Mathematical and computational modelling of biochemical mechanisms

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My research focusses on building and analysing mathematical and computational models to elucidate the mechanisms underlying various biochemical phenomena. Whenever possible, I work closely with experimentalists who gather quantitative data, the analysis of which requires the development of novel methods. Two systems ideal for study with these methods are the bacterial cell-division-regulating proteins MinCDE and the ATP-binding cassette (ABC) transporters.*******ATP-binding cassette (ABC) transporters form a broad class of transmembrane proteins that facilitate unidirectional transport of sugars, ions, lipids, amino acids, peptides and various drugs across cell membranes. Mutations in an ABC-transporter chloride ion channel are the underlying cause of cystic fibrosis. Bacterial resistance to antibiotics and cancer-cell resistance to certain drug treatments are both facilitated by ABC transporters. A detailed understanding of the biochemistry of these transporters has been emerging gradually over the last few years but a comprehensive and quantitative picture of the mechanisms by which these proteins function remains an important research goal.*******The Min proteins, MinC, MinD and MinE, form an important spatial regulator of cell division in bacteria, where they interact on the membrane to generate an oscillatory spatially alternating pole-to-pole localization. Spatial pattern formation has recently been reconstituted in vitro on flat supported membrane and in cell-shaped micro-fabricated chambers. Traveling waves and spiral waves on supported membrane and in vivo-like oscillations in cell-shaped chambers have been observed. Despite the publication of numerous models over the last decade and a half, there is still no consensus on the precise details of the protein interactions and no single quantitatively accurate model that recapitulates experimental observations both in vivo and in vitro at the level of biochemical time courses.*******The mathematical models I formulate to work on these types of problems come in many forms including ordinary, partial and integro- differential equations, discrete maps, stochastic processes, agent-based simulations and others. Some of the more common techniques that arise in analyzing the data and models are asymptotic analysis, bifurcation analysis, numerical methods, parameter estimation (nonlinear regression, model relaxation, etc.), model selection (F-test, AIC, etc.), image processing and analysis.**