Particle-Based Stochastic Reaction-Diffusion Models in Biology (14w5103)

Arriving in Banff, Alberta Sunday, November 9 and departing Friday November 14, 2014


(University of British Columbia)

Mark Flegg (Monash University)

(Boston University)

(Uppsala University)

(University of California Santa Barbara)


Broadly, the objectives of this workshop are to bring together world leaders and developing early career researchers in the area of stochastic mathematical modelling of biological systems. The workshop will be attended by the world leading experts in the various areas of stochastic reaction-diffusion simulation, analysis and application as well as junior researchers starting in the field.

Our primary aims are to:

1. Bring together international researchers developing new and innovative ways to simulate particle-based stochastic reaction diffusion processes which increase efficiency and/or accuracy in simulation outcomes.

In particular, there will be a focus on applicability of these methods to biological problems in terms of accuracy and efficiency, but also in terms of robustness to studying different types of biological processes. Groups working on each of First Passage Kinetic Monte Carlo (FPKMC), Brownian Dynamics (BD), and Reaction-Diffusion Master Equation (RDME)-based Gillespie methods will be presenting the latest advances in methodologies and biological application.

We hope to stimulate a movement to collaboratively evaluate the many numerical methods and corresponding computational implementations based on efficiency and accuracy. It is likely that the applicability of a reaction-diffusion algorithm depends on the system it is being applied to. In this case, a unification of this field of research would be to find a set of criteria which establishes the optimal simulation algorithm given particular biological conditions. By bringing this group of researchers together we hope to identify the most innovative simulation techniques and demonstrate their applicability to a range of biological phenomena. These simulation techniques must then be analyzed for sources of error that may occur in simple and complex reaction-diffusion systems. Only after we establish the optimal techniques for a range of different biological systems can we determine the most applicable approach for general biological systems of interest.

2. To facilitate interaction and future collaborations between numerical analysts and scientific computing experts developing numerical methods with mathematical modelers applying existing methods to biological problems.

Our participants include a number of members of modelling groups that have not had substantial interaction with the communities developing numerical methods and simulation algorithms. One particular focus in this regard has been the invitation of groups studying immunological processes and groups in computational neuroscience. We will introduce these groups to those working on the development of numerical methods, with the goal of stimulating new collaborations. These new applications should help to drive improvements to existing simulation methodologies. Likewise, the use of current state of the art methods should help facilitate more accurate modeling studies of larger systems for the immunology and neuroscience groups.

3. Discuss sources of numerical error in algorithms for reaction-diffusion processes and their effects on the simulation results.

There is limited rigorous numerical analysis of the errors in BD algorithms or RDME-based methods (either by mathematical analysis or well-resolved numerical simulations). Several groups which have investigated these problems will be presenting at the workshop. By bringing these researchers together we hope to stimulate more systematic studies of the accuracy of the various methods, while also disseminating their results to the broader modeling community. Understanding the accuracy and limitations of the various numerical methods is crucial when drawing biological conclusions based on simulation results.

4. Introduce hybridization simulation techniques for reaction-diffusion processes with multiple scales.

The accurate and efficient study of larger-scale biological systems such as signal transduction networks and gene regulatory networks may require the use of hybrid multiscale methods to facilitate computationally-tractable investigations. Several groups working on hybrid methods that couple more macroscopic deterministic reaction-diffusion models, or couple microscopic particle methods (BD/FPKMC) to mesoscopic RDME methods will be presenting their latest techniques at the workshop. The development of these methods is a very recent field of interest, with limited applications of these methods to the study of realistic biological systems. One goal of the workshop is to introduce modelers to the types of methods that have been developed, while simultaneously providing new biological problems to stimulate the development of improved multiscale methods.

5. To introduce early-career researchers to world leaders in the development of numerical methods and mathematical models for studying cellular processes.

One quarter of the invited speakers at the workshop are postdoctoral fellows or graduate students, with another third early-career faculty. These groups are complemented by a number of senior participants. The purpose of the emphasis on early-career participants is to develop future growth of research in stochastic mathematical modelling of biological systems.