The objective of this research project is to develop and analyze next generation stochastic simulation methods for the models found in biochemistry. Such models include gene regulatory networks, neural networks, and models of viral infection and growth. Specifically, the two main research topics considered are the efficient computation of expectations and the efficient computation of parametric sensitivities. The mathematical focus of the project will the development of Monte Carlo estimators that are unbiased, yet orders of magnitude more efficient than the current state of the art. To achieve such efficiency, novel coupling procedures, sometimes used in conjunction with the multi-level Monte Carlo framework, will be employed in both project areas.
Due in part to the appearance of new technologies, most notably fluorescent proteins, there is now a large literature demonstrating that the fluctuations arising from the effective randomness of molecular interactions can have significant consequences, including a randomization of phenotypic outcomes and non-genetic population heterogeneity. In such cases, stochastic models, combined with both analytical and computational tools, are essential if they are to be well understood. The problems that will be addressed in this project often form the bottleneck in computational experiments in systems biology. Hence, the research will make possible many realistic modeling and simulation scenarios that are beyond the range of existing techniques. As the relevant models include those for both gene networks and viral growth, this project plays a role in improving long-term human health by greatly improving the predictive power of such models.
