eGFRD in all dimensions

Biochemical reactions typically occur at low copy numbers, but at once in crowded and diverse environments. Space and stochasticity therefore play an essential role in biochemical networks. Spatial-stochastic simulations have become a prominent tool for understanding how stochasticity at the microscopic level influences the macroscopic behavior of such systems. However, 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 oftentimes imply tradeoffs between computational efficiency and biochemical accuracy. eGFRD (enhanced Green’s Function Reaction Dynamics) is an exact algorithm that evades such tradeoffs by partitioning the N -particle system into M ≤ N analytically tractable oneand 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 space while retaining access to their state variables at any moment. Here we present ”eGFRD2”, a new eGFRD version that implements the principle of eGFRD in all dimensions, thus enabling efficient simulation of biochemical reactiondiffusion 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 low particle densities, eGFRD2 is up to 3 orders of magnitude faster than optimized Brownian Dynamics. We exemplify the capabilities of eGFRD2 by simulating an idealized model of Pom1 gradient formation, which involves 3D diffusion, active transport on microtubules, and autophosphorylation on the membrane, confirming recent results on this system and demonstrating that it can efficiently operate under genuinely stochastic conditions. ∗Corresponding author; e-mail: [email protected] †Present address: Institute of Science and Technology (IST) Austria, Am Campus 1, 3400 Klosterneuburg, Austria ‡Present address: Bioquant Center, University of Heidelberg, 69120 Heidelberg, Germany §Present address: Department of Bionanoscience, Kavli Institute of Nanoscience, Faculty of Applied Sciences, Delft University of Technology, 2628 CJ Delft, The Netherlands 1 ar X iv :1 70 8. 09 36 4v 1 [ qbi o. M N ] 3 0 A ug 2 01 7