Large deviations for models in Systems Biology

Tuesday, June 5, 2018 - 2:00pm - 2:30pm
Lind 305
Lea Popovic (Concordia University)

This talk will present results for calculating the probabilities of rare events in stochastic reaction networks. Our primary focus is on rare events that are important for models in systems biology, for example reaction networks for gene-regulation and enzyme kinetics. The theory of large deviations allows one to assess events whose probabilities are exponentially small and are hence not captured by law of large number or central limit theorem results, yet in a high number of trials due to cell division are eventually likely to occur. Using tools for Markov processes we can describe the large deviation rate function for the occupation and local times of jump-diffusions with reflection on the boundaries which effectively capture the stochastic behaviour of a range of chemical reaction networks. These results involve numerically solving integro-differential equations which can be quite challenging. For that reason we also present an importance sampling scheme based on large deviation theory that is useful in designing efficient simulation algorithms for rare events.