://www.sciencedirect.com/science/article/pii/S0022519314000605"><i style="mso-bidi-font-style: normal;">Discrete and continuous models for tissue growth
and shrinkage</i></a></span><i><span style="line-height: 115%;">”, on modelling tissue growth and shrinkage using mathematical models that explicitly incorporate randomness in the tissue deformation process.</span></i></span></div>
<a name='more'></a><div style="text-align: justify;">
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<span style="font-family: inherit;"><span style="font-size: small;">The mathematical theme which underlies my research is the development of methodologies for modelling complex biological systems in which randomness (often referred to as stochasticity) plays an important role. In particular, I am interested in modelling complex processes in which the incorporation of noise can produce mean behaviour that differs significantly from the behaviour of a corresponding deterministic model. I am also interested in modelling systems for which, because of their inherent dependence on noise, there is no deterministic counterpart.</span><span style="font-size: small;">
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<span style="font-family: inherit; font-size: small;">The
incorporation of domain growth into stochastic models of biological processes
is of increasing interest to mathematical modellers and biologists alike. In
many situations, especially in developmental biology, the growth of the
underlying tissue domain plays an important role in the redistribution of
particles (be they cells or molecules) which may move and react atop the
domain. Although such processes have largely been modelled using deterministic
(non-random), continuum models, there is an increasing appetite for
individual-based stochastic (random) models, which can capture the fine detail
of the biological movement processes that are being elucidated by modern
experimental techniques, and can also incorporate the inherent stochasticity of
such systems. </span></div>
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<span style="font-family: inherit; font-size: small;">I recently had a paper published in the <a href="http://www.sciencedirect.com/science/article/pii/S0022519314000605">Journal of Theoretical Biology</a> on this subject. In this paper I study a simple stochastic
model of domain growth/shrinkage. From a basic version of this model, <a href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.88.032704">Hywood et al.</a> were able to derive a Fokker-Plank equation (FPE) (in this case, an
advection-diffusion partial differential equation on a growing domain), which
describes the evolution of the probability density of some tracer particles on
the domain. My paper extends their work so that a variety of different domain
growth mechanisms can be incorporated. I demonstrate a good agreement between
the mean tracer density and the solution of the FPE in each case. In addition
I incorporate domain shrinkage (via element death) into my individual-level
model and demonstrate that I am also able to derive coefficients for the FPE in
this case. For situations in which the drift and diffusion coefficients
are not readily available, I introduce a numerical coefficient estimation approach.</span></div>
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<span style="font-family: inherit; font-size: small;">The basic
individual-based model I use to represent tissue growth/shrinkage is a one-dimensional
domain of made up initially of contiguous elements each of length Δ. I incorporate
growth and shrinkage into this individual-level model by allowing these
elements to undergo ‘proliferation events’ and ‘death events’, which are
analogous to biological cell division and cell death. In order to better understand
the dynamics of the domain growth/shrinkage process, we can place tracer
particles on top of a subset of the domain elements. We say that these domain
elements are ‘marked’. The movement of the domain elements and the tracer
particles resulting from a growth or death event are summarised in Figures 1
and 2.</span></div>
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<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><span style="color: black; font-family: inherit;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUkJq3dXkJA4mkqyQn2DIW7mpqZ_4sVfDZTuHhKNdfmr0RX6OVSTJGfll01zFJwV4YIABnErmqE90haYp7P6nJ_049bxUYC6TDL7LPf1geyrfrvr_SZJQopvi_LXWR-c0rGKpcoy2pSIo/s1600/Slide1_crop.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUkJq3dXkJA4mkqyQn2DIW7mpqZ_4sVfDZTuHhKNdfmr0RX6OVSTJGfll01zFJwV4YIABnErmqE90haYp7P6nJ_049bxUYC6TDL7LPf1geyrfrvr_SZJQopvi_LXWR-c0rGKpcoy2pSIo/s1600/Slide1_crop.JPG" height="112" title="" width="320" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: inherit;">(a)</span></td></tr>
</tbody></table>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><span style="color: black; font-family: inherit;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5KRBZnNdw5da8JHP5LJVOCu3AazzdluZFl9bciIL-bLn3i6r8RM4XyGdXjl79_ChK7_4ZuGLfhw0FFzxJcib6gtZF1o7_iqst_CmDT2zyE1O3RdjL0fLkqnjlLC53KocY7EWzSNwEI8g/s1600/Slide2_crop.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5KRBZnNdw5da8JHP5LJVOCu3AazzdluZFl9bciIL-bLn3i6r8RM4XyGdXjl79_ChK7_4ZuGLfhw0FFzxJcib6gtZF1o7_iqst_CmDT2zyE1O3RdjL0fLkqnjlLC53KocY7EWzSNwEI8g/s1600/Slide2_crop.JPG" height="112" width="320" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: inherit;">(b)</span></td></tr>
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<span style="font-family: inherit; font-size: x-small;">Figure 1:<i> Examples of growth and division events. Domain elements
are white boxes and tracer particles are represented by smaller red boxes atop
particular ‘marked’ elements. In each subfigure the top </i><i>configuration shows a domain
before a growth event and the bottom a domain configuration after a growth
event. (a) An unmarked element is chosen to divide. It does so by pushing
itself and the intervals to its right one element length, </i>Δ<i>. Tracer particles move with the
elements and a new element (hatched) is inserted in the empty space. (b) A
marked element is selected to divide. It undergoes the
same movement procedure as for the unmarked element taking its tracer particle with
it. Again a new element (hatched) is inserted in the vacant space.</i></span></div>
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<tr><td style="text-align: center;"><span style="color: black; font-family: inherit;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgh7i7XtbAiXGvsuj70PM5f_ov3IaMuvIFsDLQUEgE0KDwRqAWgtLM2keJC6K1W2Pw8ZMKNvTLwiuiCBkhPDFvaq8aAh1-caF4MnE_TZqMlDY5IjMvoKP8eZQU_7gyjB-RG-o09IsMoSbw/s1600/Slide3_crop.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgh7i7XtbAiXGvsuj70PM5f_ov3IaMuvIFsDLQUEgE0KDwRqAWgtLM2keJC6K1W2Pw8ZMKNvTLwiuiCBkhPDFvaq8aAh1-caF4MnE_TZqMlDY5IjMvoKP8eZQU_7gyjB-RG-o09IsMoSbw/s1600/Slide3_crop.JPG" height="129" width="320" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: inherit;">(a)</span></td></tr>
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<span style="font-family: inherit;"><br /></span></div>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><span style="color: black; font-family: inherit;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrgGkd7TtQNe1mrCUsYfwkgGEvPL9aKUO-EAUsSqSBA5u6pvmwikbYOpLGLUDeW_4EKs7-og0P26JS7M3lKr7gdLVYCLmFt7Bffol9ULfhQEp22nGSgbk1_v67EmwGr0jtD39eR58HhVc/s1600/Slide4_crop.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrgGkd7TtQNe1mrCUsYfwkgGEvPL9aKUO-EAUsSqSBA5u6pvmwikbYOpLGLUDeW_4EKs7-og0P26JS7M3lKr7gdLVYCLmFt7Bffol9ULfhQEp22nGSgbk1_v67EmwGr0jtD39eR58HhVc/s1600/Slide4_crop.JPG" height="129" width="320" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: inherit;">(b)</span></td></tr>
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<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><span style="color: black; font-family: inherit;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6SW-q5M6dQ1fWDNyAS3VX4Nsql9kUJaxGGliU2bZXC5czmw9Qk16udiDjrWRPR79nnJcDnXJK9bzneaVzjB-8hh_q1fKwzDoDIf9ID4mtMoHr38qymvyc5_cXhQizojPF5AYx3Jns2vY/s1600/Slide5_crop.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6SW-q5M6dQ1fWDNyAS3VX4Nsql9kUJaxGGliU2bZXC5czmw9Qk16udiDjrWRPR79nnJcDnXJK9bzneaVzjB-8hh_q1fKwzDoDIf9ID4mtMoHr38qymvyc5_cXhQizojPF5AYx3Jns2vY/s1600/Slide5_crop.JPG" height="129" width="320" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: inherit;">(c)</span></td></tr>
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<span style="font-family: inherit; font-size: x-small;">Figure 2: <i>Examples of element
death events. Domain elements are white boxes and tracer particles are
represented by smaller red boxes atop particular ‘marked’ elements. In each
subfigure the top </i><i>configuration
shows a domain before a death event and the bottom a domain configuration after
a death event. (a) An unmarked element (hatched) is chosen to die. It is
removed from the domain and intervals to its right move leftwards by one
element length, </i>Δ<i>, to fill the space. Tracer
particles move with their elements. (b) A marked element (hatched) is chosen to
die. It is removed from the domain. However its tracer particle remains in place. The elements to the right of the dead
element move to the left one element length, </i>Δ<i>, and a previously
unmarked element becomes marked. </i><i>(c) A
marked element (hatched) dies and is removed. Its tracer particle remains where
it is and causes the already marked element that was immediately to the right
of the dead element to become doubly marked as it moves into the vacant space.
There is no limit to how many tracer particles an element can accrue.</i></span></div>
</div>
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<div style="text-align: justify;">
<span style="font-family: inherit;"><br /></span></div>
</div>
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<div style="text-align: justify;">
<span style="font-family: inherit; font-size: small;"><u>Deriving the continuum model</u></span></div>
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<div style="text-align: justify;">
<span style="font-family: inherit; font-size: small;">By changing the rate at which domain elements grow or die we can incorporate a variety of
different types of domain growth/shrinkage. For each of these different types
of tissue re-arrangement, using the first two <i>infinitesimal moments</i> (specifically the infinitesimal mean, &#956, and the infinitesimal
variance, &#963<sup>2</sup>) of the domain growth process
we can derive a continuum representation of the density of the tracer particles,
<i>C(x,t),</i> on the domain:</span></div>
</div>
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<a href="https://www.blogger.com/blogger.g?blogID=7867264995121108649" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="" border="0" height="35" 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" style="cursor: move;" width="320" /></a></div>
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<span style="font-family: inherit; font-size: small;">These infinitesimal moments can be generated by considering moment generating
functions of the corresponding birth processes.</span></div>
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<span style="font-family: inherit; font-size: small;">Our generalised method allows for the derivation of the
corresponding continuum model for a range of growth rates in the individual-based model: (i) Exponential growth, used to model elongation
of the developing intestinal tract of the quail embryo, growth of sections of
the embryos of the alligator <i>Alligator
mississippiensis, </i>the
initiation and positioning of teeth primordia in the same alligator species and
the early stages of unconstrained cancerous tumour growth); (ii) Linear growth, used to model the early
development of some fish, seeds and body sections of reptile embryos; (iii) Generalised logistic growth, used to model distance
from the dorsal neural tube midline to the distal tip of the lateral mesoderm
in chick embryos (a relevant cell migratory pathway) and the increase in mass
of reptile and bird embryos; (iv) Gompertzian growth, used to model organ
growth, tumour growth and alligator teeth patterning. Comparisons of the
individual-based models and their continuum counterparts for three different growth rates are given in Figure3.</span></div>
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<span style="font-family: inherit; font-size: small;"><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiklPMHFD3CtGjnZ2wpC6O68ytPwV2QK8aLjkj9KLwEtCSUcdOG6yOe8e4uUTSe78nJJIiI5lVOtBlgpi2JzAdu-uSPndDDQMkzVZ4To8rfYsYr6Sh5i9jIqvNjRpngWwK7z4RjHimpmss/s1600/exponential.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiklPMHFD3CtGjnZ2wpC6O68ytPwV2QK8aLjkj9KLwEtCSUcdOG6yOe8e4uUTSe78nJJIiI5lVOtBlgpi2JzAdu-uSPndDDQMkzVZ4To8rfYsYr6Sh5i9jIqvNjRpngWwK7z4RjHimpmss/s1600/exponential.jpg" height="241" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">(a)</td></tr>
</tbody></table>
</span></div>
<div style="text-align: justify;">
<span style="font-family: inherit;"><br /></span></div>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><span style="color: black; font-family: inherit;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg30MX3NEjOtNMchwHfbHN7mQA-xC-LxkQ_0n5WiFuDT3hdUKW6AqZqC18Pv4d10Mf2Ajz4dtKaZ-oyWxHvI1pCCPeP2c_nx1xnZrKvr685YfXXVDB7VR7t6dXLaliStbJEMUF-onmkjPE/s1600/linear.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg30MX3NEjOtNMchwHfbHN7mQA-xC-LxkQ_0n5WiFuDT3hdUKW6AqZqC18Pv4d10Mf2Ajz4dtKaZ-oyWxHvI1pCCPeP2c_nx1xnZrKvr685YfXXVDB7VR7t6dXLaliStbJEMUF-onmkjPE/s1600/linear.jpg" height="239" width="320" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: inherit;">(b)</span></td></tr>
</tbody></table>
<div style="text-align: justify;">
<span style="font-family: inherit;"><br /></span></div>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><span style="color: black; font-family: inherit;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEBZVDj4TX-C2MCg4-Lro11q_SiVSzWW6sJgEmstC0FPZ2l0aTTUeBrTlzC1CP7K21H_xkzcX6yn9nnic2lQ6hyD0GKa_u5JD3CkB911kkhl6VwLubwb1q6GDtky7xTeJFc5AFOGLofKs/s1600/generalised_logistic.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEBZVDj4TX-C2MCg4-Lro11q_SiVSzWW6sJgEmstC0FPZ2l0aTTUeBrTlzC1CP7K21H_xkzcX6yn9nnic2lQ6hyD0GKa_u5JD3CkB911kkhl6VwLubwb1q6GDtky7xTeJFc5AFOGLofKs/s1600/generalised_logistic.jpg" height="241" width="320" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: inherit;">(c)</span></td></tr>
</tbody></table>
<div style="text-align: justify;">
<span style="font-family: inherit;"><br /></span></div>
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<span style="font-family: inherit; font-size: x-small;">Figure 3:<i> A comparison, at different times, of the expected
occupancy of tracer particles on (a) an exponentially growing domain (b) a linearly
growing domain and (c) a domain growing in according to generalised logistic
growth. The red curves represent the solution of the Fokker-Planck equation</i> <i>and the (noisy) black
curve represents the expected density of tracer particles averaged over 10,000 realisations
of the individual based model. In all three cases </i><i>the initial
number of domain elements is </i>60<i>, each of length </i>Δ= ½,<i> with tracer particles initially between </i>15 ≤ x ≤ 20<i>. The curves are plotted at </i><i>t </i>= 15<i>, </i>30<i>, </i>45<i>, </i>60<i>. </i></span></div>
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<span style="font-family: inherit; font-size: small;"><u>Domain Shrinkage</u></span></div>
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<span style="font-family: inherit; font-size: small;">The modelling of domain shrinkage
is important for two reasons: (i) the explicit
representation of domain shrinkage is often necessary for a range of
application areas including wound healing, for example, (ii) the
incorporation of element death is important in situations where domain elements
may proliferate and die even if the net growth rate is positive. The second
point is more subtle: it might be argued that domain growth in which element
death is possible but the growth rate, <i>b</i>(<i>t</i>), outweighs the death rate, <i>d</i>(<i>t</i>), can be modelled using a purely
growing domain with a reduced positive growth rate, <i>λ</i>(<i>t</i>) = <i>b</i>(<i>t</i>) − <i>d</i>(<i>t</i>). However, this argument is
incorrect since, although the mean growth rate may be estimated correctly, the
second and higher order moments of the process will be incorrect (<i>c.f. </i>Figure 3 (a) and Figure 4 (a). Both
model exponential domain growth with the same net rate, but Figure 3 (a) shows
the results from a purely growing domain where as domain elements of the domain
used to generate Figure 4 (a) were capable of death as well as growth). In
particular, one stark difference is that the domain in which death is
incorporated explicitly will shrink to zero size with a non-zero probability,
whereas there is no possibility of this happening in the purely growing domain
with reduced net growth rate.</span></div>
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<span style="font-family: inherit; font-size: small;">In order to illustrate the
importance of domain shrinkage we incorporate elemental death into the model of
domain growth and also consider a pure domain shrinkage model (see Figure 4).
