Dr Gabriel Rosser 
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 lifethreatening infections in humans, and cause billions of pounds of damage annually in industry by biofouling.
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 E. coli, R. spaeroides and P. aeruginosa. In many flagellate bacteria, motility proceeds by a series of approximately straightline movements, interespersed by reorientation phases. Discussions with experimental collaborators from the Armitage lab (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.
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 [3]. 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.
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 [3].

References
 G. Rosser, A.G. Fletcher, 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 Rhodobacter sphaeroides. PLoS Comput. Biol. 9: e1003276.
 T. Wood, C.A. Yates, D. Wilkinson and G. Rosser (2012). Simplified multitarget tracking using the PHD filter for microscopic video data. IEEE Trans. Circuits Syst. Video Technol. 22:702713.
 G. Rosser, A.G. Fletcher, P.K. Maini and R.E. Baker (2013). The effect of sampling rate on observed statistics in a correlated random walk. J. R. Soc. Interface 10:20130273.
 G. Rosser, R.E. Baker, J.P. Armitage and A.G. Fletcher. Modelling and analysis of bacterial tracks suggest an active reorientation mechanism in Rhodobacter sphaeroides. Submitted.
A mathematical model is an abstract model that uses mathematical language to describe the behavior of a system.Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models. This page have other types of models can overlap, with a given model involving a variety of abstract structures. There are six basic groups of variables: decision variables, input variables, state variables, exogenous variables, random variables, and output variables.
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