Coupled Mesoscopic and Microscopic Simulation of Stochastic Reaction-Diffusion Processes in Mixed Dimensions

Abstract

We present a new simulation algorithm that allows for dynamic switching between a mesoscopic and a microscopic modeling framework for stochastic reaction-diffusion kinetics. The more expensive and more accurate microscopic model is used only for those species and in those regions in space where there is reason to believe that a microscopic model is needed to capture the dynamics correctly. The microscopic algorithm is extended to simulation on curved surfaces in order to model reaction and diffusion on membranes. The accuracy of the method on and near a spherical membrane is analyzed and evaluated in a numerical experiment. Two biologically motivated examples are simulated in which the need for microscopic simulation of parts of the system arises for different reasons. First, we apply the method to a model of the phosphorylation reactions in a MAPK signaling cascade where microscale methods are necessary to resolve fast rebinding events. Then a model is considered for transport of a species over a membrane coupled to reactions in the bulk. The new algorithm attains an accuracy similar to a full microscopic simulation by handling critical interactions on the microscale, but at a significantly reduced cost by using the mesoscale framework for most parts of the biological model.

Perspective: Stochastic algorithms for chemical kinetics

“…Hellander et al 93 use an RDME (mesoscopic) model in combination with a Smoluchowski GFRD (microscopic) model. The microscopic FIG.…”

Stochastic Reaction–Diffusion Processes with Embedded Lower-Dimensional Structures

“…In recent work (Mauro et al 2013; Hellander 2013), the single molecule simulation technique has been extended to 1D polymers embedded in 3D. Hybrid methods where some species are treated at the microscale and other species are modeled at the mesoscale are found in Flegg et al (2012), Hellander et al (2012a), Klann et al (2012). For small voxel sizes at the meso level, there is a breakdown of the model compared to the microscopic model (Isaacson 2009).…”

Single molecule simulations in complex geometries with embedded dynamic one-dimensional structures

“…22. In this paper, however, we only consider reflecting outer boundaries, but the methodology for simulating interactions with reactive surfaces (outer boundaries as well as internal surfaces) developed in Ref.…”

“…In this paper, however, we only consider reflecting outer boundaries, but the methodology for simulating interactions with reactive surfaces (outer boundaries as well as internal surfaces) developed in Ref. 22 can be combined with the method described in this paper. Furthermore, we could also combine this method with the hybrid method coupling microscopic and mesoscopic simulation algorithms, also developed in Ref.…”

“…[22][23][24] By restricting the microscale simulations to the species or the parts of space that are necessary for capturing the important dynamics of the system, computational time can be saved without losing a significant amount of accuracy.…”