Approximate simulation of cortical microtubule models using dynamical graph grammars.

Dynamical graph grammars (DGGs) are capable of modelling and simulating the dynamics of the cortical microtubule array (CMA) in plant cells by using an exact simulation algorithm derived from a master equation; however, the exact method is slow for large systems. We present preliminary work on an approximate simulation algorithm that is compatible with the DGG formalism. The approximate simulation algorithm uses a spatial decomposition of the domain at the level of the system's time-evolution operator, to gain efficiency at the cost of some reactions firing out of order, which may introduce errors. The decomposition is more coarsely partitioned by effective dimension 1 (d=0 to 2 or 0 to 3), to promote exact parallelism between different subdomains within a dimension, where most computing will happen, and to confine errors to the interactions between adjacent subdomains of different effective dimensions. To demonstrate these principles we implement a prototype simulator, and run three simple experiments using a DGG for testing the viability of simulating the CMA. We find evidence indicating the initial formulation of the approximate algorithm is substantially faster than the exact algorithm, and one experiment leads to network formation in the long-time behavior, whereas another leads to a long-time behavior of local alignment.