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Parameter estimation and inference for stochastic reaction-diffusion systems: application to morphogenesis in D. melanogaster

Dewar, M.A., Kadirkamanathan, V., Opper, M. and Sanguinetti, G. (2010) Parameter estimation and inference for stochastic reaction-diffusion systems: application to morphogenesis in D. melanogaster. BMC Systems Biology , 4. Art no.21. ISSN 1752-0509

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Abstract

Background: 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.

Results: 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.

Conclusions: 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.

Item Type: Article
Copyright, Publisher and Additional Information: © 2010 Dewar et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Chemical and Process Engineering (Sheffield)
The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield)
The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield)
Depositing User: Miss Anthea Tucker
Date Deposited: 30 Apr 2010 10:19
Last Modified: 05 Jun 2014 03:22
Published Version: http://dx.doi.org/10.1186/1752-0509-4-21
Status: Published
Publisher: Biomed Central
Identification Number: 10.1186/1752-0509-4-21
URI: http://eprints.whiterose.ac.uk/id/eprint/10781

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