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Center for Nonlinear Studies |
The dynamics of molecular interactions in cellular regulatory systems are sometimes challenging to model using traditional approaches, such as that of ordinary differential equations (ODEs). The molecules in these systems (viz., proteins) are composed of multiple functional components, which can each interact with multiple binding partners. The functional components can also undergo modifications that affect their behavior. The consequence is a large reachable but sparsely populated state space, which can be impractical to capture in a traditional model for biochemical kinetics. To overcome this challenge, an agent-based approach to modeling biochemical kinetics has been developed, called rule-based modeling. In this approach, rules are used to characterize the interactions of molecules in terms of local properties of molecular components, which entails coarse-graining of the kinetics of interactions, as rules tend to implicitly define and parameterize multiple reactions through inheritance. This simplification allows concise specification of models, more aligned with mechanistic understanding than, say, ODE models. The conciseness of a rule-based model derives from assumptions of component modularity, or independence. In this talk, I will describe how the modular representation of molecular components in a rule-based model allows one to apply concepts of equation-free computation to perform approximate simulations that characterize collective variables corresponding to observable quantities of interest. The approach has some similarities with renormalization in physics. Equation-free computation has the potential to make available to those who wish to analyze rule-based models the entire toolbox of numerical methods available for ODE models. In this talk, I will illustrate the potential of equation-free computation through a discussion of an accelerated simulation algorithm based on projective integration.
Host: Kipton Barros, T-4 and CNLS