UC Irvine

Dynamical graph grammars (DGGs) are capable of modeling and simulating the dynamics of complex biological systems using an exact simulation algorithm derived from a master equation; however, the exact method is slow for large systems. To accelerate the simulations of DGGs we have developed 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 rules or reactions firing out of order, which may introduce errors. The decomposition is coarsely partitioned by effective dimension (d = 0 to 2 or 0 to 3), to expose the potential for exact parallelism between different subdomains within a dimension, where most computing will happen, and to confine errors to interactions between adjacent subdomains of different effective dimensions. Additional efficiency can be achieved through maintaining an incrementally updated match data structure for all possible rule matches. To demonstrate these principles we have developed the Dynamical Graph Grammar Modeling Library (DGGML), and two DGG models for the plant cell cortical microtubule array (CMA). In the first model, we find evidence indicating that 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. In the second model, we restrict ourselves to the CMA in the periclinal face of a plant cell and explore the effects that different face shapes and boundary conditions have on local and global alignment. In the case of a square face shape, we find the array orientation to be multi-modal, and in the case of a rectangular face shape, we find that different boundary conditions reorient the array mainly between the long and short axes. The periclinal CMA DGG demonstrates the flexibility and utility of DGGML and highlights its viability to be used as a computational means of testing, screening or inventing hypotheses to explain emergent phenomena.