The infinitesimal moments required to populate the Fokker-Planck equation can
be found by generalising the moment generating function approach to birth-death
processes. </span></div>
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<tr><td style="text-align: center;"><span style="color: black; font-family: inherit;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPuH8MV1mk9tmz5U-_cWkVpPFFDN8mMcTHq7ido6E7oDfp8Ri2a_aFQmO97Y_nnmO1BVqQz7NIGdXx_OW6Xp50tawG2agBfJ6ernMCyW_Z5-qh8SLscW7VyrHqrsee4EK-mngIvQ9ZFls/s1600/exponential_birth_death.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPuH8MV1mk9tmz5U-_cWkVpPFFDN8mMcTHq7ido6E7oDfp8Ri2a_aFQmO97Y_nnmO1BVqQz7NIGdXx_OW6Xp50tawG2agBfJ6ernMCyW_Z5-qh8SLscW7VyrHqrsee4EK-mngIvQ9ZFls/s1600/exponential_birth_death.jpg" height="238" width="320" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: inherit;">(a)</span></td></tr>
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<tr><td style="text-align: center;"><span style="color: black; font-family: inherit;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhecms3kgrJdcw8joCf-pcfnH5l3cbjE-5-eprFv8OtfXyZVlfKIzLc2miTCOyP2gy3vwXY0ahB-b3NtVdZyghQhQM2iAtkIU-Ux9PegbyOhsgafADFeS-D91-Su4U_YvOtpBDSkQOuwtE/s1600/exponential_death.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhecms3kgrJdcw8joCf-pcfnH5l3cbjE-5-eprFv8OtfXyZVlfKIzLc2miTCOyP2gy3vwXY0ahB-b3NtVdZyghQhQM2iAtkIU-Ux9PegbyOhsgafADFeS-D91-Su4U_YvOtpBDSkQOuwtE/s1600/exponential_death.jpg" height="250" width="320" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: inherit;">(b)</span></td></tr>
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<span style="font-family: inherit; font-size: x-small;">Figure 4:<i> A comparison, at different times, of the expected
occupancy of tracer particles on (a) a domain growing exponentially with constant birth and death
rates, </i><i>b > d (b) </i><i>an exponentially shrinking domain with </i><i>constant death rate, </i><i>d.</i><i> Figure descriptions and initial conditions for (a) are as in Fig. </i><i>3. For
(b) </i><i>the initial number of domain elements is </i><i>600</i><i>, each of length </i><i>Δ= ½,</i><i> with tracer particles
initially between </i><i>150 </i><i>≤ </i><i>x </i><i>≤ </i><i>200. Note that for (b), the time arrow is in the opposite
direction.</i></span></div>
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<span style="font-family: inherit; font-size: small;"><u>Conclusions</u></span></div>
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<span style="font-family: inherit; font-size: small;">Our generalised method allows
the analytical derivation of the associated drift and diffusion coefficients
for any time-dependent growth rate in the individual-based model. In addition,
we have incorporated the possibility of elemental death into the
individual-based model and derived the coefficients of the corresponding PDE
for these general time-dependent birth and death rates. This approach highlights
that a process in which both elemental birth and death occur cannot simply be
approximated by a birth-only process with the reduced net growth rate since,
although the drift coefficient may be correct, the diffusion coefficient will
not be. Clearly, in situations in which the net birth rate is negative a simple
birth process will not suffice.</span></div>
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<span style="font-family: inherit; font-size: small;">For representative examples of
our pure-birth, birth-death and pure-death processes we have carried out
numerical simulations which contrast the expected tracer density in the
individual-level model with the solution of the continuous PDE model and we see
good agreement in each case.</span></div>
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<span style="font-family: inherit;"><br /></span></div>
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<div style="text-align: justify;">
<span style="font-family: inherit; font-size: small;"><span style="line-height: 115%;">As yet we have considered only the relatively straight-forward case of
uniformly growing domains in which each element is selected to proliferate or die
with equal probability. It is not immediately evident what effect, allowing anisotropic
element proliferation will have on the corresponding drift and diffusion
coefficients. </span><span style="line-height: 115%;">A further challenge will lie in the adaptation of
these methods to multivariate diffusion
processes which will correspond to higher dimensional PDEs. Since tissue growth is an important factor in the
transport of cells across the domain, and often does not occur uniaxially or
uniformly, these extensions will constitute an
important step forward in our ability to model cell migration effectively at both and individual and collective
level.</span></span></div>
Unknownnoreply@blogger.com5tag:blogger.com,1999:blog-7867264995121108649.post-45476748533900822692014-03-24T16:08:00.000+00:002014-03-24T16:45:09.225+00:00Understanding the host-virus interaction in chronic HTLV-I infection with the help of mathematical modelling<span style="font-family: inherit;"><span style="font-size: small;"><i>In this post <a href="https://www.maths.ox.ac.uk/people/profiles/aaron.lim" target="_blank">Aaron Lim</a>, a DPhil student at the WCMB and the EEID, discusses his work on within-host mathematical modelling of host-virus interactions.</i></span></span><br />
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<span style="font-family: inherit;"><span style="font-size: small;"><b>Introduction</b></span></span><br />
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<span style="font-family: inherit;"><span style="font-size: small;"><b><u><br /></u></b>I am interested in building a better understanding of the host-virus dynamics of chronic viral infections, specifically in the context of human T-cell lymphotropic virus type I (HTLV-I), which is in fact the first discovered human retrovirus, identified independently by researchers in both Japan and the United States in the late 1970's to early 1980's. I was introduced to this topic during my M. Sc. programme at the University of Alberta in Canada, under the supervision of <a href="http://www.math.ualberta.ca/~mli/" target="_blank">Prof Michael Li</a>, and was fascinated by the observation that, despite three decades of HTLV-I research, there still remained many unanswered questions about the mechanisms of viral persistence and immunopathology. After completing my M. Sc., I decided to continue my research by pursuing a DPhil here at Oxford, where I am jointly supervised by <a href="https://people.maths.ox.ac.uk/maini/" target="_blank">Prof Philip Maini</a> in the <a href="http://www.maths.ox.ac.uk/groups/mathematical-biology" target="_blank">Wolfson Centre for Mathematical Biology (WCMB)</a>, and <a href="http://www.zoo.ox.ac.uk/people/view/gupta_s.htm" target="_blank">Prof Sunetra Gupta</a> in the <a href="http://www.eeid.ox.ac.uk/" target="_blank">Evolutionary Ecology of Infectious Disease (EEID)</a> group at the Department of Zoology. It is my belief that mathematical modelling, alongside experimental advances, can help us break apart the complex mechanisms of the host-virus interaction and identify the key underlying principles of persistent infection in the presence of host immunity. In this post, I will discuss a within-host model of HTLV-I that we have developed which forms the foundation of my DPhil project.</span><span style="font-size: small;"><br /></span></span></div>
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<span style="font-family: inherit;"><span style="font-size: small;"><b><br /></b></span></span>
<span style="font-family: inherit; font-size: small;"><b>Background and Motivation</b></span><span style="font-size: small;"><br /><br /><span style="font-family: inherit;">Human T-lymphotropic virus type I (HTLV-I) is a persistent human retrovirus characterised by life-long infection and risk of developing one of two major, clinically independent diseases: adult T-cell leukaemia/lymphoma (ATL), an aggressive blood cancer, and HAM/TSP, a progressive neurological and inflammatory disease. The virus primarily infects CD4+ helper T-cells, a </span>subset<span style="font-family: inherit;"> of lymphocytes whose principal role is to enhance the function of adaptive immunity, for example, by secreting pro-inflammatory cytokines, facilitating antigen presentation, and triggering the activation of other types of immune cells. Infected individuals typically mount a large, chronically activated CD8+ cytotoxic T-lymphocyte (CTL), or so-called 'killer T-cell', response against HTLV-I-infected cells, but ultimately fail to effectively eliminate the virus. Moreover, identification of determinants to disease manifestation has thus far been elusive.</span><br /><br /><span style="font-family: inherit;">How the virus is able to evade host immunity and avoid viral clearance is a key issue in current HTLV-I research. Understanding the complex mechanisms of HTLV-I persistence is a crucial step to developing effective ways to disrupt the virus life-cycle and may help identify promising new treatment strategies to reduce the severity of HTLV-I infection and associated disease. Therefore, we focus our efforts on elucidating this issue.</span><br /><br /><b style="font-family: inherit;"> Methodology</b></span></div>
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<span style="font-family: inherit;"><span style="font-size: small;">Asquith and Bangham (2008) have recently proposed an experimental hypothesis for the persistence of HTLV-I in vivo which motivated the formulation of a mathematical model by Li and Lim (2011) that illustrates the balance between latency and activation in the target cell dynamics of the viral infection (this was work done during my M. Sc.). In the first part of my DPhil, I have extended this previous model by incorporating the role of a constantly changing anti-viral immune environment mediated by CTLs. The resulting model, which I term the 'baseline model', is a four-dimensional system of ordinary differential equations that describes the dynamic interactions among viral expression, infected target cell activation, and the HTLV-I-specific CTL response. A schematic picture of the baseline model is shown below:</span></span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDRmCi5syXt66L3tBJ1NxsQr6l9-jt7ASbJaDpzTLSrRyPaT2n8EzMhqTTk3SUKnjA1CdUUFfTlBOcabCCAUIqseVg7xZVG-RPPkPRXk_qbox8ItQSS1fYmwtw55C-7zcrsTRNtdrxDeg/s1600/schematictransferpaper.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDRmCi5syXt66L3tBJ1NxsQr6l9-jt7ASbJaDpzTLSrRyPaT2n8EzMhqTTk3SUKnjA1CdUUFfTlBOcabCCAUIqseVg7xZVG-RPPkPRXk_qbox8ItQSS1fYmwtw55C-7zcrsTRNtdrxDeg/s1600/schematictransferpaper.png" height="217" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">A schematic representation of the biological mechanism of HTLV-I infection <i>in vivo</i> that motivates the formulation of the baseline model. Figure reproduced (with slight modifications) from Lim and Maini (2014).</td></tr>
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<span style="font-family: inherit;"><span style="font-size: small;">To fully understand the dynamics of our baseline model, we have made use of standard mathematical techniques including non-dimensionalisation, stability, asymptotic, and bifurcation analyses to investigate the system. We have identified a sharp threshold parameter, the basic reproduction number for viral infection R</span><span style="font-size: xx-small;">0</span><span style="font-size: small;">, which completely characterises the global behaviour of solutions to the model: if R</span><span style="font-size: xx-small;">0</span><span style="font-size: small;"> < 1, the infection is cleared; if R</span><span style="font-size: xx-small;">0</span><span style="font-size: small;"> > 1, the infection is chronic. The global stability of the respective equilibria in each of the two cases for R</span><span style="font-size: xx-small;">0</span><span style="font-size: small;"> has been shown by constructing appropriate Lyapunov functions.<br /><br />After having established the global dynamics of the model, we asked biologically relevant questions relating to HTLV-I persistence and used the model to try and address these issues. In particular, we explored the roles of certain key parameters on the outcome of the infection dynamics using bifurcation analysis and computational methods. We focussed on three issues: (i) Why is HTLV-I not silent? In other words, what benefit does the HTLV-I provirus gain in becoming activated and expressing viral antigens? (ii) What role do CTLs play in the outcome of infection? (iii) Do our results give insights to the development of HTLV-I-associated disease?</span></span></div>
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<span style="font-family: inherit;"><span style="font-size: small;"><b><br /></b></span></span>
<span style="font-family: inherit;"><span style="font-size: small;"><b>Main Biological Conclusions</b></span></span></div>
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<span style="font-family: inherit;"><span style="font-size: small;"><br /></span></span></div>
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<span style="font-family: inherit;"><span style="font-size: small;">Our baseline mathematical model of HTLV-I infection offers important insights to the evolution of viral persistence. A few main results arising from the model are the following.</span></span><br />
<span style="font-family: inherit;"><span style="font-size: small;">
</span></span>
<br />
<ul>
<li><span style="font-size: small;">Infected target cell activation and expression of viral antigens is required for the establishment of HTLV-I infection and aids viral persistence.</span></li>
<span style="font-size: small;">
<li>The HTLV-I-specific CTL response determines proviral load despite frequent viral latency, yet is unable to completely eliminate the virus due to the small proportion of activated proviral cells that are aggressively propagating the infection. Moreover, efficient control of viraemia is dependent on a high rate of CTL-mediated lysis and not on the frequency of HTLV-I-specific immune effectors.</li>
<li>The extent of proviral activation rather than the size of the proviral load may distinguish clinical status and suggests a route for disease.</li>
</span></ul>
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<span style="font-family: inherit;"><span style="font-size: small;">
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<span style="font-family: inherit;"><span style="font-size: small;"><b>Outlook and the Road Ahead</b></span></span><br />
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<span style="font-family: inherit;"><span style="font-size: small;">The purpose of the baseline model was to develop a consistent theoretical framework that can help shed light on specific, biologically relevant questions that are of interest to experimentalists and theoretical immunologists trying to understand the complicated host-pathogen dynamics of chronic viral infections such as HTLV-I. However, we have only just scratched the surface; there are still many interesting aspects of the host-virus interaction that require deeper exploration. It is with hope that, with the rise of interdisciplinary collaborations, we can use each of our respective tools and areas of expertise to work together and build a clearer picture of all these issues.</span></span><br />
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<span style="font-family: inherit;"><span style="font-size: small;"><b>References</b></span></span></div>
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<div>
<span style="font-family: Georgia, 'Times New Roman', serif;"><span style="font-size: x-small;"><br /></span></span>
<span style="font-family: Georgia, 'Times New Roman', serif;"><span style="font-size: x-small;">B. Asquith and C. R. M. Bangham (2008). How does HTLV-I persist despite a strong cell-mediated response?, <i>Trends in Immunol.</i>, 29:4--11.</span></span></div>
<div>
<span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><br />M. Y. Li and <b>A. G. Lim</b> (2011). Modelling the Role of Tax Expression in HTLV-I Persistence in vivo. <i>Bull. Math. Biol.</i>, 73:3008-29.<br /><br /><b>A. G. Lim</b> and P. K. Maini (2014). HTLV-I infection: A dynamic struggle between viral persistence and host immunity. <i>J. Theor. Biol.</i>, http://dx.doi.org/10.1016/j.jtbi.2014.02.022i </span></div>
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Unknownnoreply@blogger.com3tag:blogger.com,1999:blog-7867264995121108649.post-25712042895027923202014-03-17T17:45:00.000+00:002014-03-17T17:45:02.953+00:00Taking randomness into account<div dir="ltr">
<span style="font-family: inherit;"><span style="font-size: small;"><i>In this post <a href="https://people.maths.ox.ac.uk/dobramysl/">Dr. Ulrich Dobramysl</a>, a Postdoctoral Research Assistant working at the WCMB, discusses stochastic modelling and randomness in biological systems.</i></span></span><br />
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<span style="font-family: inherit;">My work focusses on the modelling of biological systems involving some sort of randomness. I try to understand and quantify the relevance of random components in specific model systems. This randomness might stem from intrinsic reaction noise in biochemical systems or random influences from a complex environment in ecosystems. I will discuss some examples below.</span><br />
<span style="font-family: inherit;"><br /></span>
<span style="font-family: inherit;">Traditionally, mathematical </span>modelling<span style="font-family: inherit;"> of biological systems is done using <i>deterministic</i> techniques, which works quite well in the majority of cases. We use differential equations to provide predictions for, e.g. molecular concentrations in a given part of a cell, or the average number of animals in an ecosystem. In this case we are guaranteed to always get the same results if we start with the same initial conditions.</span><span style="font-family: inherit;"> However, we do not always know the initial conditions exactly. In laboratory conditions or <i>in vivo</i>, there is always some external noise the sources of which would be impossible to incorporate into our model. Hence, when we use deterministic modelling techniques, we need to make sure that these influences won't affect our predictions in a profound way which would render our model useless.</span></div>
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<span style="font-family: inherit;"><br /></span>
<span style="font-family: inherit;"><i>Stochastic modelling</i> is a way to incorporate randomness into mathematical models. We employ this kind of modelling when we are interested in the behaviour of only some components of a real system. This is possible, e.g. when there is a separation in time scales between the interesting parts and the rest. Take for example the movement of large biomolecules suspended in water: H2O molecules are moving extremely fast compared to the slower speeds of the biomolecules. They will collide at random with with the larger molecules, transferring momentum and energy. In this case, we can approximate the movement of the small water molecules by an <i>effective random force</i> [1]. Consequently, we do not have to track the H2O molecules and thereby can reduce the needed computational effort tremendously. Another example is the modelling of biochemical reaction, where we assume that the actual binding between reaction partners happens on much faster time scales than we are interested in. Then we are able to use <i>effective binding rates</i> in order to describe reactions such as A+B -> C [1].</span><br />
<span style="font-family: inherit;"><br /></span>
<span style="font-family: inherit;">There is a profound shift in the underlying modelling philosophy when going from a deterministic to a stochastic description, namely that now we don't know anything for certain any more. We can only make statements about <i>probabilities</i> of outcomes. For example, in a stochastic model for the diffusion of molecules, we can predict the probability of having a certain number of molecules in a given region of space. We can make statements about the <i>average</i> number and its <i>variance</i>. In principle we can derive these from the solution of the so-called <i>master equation</i>, which describes the time evolution of the probability distribution for the system to be in a particular state. However, this equation is generally not solvable by any analytical or direct numerical means, and we need to carry out numerical simulations of our model. A single run of such a simulation is called a <i>realization</i> (of the noise history, and sometimes also of the initial conditions) and we usually need to perform many such realizations in order to approximate information about the probability distribution of the quantities we are interested in.</span><br />
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<span style="font-family: inherit;">After this introduction, here are a two of my projects that can serve as an example for stochastic modelling:</span><br />
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<b>Intracellular Calcium signalling</b>: Cells can regulate their cytoplasmic concentration of calcium ions via receptor channels that are located in clusters on calcium reservoirs (in this case, the endoplasmic reticulum). These channels are opened by calcium ions binding to activating sites, and releases ions from the reservoir (this process is called <i>CICR</i> - Calcium-Induced Calcium Release). This leads to a local increase in the number of calcium ions and consequently to the opening of other channels in the cluster and to a further dramatic increase of freed calcium in the vicinity of the channel site. This excess of ions then causes them to bind to the channel's <i>inhibitory</i> binding sites which closes the channels in the cluster. To sum up, this process shows a rapid increase of the local concentration of calcium followed by an exponential decrease after the channels closed and the ions diffuse away, which we call a calcium "puff". Here is a video visualizing calcium puffs (and waves), where they imaged calcium ions in heart muscle cells:<br />
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/nYbp1vB3O-o?feature=player_embedded' frameborder='0'></iframe></div>
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It is quite clear from this video and from other experimental data, that the appearance of puffs is a random process and the cell can regulate the rate at which this process occurs. So we use a stochastic model that takes into account the randomness of the channel activation and inhibition process (i.e. a stochastic channel state model) [2,3]. We also include a way for ions to diffuse away from the channel site [3]. I am comparing various ways of including stochastic ion diffusion to "tune" the randomness and thereby assess its importance.</div>
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<b>The effect of rate randomness on predator-prey ecosystems:</b> The <i>Lotka-Volterra</i> model is a very prominent and well-studied model for the interaction between a predator (A) and a prey (B) species, where they behave according to the rules A -> 0 (mortality), B -> 2B (reproduction) and A+B -> 2A (predation) [4]. It is a wonderful example for a system that behaves differently in a a stochastic versus a deterministic modelling approach. The deterministic equations that describe this system predict perpetual oscillations in this cycle: (i) The number of prey rises because of reproduction, (ii) the number of predators rises because they feed off the prey, (iii) the predator population falls due to mortality and starvation, and (iv) the prey population recovers. But in stochastic versions of this model the oscillations are damped, and both species eventually reach co-existence population levels where they don't show oscillations any more. The frequency of the damped oscillations is also quite different from characteristic frequency in the deterministic system because of the inherent reaction randomness [5]. When we include random reaction rates, either because they vary spatially (environmental randomness) or individually (demographic randomness), both the prey and the predator population profit and their numbers increase [6,7]. This quite unexpected result lead us to eventually study the co-evolution between predators and prey in this very simple setting [7].</div>
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In addition to these projects, I am also interested in modelling cellular protrusions, called filopodia; the collective behaviour of animal swarms and crowds; as well as the development of efficient algorithms and software for the numerical simulation of these models.</div>
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I hope that I could convince you that stochastic modelling is quite interesting, and that it is important to study the influence of randomness on biological systems. </div>
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References</h4>
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<li><span style="font-size: x-small;">R. Erban, J. Chapman and P. Maini, "A practical guide to stochastic simulations of reaction-diffusion processes", Lecture Notes, available as <a href="http://arxiv.org/abs/0704.1908">http://arxiv.org/abs/0704.1908</a>, 35 pages (2007) </span></li>
<li><span style="font-size: x-small;">G. Dupont, L. Combettes, L. Leybaert, "Calcium Dynamics: Spatio‐Temporal Organization from the Subcellular to the Organ Level", International Review of Cytology 261, 193-245 (2007)</span></li>
<li><span style="font-size: x-small;">M. Flegg, S. Ruediger and R. Erban, "Diffusive spatio-temporal noise in a first-passage time model for intracellular calcium release", Journal of Chemical Physics 138, 154103 (2013)</span></li>
<li><span style="font-size: x-small;">J. D. Murray, "Mathematical Biology" Volume I, 3rd edition, pages 437-449, Springer-Verlag Berlin Heidelberg (2003)</span></li>
<li><span style="font-size: x-small;">U. C. Täuber, "Population oscillations in spatial stochastic Lotka–Volterra models: a field-theoretic perturbational analysis", Journal of Physics A: Mathematical and Theoretical 45, 405002 (2012)</span></li>
<li><span style="font-size: x-small;">U. Dobramysl and U. C. Täuber, "Spatial Variability Enhances Species Fitness in Stochastic Predator-Prey Interactions, Physical Review Letters 101, 258102 (2008)</span></li>
<li><span style="font-size: x-small;">U. Dobramysl and U. C. Täuber, Environmental Versus Demographic Variability in Two-Species Predator-Prey Models, Phys. Rev. Lett. 110, 048105 (2013)</span></li>
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Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-7867264995121108649.post-59107140886119338872014-03-11T17:23:00.001+00:002014-03-31T16:03:19.443+01:00Silver at SET for Britain<span style="font-family: inherit;"><span style="font-size: small;"><i>In this post <a href="http://people.maths.ox.ac.uk/yatesc/" target="_blank">Dr. Christian Yates</a> , a Junior Research Fellow working at the WCMB, gives us a description of his poster on locust migration which scoped the Silver Award in the Mathematics section of <a href="http://www.setforbritain.org.uk/index.asp">SET for Britain</a>, a national poster competition held in the Houses of Parliament. </i></span></span><br />
