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Center for Nonlinear Studies |
Dynamics of several biological systems, especially during morphogenesis, emerge from coupled mechanochemical processes. Modeling such processes requires accounting for a few essential aspects that render biological systems different from non-living systems. First, biological systems are kept out of equilibrium by burning a chemical fuel, and are therefore examples of active systems. Second, low copy numbers of chemical species render biological dynamics inherently stochastic. Third, biological dynamics result from nonlinear interactions between several mechanical and chemical processes. The nonlinearity renders their behavior more complex than the mere sum of parts. Fourth, biological systems are inherently coupled across several time and spatial scales. Lastly, several biological processes occur on complex and deforming surfaces that are crucial to their dynamics. In this talk, I will present computational methods for simulating mechanochemical processes and dynamics emerging from such processes. I will start by presenting a new class of highly efficient algorithms called partial-propensity methods for simulating stochastic chemical kinetics. The efficiency of these methods has allowed us to discover two novel effects of fluctuations in reaction networks. The first is called discreteness-induced concentration inversion in which fluctuations alter the ranking of chemical species as measured by their concentration levels. The second is on the effect of fluctuations on the frequency spectrum of chemical oscillators. Subsequently, I will present a hybrid particle-mesh computational method for modeling cytoskeletal mechanics central to several morphogenetic processes. In a model cytoskeleton, I will show that active stresses—due to motor proteins that generate stress upon burning a chemical fuel—induce mechanical patterns and spatiotemporal chaos. Finally, I will demonstrate how cell polarity in C. elegans embryos is a mechanochemical pattern driven by inhomogeneous curvature of the egg shell enclosing the embryo.
Host: William Hlavacek