Green’s-function reaction dynamics: A particle-based approach for simulating biochemical networks in time and space

Abstract

We have developed a new numerical technique, called Green's-function reaction dynamics (GFRD), that makes it possible to simulate biochemical networks at the particle level and in both time and space. In this scheme, a maximum time step is chosen such that only single particles or pairs of particles have to be considered. For these particles, the Smoluchowski equation can be solved analytically using Green's functions. The main idea of GFRD is to exploit the exact solution of the Smoluchoswki equation to set up an event-driven algorithm, which combines in one step the propagation of the particles in space with the reactions between them. The event-driven nature allows GFRD to make large jumps in time and space when the particles are far apart from each other. Here, we apply the technique to a simple model of gene expression. The simulations reveal that spatial fluctuations can be a major source of noise in biochemical networks. The calculations also show that GFRD is highly efficient. Under biologically relevant conditions, GFRD is up to five orders of magnitude faster than conventional particle-based techniques for simulating biochemical networks in time and space. GFRD is not limited to biochemical networks. It can also be applied to a large number of other reaction-diffusion problems.

Switching dynamics in reaction networks induced by molecular discreteness

“…In the first part of this paper, we briefly review these studies and explain other aspects of such effects. See also [13,14,15] for recent advances in the present topic by analytic methods and numerical simulations and [16,17] for simulation methods concerned.…”

Spatio-temporal correlations can drastically change the response of a MAPK pathway

“…This is a mean-field description, in which it is assumed that the system is well-stirred and that fluctuations can be neglected. Here, we perform particle-based simulations of one layer of the MAPK cascade using our recently developed GFRD algorithm (23,24). Our simulations reveal that spatio-temporal correlations between the enzyme and substrate molecules that are ignored in the commonly employed mean-field analyses can have a dramatic effect on the nature of the response.…”

Dynamics simulations for engineering macromolecular interactions

“…Other methods attempting to reach long time scales for coarsely modeling reactiondiffusion systems include the Reaction Before Move 20 BD scheme which extends previous BD methods by analytically determining the probability of two particles colliding in order to avoid missing collisions during large steps. This is related to other event-driven BD schemes such as Green's function reaction dynamics 21,22 which attempt to find the next significant interaction in the system and jump forward to it in time. These methods perform comparatively well for sparse system where regular BD approaches are forced to take many steps where no significant interactions occur, but are less advantageous in dense systems where interactions occur frequently.…”

“…[18][19][20][21][22][23] Ultimately, we hope to have a system that simulates the behavior of engineered proteins with multiple binding surfaces, including Brownian motion, binding, and dissociation events. In the present work, we focus on modeling the linker relationship between protein domains which are subject to Brownian forces, varying linker stiffness and binding events (on-events).…”