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<span style="font-family: inherit;"><span style="font-size: small;">On the 17th of March I headed down to London, more specifically to the Houses of Parliament, to present a poster of my work [1] on modelling locust migration to leading scientists and MPs as part of the national “<a href="http://www.setforbritain.org.uk/index.asp">SET for Britain</a>” pos</span></span>ter competition.<br />
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The aim of for SET for Britain is to encourage, support and promote Britain's early-career research scientists, engineers, technologists and mathematicians, who represent Britain's future scientific and technological leaders. The event was well attended by both politicians and researchers. Presenters are entered into the engineering, biological and biomedical sciences, physical sciences (chemistry), physical sciences (physics), or mathematics session, depending on the researcher’s specialism.<br />
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<span style="font-family: inherit;"><span style="font-size: small;">This
year, for the first time, SET for Britain was open to mathematicians,
so I was delighted to have been selected to present my poster
in the inaugural competition. It’s important, as mathematical
biologists, that we can explain and justify the work we do. I think SET for Britain presents a great opportunity do that by communicating my work to a wider
audience, including the people who make high-level decisions about
research funding. </span></span><br />
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<span style="font-family: inherit;"><span style="font-size: small;">On the day approximately 210 early-career researchers (including 30 in the Mathematics section) turned up to present their work. Over a two hour session in the Churchill room (click <a href="http://360.io/ZPaAcQ">here</a> to see an interactive panorama of the room taken at a previous event) we were visited by politicians, academics, education specialists and, of course, the all important judges (Professor John McWhirter (Cardiff University), Dr Vincent Knight, (Cardiff University), Professor Kevin McConway (The Open University), Professor Tim Pedley (Universiy of Cambridge) and Professor Nick Woodhouse (University of Oxford)).</span></span><br />
<span style="font-family: inherit;"><span style="font-size: small;"><br /></span><span style="font-size: small;">After spending two hours convincing the judges that increasing the noisiness of their motion can help to keep locust swarms aligned for longer, I was presented with the Silver award in the Mathematics competition.</span></span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkVfqBj4W0BoMnwTStxfWZ6jjCEgE3UIRDJOFFo69xge-zoXlP0xQPu5PvEOFCW45ZcyldZjDdVVG9DHVDnKyvDJfjkcMJE5IlK7b98km7WBKMm-zwXWzR1jbZTsvd4ree7FJP_FFuofU/s1600/Set_4_britain_Christian_Yates.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkVfqBj4W0BoMnwTStxfWZ6jjCEgE3UIRDJOFFo69xge-zoXlP0xQPu5PvEOFCW45ZcyldZjDdVVG9DHVDnKyvDJfjkcMJE5IlK7b98km7WBKMm-zwXWzR1jbZTsvd4ree7FJP_FFuofU/s1600/Set_4_britain_Christian_Yates.JPG" height="213" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Receiving my award from Professor Sir Adrian Smith and Andrew Miller MP, the sponsor of the event.</td></tr>
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<span style="font-family: inherit;"><span style="font-size: small;">Below is a copy of the poster and the abstract that I submitted for the pre-selection process, which summarises the work I presented in my poster and hopefully captures the essence of the project without being too mathematical.</span></span><br />
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<b><span style="font-family: inherit;"><span style="font-size: small;">United by Noise: Randomness helps swarms stay together</span></span></b><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaPgpxH9ac9-oIm3qIGEKdbUDPiy-bbuySn8APtOFoW9iQvYKuNUu3b0ON-AHxNmthnw2srXineKUynvPBDgyrRIgJcAsiN6KLuNpRkdeiODGmyH53HAJ5aWjMCbEDA5hBGMSBJkHfrYY/s1600/Set_for_britian_Locusts_Christian_Yates.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaPgpxH9ac9-oIm3qIGEKdbUDPiy-bbuySn8APtOFoW9iQvYKuNUu3b0ON-AHxNmthnw2srXineKUynvPBDgyrRIgJcAsiN6KLuNpRkdeiODGmyH53HAJ5aWjMCbEDA5hBGMSBJkHfrYY/s1600/Set_for_britian_Locusts_Christian_Yates.jpg" height="320" width="226" /></a></div>
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<b><span style="font-family: inherit;"><span style="font-size: small;">Devastating consequences</span></span></b><br />
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<span style="font-family: inherit;"><span style="font-size: small;">During plagues, desert locusts may migrate over or into parts of 60 countries, covering more than 20% of the total land surface of the world. A typical swarm can be one kilometre wide and up to three kilometres long. With typical densities of 80,000 locusts per square kilometre swarms can comprise up to a quarter of a million locusts each eating their own weight (2g) in food every day. Given such voracious appetites and such large numbers it is easy to understand the devastating effect locust swarms can have on the lands they ravage and consequently on the livelihoods of the 10% of the world's population who encounter them. Strategies to understand the formation and cohesion of locust swarms are therefore of great importance. We present a collaborative interdisciplinary approach in which mathematical modelling is combined with experimental investigations. Our work leads to novel and counter-intuitive strategies for controlling locust swarming.</span></span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcup8SLK1wOtkKpGXwjSlIbSRULA_iSnN5l_rxLF2OItHBQmCV65xxzNXWR4zbR2ba4HRwkuG25H_o7JkXVwnASkQ3uBpu_D9oV84vEfor89_EmnqPfcHuiZzMcZDcOc3ghfZj_7pNtXE/s1600/locust-cannibals.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcup8SLK1wOtkKpGXwjSlIbSRULA_iSnN5l_rxLF2OItHBQmCV65xxzNXWR4zbR2ba4HRwkuG25H_o7JkXVwnASkQ3uBpu_D9oV84vEfor89_EmnqPfcHuiZzMcZDcOc3ghfZj_7pNtXE/s1600/locust-cannibals.jpg" height="239" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Locusts.</td></tr>
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<b><span style="font-family: inherit;"><span style="font-size: small;">Experimental Evidence</span></span></b><br />
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<span style="font-family: inherit;"><span style="font-size: small;">To investigate swarming dynamics, locusts were placed in a ring-shaped arena it was observed that they marched together in the same direction (clockwise or anticlockwise) around the arena before spontaneously and collectively switching the direction of their marching. The switching rate can be though of as a measure of the stability of the locust group, with larger, more stable groups switching less often and smaller more volatile groups switching more frequently.</span></span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJtWxjD68gn3HklF-rj3Q3ieZqIC-jirosGP9pQdBw_1MPMaYbg1PErLD2LpCWV1wR5THCbLIfvkOVGc8AmZqtRBpIDoA3TeTPfIvtu2lQI4C6R9JyrJJqdkSswTSfrZKR5JQqeJZZlsU/s1600/locust_set_up.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJtWxjD68gn3HklF-rj3Q3ieZqIC-jirosGP9pQdBw_1MPMaYbg1PErLD2LpCWV1wR5THCbLIfvkOVGc8AmZqtRBpIDoA3TeTPfIvtu2lQI4C6R9JyrJJqdkSswTSfrZKR5JQqeJZZlsU/s1600/locust_set_up.jpg" height="238" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: inherit;"><span style="font-size: small;"> <span style="font-size: x-small;">The ring-shaped experimental arena with 100 locusts (black dots).</span></span></span></td></tr>
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<b><span style="font-family: inherit;"><span style="font-size: small;">A Mathematical Model</span></span></b><br />
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<span style="font-family: inherit;"><span style="font-size: small;">By carefully analysing the experimental data on the switching behaviour of locusts we are able to build accurate individual-based mathematical models of locust movement. In these “self-propelled particle models” each locust is represented as an individual with a position and a velocity. These properties are updated at discrete time-steps according to the behaviour of neighbouring locusts. Noise is added to the model to mimic the natural randomness of such systems. </span></span><br />
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<b><span style="font-family: inherit;"><span style="font-size: small;">Predictive power</span></span></b><br />
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<span style="font-family: inherit;"><span style="font-size: small;">Such models have great predictive power and are able to forecast the nature of the density dependent switching phenomenon seen in the experiments. We use bespoke mathematical techniques (the Fokker-Planck coefficient estimation approach) in order to further investigate our model and to validate it by comparing it, in detail, to the experimental data. The results of our analysis suggest that the locusts decrease the randomness in their motion when they find themselves in alignment with their neighbours, but increase the noisiness when they find themselves out of line. For some reason the locusts panic when not aligned with their neighbours.</span></span><br />
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<b><span style="font-family: inherit;"><span style="font-size: small;">Cannibalism</span></span></b><br />
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<span style="font-family: inherit;"><span style="font-size: small;">One possible explanation for this phenomenon is cannibalism. The best way for locusts to get protein and salt into their diet is to eat other locusts. Experiments have been carried out on Mormon Crickets which suggest that an individual’s sides are vulnerable to cannibalistic attack. Based on our model we therefore hypothesise that, if a locust finds itself out of line with its neighbours, it will increase the randomness of its motion to avoid being eaten. Conversely locusts will reduce the randomness of their motion once in an aligned state so that they might stay in that state for longer. It is also known that cannibalism is a significant force in driving swarms forward. Individuals dare not sit still for too long for danger of being eaten by the locusts behind them!</span></span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQexlv6NiArmdCIhuzkLcivHhbtShU4nQcWmtzLBrUi0tGZEFzyERzd2Mf4XPgcYm_kkPG-kW47Qi5XLYD1L9Npc6XgB4S31MJRf0-icVvupcLSIqpYi3dMHUdGIaIiri9YcYwNwYZwTc/s1600/locust_cannibalism.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQexlv6NiArmdCIhuzkLcivHhbtShU4nQcWmtzLBrUi0tGZEFzyERzd2Mf4XPgcYm_kkPG-kW47Qi5XLYD1L9Npc6XgB4S31MJRf0-icVvupcLSIqpYi3dMHUdGIaIiri9YcYwNwYZwTc/s1600/locust_cannibalism.jpg" height="219" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: inherit; font-size: x-small;">Cannibalism provides an efficient way for locusts to get protein into their diet.</span></td></tr>
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<span style="font-family: inherit;"></span><b><span style="font-family: inherit;"><span style="font-size: small;">Managing locust plagues</span></span></b><br />
<span style="font-family: inherit;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: inherit;"><span style="font-size: small;"> Our model suggests that, if cannibalism could be reduced, the penalty for a locust who is out of line with his neighbours will also be reduced leading to less stable swarms. Providing alternative, protein- and salt-rich food sources may reduce cannibalism, leading to less cohesion and marching motivation in locust swarms and potentially to their eventual break-up. In addition our model suggests locusts are extremely susceptible to noise and explains why strategies which increase the overall randomness of a swarm (flying aeroplanes low overhead to that their wing-tip vortices disrupt the locusts) are currently being employed in an attempt to disorient and disperse swarms.</span></span><br />
<span style="font-family: inherit;"><br class="Apple-interchange-newline" /></span><span style="font-family: inherit;"></span><b>References</b><br />
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<li><span style="background-color: white;">C.A. Yates, R. Erban, C. Escudero, I. Couzin, J. Buhl, I. Kevrekidis, P. Maini and D. Sumpter, (2009). "<a href="http://people.maths.ox.ac.uk/yatesc/inherentnoise.pdf"><b>Inherent noise can facilitate coherence in collective swarm motion</b></a>". <i>PNAS</i>106(14) 5464-5469.</span></li>
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Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-7867264995121108649.post-88682036554541301302014-03-09T10:30:00.000+00:002014-03-11T17:34:15.395+00:00Chemical reactions, spatial information processing, and model invalidation, oh my!<div style="font-family: Arial; font-size: 16px;">
<span style="font-family: inherit;"><span style="font-size: small;"><i>In this post <a href="http://www.maths.ox.ac.uk/people/profiles/heather.harrington">Dr Heather Harrington</a>, Hooke Research Fellow and EPSRC Postdoctoral Fellow at the WCMB, discusses her research interests.</i></span></span><br />
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Much of my work is motivated by cellular decision making - such processes require balanced and nuanced responses to environmental, physiological and developmental signals. In many organisms, this involves the interplay and concerted action of a number of molecular players, that receive external signals, broadcast them further into the cytoplasm, and, if a transcriptional response is called for, shuttle into the nucleus and activate the transcriptional machinery. </div>
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One of my interests is studying the role that spatial organisation plays on cellular decisions. To do this, we've focus on the mitogen activated protein (MAP) kinase family of proteins, which is involved in regulating cellular fate activities such as proliferation, differentiation and apoptosis. Their fundamental importance has attracted considerable attention on different aspects of the MAP kinase signalling dynamics; this is particularly true for the Erk/Mek system, which has become the canonical example for MAP kinase signalling systems. Inspired by experiments from mouse cells, we've constructed and parameterised a mathematical models of sub-cellular localisation of Erk/Mek. Borrowing tools from chemical reaction network theory and dynamical systems, we showed that the existence of distinct compartments plays a pivotal role in whether a system is capable of multistationarity. Working with collaborators <a href="http://www.math.ku.dk/~efeliu/">Elisenda Feliu</a>, <a href="http://www.math.ku.dk/~pbx512/%E2%80%8E">Carsten Wiuf</a> (Copenhagen), and my postdoc advisor, <a href="http://www.theosysbio.bio.ic.ac.uk/people/michael-stumpf/">Michael Stumpf</a>, we gave necessary conditions for multistationarity. This was based on studying the Jacobian of the system and determining whether the model was injective. (Since this, Elisenda and her co-authors have generalised these results <a href="http://arxiv.org/abs/1311.5493">here</a>.)</div>
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Interestingly, we found that cellular <span style="background-color: white;">information</span> processing can be altered by including spatial organisation via compartments. Recently, this model has been adapted and compared qualitatively to experimental Mek/Erk data from chick and mouse embryo (with collaborators from the Weizmann Institute).</div>
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Another one of my primary interests is developing methods for linking data and models. In collaboration with <a href="http://www.stanford.edu/~klho/">Ken Ho</a> (Stanford), we proposed a competing model of cell death activation. One question that reoccurred was "which model is best?" Ultimately this was my focus for a couple years working with <a href="http://www.theosysbio.bio.ic.ac.uk/">Michael Stumpf</a> in Theoretical Systems Biology, Imperial College ( twitter: <a href="https://twitter.com/theosysbio">@theosysbio</a>) . In the case of comparing these apoptosis models, there was no knowledge of parameter values which led Ken Ho, Tom Thorne (Edinburgh) and I to transform our model into only 'theoretically' observable variables via Groebner Bases (a multivariate Gaussian elimination) and then use a statistical test to determine whether the transformed data lie on the same plane as the transformed model. This parameter-free approach falls on one end of the spectrum with Bayesian approaches in the middle (integrating out parameters), and finally, parameter fitting+information criterion on the other end. Developing parameter-free model discrimination is still an ongoing area of research.</div>
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The usefulness of Groebner Bases and other techniques from algebra and geometry have attracted me venture into a pure mathematician's toolbox and ask how these tools complement many of the existing approaches for analysing biological systems. For example, I have really enjoyed learning about chemical reaction network theory, with the rich theory developed since the 1970s by Feinberg, Horn, and Jackson and more recently a larger body of <a href="http://reaction-networks.net/wiki/Mathematics_of_Reaction_Networks">researchers</a>. The primary focus of CRNT is to analyse models arising from chemical reactions in a systematic, generalised approach that can provide information about the dynamics of the system (existence, uniqueness, multiplicity and stability of fixed points) as well as oscillatory behaviour, and more recently extending to stochastic and spatial dynamics (e.g. Turing instabilities). The appeal of the theories developed in CRNT is their ability to preclude behaviour as well as determine the capacity for certain results; often this analysis is performed irrespective of parameter values. Last year I attended a workshop at <a href="http://aimath.org/">AIM</a>, which has sparked collaborations and discussions with many mathematicians around the world working on using algebraic and geometric approaches to analyse such systems. </div>
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At Oxford I'm particularly interested in finding problems (with data) that would benefit from spatial analysis, model discrimination and/or use ideas from chemical reaction network theory to better understand the system. I will also continue developing methods for data; which has been kickstarted by the workshop funding by OCCAM, enabling a small group of academics around Oxford to meet to discuss challenges in inference and identifiability with data. In the past six months, I've become involved in studying biological systems using combinatorics, networks, and computational topology, and hope to continue to develop links to other areas of mathematics in my research. Furthermore, I'm very grateful to be welcomed into WCMB so warmly and involved in many interesting and exciting projects. </div>
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Currently reading:</div>
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Pleasure: <a href="http://www.nytimes.com/2007/04/15/books/review/Wood.t.html?pagewanted=all&_r=0">Savage Detectives</a> (Los Detectives Salvajes) by Roberto Bolaño. </div>
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Work: <a href="http://arxiv.org/pdf/1309.0049v2.pdf">The Euclidean Distance Degree of an Algebraic Variety</a> (Jan Draisma, Emil Horobet, Giorgio Ottaviani, Bernd Sturmfels and Rekha R. Thomas) </div>
Anonymoushttp://www.blogger.com/profile/14460349668510418485noreply@blogger.com1tag:blogger.com,1999:blog-7867264995121108649.post-57369174338317471282014-03-02T16:29:00.001+00:002014-03-02T17:07:01.134+00:00Interdisciplinary communication: stuck in the middle?<i>In this post D.Phil. student <a href="http://www.dtc.ox.ac.uk/people/11/schumacher/" target="_blank">Linus Schumacher</a> sums up recent thoughts on interdisciplinary communication and science career paths.</i><br />
<a name='more'></a><br />
This January I had the opportunity to present a research scientist's perspective on the <a href="https://www.writelatex.com/blog/83-join-us-at-the-british-library-in-january-to-celebrate-a-new-year-for-science-and-publishing" target="_blank">future of science and publishing</a> at the British Library in London, as part of an event hosted by <a href="https://www.writelatex.com/" target="_blank">writeLaTeX</a>. My outlook for 2014 and beyond was, in summary:<br />
<ul>
<li>There’ll be more scientists working as translators, or <a href="http://cancerconnector.blogspot.co.uk/" target="_blank">connectors</a>, between disciplines.</li>
<li>We’d like even better software for communicating and sharing data with our collaborators, especially for those overseas.</li>
<li>A hope that more biologists will use tools for collaborative writing, as well as preprint servers.</li>
<li>How are we going to acknowledge conceptual insights from extradisciplinary ways of thinking as contributions to joint research?</li>
</ul>
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-INRJEYmu4Bs/UuJamo5wH6I/AAAAAAAABZ8/N2W-_eAe3Bw/w381-h571-no/AX7A8414.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://4.bp.blogspot.com/-INRJEYmu4Bs/UuJamo5wH6I/AAAAAAAABZ8/N2W-_eAe3Bw/w381-h571-no/AX7A8414.jpg" height="200" width="131" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">A one slide talk. <a href="https://www.writelatex.com/blog/85-photos-from-the-launch-event" target="_blank">More photos from the event.</a></td></tr>
</tbody></table>
<br />
Afterwards, I was offered the chance to expand on these thoughts in a <a href="http://blogs.nature.com/naturejobs/2014/02/21/stuck-in-the-middle" target="_blank">guest post for the Nature jobs blog</a>. I quickly noticed that I was one of three to post about these issues in the space of three days, joined by <a href="http://www.theguardian.com/higher-education-network/blog/2014/feb/19/interdisciplinary-research-universities-academic-careers" target="_blank">Sarah Byrne</a> and <a href="http://p-gerlee.blogspot.co.uk/2014/02/the-role-of-mathematical-oncology.html" target="_blank">Philip Gerlee</a>, all three <a href="http://cancerevo.wordpress.com/2014/02/24/on-interdisciplinary-research/" target="_blank">summarised by David Basanta</a>. As I had drawn heavily on the experience of colleagues and peers in my talk and post, it was not too surprising to see similar ideas expressed elsewhere.<br />
<br />
One of the specific issues I talked and wrote about was that there were perhaps too few career examples to follow for someone becoming a connector:<br />
<blockquote class="tr_bq">
"This new connector-niche presents an opportunity for pluripotent
interdisciplinary researchers to stay undifferentiated, but also a risk
of undetermined career fate decision.<b> </b>The problem is that
we lack example career paths of these connectors’ that scientists in
training can follow."</blockquote>
So we need more lineage tracing data (to continue the metaphor). As it happened, just a few days after the above mentioned blog posts, the website <a href="http://myscicareer.com/">myscicareer.com</a> launched as a place for first-person science career stories. It currently features more than a dozen examples of research and other science careers, and it would be great to see some stories of connectors there. So if you are a scientist with an unusual career path, or know someone with an interesting story, please do <a href="http://myscicareer.com/contact/" target="_blank">contact myscicareer to contribute</a>. <br />
<br />Linus Schumacherhttp://www.blogger.com/profile/09580921538587285737noreply@blogger.com1tag:blogger.com,1999:blog-7867264995121108649.post-9824179830481292712014-02-24T14:39:00.002+00:002014-03-17T16:39:24.876+00:00Ten simple rules for effective computational research<i>With the increasing use of computational techniques in the life sciences, a wide range of scientists are finding that software development plays an increasing role in their day-to-day research. In this post <a href="http://people.maths.ox.ac.uk/fletcher/">Dr Alexander Fletcher</a> discusses a forthcoming article on best practice when developing and using software for scientific research.</i><br />
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Introduction</span></h4>
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<span lang="en-GB"><span style="text-align: justify;">To try to understand the dazzling complexity that is inherent in nature, mathematical and computational
techniques are being used more and more widely in the life sciences. Computer programming is becoming unavoidable
for scientists who want to stay up-to-date with the latest quantitative developments
in their field. Yet the degree of practical training on this topic remains low in many degree courses. While a number of guides to software development exist, they are often aimed at computer scientists or concentrate on large open source projects. There is thus a need for guidance in this area aimed specifically at the vast majority of scientific researchers: those without formal training in computer science.</span></span></div>
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<span lang="en-GB">To address this issue, I and other postdoctoral Research Fellows associated with the <a href="http://www.2020science.net/">‘2020 Science’ project</a>, funded jointly by the EPSRC and Microsoft Research Ltd, have come up with a jargon-free guide to best practice when developing and using software for scientific research. This guide [1], consisting of "ten simple rules", is due to appear in a forthcoming issue of <i>PLoS Computational Biology</i>. It is based on our collective experience of the challenges associated with
carrying out multidisciplinary computation-based science. These "rules" are shown in more or less the order in which they should be considered, starting from <i>before</i> a computational scientists should even think about writing any code.</span></div>
<div style="text-align: left;">
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<div style="text-align: left;">
<span lang="en-GB">A brief summary of our "rules" is provided below. The manuscript has not been uploaded to a preprint server (not because we disagree with <a href="http://wcmb-oxford.blogspot.co.uk/2013/12/pre-print-servers-dangerous-ways-to.html">Jacob Scott's opinion</a> on the issue, but I am afraid because no-one has gotten around to it), though a version has been self-archived by Kit Yates and can be found <a href="http://people.maths.ox.ac.uk/yatesc/10SimpleRules.pdf">here</a>. There are many other useful guides in the "Ten simple rules" series worth checking out [2, 3, 4, 5], as well as a recent <i>PLoS Biol. </i>community page on best practices for scientific computing [6].</span></div>
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<span lang="en-GB"><b>Rule 1: Look before you leap</b></span></h4>
<span lang="en-GB" style="font-family: inherit;"><span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;"><br /></span></span>
