Sunday, 9 March 2014

Chemical reactions, spatial information processing, and model invalidation, oh my!

In this post Dr Heather Harrington, Hooke Research Fellow and EPSRC Postdoctoral Fellow at the WCMB, discusses her research interests.

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. 

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 Elisenda Feliu, Carsten Wiuf (Copenhagen), and my postdoc advisor, Michael Stumpf, 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 here.)
Interestingly, we found that cellular information 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).

Another one of my primary interests is developing methods for linking data and models. In collaboration with Ken Ho (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 Michael Stumpf in Theoretical Systems Biology, Imperial College ( twitter: @theosysbio) . 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.

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 researchers. 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 AIM, which has sparked collaborations and discussions with many mathematicians around the world working on using algebraic and geometric approaches to analyse such systems. 

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. 

Currently reading:
Pleasure: Savage Detectives (Los Detectives Salvajes) by Roberto BolaƱo. 

Work: The Euclidean Distance Degree of an Algebraic Variety (Jan Draisma, Emil Horobet, Giorgio Ottaviani, Bernd Sturmfels and Rekha R. Thomas) 

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