Session B1 - Computational Dynamics
July 15, 16:00 ~ 16:30 - Room 111
Model rejection and parameter reduction via time series
Montana State University, United States - firstname.lastname@example.org
We discuss a new approach to Dynamic Signatures Generated by Regulatory Networks (DSGRN) provides a queryable description of global dynamics over the entire parameter space. We perform a model validation within this class of dynamical systems. We show how a graph algorithm for finding matching labeled paths in pairs of labeled directed graphs can be used to reject models that do not match experimental time series. In particular, we extract a partial order of events describing local minima and local maxima of observed quantities from experimental time-series data from which we produce a labeled directed graph we call the pattern graph for which every path from root to leaf corresponds to a plausible sequence of events. We then consider the regulatory network model, which can be itself rendered into a labeled directed graph we call the search graph via techniques previously developed in computational dynamics. Labels on the pattern graph correspond to experimentally observed events, while labels on the search graph correspond to mathematical facts about the model. We give a theoretical guarantee that failing to find a match invalidates the model. As an application we consider gene regulatory models for the yeast S. cerevisiae.
Joint work with Bree Cummins (Montana State University), Shaun Harker (Rutgers University) and Konstantin Mischaikow (Rutgers University).