<span lang="en-GB" style="font-family: inherit;"><span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;">Before developing new code, it is worth performing a survey of what existing </span></span><span style="font-family: inherit; line-height: 18.399999618530273px; text-align: justify;">software toolboxes and libraries are out there that might be able to tackle your chosen problem. </span><span lang="en-GB" style="font-family: inherit; line-height: 18.399999618530273px; text-align: justify;">Software repositories such as </span><span style="font-family: inherit; line-height: 18.399999618530273px; text-align: justify;"><a href="https://github.com/">GitHub</a></span><span style="font-family: inherit; line-height: 18.399999618530273px; text-align: justify;"> and </span><span style="font-family: inherit; line-height: 18.399999618530273px; text-align: justify;"><a href="http://sourceforge.net/">SourceForge</a></span><span style="font-family: inherit; line-height: 18.399999618530273px; text-align: justify;"> </span><span lang="en-GB" style="font-family: inherit; line-height: 18.399999618530273px; text-align: justify;">are a good place to begin (as are your colleagues in the field).</span><br />
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</span></div>
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<h4>
<b style="font-family: inherit;">Rule
2: Develop a prototype first</b></h4>
<span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;"><br /></span>
<span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;">Before writing any code it is essential to be clear about what you are trying to implement: what functionality do you require, and what interfaces do you need? W</span><span style="line-height: 18.399999618530273px; text-align: justify;">hether extending existing code or starting from scratch, it is helpful to begin by considering a </span><span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;">prototype (a simplified version of the full system or algorithm) to guide the next steps in code development. </span><span style="line-height: 18.399999618530273px; text-align: justify;">From a practical point of view it is often easier to prototype methods in a ‘higher level’ language such as MATLAB or R; the straightforward nature and built-in functionality in these languages can mean </span><span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;">that you spend less time expressing your ideas in code and searching for bugs.</span><br />
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<h4 style="text-align: left;">
<span lang="en-GB">
<span style="font-family: inherit;"><b>Rule 3: Make
your code understandable by others (and yourself)</b></span></span></h4>
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<div style="text-align: left;">
<span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;">The absence of documentation and comments can cause a lot of grief when revising or adapting existing code! Such documentation not only makes your code more understandable to others but also to your future self (put simply, the code tells you ‘how’, the comments tell you ‘why’). The program code itself can be made more understandable by using meaningful variable names</span><span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;"><i> </i></span><span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;">and formatting the code consistently. While commenting and documentation is often neglected when faced with deadlines, developing and maintaining a standardised way of commenting your code will be of great benefit.</span></div>
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<b style="font-family: inherit;"><span lang="en-GB">Rule 4</span><span lang="en-GB">:
Don’t underestimate the complexity of your task </span></b></span></h4>
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<span style="line-height: 18.399999618530273px; text-align: justify;"><span lang="en-GB"><br /></span></span>
<span style="line-height: 18.399999618530273px; text-align: justify;"><span lang="en-GB">When developing your code you should keep a record of your work. This could be in the form of a ‘log-book’ file or a paper-based note-book where you store commonly used commands and other notes; another good option is an online tool such as <a href="http://evernote.com/">Evernote</a>. </span></span><span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;">You will often find that you have to choose between spending a long time doing a task by hand and possibly spending longer learning how to automate it. </span><span style="line-height: 18.399999618530273px; text-align: justify;">A good rule to follow is “the rule of three”: once you have had to do the same thing twice already, automate it.</span></div>
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<h4>
<span lang="en-GB"><span style="font-family: inherit;"><span lang="en-GB">Rule
5: Understand the mathematical, numerical and computational methods
underpinning your work</span></span></span></h4>
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<span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;">When solving any computational model, you should always ensure that you are using the appropriate numerical method for your problem, and that any constraints and conditions are satisfied. A basic understanding of numerical analysis and in particular the concepts of rate of convergence, order, and stability of numerical methods will pay dividends. </span><span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;">By fully understanding the mathematical and numerical methods being used you can be confident that your results reflect the true behaviour of the underlying model and are not numerical or computational artefacts.</span></div>
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<h4>
<span lang="en-GB"><span style="font-family: inherit;"><span lang="en-GB">Rule 6: </span><span lang="en-GB">Use
</span>pictures: they really are worth a
thousand words</span></span></h4>
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<span style="line-height: 18.399999618530273px; text-align: justify;"><br /></span>
<span style="line-height: 18.399999618530273px; text-align: justify;">Visualisation and graphics are fundamental to developing understanding and testing hypotheses, and are indispensable for verifying and validating computational methods. It is worthwhile spending time developing the visual components of your work. Learn, develop and use visualisation software and tools to ensure that you understand your research outputs and can effectively communicate your findings. You may well need to develop novel visualisations for your work, but keep the basic figures. You needed them to understand your results, model, and implementation and so will anyone else.</span></div>
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<h4>
<span lang="en-GB" style="font-family: inherit;">Rule 7: Version control</span><span lang="en-GB" style="font-family: inherit;"><i>
everything</i></span></h4>
<div style="text-align: left;">
<span lang="en-GB"><span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;"><br /></span></span>
<span lang="en-GB"><span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;">Version control systems such as </span></span><span style="line-height: 18.399999618530273px; text-align: justify;"><a href="http://subversion.tigris.org/">Subversion</a> </span><span style="line-height: 18.399999618530273px; text-align: justify;">and <a href="http://www.github.com/">Git</a> </span><span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;">offer an easy way to store </span><span style="line-height: 18.399999618530273px; text-align: justify;">and backup</span><span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;"> not only the current version of your code that you are working on but also every previous version of the code (in what’s known as a repository). This not only saves you from having to keep multiple copies of the same file but also allows you to ‘roll back’ to an older ‘working’ version of the code if things go wrong. Version control systems </span><span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;">also allow you to share material between multiple machines, operating systems and more importantly users in a simple and robust manner. </span><span style="line-height: 18.399999618530273px; text-align: justify;">Cloud storage such as <a href="http://www.dropbox.com/">Dropbox</a></span><span style="line-height: 18.399999618530273px; text-align: justify;"> and </span><span style="line-height: 18.399999618530273px; text-align: justify;"><a href="http://www.skydrive.live.com/">SkyDrive</a></span><span style="line-height: 18.399999618530273px; text-align: justify;"><u> </u></span><span style="line-height: 18.399999618530273px; text-align: justify;">offer basic file sharing and backup facilities, but don’t offer the code management features of true version control systems.</span></div>
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<h4 style="text-align: left;">
<span lang="en-GB">
<span lang="en-GB" style="font-family: inherit;">Rule
8: Test </span><span lang="en-GB" style="font-family: inherit;"><i>everything</i></span></span></h4>
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</span>
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<div style="text-align: left;">
<span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;">Any non-trivial computer program will have bugs when first written, often subtle ones that are hard to detect, which may lead to incorrect results. Simple tests that the software behaviour matches expectations are essential for ensuring robust results, minimising the presence of bugs and gaining confidence in your code (for you and others). As a result of the time pressures inherent in academia, often software testing is performed manually in an </span><span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;"><i>ad hoc</i></span><span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;"> manner, to determine whether results ‘look roughly right’.</span><span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;"> However, a systematic approach to testing can pay dividends.</span></div>
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<br /></div>
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<h4 style="text-align: left;">
<span lang="en-GB">
<span lang="en-GB" style="font-family: inherit;">Rule
9: Share </span><span lang="en-GB" style="font-family: inherit;"><i>everything</i></span></span></h4>
</div>
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</span><span lang="en-GB"><span lang="en-GB" style="line-height: 18.399999618530273px; text-align: justify;"></span></span>
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<div style="text-align: left;">
<span style="line-height: 18.399999618530273px; text-align: justify;">If an important part of your research involves developing new software tools and/or collecting new data, then you should consider sharing these. Based on our collective experience, we advocate an open approach of sharing source code, data and results as freely as possible. You should ask yourself, ‘why not share?’ If the answer is that, ‘I am worried that people would find mistakes in it’ then, as a scientist, this should be the strongest argument in favour of sharing it!</span></div>
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<h4 style="text-align: left;">
<span lang="en-GB">
<span style="font-family: inherit;">Rule
10: Keep going!</span></span></h4>
</div>
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</span><span lang="en-GB">
</span><br />
<div style="line-height: 115%; margin-bottom: 0cm; text-align: justify;">
<div style="text-align: left;">
<span lang="en-GB" style="font-family: inherit; line-height: 115%;">Our advice arises from our collective experience, and we continue to strive to obey these rules in our work. Scientists have a wide variety of demands (researching, writing papers</span><span lang="en-GB" style="font-family: inherit; line-height: 115%;">, teaching</span><span lang="en-GB" style="font-family: inherit; line-height: 115%;">, applying for grants, admin) and have to make the most of limited resources. Becoming more technically effective can seem daunting without strategies for making progress and keeping motivated. So, prioritise in a way that suits you and your projects and career aspirations. One strategy is to implement another of these rules each time you start a new project, to build a growing repertoire, rather than trying to do everything at once. Take every opportunity to teach and help others to do what you have learnt. </span></div>
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<span lang="en-GB">
<span style="font-family: inherit;"><a href="https://www.blogger.com/null" name="h.ujpq24uz3t66"></a></span></span></h2>
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References</span></h4>
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<ol>
<li><span style="font-family: inherit; font-size: x-small;">J.M. Osborne, M.O. Bernabeu, M. Bruna, B. Calderhead, J. Cooper, N. Dalchau, S.-J. Dunn, A.G. Fletcher, R. Freeman, D. Groen, B. Knapp, G.J. McInerny, G.R. Mirams, J. Pitt-Francis, B. Sengupta, D.W. Wright, C.A. Yates, D.J. Gavaghan, S. Emmott, C. Deane (2013). Ten simple rules for effective computational research. <i>PLoS Comput. Biol.</i> In press.</span></li>
<li><span style="font-family: inherit; font-size: x-small;">W. Zhang (2014). Ten simple rules for writing research papers. </span><i style="font-family: inherit;"><span style="font-size: x-small;">PLoS Comput. Biol. </span></i><span style="background-color: white; font-family: inherit; line-height: 18.0049991607666px;"><span style="font-size: x-small;">10(1): e1003453. doi:10.1371/journal.pcbi.1003453</span></span></li>
<li><span style="background-color: white; font-family: inherit; font-size: x-small; line-height: 18.0049991607666px;">G.K. Sandve, A. Nekrutenko, J. Taylor, E. Hovig (2013). Ten simple rules for reproducible computational </span><span style="font-family: inherit; font-size: x-small;"><span style="background-color: white; line-height: 18.0049991607666px;">research. </span><i style="background-color: white; line-height: 18.0049991607666px;">PLoS Comput. Biol.</i><span style="background-color: white; line-height: 18.0049991607666px;"> 9(10): e1003285. doi:10.1371/journal.pcbi.1003285</span></span></li>
<li><span style="background-color: white; font-family: inherit; font-size: x-small; line-height: 18.0049991607666px;">A. Prlić, J.B. Procter (2012). Ten simple rules for the open development of scientific software. <i>PLoS Comput. Biol.</i></span><span style="background-color: white; font-family: inherit; font-size: x-small; line-height: 18.0049991607666px;"> 8(12): e1002802. doi:10.1371/journal.pcbi.1002802</span></li>
<li><span style="background-color: white; font-family: inherit; font-size: x-small; line-height: 18.0049991607666px;">P.E. Bourne (2011). Ten simple rules for getting ahead as a computational biologist in academia. <i>PLoS Comput. Biol. </i></span><span style="background-color: white; font-family: inherit; font-size: x-small; line-height: 18.0049991607666px;">7(1): e1002001. doi:10.1371/journal.pcbi.100200</span></li>
<li><span style="background-color: white; font-family: inherit; font-size: x-small; line-height: 18.0049991607666px;">G. Wilson, D.A. Aruliah, C.T. Brown, N.P. Chue Hong, M. Davis, R.T. Guy, S.H.D. Haddock, K.D. Huff, I.M. Mitchell, M.D. Plumbley, B. Waugh, E.P. White, P. Wilson</span><span style="background-color: white; font-family: inherit; font-size: x-small; line-height: 18.0049991607666px;"> (2014). Best practices for scientific computing. <i>PLoS Biol.</i></span><span style="background-color: white; font-family: inherit; font-size: x-small; line-height: 18.0049991607666px;"> 12(1): e1001745. doi:10.1371/journal.pbio.1001745</span></li>
</ol>
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</span></div>
Anonymoushttp://www.blogger.com/profile/06781843200914952471noreply@blogger.com4tag:blogger.com,1999:blog-7867264995121108649.post-40935527469508188862014-02-16T16:35:00.003+00:002014-02-16T16:35:33.558+00:00Mid-term updateWe're halfway through term here in Oxford, and at the WCMB we've had a busy week with excellent talks by <a href="http://www.2020science.net/people/zhuoyi-song" target="_blank">Zhuoyi Song</a> and <a href="http://lucacardelli.name/" target="_blank">Luca Cardelli</a>. Next week <a href="http://www.math.leidenuniv.nl/~frits/" target="_blank">Frits Veerman</a> and <a href="http://www.maths.ox.ac.uk/contact/details/maclean" target="_blank">Adam McLean</a> are speaking at Monday's group meeting, while Friday's research seminar will be given by <a href="http://www.birmingham.ac.uk/staff/profiles/maths/smith-david.aspx" target="_blank">David Smith</a>.<br />
<br />
Our blog admins have been hit by scheduling delays this week, so there's no new post from us. But why not check out some of our group's very successful individual blogs, <a href="http://laughmaths.blogspot.co.uk/" target="_blank">The Laughing Mathematician</a> and <a href="http://cancerconnector.blogspot.co.uk/" target="_blank">Cancer Connector</a>.<br />
<br />
We've got some exciting posts in the pipeline for the rest of this and next month, and will be back for you all next Sunday.Linus Schumacherhttp://www.blogger.com/profile/09580921538587285737noreply@blogger.com1tag:blogger.com,1999:blog-7867264995121108649.post-71342256573133658592014-02-10T02:35:00.000+00:002014-02-10T21:13:05.958+00:00Hamilton’s haplodiploidy hypothesis and the females who do all the work<!--[if gte mso 9]><xml>
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<br />
<i>In this post <a href="http://www.maths.ox.ac.uk/contact/details/davies">Nick Davies</a>, who is doing his DPhil between the WCMB and the <a href="http://zoo-kfoster.zoo.ox.ac.uk/node/42">Foster lab</a> in Zoology, provides some history on the long-standing question of why worker castes in social colonies of wasps, bees, and ants are exclusively female.</i><br />
<a name='more'></a><br />
<blockquote class="tr_bq">
<i><span lang="EN-GB"><span style="font-family: inherit;">“also they put a litle of the Sugar in
a porrenger, and that in the midst of a flatter Dish filled with Water: and
[...] these Wonderfull Creatures discerning it to be there, (whether by
Instinct or Smell I cannot say [...]) they came about the Dish, and at last put
forward into the Water, till so many were drowned that they made a Bridge with
their Bodies for their fellows, over which they went to and fro till they had
carried away the Sugar. This another Knight, his brother, and all the Famelie
testified. Which if true, it shews these litle Generous Creatures to be very
resolute in Sacrificing their Lives for the Benefit of their Country, and very
magnanimous in despising their privat Satisfaction, in comparison of the
Advantage of all the Societie, as well as faithfull in their Trust, and of very
great and public spirits: being free from that vice wherby men are apt having
found a Treasure to appropriat it all by stealth to themselvs, and to envy
others the Enjoyment of it.”</span></span></i></blockquote>
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<i>— Thomas Traherne (1637–1674), </i>Commentaries of Heaven<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://images.nationalgeographic.com/wpf/media-live/photos/000/350/cache/fire-ants-form-life-rafts-edge_35040_600x450.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://images.nationalgeographic.com/wpf/media-live/photos/000/350/cache/fire-ants-form-life-rafts-edge_35040_600x450.jpg" height="302" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fire ants forming a raft. Source: <a href="http://news.nationalgeographic.com/news/2011/04/pictures/110425-fire-ants-life-rafts-swarms-science-proceedings/">National Geographic</a>.</td></tr>
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<br /></div>
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<i><br /></i></div>
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<span lang="EN-GB"><span style="font-family: inherit;">The
social hymenoptera—ants, bees, and wasps living in tightly regulated colonies where
a specialized, sterile worker caste devotes itself to raising its siblings—have
long fascinated naturalists. The above anecdote about ants from the
17th-century poet and clergyman Thomas Traherne illustrates one of the defining
characteristics of the social hymenoptera: self-sacrifice for the “</span><span lang="EN-GB"><span style="font-family: inherit;">Advantage of all the Societie</span></span><span style="font-family: inherit;">”. As with other examples of altruism, these acts can seem, at face
value, to contradict what we know about natural selection. If survival of the
fittest requires individuals to maximise their own reproductive success, why
are these “Wonderfull Creatures” so willing to lay down their own lives in
order to help others?</span></span><br />
<span lang="EN-GB"><span style="font-family: inherit;"></span></span></div>
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<br /></div>
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<span lang="EN-GB"><span style="font-family: inherit;">The
answer, as we now know, lies in kin selection. Behaviour is influenced by genes, and
we normally expect a gene variant that brings harm to its host—say, by increasing curiosity about a natural predator—will not spread through a
population. But could a gene that harms its host nevertheless succeed at
spreading through natural selection? It turns out that there are a number of ways this can work. One of these ways is kin selection, which relies on the fact that </span></span>genes tend to be more closely shared between relatives<span style="font-family: inherit;">. If there is an altruistic action which greatly benefits an individual’s close relatives, then even if it causes harm to the altruist, a gene encoding that action can still be favoured by natural selection, because the altruist’s relatives have a high probability of also having the gene for the altruistic behaviour, and their fitness is increased by the altruistic individual’s behaviour.</span><br />
<span style="font-family: inherit;"><br /></span>
<span style="font-family: inherit;">This is how we
explain behaviours like alarm calls. If
a ground squirrel spots an approaching coyote, and the squirrel has a gene that
causes him to emit a loud trill at this sign of jeopardy, the noise may draw the
coyote’s attention to him and could well endanger his life. However, if the
warning saves the lives of his brother and sister squirrels, many of whom will share
the alarm-call gene, they may be more likely than other squirrels in the larger population to survive to reproductive age, thus indirectly passing on the altruist’s alarm-call gene.
Crucially, the more closely related a pair of individuals is, the more likely
they are to share any given gene; hence the geneticist J. B. S. Haldane’s tongue-in-cheek (and
possibly apocryphal) remark, in response to being asked whether he would
sacrifice his life to save a drowning brother: “No, but I would to save </span><i style="font-family: inherit;">two</i><span style="font-family: inherit;"> brothers, or eight cousins”.</span><br />
<span style="font-family: inherit;"><br /></span>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td><a href="http://upload.wikimedia.org/wikipedia/commons/f/f1/Spermophilus_beldingi.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://upload.wikimedia.org/wikipedia/commons/f/f1/Spermophilus_beldingi.jpg" height="400" width="327" /></a></td></tr>
<tr><td class="tr-caption"><span style="font-size: x-small;">A Belding’s ground squirrel watches for approaching predators. Source: <a href="http://en.wikipedia.org/wiki/Belding%27s_Ground_Squirrel">Wikipedia</a>.</span></td></tr>
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</div>
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<span lang="EN-GB"><span style="font-family: inherit;"><br /></span></span>
<span lang="EN-GB"><span style="font-family: inherit;"><br /></span></span>
<span lang="EN-GB"><span style="font-family: inherit;">As
with many 20th-century developments in evolutionary theory, the idea of kin selection can readily be
traced back to Darwin. In a famous passage in the <i>Origin of Species</i> (1859), he wrote:</span></span></div>
<blockquote class="tr_bq">
<i><span lang="EN-GB"><span style="font-family: inherit;">“a well-flavoured vegetable is cooked,
and the individual is destroyed; but the horticulturist sows seeds of the same
stock, and confidently expects to get nearly the same variety: breeders of
cattle wish the flesh and fat to be well marbled together; the animal has been
slaughtered, but the breeder goes with confidence to the same family. I have
such faith in the powers of selection, that I do not doubt that a breed of cattle,
always yielding oxen with extraordinarily long horns, could be slowly formed by
carefully watching which individual bulls and cows, when matched, produced oxen
with the longest horns; and yet no one ox could ever have propagated its kind.”</span></span></i></blockquote>
<div class="MsoNormal">
<span lang="EN-GB"><span style="font-family: inherit;">(This
example is made clearer when we remember that an ox is a castrated bull.)<o:p></o:p></span></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span lang="EN-GB"><span style="font-family: inherit;">It
was the evolutionary biologist W. D. Hamilton (1936–2000), however, who was
largely responsible for formalizing and popularizing kin selection, in the
1960s. He formulated the inequality now known as ‘Hamilton’s Rule’: if a trait costs
<i>C</i> units of reproductive success to one
individual, but provides <i>B</i> units of
benefit to a second individual or class of individuals, who is/are related to the first individual by a
relatedness coefficient of <i>r</i>, and the
inequality<o:p></o:p></span></span></div>
<div class="MsoNormal" style="text-align: center;">
<span style="font-family: inherit;"><i><span lang="EN-GB">rB</span></i><span lang="EN-GB"> > <i>C</i><o:p></o:p></span></span></div>
<div class="MsoNormal">
<span lang="EN-GB"><span style="font-family: inherit;">holds,
then the trait will be favoured by natural selection. When <i>rB</i> = <i>C</i>, the trait is selectively neutral, and when <i>rB </i>< <i>C</i>, it will be disfavoured. For example, in humans, brothers are related by <i>r</i> = 1/2, whereas cousins are related by <i>r</i> = 1/8. This is why Haldane professed that he was willing to give his own life (a cost of <i>C</i> = 1) to save two brothers (<i>B</i> = 2) or eight cousins (<i>B</i> = 8). In the hymenoptera, kin
selection explains why sterile workers might be willing to raise their siblings despite that it seems
to provide them with no <i>direct </i>benefit:
their altruistic behaviour towards reproductive siblings (drones and queens)
indirectly helps pass on their genes.<o:p></o:p></span></span></div>
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<div class="MsoNormal">
<span lang="EN-GB"><span style="font-family: inherit;">To
summarize thus far: we can use kin selection to explain why natural selection
might favour certain altruistic traits, including why we might expect the
production of a self-sacrificing, sterile worker caste to be favoured by
natural selection; and kin selection can be formally described by Hamilton’s
Rule. But Hamilton put his rule to more subtle use in the paper that introduced
it (Hamilton 1964) to explain a striking feature of social insects. In the
hymenoptera, colony life does not have a single origin; rather, social lineages
evolved from solitary lineages 9 times independently (Ross <i>et al.</i> 2013).
