Parameter estimation and inference for stochastic reaction-diffusion systems: application to morphogenesis in D. melanogaster
1 Department of Applied Physics and Applied Mathematics, Columbia University, New York, USA
2 Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, UK
3 Fakultät Elektrotechnik und Informatik, Technische Universität Berlin, Berlin, Germany
4 Department of Computer Science, University of Sheffield, Sheffield, UK
5 ChELSI Institute, Department of Chemical and Process Engineering, University of Sheffield, Sheffield, UK
6 School of Informatics, The University of Edinburgh, Edinburgh, UK
BMC Systems Biology 2010, 4:21 doi:10.1186/1752-0509-4-21Published: 10 March 2010
Reaction-diffusion systems are frequently used in systems biology to model developmental and signalling processes. In many applications, count numbers of the diffusing molecular species are very low, leading to the need to explicitly model the inherent variability using stochastic methods. Despite their importance and frequent use, parameter estimation for both deterministic and stochastic reaction-diffusion systems is still a challenging problem.
We present a Bayesian inference approach to solve both the parameter and state estimation problem for stochastic reaction-diffusion systems. This allows a determination of the full posterior distribution of the parameters (expected values and uncertainty). We benchmark the method by illustrating it on a simple synthetic experiment. We then test the method on real data about the diffusion of the morphogen Bicoid in Drosophila melanogaster. The results show how the precision with which parameters can be inferred varies dramatically, indicating that the ability to infer full posterior distributions on the parameters can have important experimental design consequences.
The results obtained demonstrate the feasibility and potential advantages of applying a Bayesian approach to parameter estimation in stochastic reaction-diffusion systems. In particular, the ability to estimate credibility intervals associated with parameter estimates can be precious for experimental design. Further work, however, will be needed to ensure the method can scale up to larger problems.