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 (http://epubs.siam.org/doi/abs/10.1137/110832148), 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 https://arxiv.org/abs/1709.00475

At Isaac Newton Institute

I will be spending Feb 15-March 17 at the Isaac Newton Institute, Cambride, UK, for a program on Stochastic Dynamical Systems in Biology: Numerical Methods and Applications. Big thanks to the organizers,Radek Erban (Oxford), David Holcman (ENS – Paris), Samuel Isaacson (Boston) and Konstantinos Zygalakis (Southampton) for organizing this amazing opportunity to gather many creative people in our field at the same place!

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).

Multiscale and hybrid algorithms for stochastic chemical kinetics

Many biochemical network models display scale separation with respect to reaction rates and/or molecular copy numbers. Depending on the type of question under study, different models are best suited to simulate the system. For some parts of the system, a macroscopic model might be appropriate. For other parts, a mesoscopic model may provide additional insight into the models dynamics. In other cases, a microscopic model might be needed to capture the fine-grained features of the model. To efficiently simulate systems that have different requirements with respect to modeling levels, hybrid methods offer an attractive approach.