Despite these multiple origins, each evolutionarily ‘new’ instance of sociality
shares remarkably similar features. One particular such feature involves the sex of workers: the worker castes among all social hymenoptera are always
composed exclusively of females. Males, with very few exceptions, are never workers
and generally contribute little to colony life. Why has this sex bias reliably
recurred?<o:p></o:p></span></span><br />
<span lang="EN-GB"><span style="font-family: inherit;"><br /></span></span>
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://upload.wikimedia.org/wikipedia/en/a/a4/Honeybee02.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://upload.wikimedia.org/wikipedia/en/a/a4/Honeybee02.jpg" height="228" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Female worker honey bees return from foraging. Source: <a href="http://en.wikipedia.org/wiki/Honey_bee">Wikipedia</a>.</td></tr>
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<span lang="EN-GB"><span style="font-family: inherit;"><br /></span></span>
<span lang="EN-GB"><span style="font-family: inherit;">W.
D. Hamilton theorized that the relatedness term in his famous inequality was responsible. Most
animals familiar to us are diploid, which means that both males and females
have two sets of chromosomes: one from their mother and one from their father.
Full siblings under diploidy will have a relatedness coefficient of <i>r</i> = 1/2, because they each inherit half
of their mother’s genes and half of their father’s genes, and so the
probability that, at a particular locus, a randomly-selected allele from one
sibling and a randomly-selected allele from the other sibling are identical by
descent is 1/2. (It is possible to interpret the relatedness coefficient in a
number of ways, but this description suffices for our
purposes.) Hymenoptera, however, are not diploid but haplodiploid: males are
produced from unfertilized eggs and are haploid, with just one set of
chromosomes they inherit maternally; females are produced from fertilized eggs,
and are therefore diploid, with one set of chromosomes from each parent.<o:p></o:p></span></span></div>
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<br /></div>
<div class="MsoNormal">
<span lang="EN-GB"><span style="font-family: inherit;">This
leads to unusual relatedness relationships between siblings of different
sexes. For example, under haplodiploidy, two full sisters have a 3/4
probability of an allele at a given locus being identical, because they inherit
their father’s full complement of genes alongside half of their mother’s
genes. Therefore, a female is more related to her sisters (<i>r</i> = 3/4) than to her daughters (<i>r</i> = 1/2). (This differs from the case in diploids, where a female is equally related to her sisters and to her daughters, with <i>r</i> = 1/2 in both cases.) Hamilton hypothesized that
this could explain the sex bias in hymenopteran worker castes. After all, this
means that a female can more efficiently pass on her genes by raising her
mother’s daughters than her own, whereas males have no similar reason to favour their siblings over their offspring.<o:p></o:p></span></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span lang="EN-GB"><span style="font-family: inherit;">However,
under haplodiploidy, a female has only <i>r</i>
= 1/4 relatedness to her full brothers, because her brothers don’t inherit any
genes from her father at all. So, averaged across both sexes, females are actually equally related to their siblings (brothers and sisters) and offspring (sons and daughters), with an average relatedness coefficient of <i>r</i> = 1/2 in both cases. This realization deflated enthusiasm for
Hamilton’s haplodiploidy hypothesis. Nonetheless, despite the lack of
theoretical support, it still features prominently in many textbooks, and
indeed, even on the relevant Wikipedia pages.<o:p></o:p></span></span></div>
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<br /></div>
<div class="MsoNormal">
<span lang="EN-GB"><span style="font-family: inherit;">It
is important to note that this </span>rare mistake by an exceptionally gifted biologist<span style="font-family: inherit;"> has no bearing on whether the overall theory of kin selection is ‘true’: Hamilton’s haplodiploidy hypothesis may have fallen out of favour, but kin selection is still the logical conclusion of a gene-centred view of evolution. However, it does seem
that relatedness coefficients in and of themselves do not explain why
hymenopteran workers are only ever female. Rather, the most plausible theory is that hymenopteran workers are female because of
the ancestral pattern of parental care among their solitary ancestors (Bourke
& Franks 1995). Social hymenoptera evolved from solitary-living wasps, the
females of which provide care to their offspring in the form of food and
shelter. In contrast, paternal care in this clade is exceedingly rare. A
longstanding observation maintains that sib-rearing behaviours in social
hymenoptera look a lot like brood care in solitary hymenoptera, except
redirected toward brothers and sisters (<i>e.g.</i>,
Wheeler 1928). Furthermore, new genetic evidence suggests that maternal care
and sib care are controlled largely by the same genes (Amdam <i>et al.</i> 2006; Toth <i>et al.</i> 2007). This simple hypothesis, that females and not males
were pre-adapted to perform altruistic sib-rearing, and so it was females who
were better suited to the worker role, seems to explain patterns of sex biases
in worker castes across all eusocial lineages where brood care is the primary
function of workers, not just among the hymenoptera (Ross <i>et al.</i> 2013).<o:p></o:p></span></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span lang="EN-GB"><span style="font-family: inherit;">However,
it is still possible that haplodiploidy influenced the ancestral pattern of
parental care, precisely by predisposing female solitary wasps—and not males—to
provide care to their offspring. If it could be shown that haplodiploids are
more readily able to evolve maternal care than diploids, haplodiploidy could
still have played an evolutionary role in determining the sex of hymenopteran workers. This
possibility is the subject of some of my work with Andy Gardner, the results of
which I will share here in the near future.<o:p></o:p></span></span></div>
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<br /></div>
<div class="MsoNormal" style="text-align: center;">
<span style="font-family: inherit;"><span lang="EN-GB"><b>REFERENCES</b></span><o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: inherit;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: inherit;">Amdam, G.V., Csondes, A., Fondrk, M.K. & Page, R.E. 2006. Complex
social behaviour derived from maternal reproductive traits. <i>Nature</i> <b>439</b>:
76–78.<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-family: inherit;"><span lang="EN-GB">Bourke,
A.F.G. & Franks, N.R. 1995. <i>Social Evolution in Ants</i>. Princeton
University Press, Chichester.</span><o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-family: inherit;"><span lang="EN-GB">Hamilton,
W.D. 1964. The genetical evolution of social behaviour. I, II. <i>J.
Theor. Biol.</i> <b>7</b>: 1–52.</span><o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-family: inherit;"><span lang="EN-GB">Ross,
L., Gardner, A., Hardy, N. & West, S.A. 2013. </span>Ecology, not
the genetics of sex determination, determines who helps in eusocial populations<span lang="EN-GB">. <i>Curr. Biol.</i> </span><b>23</b>: 2383–2387.<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-family: inherit;">Toth, A.L., Varala, K., Newman, T.C., Miguez, F.E., Hutchison, S.K.,
Willoughby, D.A. <i>et al</i>. 2006. Wasp gene expression supports an
evolutionary link between maternal behavior and eusociality. <i>Science</i> <b>318</b>:
441–444.<o:p></o:p></span></div>
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<br /></div>
<span style="font-family: inherit;">Wheeler,
W.M. 1928. <i>The Social Insects</i>. Kegan Paul, Trench, Trubner & Co., London.</span><!--EndFragment-->Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-7867264995121108649.post-51484746887073458222014-02-02T09:00:00.000+00:002014-03-17T16:39:38.099+00:00Blabbing about blebbing: Oxford University’s Mathematical Institute conference on membrane dynamics and blebbing, September, 2013.<div style="text-align: justify;">
<i>In this post <a href="http://people.maths.ox.ac.uk/woolley/">Dr Thomas Woolley</a> reviews a recent conference he organised in Oxford. Bringing together experimentalists and theoreticians from around the world they had one focus: blebbing cells! </i> </div>
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If you have never heard of blebbing, you can be forgiven. Indeed, for a long time blebs were completely ignored as it was thought that they were signs of cell death. However, over the last twenty years experimentalists and theoreticians have been working hard to change the image of the humble bleb, from a simple nuisance to a sign of incredibly complex dynamics. This conference brought together the world’s leading experts in blebbing with the hope of not just simply offering new insights but also the chance to develop new contacts and breed new interdisciplinary collaborations.</div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDDfcRNmFc8bS8OxJIyLC2WEknTckSAtiEUB7_iZe06DvHmAqULkqwtUpAsJ6JooVBO5FrT_fIR08HdXqheFPeGSsb6aUZfn6l0aT-zOUpEJLITYsmjvn-WQDnAAuROYm4V9OMMfn2VKw/s1600/Fig2.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDDfcRNmFc8bS8OxJIyLC2WEknTckSAtiEUB7_iZe06DvHmAqULkqwtUpAsJ6JooVBO5FrT_fIR08HdXqheFPeGSsb6aUZfn6l0aT-zOUpEJLITYsmjvn-WQDnAAuROYm4V9OMMfn2VKw/s1600/Fig2.jpg" height="276" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1. The dynamic cycle of blebbing. © Thomas Woolley.</td></tr>
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To understand what a bleb is we must first understand a little about the structure of a cell. At its simplest, the cell can be characterised as an extremely thin and weak membrane which is attached to a stiffer actin cortex through adhesion proteins. These structures surround a pressurised fluid, known as cytosol. If the membrane becomes unstuck from the cortex, the intercellular pressure is able to push the membrane into a hemispherical blister, known as a bleb. Over time, cortex reforms in the bleb, which is then slowly retracted (see Fig 1). Although this may sound simple, certain cells are able to produces these protrusions rapidly and randomly all over the membrane (see Fig 2) and the processes that control each of these stages is not fully understood.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1wjZsiyxD9SpH_JSe1J1uXy6mOjyExv9qctHtsxYEVn7DamZAJXG7Lngfw3_G213sDsBs-EOxRs62ckFBDhoQra8xq9T6XLWZI5_XSCPRXnoaMGHMRIl86BSdHKZmR-TR402k7sooaK4/s1600/Cell.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1wjZsiyxD9SpH_JSe1J1uXy6mOjyExv9qctHtsxYEVn7DamZAJXG7Lngfw3_G213sDsBs-EOxRs62ckFBDhoQra8xq9T6XLWZI5_XSCPRXnoaMGHMRIl86BSdHKZmR-TR402k7sooaK4/s1600/Cell.jpg" height="179" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 2. A single cell that has produced a number of blebs. Electron
microscopy photo courtesy of the Skeletal Muscle Development Group,
University of Reading.</td></tr>
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Now-a-days blebs are known to aid in cell spreading, division, motility and many other processes besides. It was with this knowledge that experts from each of these blebbing fields were gathered together in the brand new Mathematical Institute of the University of Oxford. If you are wondering why we were in the mathematical department and not the biology department, it is simply because blebbing has a proud tradition of being a very multidisciplinary research area. Many of the field’s leading papers have both theoretical and experimental authors demonstrating what can be achieved when biological insights are tested mathematically, which, in turn leads to new predictions for experimentation.</div>
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The conference was opened with a wonderful plenary talk delivered Ewa Paluch. Being one of the field’s leading experimentalists she masterfully wove together the complex history of blebbing with modern insights, finally leading to new exciting work dealing with cells that are able to rapidly oscillate between bulging states. Her talk was then followed by Guillaume Salbreaux, one of her theoretical collaborators, who presented a number of mathematical frameworks in which these experiments could be understood.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQVRcRzNiwxJAXp3QmyzDOkn9-uYnRocSdbegKL5UDtINnXEtrIwzi0xUva_M7vsVRrN8LoiHX1rBaTouEmKJMSWKgjCDNiO-_HBcYuCT1vvH0D7P_TdswFQcEDRJ-641HLMp_RBw7ZuI/s1600/IMG_6143.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQVRcRzNiwxJAXp3QmyzDOkn9-uYnRocSdbegKL5UDtINnXEtrIwzi0xUva_M7vsVRrN8LoiHX1rBaTouEmKJMSWKgjCDNiO-_HBcYuCT1vvH0D7P_TdswFQcEDRJ-641HLMp_RBw7ZuI/s1600/IMG_6143.JPG" height="213" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 3. Ewa Paluch, University College London, entertaining a captive audience.</td></tr>
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Different blebbing cell were introduced by Ketan Patel and Henry Collins-Hooper, who demonstrated that the healing of muscle damage depends crucially on the ability of muscle stem cells to bleb. Working with Thomas Woolley of the Oxford Mathematical Institute, who also spoke, they were able to produce some ground breaking conclusions on how to regenerate the blebbing characteristics of older cells, thereby potentially allowing wounds to heal quicker. Phil Dash then presented the next stages of their work, involving a new direction considering membrane pores called “aquaporins”. Aquaporins let water in and out of the cell and have the potential to revolutionise the way we control bleb location and therefore cell motion.</div>
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One of the most exciting presentations of the day was from Robert Grosse. Robert surprised everyone by showing recent experiments of cells that were able to use blebs to invade other cells. His results were so new that there were gasps of amazement from the audience!</div>
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Another theoretical/experimental team from Cancer Research UK then presented some beautifully realistic simulations of blebbing cells and there corresponding experimental analogues. The work of Paul Bates, Melda Tozluoğlu and Erik Sahai, recently published in Nature Cell Biology, has set a new precedent, by which all new work will be measured. In particular they characterised why different methods of motility help the cell travel faster in different environments.</div>
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The second day was also predominantly about blebbing, with talks from Guillaume Charras on the adhesions that fix the membrane and cortex together and Wanda Strychalski presenting a simple but effective mathematical model that tests different assumptions about the fluid interior. The day also saw some more general cellular motion and membrane dynamic talks from Laura Kimpton and Marrino Arroyo, respectively. Laura’s prize winning work considers the crawling dynamics of cells and has much potential to be extended. Marrino’s cutting edge numerical methods offered simple reasons behind extremely complex membrane protrusions.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfX7iwSB8WSl7p7fV1Y4My7tddPb50ayew3qbJ5abfgruWu6M0U1x5441PvLf5VCjbBIGwOKWALrT7LPWVzWgvLJIbH894OYyxcF5aIWwHwZU8_GiJpfI7LZ22cf8_QrT16no7ISsPQbc/s1600/IMG_6177.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfX7iwSB8WSl7p7fV1Y4My7tddPb50ayew3qbJ5abfgruWu6M0U1x5441PvLf5VCjbBIGwOKWALrT7LPWVzWgvLJIbH894OYyxcF5aIWwHwZU8_GiJpfI7LZ22cf8_QrT16no7ISsPQbc/s1600/IMG_6177.JPG" height="320" width="213" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 4. Robert Kay, MRC Laboratory of Molecular Biology, speaking with passion about blebs in dictyostelium cells.</td></tr>
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The final talk by Robert Kay once again challenged our preconceived notions of cellular motion. He supplied convincing evidence suggesting a link between blebs and other cellular protrusions known as “lamellipodia”. Previously, it had been assumed that lamellipodia were quite different to blebs as lamellipodia were pushed out by the actin cortex, whilst blebs are simply driven by the pressure difference. However, Robert’s work suggests that the membrane of the lamellipodia may also be pushed out due to pressure gradients, whilst the actin skeleton fills in the space behind the membrane, thereby not actually pushing the membrane at all!</div>
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The two days were a wonderful meeting of minds. The focused direction of all of the participants led to much discussion of new ideas, new twists of old ideas and hopefully new collaborations. For myself, the take home message from the conference was that although we may all refer to our membrane protrusions as blebs, the protrusions come in many different shapes and sizes. Some look like small spherical hemispheres that grow randomly over the entire cell, whilst others are large amorphous expansions that are able to flow along chemical gradients.</div>
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Whatever the future may hold for blebs and membrane dynamics, it is certain that we are still generating more questions than answers.
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Thomas Woolleyhttp://www.blogger.com/profile/07895826981003298350noreply@blogger.com2tag:blogger.com,1999:blog-7867264995121108649.post-35051216990129068392014-01-30T09:00:00.000+00:002014-01-30T09:00:00.874+00:00Poster: Investigating bacterial ecology and evolution in complex environments<i>Another recent poster from <a href="http://www.maths.ox.ac.uk/contact/details/coyte" target="_blank">Katharine Coyte</a>, who is doing her DPhil between the WCMB and the <a href="http://zoo-kfoster.zoo.ox.ac.uk/node/32" target="_blank">Foster lab</a> in Zoology. This poster wan an award at the <a href="http://id2conference.org/" target="_blank">id2 conference</a>.</i><br />
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<i> </i>Linus Schumacherhttp://www.blogger.com/profile/09580921538587285737noreply@blogger.com1tag:blogger.com,1999:blog-7867264995121108649.post-73497035211285659132014-01-26T09:00:00.000+00:002014-03-17T16:39:48.729+00:0021st Century Turing<div style="text-align: justify;">
<i>In this post <a href="http://people.maths.ox.ac.uk/woolley/">Dr Thomas Woolley</a> describes one of the original, biggest and most outrageous ideas of mathematical biology. Thomas achieved his doctorate working on mathematical pattern formation within the WCMB in 2012, under the supervision of Prof. Philip Maini, Dr Ruth Baker and Dr Eamonn Gaffney. He is currently a <a href="http://www.sjc.ox.ac.uk/660-6315/Dr-Thomas-Woolley.html">Junior Research Fellow</a> for St John’s College, Oxford and works on the solid mechanics behind cellular motion. However, he still likes to keep an eye on pattern formation. He runs his own <a href="http://laughmaths.blogspot.co.uk/">mathematical outreach website</a> as well as working as a mathematical consultant on the TV show “Dara O’Briain’s School of Hard Sums”.</i> </div>
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On the 7th June 1954, just a couple of weeks before his 42nd birthday, the world lost one of its greatest mathematicians. Betrayed by the very government that he had fought so hard to protect during World War II, Alan Mathison Turing (Figure 1) took his own life by eating an apple laced with cyanide. Although his tale is an extremely sad one, this post is designed to focus on his achievements and genius, rather than his depression and death.<br />
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<tr><td class="tr-caption" style="text-align: center;">Figure 1. A black and white vector portrait of Alan Turing. © Thomas Woolley.</td></tr>
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Although Turing is well known as an eminent figure in computation, logic and cryptography, he is my hero because of the work he did just two years before his untimely death. Specifically, he was interested in such questions as:</div>
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<li>Why is there something rather than nothing?</li>
<li>How are complex structures formed from simple components?</li>
<li>Why doesn't everything tend to a state of uniformity?</li>
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In 1952 he published a paper, <a href="http://www.dna.caltech.edu/courses/cs191/paperscs191/turing.pdf">The Chemical Basis of Morphogenesis</a>, trying to answer these questions. His ideas were revolutionary and not fully appreciated at the time. However, his paper was the start of a whole new field of mathematics, which 60 years later still uses his ideas as their foundation.</div>
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In order to produce patterns, Turing coupled two components together that individually would not lead to patterning. First, he considered a stable system of two chemicals. The chemicals reacted in such a way that if they were put in a small container the system eventually produced a uniform density of products, thus, no patterns. Second, he added the mechanism of diffusion. This meant that the chemicals could move. Incredibly, he showed that if the chemicals are put in a larger container, then diffusion could make the equilibrium state unstable, leading to a spatial pattern. This process is now known as a diffusion-driven instability.</div>
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To see how remarkable this is, consider putting a spot of ink in water, without stirring (Figure 2). The ink will diffuse throughout the water and eventually the solution will be one shade of colour. There will be no patches that are darker or lighter than the rest. However, in Turing’s mechanism diffusion does create patterns. When this happens the system is said to have self-organised and the resultant pattern is an emergent property. In this respect, Turing was many years ahead of his time: he showed that understanding the integration of the parts of a system plays a role as important (if not more so) as the identification of the parts themselves. </div>
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Figure 2. A 3D rendering of diffusion of purple dye in water. Image used under the Creative Commons License. Original from <a href="http://en.wikipedia.org/wiki/File:Blausen_0315_Diffusion.png">here</a>.</div>
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Turing termed the chemicals in his framework morphogens and hypothesised that cells would adopt a certain fate if the individual morphogen concentrations breached a certain threshold value. In this way, the spatial pattern in morphogen concentration would serve as a pre-pattern to which cells would respond by differentiating accordingly.</div>
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Of course, it is possible to produce patterns by other means. One such mechanism is known as the <a href="http://en.wikipedia.org/wiki/French_flag_model">French flag model</a>. Suppose that a row of cells has a constant source of morphogen at its left-hand boundary. If this morphogen is allowed to diffuse outwards from the source it produces a concentration profile, or gradient, that is higher on the left than the right (Figure 3). The cells on the left sense a higher concentration of morphogen and respond in some way, e.g. they turn red. The central cells sense an intermediate concentration and the right-hand cells sense a low concentration, and so they produce different responses, e.g. they turn white and blue, respectively. Hence, through the diffusion of a single morphogen we are able to produce the so-called French flag pattern. Importantly, we do not need the morphogens to react.</div>
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Figure
3. French flag model pattern producible by a source of diffusible
chemical assumed to lie along the left-hand boundary. The source
produces an exponentially decreasing profile similar to that shown in
the top image. The different levels of concentration sensed by the
polygons (denoting cells) are visualised by their given colour in the
bottom image. The cells are red if they can sense a high concentration,
white for medium concentrations and blue for low concentrations. ©
Thomas Woolley.</div>
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However, the French flag pattern fundamentally assumes the heterogeneous localisation of a source. Namely, if the source was not only along one side, but instead uniform everywhere then no pattern would emerge. The Turing mechanism of pattern formation needs no such assumption. The reactions and diffusion are defined to happen equally everywhere across the domain. Yet heterogeneity can be produced (Figure 4).</div>
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<tr align="justify"><td class="tr-caption">Figure 4. An evolving morphogen concentration producing a Turing
pattern. The <i>x</i>-axis shows the space, whilst the <i>y</i>-axis shows the concentration of one of the interacting morphogens, <i>u</i>. The
simulation starts from a random initial condition and tends to a three-peak Turing pattern. © Thomas Woolley.</td></tr>
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Hopefully, my next post on this blog will detail how mathematical biologists use these patterns to understand animal skin pigmentation, limb formation and maybe even heart attacks.
