Matthew Hur (University of California, Irvine), Eric Mjolsness (University of California, Irvine)

Dendritic (postsynaptic) spine head size changes can strengthen or weaken the synaptic connection in response to the temporal correlation of signals between two neurons. This morphology can be expressed as an underlying graph due to dynamics of the actin cytoskeleton. In this project, we seek to use Dynamical Graph Grammars (DGGs) implemented within a computer algebra system in Mathematica package to model actin filament networks. In this package, rules, which can depend on matching object parameters, declare how to evolve a network at time steps. Then, a symbolically defined propensity function of the parameters weights the rule firing probability. We implemented several DGG sub-grammar mathematical models to regulate the generation and deletion of graph objects for actin network remodeling. They also incorporate additional rules for changing parameters including anisotropic filament forces, filament-membrane mechanical interaction, and Hessian Boltzmann sampling of random molecular displacements. Rules, based on viscous dynamics of potential derived forces, function as energy minimizer of the system into a stochastic simulation of evolving graphs. We refined this model by incorporating rate constants used in previous models.