Numerical Methods with Applications to Biochemical Networks

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My research is in the area of numerical analysis and scientific computing. The main objectives of this proposal are to develop and analyze numerical methods for approximating the solution of mathematical models of well-stirred and spatially distributed biochemical networks. This research will contribute to the improvement of existing software and will allow researchers in a crucial area of life sciences to solve more challenging problems than was previously possible, to effectively and reliably approximate the solution to their models and to analyze and predict the behaviour of complex systems. In the past, my research focused on the development of efficient strategies for solving numerically initial value problems for stochastic models of well-stirred and spatially distributed biochemical networks and initial value problems for differential algebraic equations. The application of mathematical modelling and simulations to study critical biological processes is an exciting and new area of research. Stochastic models of biochemical networks are of high interest today, due to their wide variety of important practical applications. Often, these mathematical models are highly complex. They may be non-linear and exhibit mathematical stiffness, due to the presence of multiple scales in time and molecular population numbers. Typically, such models cannot be solved by analytic mathematical tools. Then, numerical strategies are necessary to approximate their solution. Designing fast simulation techniques for studying complex stochastic models of biochemical systems which are also stiff is a challenging task. This proposal aims to (1) extend my previous work on stochastic models of well-stirred and spatially distributed biochemical systems, to improve the numerical methods for biologically relevant models, using adaptive time-stepping schemes and higher-order techniques, (2) design hybrid methods for approximating the solution of discrete stochastic models of reaction-diffusion systems, (3) develop effective and accurate strategies for sensitivity analysis of discrete stochastic models of biochemical systems, and (4) construct reliable and effective numerical techniques for identifiability analysis of discrete stochastic biochemical kinetic models.