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Thomas Woolleyhttp://www.blogger.com/profile/07895826981003298350noreply@blogger.com0tag:blogger.com,1999:blog-7867264995121108649.post-54736985126065359952014-01-22T16:54:00.000+00:002014-03-17T16:39:58.084+00:00Poster: The fractured bacterium: how horizontal gene transfer and selection divide the genome<i>Another poster from the DTC 4th year conference, by <a href="http://zoo-kfoster.zoo.ox.ac.uk/node/33" target="_blank">Rene Niehus</a> who is co-supervised between the WCMB and <a href="http://zoo-kfoster.zoo.ox.ac.uk/" target="_blank">the Foster lab in the Department of Zoology</a>.</i><br />
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Linus Schumacherhttp://www.blogger.com/profile/09580921538587285737noreply@blogger.com0tag:blogger.com,1999:blog-7867264995121108649.post-63855873711292345582014-01-19T00:06:00.002+00:002014-01-22T16:55:26.151+00:00Workshop on "Mechanics and growth of tissues: from development to cancer"<i>In this post Dr Alexander Fletcher, Research Fellow in Computational Science at the WCMB, discusses the workshop "<a href="https://mgt2014.curie.fr/">Mechanics and growth of tissues: from development to cancer</a>", which took place at the Institut Curie in Paris on 13-16 January 2014, and describes the content of his poster contribution.</i><br />
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Workshop overview</h4>
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Over the last few years, scientists have increasingly sought a <i>quantitative </i>understanding of the mechanisms underlying the dynamic behaviour of tissues during growth and disease. The aim is to elucidate how cells collectively self-organise into tissues and maintain configurations through different celllular signalling systems. To accelerate this endeavour, the workshop brought together biologists, physicists and mathematicians to discuss recent developments in this field: from experimental advances such as optogenetics; through improvements in live-imaging and microscopy; to new integrative approaches to studying the interplay between cell mechanics and signalling, combining <i>in vivo</i> observations with computational modelling.<br />
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The workshop comprised 23 invited talks, 12 selected talks and 100 posters (including one by me). It also included one lunchtime session featuring <a href="http://www.weizmann.ac.il/mcb/UriAlon/homepage">Uri Alon</a> playing guitar. Over four days, the workshop covered five broad themes: "tissue homeostasis and cancer", including tissue mechanics and signalling; "development", including tissue patterning and shape; "dynamics and gene networks"; "cell division" and "new experimental aspects". </div>
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<span style="font-family: inherit;">Some highlights from the workshop</span></h4>
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<span style="font-family: inherit;">The workshop included several excellent talks, of which I would like to highlight three in particular: those of Uri Alon, Buzz Baum and Boris Shraiman. These talks ranged from evolutionary trade-offs, to cell shape changes during mitosis, to the role of mechanics in tissue growth.</span><br />
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<span style="font-family: inherit;">The workshop opened with an excellent talk by <a href="http://www.weizmann.ac.il/mcb/UriAlon/homepage">Uri Alon</a> (Weizmann Institute of Science) on "<a href="http://www.weizmann.ac.il/mcb/UriAlon/sites/mcb.UriAlon/files/shoval2012.pdf">Evolutionary tradeoffs and the geometry of phenotype space</a>". This described his group's work that used the <a href="http://en.wikipedia.org/wiki/Pareto_front">Pareto front</a> concept from multi-objective optimization to establish best-trade-off phenotypes as weighted averages of phenotypes specialized for single tasks (termed 'archetypes'). For two tasks for instance, phenotypes fall on the line connecting the two archetypes. An intriguing consequence of this work is a significant dimensional reduction in the trait space explored by phenotypes. One impressive example of this was provided in the form of <a href="http://www.nature.com/nmeth/journal/v3/n8/abs/nmeth895.html"><i>E. coli</i> gene expression data</a>, which (with appropriate transformation) were found to lie on a line between two points corresponding to 'growth' and 'survival' phenotypes, even though the measured phenotype space was 2,000-dimensional. This motivates the interesting suggestion that the vertices of polyhedra fit to such datasets might provide information or intuition on the tasks that may be present.</span><br />
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<span style="font-family: inherit;">In a talk titled "The importance of being well-rounded", <a href="http://www.ucl.ac.uk/lmcb/research-group/buzz-baum-research-group">Buzz Baum</a> (UCL) discussed work done by his and Matthieu Piel's labs to investigate <a href="http://www.sciencedirect.com/science/article/pii/S1534580713001858">the function of mitotic cell rounding</a>. They found that mitotic rounding generates a space in which to form and correctly position the spindle, and that cancer cells seem to have a greater requirement for rounding (possibly due to ploidy). It was also <a href="http://www.sciencedirect.com/science/article/pii/S1534580712002766">established </a>through RNAi and optical stretching that cells change shape very early during mitosis, and that this is driven by relocalisation of the protein ECT2. This work highlighted the exciting advances that are being made in elucidating the mechanisms coupling mitotic cell shape changes to cell cycle progression and provided much food for thought for future computational models of proliferation within epithelial tissues.</span><br />
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<span style="font-family: inherit;"><a href="http://www.kitp.ucsb.edu/shraiman/">Boris Shraiman</a> (KITP) gave a talk titled "Mechanics of epithelial morphogenesis: from theory to experiment and back", which began with an excellent discussion of how theorists can contribute to our understanding of developmental processes. This included a reference to Alan Turing's seminal 1952 <a href="http://rstb.royalsocietypublishing.org/content/237/641/37.abstract">paper</a> on morphogenesis, which made it onto the Nature-sanctioned list of <a href="http://www.nature.com/milestones/development/milestones/index.html">milestones in development</a>. After describing his earlier work exploring how <a href="http://www.pnas.org/content/102/9/3318.short">mechanical feedback could regulate tissue growth</a>, Shraiman went on to describe experimental validation for this work, including a <a href="http://dev.biologists.org/content/140/19/4051.short">quantitative map of strain</a> in the case of the <i>Drosophila</i> wing imaginal disc (a model system in development). He also discussed some <a href="http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371%2Fjournal.pcbi.1002512">recent work</a> on inferring stresses from static images based on a 'mechanical inverse' method, which overcomes issues associated with more invasive experimental protocols such as <a href="http://www.sciencedirect.com/science/article/pii/S0960982209018405">laser ablation of cell junctions</a>. <span lang="EN-US">Similar approaches are likely to become more widely used, as </span><span lang="EN-US">an increasing number of integrative
studies try to place computational models on a quantitative footing through
validation against experimental measurements of forces within tissues.</span></span></div>
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<span style="font-family: inherit;">Our contribution</span></h4>
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<span style="font-family: inherit;">The title of the poster that I presented at the workshop is "Implementing vertex models of epithelial sheets in a consistent computational framework".</span><span style="font-family: inherit;"> This poster is based on our recent publication of the same title [</span><a href="http://www.sciencedirect.com/science/article/pii/S0079610713000989" style="font-family: inherit;">1</a><span style="font-family: inherit;">]. </span><br />
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<tr><td class="tr-caption" style="text-align: center;"><span style="background-color: white;"><span style="color: black; font-family: inherit; font-size: x-small;">Full-size poster available <a href="http://dx.doi.org/10.6084/m9.figshare.899202">here</a>.</span></span></td></tr>
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<span style="font-family: inherit;">Vertex models consider cells as individual objects and assume that </span><span style="font-family: inherit;">epithelial mechanics are dominated by forces acting within the </span><span style="font-family: inherit;">plane of cellular junctions (adherens junctions). Cells are considered as two-dimensional polygons representing cellular </span><span style="font-family: inherit;">interfaces, with vertices forming where three or more polygons meet (figure </span><b style="font-family: inherit;">a</b><span style="font-family: inherit;"> below). Every vertex moves in response </span><span style="font-family: inherit;">to forces due to growth, interfacial tension and hydrostatic pressure within each cell (figure </span><b style="font-family: inherit;">b</b><span style="font-family: inherit;"> below). </span><span style="font-family: inherit;">The precise forces </span><span style="font-family: inherit;">considered and the method of implementation vary across models. </span><span style="font-family: inherit; text-align: justify;">In order to accurately describe
epithelial dynamics, cells must be allowed to form and break bonds, and be
prevented from (self) intersecting. This is implemented through simple
operations, such as cell intercalation (also called neighbour exchange or T1 transition; figure <b>c</b> below). The evolution
of the system is thus a combination of relaxation to mechanical equilibrium and
changes in tissue connectivity according to prescribed cell rearrangement
processes.</span><br />
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<tr><td class="tr-caption" style="text-align: center;">Schematic illustrating the basic assumptions of vertex models. Image reproduced from [2].</td></tr>
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<span style="font-family: 'Times New Roman', serif;"><br /></span>
<span style="font-family: inherit;">Vertex models are increasingly used to study cellular </span><span style="font-family: inherit;">processes within epithelia, including cell motility, cell–cell adhesion, mitosis, delamination and apoptosis</span><span style="font-family: inherit;"> [3].</span><span style="font-family: inherit;"> However, a major barrier to the wider use of such models as a </span><span style="font-family: inherit; text-align: justify;">computational tool by the scientific community is the </span><span style="font-family: inherit; text-align: justify;">lack of standards or benchmarks. It is still the case that previously developed models and methods are often not re-used effectively, since they are typically not available as rigorously tested, open source simulation software. It is therefore difficult to guara</span><span style="text-align: justify;"><span style="font-family: inherit;">ntee the reproducibility of computational results.</span></span><br />
<span style="text-align: justify;"><span style="font-family: inherit;"><br /></span></span>
<span style="font-family: inherit;"><span style="text-align: justify;">Our work has sought to address this problem by providing </span><span style="text-align: justify;">an open source C++ implementatio</span><span style="text-align: justify;">n of vertex models of epithelial tissues</span><span style="text-align: justify;"> within <a href="http://www.cs.ox.ac.uk/chaste/">Chaste</a> [<a href="http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371%2Fjournal.pcbi.1002970">4</a>]. </span><span style="background-color: white; line-height: 20px; text-align: justify; word-spacing: -1.0499999523162842px;">Chaste comprises fully tested, industrial-grade software that has been developed using an agile approach. This computational framework allows one to easily change assumptions regarding force generation and cell rearrangement processes within these models. In our paper we illustrate the versatility and generality of this framework using a number of biological examples, with a focus on providing full details of all technical aspects of our model implementations. Of course, this work is ultimately driven by some concrete scientific problems arising in the study of epithelial dynamics, which I hope to discuss in more detail in a future blog post.</span></span><br />
<span style="font-family: inherit;"><br /></span>
<br />
<h4>
<span style="font-family: inherit;">Archiving research posters</span></h4>
<h4>
<span style="font-family: inherit; font-weight: normal;"><br /></span></h4>
<h4>
<span style="font-family: inherit; font-weight: normal;">In the spirit of open science, I have uploaded my workshop poster to Figshare. You can find it </span><a href="http://dx.doi.org/10.6084/m9.figshare.899202" style="font-family: inherit; font-weight: normal;">here</a><span style="font-family: inherit; font-weight: normal;">. Personally, </span><span style="font-family: inherit; font-weight: normal;">I will try to do this with all my research posters in future and hope that this becomes the norm for conferences, if not using Figshare then with some other form of online repository. It would seem that everyone benefits: the presenter benefits from their research output being accessible as well as citable (all Figshare content has its own DOI), and is able to link to and update other relevant material; other conference attendees benefit, who may not have time to make it to all the posters they wish to view or may overlook a poster, for example due to a misleading title; and the wider scientific community also benefits, who did not or could not attend the conference but may be interested in reading the poster.</span></h4>
<br />
<h4>
References</h4>
<ol>
<li><span style="font-size: x-small;">A.G. Fletcher, J.M. Osborne, P.K. Maini and D.J. Gavaghan (2013). Implementing vertex dynamics models of cell populations in biology within a consistent computational framework. <i>Prog. Biophys. Mol. Biol.</i> doi:10.1016/j.pbiomolbio.2013.09.003</span></li>
<li><span style="font-size: x-small;">J.-P. Vincent, A.G. Fletcher and L.A. Baena-Lopez (2013). Mechanisms and mechanics of cell competition in epithelia. <i>Nat. Rev. Mol. Cell Biol.</i> 14:581-591.</span></li>
<li><span style="font-size: x-small;">A.G. Fletcher, M. Osterfield, R.E. Baker and S. Shvartsman (2013). Vertex models of epithelial morphogenesis. <i>Biophys. J. </i>(in press)</span></li>
<li><span style="font-size: x-small;"><span style="background-color: white; font-family: inherit; text-align: justify;">G.R. Mirams, C.J. Arthurs, M.O. Bernabeu, R. Bordas, J. Cooper, A. Corrias, Y. Davit, S-J. Dunn,</span><span style="background-color: white; font-family: inherit; text-align: justify;">A.G. Fletcher</span><span style="background-color: white; font-family: inherit; text-align: justify;">, D.G. Harvey, M.E. Marsh, J.M. Osborne, P. Pathmanathan, J. Pitt-Francis, J. Southern, N. Zemzemi and D.J. Gavaghan (2013). Chaste: an open source C++ library for computational physiology and biology. </span><i style="background-color: white; font-family: inherit; text-align: justify;">PLoS Comput. Biol.</i><span style="background-color: white; font-family: inherit; text-align: justify;"> 9:e1002970. doi:</span><span style="background-color: white; line-height: 18.0049991607666px;"><span style="font-family: inherit;">10.1371/journal.pcbi.1002970</span></span></span></li>
</ol>
Anonymoushttp://www.blogger.com/profile/06781843200914952471noreply@blogger.com0tag:blogger.com,1999:blog-7867264995121108649.post-25142231998054024902014-01-16T10:37:00.000+00:002014-01-22T16:56:05.461+00:00Poster: A simple model of wound healing in normal and diabetic mice<i>We will try and upload most posters that members of the WCMB present at conferences. The DTC 4th year conference is coming up, for which <a href="http://www.maths.ox.ac.uk/contact/details/bowden">Lucie Bowden</a> has prepared the poster below.</i><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8JnYSP_W4P8myOBZMuwIQXbyYscYrKGLQVDU1DxC-QTTpz4ua74spTO1NH8ZJltAl1ii_P0ihwzfj3eeNDPH8FgDV91-AkH-4Mt_pmVsKuK8O5WvG8gHXCzs2zlQ6QNl0OxZW_DPzmPrX/s1600/luciebowden_poster.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8JnYSP_W4P8myOBZMuwIQXbyYscYrKGLQVDU1DxC-QTTpz4ua74spTO1NH8ZJltAl1ii_P0ihwzfj3eeNDPH8FgDV91-AkH-4Mt_pmVsKuK8O5WvG8gHXCzs2zlQ6QNl0OxZW_DPzmPrX/s400/luciebowden_poster.png" height="280" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">(click for larger version)</td></tr>
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<br />Linus Schumacherhttp://www.blogger.com/profile/09580921538587285737noreply@blogger.com0tag:blogger.com,1999:blog-7867264995121108649.post-69078970006470318982014-01-13T06:15:00.000+00:002015-04-22T17:30:25.737+01:00Mathematical modelling of oxygen transport in cardiac and skeletal muscle tissues<!--[if gte mso 9]><xml>
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</xml><![endif]--><i>In this post <a href="http://www.maths.ox.ac.uk/contact/details/alshammari">Abdullah Al-Shammari</a> describes the DPhil project he worked on at the WCMB during the last 4 years. This project was supervised by Dr <a href="http://people.maths.ox.ac.uk/~gaffney/">Eamonn Gaffney</a> in close collaboration with Prof Stuart Egginton, whose labs in <a href="http://www.birmingham.ac.uk/staff/profiles/cem/CVRS/Egginton-Stuart.aspx">Birmingham</a> and <a href="http://www.fbs.leeds.ac.uk/staff/profile.php?tag=Egginton_S">Leeds</a> kindly provided us with biological datasets and interpretation of our modelling results.</i><br />
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<a name='more'></a><span style="font-family: inherit;"><span style="font-size: small;">I am generally interested in exploring the effects of
incorporating the spatial heterogeneities in skeletal and cardiac muscles on
the transport of oxygen (O2), with
the aim of developing indices and research tools that allow an objective
assessment of tissue oxygenation. By ''heterogeneity'' here I mean basing my mathematical
modelling on the micro-geometry extracted from images based on the histology of
muscle tissue biopsies (Fig. 1A). This work has implications on muscle
physiology and pathology [1-4], e.g. muscle fibre re-modelling, the spatial
organisation of adaptive angiogenesis (capillary
growth from pre-existing capillary bed), and muscle <i>ischaemia</i>. Moreover,
it allows for <i>in silico</i> examination of the relative efficiency of
changes in different components within the pathway of O2 transport to tissue [5], thus providing a framework for assessing experimental
modulations in pathological situations.</span></span></div>
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<![endif]-->Before delving into the details of my work, I will begin by
emphasising the importance of O2 transport to muscles,
among other tissues. The availability of energy within muscle cells (fibres) is
essential for sustaining healthy functions, e.g. muscle contraction and heat
production, where the preference is generally for aerobic (<i>oxidative</i>)
respiration which generates large amounts of energy in the form ATP through oxidative phospohrylation in mitochondria. Hence, a
continuous local supply of O2 to muscle fibres is necessary for matching their
oxidative demand for energy.</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-GB; mso-ascii-theme-font: major-bidi; mso-bidi-language: HI; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: KHTDVD+CMR10; mso-fareast-language: ZH-CN; mso-hansi-theme-font: major-bidi;"> </span> </span></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbBKDOrz67BIVYnjral-mNxA_gWIy0r6dCPVb3_N5mX_ag_Ql5ozZpSsbvlgmQm-c_qPnkvaYdhJdELE9pPpXWdQIHKBfQqJKEpedF1XYFW5CHiKhu8K-X-2jpPhoUBgLvRVJthadJJTU/s1600/fig1.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbBKDOrz67BIVYnjral-mNxA_gWIy0r6dCPVb3_N5mX_ag_Ql5ozZpSsbvlgmQm-c_qPnkvaYdhJdELE9pPpXWdQIHKBfQqJKEpedF1XYFW5CHiKhu8K-X-2jpPhoUBgLvRVJthadJJTU/s1600/fig1.png" height="242" width="400" /></a></td></tr>
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<div style="text-align: justify;">
<span style="font-size: small;"><b><span style="font-family: "Times New Roman","serif";">Figure 1. (A)</span></b><span style="font-family: "Times New Roman","serif";"> typical tissue cross
section of rat skeletal muscle (m. extensor digitorum longus) with capillary
location identified by alkaline phosphatase staining. The dark structures are
capillaries, the lighter objects are muscle fibres, and the lightest region is
the interstitial space. The scale bar corresponds to 50 µm. <b>(B)</b> An
expanded region of the original image on which Voronoi polygons are superimposed
by dotted blue lines. A central Voronoi polygon is highlighted in dark gray and
overlaps adjacent fibres, where the overlaps represent the fractional supply
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<div class="Standard" style="text-align: justify; text-autospace: none;">
<span style="font-family: inherit;"><span style="font-size: small;">Such an
aerobic respiration is contingent on a local capillary bed ensuring adequate O2 delivery within short diffusion distances of muscle fibres (Fig. 1B). In
particular, the microvascular transport of oxygen to tissue depends on numerous
factors including the distribution, permeability and tortuosity of capillaries;
the location of mitochondria; variations in the capillary blood flow and
haematocrit; the anatomical details of interstitial and cellular geometry; the
levels of intracellular facilitated diffusion; the temperature and the interaction
of haemoglobin and oxygen. How such factors orchestrate so as to dictate O2 functional capillary supply (FCS) to striated muscles, and whether this
is particularly sensitive to one or more of these factors, are important
questions that to date have far from a complete answer.</span></span></div>
<div class="Standard" style="text-align: justify;">
<span style="font-family: inherit;"><span style="font-size: small;"><br /></span></span></div>
<span style="font-family: inherit;"><span style="font-size: small;">Consequently, our current understanding of experimental
interventions to enhance FCS in diseased tissue, such as chronic ischaemia in skeletal and cardiac muscles, is far from complete [3, 6]. In particular, while treatment of such pathologies would certainly
benefit from local enhancement of FCS of oxygen by inducing angiogenesis to match the local tissue demand, the
classification of oxygen and metabolite supply that is based on conventional FCS measures can give conflicting
results, thus leading to poor interpretations [6]. To this end, there has been
a growing interest in improving the characterisation of FCS in effort to improve the interpretation of
studies assessing pharmacological modulations of angiogenesis in response to
skeletal or cardiac muscle pathologies (Fig. 1B).</span></span></div>
<div class="Standard" style="text-align: justify; text-autospace: none;">
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<span style="font-size: small;"><b><span style="font-family: "Times New Roman","serif";">Figure
</span><span style="font-family: "Times New Roman","serif";">2</span></b><span style="font-family: "Times New Roman","serif";"><b>:</b> </span><span lang="EN-US" style="font-family: "Times New Roman","serif";">A direct numerical exploration of the oxygen
transport problem within tissue cross sections (<b>A</b>) can be pursued via
image capture, overlaying a mesh which is faithful to the geometry captured
from biopsies (<b>B</b>) and refined within regions of complex geometry (<b>C</b>).
