Mesoscopic-microscopic hybrid algorithm with automatic partitioning

We have developed a multiscale method coupling the mesoscopic and microscopic scales. On the mesoscopic scale, systems are modeled as discrete jump processes on a structured or unstructured grid, while on the microscopic scale, molecules are modeled by hard spheres diffusing in continuous space.

Microscopic simulations are accurate but computationally expensive. In this paper we try to automatically detect which parts of a system that need high accuracy to be accurately resolved, and which parts can be simulated on the coarser mesoscopic scale. We also extend a previously developed hybrid algorithm (, to improve its convergence properties.

This new algorithm makes it possible to simulate larger systems with greater accuracy than before, thus significantly widening the scope of problems that can be simulated at the particle level.

The manuscript has been submitted and is under review. It is available on Arxiv at

StochSS 1.4: Introducing Spatial Stochastic Modeling and Simulations

We are excited to announce the release of StochSS 1.4

Version 1.4 includes spatial stochastic simulation capabilities powered by  PyURDME (

Details and instructions on how to obtain the code can be found on the Download page

Tutorials are available on the Documentation page

Linda Petzold and Chandra Krintz – University of California Santa Barbara

Per Lotstedt and Andreas Hellander – Uppsala Universitet

Give it a go and let us know what you think! Ways to communicate with us include our Google Group:

or visit us on GitHub:


After more than a year of development, we are happy to announce the release of PyURDME 1.0.0! PyURDME is a Python module for spatial stochastic simulation model development and simulation. PyURDME is connected to URDME in that is uses a modified version of its core solver. While URDME is mainly designed as an interactive Matlab toolbox that makes use of the tight connection between Comsol Multiphysics to provide an interactive modeling environment, PyURDME is an object oriented API relying only on open source software, in particular the FeniCS/Dolfin project, providing great flexibility for modelers and developers to customize computational experiments.

PyURDME has also been designed with Cloud/Distributed computing in mind, and in particular it integrates well with the IPython tools, such as IPython Notebook. We are currently working on a platform for deploying PyURDME as a Cloud appliance, with support for interactive parallel computational experiments via IPython Parallel, so check back soon for updates on this project. We are also working on integration with StochSS, which ill provide an easy-to-use UI assisted endpoint to PyURDME.

PyURDME is a collaboration with Brian Drawert at UCSB.

PhD and Postdoc positions

The Center for Applied Mathematics (CIM) in Uppsala are looking for up to 3 PhD students in applied mathematics. Within this call there is an opportunity to joint the group working on the project From cell-cell interactions to embryo development: Multiscale models and simulation in systems biology. This project is a collaboration with Carolina Wählby.

The division of Scientific Computing are looking for 3 PhD students in numerical analysis/scientific computing. Here, a variant of the above project more focused on the multiscale method development is also available: Stochastic simulation of gene expression: From individual to interacting cells.

We are also looking for a Postdoc in Scientific Computing. This is an open position where the candidate will formulate a research plan (within the areas of interests in the department).

Spatial Stochastic Simulation of the Hes1 gene regulatory network

Individual mouse embryonic stem cells have been found to exhibit highly variable differentiation responses under the same environmental conditions. Recent experimatal evidence suggest that the noisy cyclic expression of Hes1 and its downstream genes are  responsible for this, but the mechanism underlying this variability in expression is not well understood.

Together with Mark Chaplain’s group, we have recenly published a new paper in Journal of the Royal Society Interface, where we propose a spatial stochastic model of the Hes1 regulatory network. Simulations of this model with URDME suggest that the Hes1 oscillations will intrinsically give rise to broad period distributions, and hence very heterogenous cell popuations with respect to Hes1 expression. Our work suggests a simple mechanism to explain the observations that cells that were sorted according to high or low expression of Hes1 relaxed back to a heterogenous mixture of Hes1 expression. We also propose experiments to control the precise differentiation response using drug treatment.


URDME paper in BMC Systems Biology

Ever since the first version of URDME, a software framework based on our theoretical work on RDME simulations on unstructured meshes, was made public in 2008, we have wanted to write up a journal publication that describes the software. For variuos reasons we have not gotten around to it, until now.

The paper, published in BMC systems Biology, contains two modeling examples and one example that illustrates how one can use the framework as a tool in methods development. We also discuss the relationship between URDME and two other great RDME simulators, mesoRD and STEPS.


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.