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Research Interests

My main research interests are in using mathematical modelling/statistics to understand complex biology processes and biological data sets (fluorescence imaging and omics data). Methodologies include dynamical systems, partial differential equations, stochastic models (eg random walks, queuing theory), large deviation methods and Markov chain Monte Carlo techniques. This page gives a brief summary of my interests, additional details can be found on the associated links.

UNDER CONSTRUCTION

Cellular Biology

Microtubule dynamics and kinetochore oscillations. With Andrew McAinsch (Warwick Medical School), we are using systems approaches to understand microtubule dynamics.

Cytoskeleton dynamics and regulation.

Actin dynamics and the ability to produce coordinated movement from polymerisable fibers is a major challenge to mathematical models. We are using a variety of techniques from statistical mechanics, structured models, PDEs and dynamical systems to tackle these issues.

Previous areas of research.

Mathematical Immunology

The aim of mathematical immunology is to aid understanding of the complexities of the immune system through mathematical modelling. Control and regulation is fundamental to the proper functioning of the imune systems, ie delivering an appropriate response to a stimulous. Much of the research in this area involves an analysis of mechanisms of control, selection and activation, often extrapolating between scales, i.e. molecular to cellular, or cellular to repertoire; simulating and predicting effects of mechanisms at the lower level on the upper. We work hard at the following research projects -

The immunological synapse and differential enrichment

T cell conjugation with an antigen presenting cell involves a redistribution and segregation of important signalling and adhesion molecules in the contact interface. A model based on reaction diffusion equations incorporating thermodynamic effects of membranes is being investigated through simulations, mathematical analysis and analysis of experimental data. We have found criteria for segregation involving a balance of thermodynamic effects, which reproduce realistic segregation patterns. This model is being tested by fitting to 3D fluorescent images.

PLoS ONE 5(11): e15374. doi:10.1371/journal.pone.0015374. Köhler K, Xiong S, Brzostek J, Mehrabi M, Eissmann P, et al. (2010) Matched Sizes of Activating and Inhibitory Receptor/Ligand Pairs Are Required for Optimal Signal Integration by Human Natural Killer Cells.

Immunological Reviews, 189 (2002) 64-83. C. Wulfing, I. Tskvitaria-Fuller, N.J. Burroughs, M.D. Sjaastad, J. Klem and J.D. Schatzle. Interface accumulation of receptor/ligand couples in lymphocyte activation: Methods, mechanisms and significance.

Biophysical Journal, 83 (2002), 1784-1796. N.J. Burroughs and C. Wulfing. Differential segregation in a cell:cell contact interface - the formation of the immunological synapse.

FIGURE: Simulation of a T cell APC contact interface: MHC green, ICAM1 red.

Segregation through free energy minimisation occurs within a minute. Membrane adjusts locally to optimise binding of short and long bonds. Domains do not coalesce without another mechanism, eg cytoskeletal transport.

The role of the synapse is large unknown, but likely to play a key role in signalling. Micro patternation as a means to transduce signals was investigated using a mathematical model of Brownian motion.This demonstrated that a physical process of segregation can underpin a signaling mechanism, i.e. conformation changes for example are not needed.

Immunological Reviews, (2007), 216: 69-80. Stochasticity and spatial heterogeneity in TCR activation. NJ Burroughs and PA van der Merwe.

Ligand detection and discrimination by spatial relocalisation: a kinase-phosphatase segregation model of TCR activation. NJ. Burroughs, Z. Lazic, PA van der Merwe. (2006) BJ, 91: 1619-1629.

Plants and Pollination

With global crises looming, civil unrest over food and water shortages, and global climate deterioration through global warming, my personal scientific priorities have shifted. I have a number of projects that may contribute to alleviating some of these problems. This includes:

Unravelling the impact of the mite Varroa destructor on the interaction between the honeybee and its viruses. Here we use molecular biology techniques and mathematical modelling to try and understand the destructive impact that the varroa mite is having on bee colonies world wide. This is in collaboration with Warwick Life Sciences, David Evans (PI) and Eugene Ryabov.

Comparative cell-specific profiling to understand the molecular basis of nodulation. Nitrogen is a major limiting factor of crop yield; the production of nitrogen fertilisers being a major financial and energy cost to agriculture whilst ultimately also contributing to land and river pollution. Thus, an understanding of how nodules form in the legumes, which harbour nitrogen fixing bacteria, could potentially open the way for transfer of this ability to other crops, and thus eliminate the need for applying nitrogen fertilisers. This is in collaboration with Warwick Life Sciences, Miriam Gifford on the WHRI campus.

Engineering and Physical Sciences Research Council

Biotechnology and Biological Sciences Research Council

Address:
Warwick Systems Biology
Coventry House

University of Warwick
Coventry CV4 7AL
United Kingdom