eGFRD in all dimensions

Biochemical reactions often occur at low copy numbers but at once in crowded and diverse environments. Space and stochas-ticity therefore play an essential role in biochemical networks. Spatial-stochastic simulations have become a prominent tool forunderstanding how stochasticity at the microscopic level influences the macroscopic behavior of such systems. While particle-based models guarantee the level of detail necessary to accurately describe the microscopic dynamics at very low copy numbers,the algorithms used to simulate them typically imply trade-offs between computational efficiency and biochemical accuracy.eGFRD (enhanced Green’s Function Reaction Dynamics) is an exact algorithm that evades such trade-offs by partitioning theN-particle system intoM≤Nanalytically tractable one- and two-particle systems; the analytical solutions (Green’s functions)then are used to implement an event-driven particle-based scheme that allows particles to make large jumps in time and spacewhile retaining access to their state variables at arbitrary simulation times. Here we present “eGFRD2,” a new eGFRD version thatimplements the principle of eGFRD in all dimensions, thus enabling efficient particle-based simulation of biochemical reaction-diffusion processes in the 3D cytoplasm, on 2D planes representing membranes, and on 1D elongated cylinders representative of,e.g., cytoskeletal tracks or DNA; in 1D, it also incorporates convective motion used to model active transport. We find that, for lowparticle densities, eGFRD2 is up to 6 orders of magnitude faster than conventional Brownian dynamics. We exemplify the capa-bilities of eGFRD2 by simulating an idealized model of Pom1 gradient formation, which involves 3D diffusion, active transport onmicrotubules, and autophosphorylation on the membrane, confirming recent experimental and theoretical results on this systemto hold under genuinely stochastic conditions.

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