This allows a numerical solution of oxygen transport equations, which capture
the biophysics of oxygen delivery while accounting for histological details.
However, the complexity at the microvascular level limits the length scales
which may be readily explored in this manner, especially for 3-D simulations,
or for simulations within a large parameter space [7-9]. </span></span></div>
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<br />
My work, in particular, seeks to isolate the important factors which govern oxygen supply and highlight factors whose influence is relatively weak. For example, I address the effect of detailed muscle micro-geometry such as incorporating (<i>i</i>) the distribution of capillaries [7], (<i>ii</i>) the distribution of muscle fibres, their sizes, and their different types [8], (<i>iii</i>) the detailed distribution of mitochondria within muscle fibres [11], and (<i>iv</i>) the facilitated diffusion by myoglobin [9, 11]. In addition, I seek to explain the relationship between muscle fibre size and mitochondria distribution, which influences O2 diffusivity and demand. This is better suited for finite elements models where a mathematical framework is used to simplify such investigations on complicated geometries and relatively large domain sizes, thus allowing their application to larger biological imaging datasets (Fig. 2). <br />
<br />
<span style="font-size: small;"><span style="font-family: inherit;">
My results highlight the relative importance of
such heterogeneities in partitioning capillary O2 supply to muscle
fibres, and emphasise that the extent of diffusion areas, rather than 1D
diffusion distances, may better elucidate the link between capillary supply and
tissue demand. In particular, the distributions of areas diffusively supplied
by individual capillaries (capillary supply areas) provide a means to identify <i>where</i>
deficient supply to tissue may occur (Fig. 3B), thereby naturally giving a
methodological way to localise potential compensatory growth of new capillaries
[8]. The possibility of such a localisation of angiogenesis is a direct result of modelling O2 supply in terms capillary supply areas. Indeed, everything else fixed, the
larger the capillary supply area the lower the O2 levels [10]. This
explains the usual pattern observed in skeletal muscle of all vertebrates,
namely that capillary supply (O2 levels) scales with respect to
fibre size [4]. Moreover, modifications to this basic growth process due to experimental
modulations or pathologies can be conveniently explored within the framework of
capillary supply areas [9].</span></span><br />
<br />
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<span style="font-size: small;"><b><span style="font-style: normal;">Figure </span><span style="font-style: normal;">3</span></b><span style="font-style: normal;"><b>:</b> Investigation of metabolic and
anatomic heterogeneities. <b>(A)</b> A tissue with heterogeneous distribution
of fibre sizes and types (red shading = oxidative fibers; blue shading =
glycolytic fibres; red polygons = Voronoi polygons; black = trapping regions). <b>(B)</b>
Distribution of capillary supply areas (Voronoi polygons & trapping regions).
<b>(C)</b> Area histograms of oxygen tension for the same tissue. <b>(D)</b> A
heat map visualising the spatial distribution of oxygen established by diffusion from capillaries and consumption by
tissue (mitochondria).</span></span></div>
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<br />
<span style="font-family: inherit;"><span style="font-size: small;">Also, of key interest is using this framework to
investigate the appropriateness of common oxygen supply indices (e.g. Voronoi
polygons; Figs. 1B, 3A-B) that are aimed at specifying estimates for functional
capillary supply, especially in the presence of the aforementioned
heterogeneities (see [6] for a detailed list of indices). While such polygons are typically assumed
to represent the actual supply area of individual capillaries in physiological
studies, their use has yet to be fully validated by mathematical models of oxygen transport.</span></span><br />
<span style="font-family: inherit;"><br /></span>
<span style="font-family: inherit;"><span style="font-size: small;">I explored this question by calculating O2 supply regions (trapping regions) from the oxygen flux lines established by diffusion from capillaries; this is an intensive computational alternative to Voronoi polygons (Fig. 4). My results [8-9] indicated that methods based on Voronoi polygons may be useful for assessing capillary supply in homogeneous and heterogeneous muscle tissues (Fig. 3A-B), but their use may become problematic in the presence of extensive capillary rarefaction (localised low capillary density), substantial spatial differences in O2 extraction capacities, and where extensive non-uniformity in capillary O2 content occurs. In such cases, trapping regions provide a more general representation of capillary supply areas. In addition, trapping regions can account for additional influences of heterogeneity that are absent in the consideration of Voronoi polygons (e.g. differences in local metabolism or muscle fibre size).</span></span><br />
<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnoo_5GlnKeCWRMTz09A2PhVlIO3bBjEAEbnE1BUmoqd1j3xrS92oc8Acp7tRNEjVa2TDwEyDbvFOOnf7xG27SZNsj4xr2spkcp08GO-wxr3QUJd_qMW1nviVfMkmnSgLR8kWL6fyAdko/s1600/fig4.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnoo_5GlnKeCWRMTz09A2PhVlIO3bBjEAEbnE1BUmoqd1j3xrS92oc8Acp7tRNEjVa2TDwEyDbvFOOnf7xG27SZNsj4xr2spkcp08GO-wxr3QUJd_qMW1nviVfMkmnSgLR8kWL6fyAdko/s1600/fig4.png" height="317" width="320" /></a></td></tr>
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<span style="font-size: small;"><b><span style="font-style: normal;">Figure </span><span style="font-style: normal;">4</span></b><span style="font-style: normal;"><b>:</b> Computation of the biophysical
modelling predictions of oxygen capillary supply areas (trapping regions) in 2D
muscle tissue. Trapping regions (black lines) characterise capillary supply by
delimiting the oxygen flux lines (red lines) diffusing from capillaries (red
disks).</span></span></div>
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<span style="font-family: inherit;"><span style="font-size: small;"><br />Nonetheless, I also observed that the correlation between Voronoi polygons and trapping regions can provide insight into the control of local tissue remodelling in striated muscles [8]. For example, in aerobic muscle, this correlation suggests a sensitive local control of angiogenesis on the length scale of fibre diameter. In particular, in mixed muscles, the effect of capillary loss becomes insignificant when localised to glycolytic fibres, suggesting that such rarefactions may be mitigated by reducing fibre O2 consumption.<br /><br /> The aforementioned models and computational framework have been coded, optimised, packaged, and made available in Matlab for easy use in Prof Egginton's experimental laboratory at the University of Leeds. </span></span><br />
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<b><span style="font-family: Times, Times New Roman, serif;">References</span></b></div>
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<ol><span style="background-color: white;"><span style="font-family: Times, Times New Roman, serif;">
</span></span>
<li><span style="background-color: white; font-family: Times, Times New Roman, serif;">Hudlická
O, Brown M, Egginton S. Angiogenesis in skeletal and cardiac muscle. <i>Physiological
Reviews</i>, 1992; 72(2):369-417.</span></li>
<span style="background-color: white;"><span style="font-family: Times, Times New Roman, serif;">
</span></span>
<li><span style="background-color: white; font-family: Times, Times New Roman, serif;">Badr
I, Brown M, Egginton S, Hudlická O, Milkiewicz M, Verhaeg J. Differences in
local environment determine the site of physiological angiogenesis in rat
skeletal muscle. <i>Experimental Physiology</i>, 2003; 88(5):565-568. </span></li>
<span style="background-color: white;"><span style="font-family: Times, Times New Roman, serif;">
</span></span>
<li><span style="background-color: white; font-family: Times, Times New Roman, serif;">Deveci D, Egginton S. Muscle
ischaemia in rats may be relieved by overload-induced angiogenesis. <i>Experimental
Physiology</i>, 2002; 87(4):479-488. </span></li>
<span style="background-color: white;"><span style="font-family: Times, Times New Roman, serif;">
</span></span>
<li><span style="background-color: white; font-family: Times, Times New Roman, serif;">Wüst RCI, Gibbings SL, Degens H,
Fiber capillary supply related to fiber size and oxidative capacity in human
and rat skeletal muscle. In: Liss, P and Hansell, P and Bruley, D F and
Harrison, D K, editor. Oxygen Transport to Tissue XXX. vol. 645 of Advances in
Experimental Medicine and Biology; 2009, pp. 75-80.</span></li>
<span style="background-color: white;"><span style="font-family: Times, Times New Roman, serif;">
</span></span>
<li><span style="background-color: white; font-family: Times, Times New Roman, serif;">Hauton D, Winter J, <b>Al-Shammari AA</b>, Gaffney
EA, Evans RD, Egginton S, <span style="text-align: start;">Changes to both metabolism and performance accompany acute reductions in functional capillary supply. Biochimica et Biophysica Acta (BBA)-General Subjects, 2015, 1850(4): 681-690</span>. DOI: </span><a href="http://dx.doi.org/10.1016/j.bbagen.2014.12.014">10.1016/j.bbagen.2014.12.014</a></li>
<span style="background-color: white;"><span style="font-family: Times, Times New Roman, serif;">
</span></span>
<li><span style="background-color: white; font-family: Times, Times New Roman, serif;"><span lang="EN-US">Egginton S, <i>Morphometric
analysis of tissue capillary supply</i>. In: Boutilier, RG (ed) Vertebrate Gas
Exchange from Environment to Cell.
Advances in Comparative and Environmental Physiology, 1990: 6, 73-141.</span><span lang="EN-US"> </span></span></li>
<span style="background-color: white;"><span style="font-family: Times, Times New Roman, serif;">
</span></span>
<li><span style="background-color: white; font-family: Times, Times New Roman, serif;"><span lang="EN-US">Egginton S, Gaffney EA,
Tissue capillary supply – it’s quality not quantity that counts! Experimental
Physiology, 2010; 95(10): 971-979.</span><span lang="EN-US"> </span></span></li>
<span style="background-color: white;"><span style="font-family: Times, Times New Roman, serif;">
</span></span>
<li><span style="background-color: white;"><span style="font-family: Times, Times New Roman, serif;"><b>Al-Shammari AA</b>, Gaffney EA, Egginton S, Re-evaluating
the use of Voronoi tessellations in the assessment of oxygen supply from
capillaries in muscle. <i>Bulletin of Mathematical Biology</i>, 2012; 74(9): 2204-223.<span lang="EN-US"> </span>DOI: <a href="http://dx.doi.org/10.1007/s11538-012-9753-x" target="_blank">10.1007/s11538-012-9753-x</a></span></span></li>
<span style="background-color: white;"><span style="font-family: Times, Times New Roman, serif;">
</span></span>
<li style="text-align: left;"><div style="text-align: left;">
<div style="text-align: justify;">
<span style="font-family: Times, Times New Roman, serif;"><b>Al-Shammari AA</b><span style="background-color: white;">, Gaffney EA, Egginton S, Modelling capillary oxygen supply capacity in mixed muscles: </span></span><span style="background-color: white; font-family: Times, 'Times New Roman', serif;">Capillary domains revisited. </span><i style="font-family: Times, 'Times New Roman', serif;">Journal of Theoretical Biology</i><span style="background-color: white; font-family: Times, 'Times New Roman', serif;">, </span><span style="font-family: Times, 'Times New Roman', serif; white-space: pre-wrap;">2014; 356:47-61. D</span><span style="background-color: white; font-family: Times, 'Times New Roman', serif;">OI: </span><a href="http://dx.doi.org/10.1016/j.jtbi.2014.04.016" style="font-family: Times, 'Times New Roman', serif;" target="_blank">10.1016/j.jtbi.2014.04.016</a><span style="background-color: white; font-family: Times, 'Times New Roman', serif;">.</span></div>
</div>
</li>
<span style="background-color: white;"><span style="font-family: Times, Times New Roman, serif;">
</span></span>
<li><span style="background-color: white; font-family: Times, Times New Roman, serif;"><b>Al-Shammari AA</b>, Gaffney EA, Egginton S, <i>Modelling
oxygen capillary supply to striated muscle tissues.</i> Advances in Applied Mathematics. Springer International Publishing, 2014. 13-21. DOI: </span><span style="font-family: Times, Times New Roman, serif;"><a href="http://dx.doi.org/10.1007/978-3-319-06923-4_2">10.1007/978-3-319-06923-4_2</a></span></li>
<span style="background-color: white;"><span style="font-family: Times, Times New Roman, serif;">
</span></span>
<li><span style="background-color: white; font-family: Times, Times New Roman, serif;"><b>Al-Shammari AA</b>, Gaffney EA, Egginton S, The effect
of heterogeneity in mitochondrial spatial distribution on oxygen transport in mixed
muscles, (to appear).</span></li>
</ol>
</div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7867264995121108649.post-77311367653605143732014-01-05T10:00:00.000+00:002014-03-17T16:39:14.185+00:00Mathematical modelling and analysis of bacterial motility<i>In this post <a href="http://www.2020science.net/profile/gabriel-rosser">Gabriel Rosser</a>, who completed his D.Phil. at the WCMB in early 2013, describes his research in bacterial motility.</i><br />
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<tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-X2md0iyPKKM/UqBxt-hpOVI/AAAAAAAAAG0/DhdAM6vT1K4/s1600/image.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://1.bp.blogspot.com/-X2md0iyPKKM/UqBxt-hpOVI/AAAAAAAAAG0/DhdAM6vT1K4/s200/image.png" height="200" width="154" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Dr Gabriel Rosser</td></tr>
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Bacteria have evolved myriad means of transporting themselves from one location to another. Twitching, gliding, floating and swimming are all methods seen in nature in some bacterium or other. Presumably the different mechanisms have evolved as different optimal solutions to the various needs of bacteria in their natural habitats, which include foraging for nutrients, escaping potentially harmful toxins and searching for new habitats to colonise. This is of more than simply academic interest: colonies of bacteria are responsible for life-threatening infections in humans, and cause billions of pounds of damage annually in industry by biofouling.<br />
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During my D.Phil., I focused on one particularly prevalent form of motility: swimming through a liquid medium mediated by one or more flagella. This is exemplified by many of the model bacterial species studied in recent years, including <i>E. coli</i>, <i>R. spaeroides</i> and <i>P. aeruginosa</i>. In many flagellate bacteria, motility proceeds by a series of approximately straight-line movements, interespersed by reorientation phases. Discussions with experimental collaborators from the <a href="http://www.bioch.ox.ac.uk/aspsite/index.asp?pageid=565">Armitage lab</a> (Department of Biochemistry) early on in my project indicated that experimental methods had progressed to the stage where it is possible to gain large amounts of microscopy video data from bacteria swimming in a glass capillary. Some example footage is shown below.<br />
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This process results in the availability of rich datasets containing tracks derived from bacteria swimming in a controlled medium, which is of great value in addressing many of the open questions about bacterial motility, such as the mechanism of reorientation, the effect of viscosity on swimming and how bacterial motility changes close to a surface. However, the limiting factor was the ability to analyse these tracking datasets meaningfully. I first turned my attention to this problem, developing novel Bayesian statistical analysis methods to automatically distinguish reorientation phases in the tracks [<a href="http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371%2Fjournal.pcbi.1003276">1</a>]. This made use of a recently developed multitarget tracker based on a PHD filter [<a href="http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6093957&tag=1">2</a>]. The same example footage as above, this time overlaid with computed cell tracks, is shown below.<br />
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A second area of interest is in the optimisation of experimental methods. This is a particularly important area, since it may have a significant impact on the effectiveness of an experimental technique. This is an area of research that benefits from the application of mathematical models; it is neither practical nor economical to test too many variants of a given experimental protocol, yet the application of an appropriate model of the process allows us to consider the impact of a wide variety of parameters, with no restriction on the number of combinations we may test. I used a model of bacterial motion known as the correlated random walk to test the effect of the microscope camera sampling frequency on the observed process [<a href="http://rsif.royalsocietypublishing.org/content/10/85/20130273.short">3</a>]. Tracks that are captured with a low sampling frequency will not be sufficiently detailed (see Figure 1). In this study, I showed that the apparent distributions of speeds and angle changes in bacterial tracks vary significantly with the sampling frequency. In particular, when finite duration stationary reorientation phases are included in the model of motion, the effects become more severe.<br />
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<tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-LVYNMypujJc/UqCA7UvCWxI/AAAAAAAAAHE/rNuiLmlGVuM/s1600/illustration_1.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://4.bp.blogspot.com/-LVYNMypujJc/UqCA7UvCWxI/AAAAAAAAAHE/rNuiLmlGVuM/s320/illustration_1.png" height="319" width="320" /></a></td></tr>
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<span style="background-color: white; font-size: 12px; line-height: 18px; text-align: left;"><span style="font-family: inherit; font-size: x-small;">Figure 1: The effect of sampling on apparent motion. The lower track is simulated using a correlated random walk model of bacterial motion, in which bacteria are assumed to reorientate instantaneously. Circles indicate reorientation events, crosses indicate sampling points and two run lengths and a turning angle are shown. The upper panel shows the circled portion in greater detail. This is the observed track, with two apparent displacements and two apparent angle changes marked. Details of the notation used can be found in [<a href="http://rsif.royalsocietypublishing.org/content/10/85/20130273.short">3</a>].</span></span></div>
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Finally, I considered the effect that Brownian motion has on bacterial motility. It has long been known that bacteria are sufficiently small that their movements are affected by the buffeting motion of the molecules in the surrounding liquid, characterised by translational and rotational diffusion of the bacterium (see Figure 2). However the exact nature of this effect is not fully understood.<br />
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<tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-_IWGXqFpxoM/UqCC3zDxiRI/AAAAAAAAAHQ/FuDq52Hf20k/s1600/Figure_CartoonOfDiffusionModes_Greyscale.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://4.bp.blogspot.com/-_IWGXqFpxoM/UqCC3zDxiRI/AAAAAAAAAHQ/FuDq52Hf20k/s400/Figure_CartoonOfDiffusionModes_Greyscale.png" height="145" width="400" /></a></td></tr>
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<span style="text-align: start;"><span style="font-family: inherit; font-size: x-small;">Figure 2: Illustration of a single bacterium undergoing translational (left) and rotational (right) </span></span><span style="font-family: inherit; text-align: left;">diff usion. Increasing transparency represents position and orientation in the more distant past. </span><span style="font-family: inherit; text-align: left;">Dashed lines trace the trajectory of the cell centroid (left) or a point on the flagellum to show </span><span style="font-family: inherit; font-size: x-small; text-align: left;">the angle changes (right).</span></div>
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Modelling a bacterium as a 'self-propelled particle' subjected to Brownian rotational buffeting, I interrogated the tracking data discussed previously. The model agrees well with the tracks of a bacterial mutant that does not exhibit reorientation phases. Considering tracks from a bacterium that does exhibit such reorientations, however, indicates that the reorientation mechanism cannot occur passively - the bacterium wouldn't change direction sufficiently if it simply waited for Brownian rotation to do the hard work. Based on these findings, I proposed several possible phenomenological explanations for the discrepancy, and demonstrated that a small change to the model of motion that incorporates an active reorientation mechanism agrees much better with the data [4].<br />
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<b>References</b>
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<ol>
<li><span style="font-family: inherit; font-size: x-small;"><span style="background-color: white; text-align: justify;">G. Rosser, </span><span style="background-color: white; text-align: justify;">A.G. Fletcher</span><span style="background-color: white; text-align: justify;">, D.A. Wilkinson, J.A. de Beyer, C.A. Yates, J.P. Armitage, P.K. Maini and R.E. Baker (2013). Novel methods for analysing bacterial tracks reveal persistence in </span><i style="background-color: white; text-align: justify;">Rhodobacter sphaeroides</i><span style="background-color: white; text-align: justify;">. </span><i style="background-color: white; text-align: justify;">PLoS Comput. Biol.</i><span style="background-color: white; text-align: justify;"> 9: e1003276.</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: inherit;"><span style="background-color: white; text-align: justify;">T. Wood, C.A. Yates, D. Wilkinson and G. Rosser (2012). Simplified multitarget tracking using the PHD filter for microscopic video data. </span></span><i>IEEE Trans. Circuits Syst. Video Technol.</i> 22:702-713.</span></li>
