Algorithms and software for mechanistic modelling of biochemical networks

In experimental systems biology, the majority of high throughput experimental data is of molecular abundance and the minority is of reaction rates. We seek a modelling framework flexible enough to integrate experimental data on both rates and abundance. Established genome-scale modelling methods do not explicitly represent the abundance of each molecule. Without explicitly representing abundance, the incorporation of experimental constraints from measurements of molecular abundance is

always an approximation. Such approximation may be useful in the short to medium term, but ultimately we seek a computational model of biochemical reaction networks to explicitly represent the abundance of each molecule and the rate of each reaction. We are developing a novel approach to model stationary state reaction kinetics for large systems of reactions based on nonlinear continuous optimization algorithms. These variational kinetic models aim to preserve the computational tractability associated with numerical optimization and add the biochemical realism typical of kinetic models. Our general approach is to focus on the development of biochemically tailored polynomial-time optimization algorithms with guaranteed convergence properties. This effort requires the development and application of mathematical concepts at the intersection of Variational Analysis, Continuous Nonlinear Optimization, Generalised Convexity and Numerical Analysis. In tandem with mathematical algorithm development, we prototype numerical analysis software and then test its performance when applied to a set of low, medium and high-dimensional biochemically relevant modelling problems.