Abstract: Motivated by the observation that several biological
processes can be conveniently modeled through the interaction of
continuous and discrete phenomena, there has been a growing interest
recently in the application of hybrid systems techniques to biological
modeling and analysis. It has also been recognized that many biological
processes are intrinsically uncertain; stochastic phenomena have in
fact been shown to be instrumental in improving the robustness of
certain biological processes, or in inducing variability in an
otherwise homogeneous population. In this talk we will describe the
development of stochastic hybrid models for two classes of biological
processes: Gene regulatory networks and DNA replication. In gene
regulatory networks, stochastic hybrid systems offer a promising
alternative, bridging the gap between more traditional nonlinear
differential equation models and stochastic models based on the Master
equation. We will discuss the development of models and parameter
identification algorithms in this framework and demonstrate the results
on an in-silico case study of the nutritional stress response of E.
coli. For DNA replication, we will describe the development of a
genome-wide model of the “mechanics” of the process. We will present
analysis results on the instantiation of the model for the fission
yeast. The results suggest that the predictions of the model do not
match conventional biological wisdom and experimental evidence;
interestingly, the problem appears to be not in the model, but in
conventional biological wisdom. We will discuss how this observation
has motivated follow-on experiments (in vitro and in silico) to test
two competing biological hypotheses that could explain the discrepancy.
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