<li><span style="font-size: x-small;"><span style="background-color: white; font-family: inherit; text-align: justify;">G. Rosser</span><span style="background-color: white; font-family: inherit; text-align: justify;">, </span><span style="background-color: white; font-family: inherit; text-align: justify;">A.G. Fletcher</span><span style="background-color: white; font-family: inherit; text-align: justify;">, P.</span><span style="background-color: white; font-family: inherit; text-align: justify;">K. Maini and R.E. Baker (2013). The effect of sampling rate on observed statistics in a correlated random walk.</span><span style="background-color: white; font-family: inherit; text-align: justify;"> </span><i style="background-color: white; font-family: inherit; text-align: justify;">J. R. Soc. Interface</i><span style="background-color: white; font-family: inherit; text-align: justify;"> </span><span style="background-color: white; font-family: inherit; text-align: justify;">10:20130273.</span></span></li>
<li><span style="font-size: x-small;"><span style="background-color: white; font-family: inherit; text-align: justify;">G. Rosser, R.E. Baker, J.P. Armitage and A.G. Fletcher. </span><span style="text-align: justify;">Modelling and analysis of bacterial tracks suggest an active </span><span style="text-align: justify;">reorientation mechanism in <i>Rhodobacter sphaeroides</i>. Submitted.</span></span></li>
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Anonymoushttp://www.blogger.com/profile/06781843200914952471noreply@blogger.com1tag:blogger.com,1999:blog-7867264995121108649.post-49166727733111469392013-12-29T11:00:00.000+00:002013-12-29T11:00:00.480+00:00Turing's theory of developmental pattern formation (Video lecture)<div class="separator" style="clear: both; text-align: center;">
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<i>In this talk given at the <a href="http://www.ed.ac.uk/" target="_blank">University of Edinburgh</a> in 2012, our director <a href="http://people.maths.ox.ac.uk/maini/">Prof. Philip Maini</a></i><br />
<i>gives an overview of the principles of pattern formation in mathematical biology.</i><br />
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Another lecture on "<a href="https://beta.mbi.ohio-state.edu/video/player/?id=1548&title=Modelling+invasive+processes+in+biology" target="_blank">Modelling invasive processes in biology</a>" was given by Philip Maini in the same year. This was part of the <a href="http://mbi.osu.edu/" target="_blank">MBI</a>'s event<a href="http://beta.mbi.ohio-state.edu/video?view=events&id=166&item=Math%20Biology:%20Looking%20at%20the%20Future" target="_blank"> "Math Biology: Looking at the Future</a>" and showcases some of the more recent research of our group.Linus Schumacherhttp://www.blogger.com/profile/09580921538587285737noreply@blogger.com0tag:blogger.com,1999:blog-7867264995121108649.post-71519517120351011542013-12-22T10:30:00.000+00:002013-12-22T10:30:00.891+00:00Perspective on mathematical biology - Going back to go forward<br />
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--></style><i>This post by the Director of the WCMB, <a href="http://people.maths.ox.ac.uk/maini/">Prof. Philip Maini</a>, is an extended version of his recent article in the <a href="http://www.smb.org/publications/newsletter.shtml">SMB Newsletter</a>.</i><br />
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<tr><td style="text-align: center;"><a href="http://depts.washington.edu/amath/people/faculty/murray/murray.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="200" src="http://depts.washington.edu/amath/people/faculty/murray/murray.jpg" width="136" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;"><span style="font-family: inherit;">James D. Murray</span></span></td></tr>
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<span style="font-family: inherit;"><span style="font-size: small;">This year marks the 30th anniversary of the Oxford Centre for Mathematical Biology (now renamed the Wolfson Centre for Mathematical Biology). Such landmark birthdays naturally make one pause for thought. The Centre was founded by <a href="https://www.maths.ox.ac.uk/people/profiles/james.murray" target="_blank">Professor J.D. Murray</a>, FRS. He was awarded a grant from the Science and Engineering Research Council (SERC) to set up a centre to promote mathematical biology in the UK. The freedom he was given is unimaginable in today’s government funding environment. Basically, if he came into contact with someone (via a conference or research paper) who looked interesting, he could invite them to come to Oxford and pay for them out of the grant. </span></span><br />
<span style="font-family: inherit;"></span><span style="font-family: inherit;"><span style="font-size: small;"><br />Thirty years on and the <a href="http://www.epsrc.ac.uk/" target="_blank">Engineering and Physical Sciences Research Council</a> (EPSRC – which is what SERC became) announced a new model for funding graduate studies in the UK, called <a href="http://www.epsrc.ac.uk/skills/students/centres/Pages/centres.aspx" target="_blank">Centres for Doctoral Training</a> (CDT), with over 60 theme areas. The only one that contained the words “mathematics” and “biology” was the one: “New mathematics in biology and medicine”. To my mind, this totally misses the point as mathematics should be used to discover new biology and medicine and, in the process, inevitably new mathematics arises. The “winners” were <a href="http://www.epsrc.ac.uk/newsevents/news/2013/Pages/phdnewcentres.aspx" target="_blank">announced</a> three weeks ago and of the over 70 CDTs awarded, not one was for mathematical biology. So, is this a bad time for mathematical biology in the UK? One can argue both ways – several of the CDTs will implicitly use mathematical biology for applications in industry and healthcare, so does this mean that mathematical biology is now such an integral part of science that it does not need special treatment, or that it is having to be slipped in under the radar? Only time will tell, but the fact is that, just as the subject area is growing at its fastest rate, so the number of UK graduates in the subject will fall.</span></span><br />
<span style="font-family: inherit;"><span style="font-size: small;"><br />Both mathematics and biology have changed enormously over the past 30 years. For example, computing power has increased so much that one can do in seconds what would previously have taken months. At the same time, advances in biotechnology have led to huge amounts of data, and “big data” is the phrase everyone uses nowadays. However, mathematical biology has not kept pace with these advances. Why? I would argue that most data that are being generated are not appropriate for the sort of mathematical biology practised by the <a href="http://www.smb.org/" target="_blank">SMB</a> community. We focus on mechanism and develop models that are typically spatiotemporal in nature, yet most data are static. This, I feel is one reason why we have been overtaken by bioinformatics where the methodology can use the data presently being generated and great advances have been made in this field. However, I feel that we are now on the threshold of very exciting times in mathematical biology, as advances in imaging and staining etc. now mean that, for the very first time, there is the chance that we will acquire the data that our models need. </span></span><br />
<span style="font-family: inherit;"><span style="font-size: small;"><br />To take full advantage of this new opportunity will, in many cases, involve us having to go back to go forward. Certainly in <a href="http://people.maths.ox.ac.uk/maini/" target="_blank">my area</a> of <a href="http://www.maths.ox.ac.uk/groups/mathematical-biology/research" target="_blank">mathematical biology </a>(developmental biology, wound healing and cancer) many of the models proposed over the past 30 years were way beyond what could be verified experimentally and therefore they could not be validated. Now that they will, in principle, be verifiable, we must revisit them. This poses a challenge, as we are always under pressure to move “forward” in developing new mathematics, new models and collect new data. Under this system, funding to revisit old models would not be granted. But, we are the system, and we must do something about this!</span></span><br />
<span style="font-family: inherit;"><span style="font-size: small;"><br />There are many positives regarding mathematical biology. In more and more talks, it is becoming difficult to spot where the mathematics ends and the biology begins, such is the close integration. We also publish more in scientific journals, so that our work reaches the application areas. Certainly in many Mathematics Departments, this is very unusual, even for “applied” mathematics. The journal <a href="http://cancerres.aacrjournals.org/" target="_blank">Cancer Research </a>has several mathematical biologists on its Editorial Board. </span></span><span style="font-family: inherit;"><span style="font-size: small;"><span style="font-family: inherit;"><span style="font-size: small;"><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="http://labpages.moffitt.org/andersona/images/sandy.png" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="200" src="http://labpages.moffitt.org/andersona/images/sandy.png" width="166" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Alexander "Sandy" R. A. Anderson</td></tr>
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</span></span>The <a href="http://www.moffitt.org/" target="_blank">Moffitt Cancer Center</a> in Tampa has, within it, the <a href="http://www.moffitt.org/research--clinical-trials/research-disciplines/departments/integrated-mathematical-oncology/" target="_blank">Integrated Mathematical Oncology Department</a>, chaired by <a href="http://labpages.moffitt.org/andersona/" target="_blank">Dr Sandy Anderson</a>, a mathematician.They sit next to experimentalists and work closely with them. Then there is the recent appoint of <a href="http://mathematicalneurooncology.org/" target="_blank">Dr Kristin Swanson</a> (a mathematician) as Professor in Neurological Surgery and Vice Chair of Research for Neurosurgery at the <a href="http://www.feinberg.northwestern.edu/" target="_blank">Northwestern School of Medicine</a>.</span></span><span style="font-family: inherit;"><span style="font-size: small;"><span style="font-family: inherit;"><span style="font-size: small;"><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="http://ec2-107-22-238-17.compute-1.amazonaws.com/wp-content/uploads/2010/06/swansonbrain-200x300.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="200" src="http://ec2-107-22-238-17.compute-1.amazonaws.com/wp-content/uploads/2010/06/swansonbrain-200x300.jpg" width="133" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Kristin R. Swanson</td></tr>
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</span></span> These are just two examples of the growing number of mathematical research groups embedded in medical schools/<a href="http://cbio.mskcc.org/" target="_blank">institutes</a>, adding to the numbers embedded already in the more traditional haunts of physiology, zoology, ecology and epidemiology departments. In Europe, <a href="http://www.bioms.de/" target="_blank">BIOMS</a> in Heidelberg is just one of the growing numbers of institutes in which mathematicians and experimentalists work side by side. The subject is informing government strategies on epidemiology and general ecological management. Mathematical biologists are beginning to be invited to present at biology/medical/healthcare conferences and departments. In this day and age when there is so much political, as well as social, ignorance of relevance of mathematics in the real world, I think that the engagement of mathematical biology with the “user” partners (most mathematical biology is not done in mathematical departments) is an excellent riposte.</span></span><br />
<span style="font-family: inherit;"></span><span style="font-family: inherit;"><span style="font-size: small;"><br />Then of course there is <a href="http://www.nimbios.org/" target="_blank">NIMBioS</a> and the <a href="http://mbi.osu.edu/" target="_blank">MBI</a>, two centres that have greatly contributed to the growth of mathematical biology. I remember when I started as a graduate student in 1982, my supervisor, Professor Jim Murray, handed me a small number of papers and told me that I should be able to read them by Christmas and then I would basically be able to start research as I would know all the important literature. In those days, one was aware of everything going on in the subject. Now, it is impossible to keep up even in one’s own very specialised part of mathematical biology.</span></span><br />
<span style="font-family: inherit;"></span><span style="font-family: inherit;"><span style="font-size: small;"><br />As well as being interdisciplinary, mathematical biology is becoming more intradisciplinary. For example, understanding network requires ideas from graph theory; work on viral capsids requires group theory; fitting models to data requires ideas from algebra, probability and statistics. Therefore I see a further exciting era of more pure mathematicians getting involved in mathematical biology. One of our responsibilities is to find a way to make this community aware of these exciting opportunities.</span></span><br />
<span style="font-family: inherit;"><span style="font-size: small;"><br />As the subject area continues to grow in breadth and depth there are inevitable questions about training. Should there be undergraduate degrees in mathematical biology, or is it at the graduate level, or postdoctoral level that a student should broaden out. I would say that for interdisciplinary research one should have at least a discipline and so it is at graduate level that one should begin interdisciplinary research, but I know many people who disagree with that, arguing that this is too late or, indeed, too early.</span></span><br />
<span style="font-family: inherit;"><span style="font-size: small;"><br />Then there is the question of at what level can the sort of mathematics we do be applied. My own approach more recently has been, by and large, to focus on a particular biological question that cannot be answered purely by experiment and then work closely with experimentalists in a predict-test-refine-predict iterative cycle. I have tried to resist the temptation to include too many things in the model as I feel that such models are difficult to parametrise and that it is also difficult to learn a great deal from them. The models that have been the most influential to date (for example, <a href="http://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equation" target="_blank">Lotka-Volterra</a>, <a href="http://en.wikipedia.org/wiki/Fisher_equation" target="_blank">Fisher</a>, <a href="http://en.wikipedia.org/wiki/Hodgkin%E2%80%93Huxley_model" target="_blank">Hodgkin-Huxley</a>, <a href="http://en.wikipedia.org/wiki/Turing_pattern" target="_blank">Turing</a>, to name only the classical ones) have all had few equations but have changed the way people think. Of course, this is an unfair comparison as these models have been around a lot longer than the more detailed models presently being developed. For example, some of the <a href="http://www.cs.ox.ac.uk/activities/Heart/" target="_blank">heart modelling</a> is now being incorporated by some drug companies are part of their drug testing protocol. It remains to be seen how these more detailed models develop.</span></span><br />
<span style="font-family: inherit;"><span style="font-size: small;"><br />In my first year back in Oxford as a faculty member I was sitting at lunch one day and overheard a senior colleague paraphrasing Max Planck, “science advances one funeral at a time” (according to <a href="http://en.wikiquote.org/wiki/Max_Planck" target="_blank">Wikiquote</a>, the full statement is, “A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.”). I must admit that, at the time, this made no sense to me and I felt it totally irrelevance. Twenty- three years on, I think it is one of the most enlightened statements I have ever heard and it has become as sort of mantra – especially when faced with the sort of problems I mentioned at the beginning of this piece.</span></span><br />
<span style="font-family: inherit;"></span><span style="font-family: inherit;"><span style="font-size: small;"><br />I think that the new generation of scientists coming into this field are more open and, while there undoubtedly are challenges in the immediate future (particularly of a financial kind faced by all of society, and caused by another field of mathematics), the fact that the number of people in the non-mathematical sciences who feel mathematics is important is growing, the future looks promising for our field.<span lang="EN-GB"><a href="http://www.blogger.com/null" name="_GoBack"></a></span></span></span>
Linus Schumacherhttp://www.blogger.com/profile/09580921538587285737noreply@blogger.com0tag:blogger.com,1999:blog-7867264995121108649.post-54202586193370615382013-12-18T11:20:00.000+00:002013-12-18T11:21:59.601+00:00Handling collaborative projects in the age of the cloud - how to manage without spending any money!<i>In this mid-week extra, <a href="http://www.maths.ox.ac.uk/node/17606">Dr Jacob Scott</a> discusses cloud storage services for collaborative science projects, which we also wrote about in his <a href="http://cancerconnector.blogspot.co.uk/2013/12/how-i-manage-collaborative-projects.html" target="_blank">own blog</a>.</i><br />
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As a clinician cum scientist, I am almost always involved in
collaborations with multi-disciplinary groups. And, as an American who
has done some training in the UK, many of those groups are NOWHERE
REMOTELY NEAR one another. To keep myself, and my collaborators sane,
I've been constantly experimenting with different combinations of cloud
based repositories so that we can all work on things together.<br />
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So, I started out with <a class="g-profile" href="https://plus.google.com/103316200298703443962" target="_blank">+Dropbox</a> by itself, but quickly found that, without spending money, I quickly filled up my allotted space. Even after totally maxing out the freebie upgrades (I think I have like 35Gb or something thanks to some promo at Oxford, referring everyone I know and being a shameless social media promoter - every Mb counts!), I still am limited. So I added <a class="g-profile" href="https://plus.google.com/112567260833137438263" target="_blank">+SugarSync</a> for my personal files, to clear off dropbox and leave it for just collaboration. Well, that filled up pretty quick too, and as I haven't found sugarsync to be as easy to navigate as dropbox, I haven't worked as hard to maximize my space there. I muddled along with these two but still struggled with things like version control and the desire for contemporaneous editing. Which led to...<br />
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Google drive and google docs. So, with google drive, you get 25Gb or something, but I started to get confused as to where things were. When I wanted to collaborate real time though, I was stuck, as google docs was really the best thing going (and still is, for many things). However, in the last few months, I discovered <a class="g-profile" href="https://plus.google.com/107817414043832561351" target="_blank">+writeLaTeX</a>, which has really changed the way I do business. This is a (mostly) free service (I haven't hit the wall yet, and it is pretty big considering that you don't store data there really) in which you can create, manage and edit LaTeX documents with as many people as you like. For me, as a mathematical biologist, this was great - so long as my collaborators were also theorists who were tex-savvy. Recently though, as in, in the last few days, they have added a Rich Text formatting layer which, I think, will change everything again. No longer will I have to give the link to a document to my biological/clinical collaborator with the caveat 'just ignore everything that isn't text - squint a bit if you have to'. Now, they can just go ahead and edit away just like they are in word or whatever, but I can come in behind and have the full functionality of LaTeX. So that aspect seems solved.<br />
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The only issue left for me is, now that I'm cranking TONS of simulations in (what I hope is) the final push toward this whole PhD thing, how to work on a DATA-HOG of a project on two computers (I can't stay at work late because I want to go home to my super sweet little kids, but then I DO want to work after they go to bed without driving back to work) or to share this with someone else. I thought, at first, that I'd just clear out my dropbox a bit, and try to be parsimonious with what I saved... but, as the output for my simulations is \mathcal{O} 30Gb/simulation, this quickly became unfeasible.<br />
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Enter <a href="http://www.bittorrent.com/sync">bittorrentsync</a> - my saviour. This little gem (free) lets you have a synced drive on as many computers as you like. The freeing move here is that there is no cloud interaction, so there is NO SPACE LIMITATION. (There is also no auto-backup for the same reason... but this is obviated if you use Time Machine or something similar). All you do is download the software (a couple Mb's) and then, to set up a shared directory, it generates a 'secret' which you share with whomever you want to share. The secret is a massive string of letters/numbers that is auto-generated - and I bet even the guy at <a href="http://xkcd.com/">xkcd.com</a> would <a href="http://xkcd.com/936/">approve</a>.<br />
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So, now I'm set and I don't have to think too hard. I also don't forsee ever having to spend any money (until maybe I have a lab or my own and lots of people, but by then - if that time ever comes - I will have grant money to spend on such things... ?).<br />
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Summary: I use <a href="https://www.dropbox.com/login?cont=https%3A%2F%2Fwww.dropbox.com%2Fhome">dropbox</a> for shared/travelling talks, figures, syncing my <a href="http://www.papersapp.com/mac/">papers library</a>, shared simple code (matlab, etc). I use <a href="https://www.sugarsync.com/">sugarsync</a> for my personal documents (though I might phase this out...). I use <a href="https://www.writelatex.com/">writelatex</a> for (now and going forward) ALL papers I write and bittorrent sync for shared working directories (also home/office syncing of working directories).Jacob Scotthttp://www.blogger.com/profile/12788368243256158841noreply@blogger.com0