On the reaction-diffusion master equation in the microscopic limit

The RDME will break down in the limit of vanishing voxel sizes, in the sense that contributions from bimolecular reactions will be lost. The problem sets on earlier (for larger voxels), the more diffusion limited the reaction is. This is a problem that has attracted a lot of interest since it was pointed out by Samuel Isaacson  in this paper.
Recently, corrections to the bimolecular rates that are explicitly mesh-dependent has been proposed to deal with the problem. Erban and Chapman finds an expression in 3D that works down to a critical size of the mesh.
In this paper, we use a theorem from Montroll to show that there will always be such a critical mesh size for which no local correction to the RDME can make it agree with the Smoluchowski model in the sense that the mean binding time between two particles should be the same in both models. In the limit of perfect diffusion control, we find analytical values for the critical size in both 2D and 3D. Interestingly, the value we find in 3D agrees with the value found by Erban and Chapman. We also discuss the relationship between the local corrections of Erban and Chapman and ours to those derived by Fange et. al.

Extending URDME

The first version of StochSS will support well mixed stochastic simulation using solvers from StochKit2 , but the work to incorporate spatial stochastic solvers are starting already now. For the spatial solvers, we will use algorithms from URDME as a computational backend. URDME is a modular framwork with a Matlab frontend, and uses Comsol Multiphysics to define and construct the spatial components of the model. Currently, its main use is as an interactive environment functioning much as a Matlab toolbox. Models are specified using a Matlab/Comsol API.
To make the solvers of URDME readily available to StochSS we are currently working on extending URDME to support open-source software for geometry modelling and meshing, and on a Python API for model specification. This Python interface will also be made available as an alternative frontend to URDME.

Welcome to StochSS

Welcome to the StochSS site! StochSS (Stochastic Simulation as a Service)
is our NIBIB-funded project to make discrete stochastic simulation easy and accessable. In the first version of StochSS we are focusing on simulation capabilities for cell biology. Our goal is to enable you to build a model (or models), scale it up to increasing complexity including incorporating spatial dependence, characterization or rare events, and parameter estimation, and explore the parameter space.
StochSS will be available on your desktop as a web app. As your computational needs grow, StochSS will be able to seamlessly deploy the appropriate computing resources as needed, via cloud computing. The foundation of the cloud computing capabilities is the AppScale open source cloud platform, developed by the Krintz group at UCSB. Appscale can link to a variety of commercial clouds, or you can turn your local cluster into a cloud.
Stay tuned for StochSS v1.0, coming soon!
The StochSS team
Linda Petzold, Chandra Krintz, Andreas Hellander, Per Lötstedt, Ben Bales, Bernie Daigle, Sheng Wu, Jin Fu, Chris Bunch, Brian Drawert, Hiranya Jayathilaka, Stefan Hellander