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Parameter estimation and determinability analysis applied to Drosophila gap gene circuits.

ABSTRACT: Mathematical modeling of real-life processes often requires the estimation of unknown parameters. Once the parameters are found by means of optimization, it is important to assess the quality of the parameter estimates, especially if parameter values are used to draw biological conclusions from the model.In this paper we describe how the quality of parameter estimates can be analyzed. We apply our methodology to assess parameter determinability for gene circuit models of the gap gene network in early Drosophila embryos.Our analysis shows that none of the parameters of the considered model can be determined individually with reasonable accuracy due to correlations between parameters. Therefore, the model cannot be used as a tool to infer quantitative regulatory weights. On the other hand, our results show that it is still possible to draw reliable qualitative conclusions on the regulatory topology of the gene network. Moreover, it improves previous analyses of the same model by allowing us to identify those interactions for which qualitative conclusions are reliable, and those for which they are ambiguous.

SUBMITTER: Ashyraliyev M

PROVIDER: S-EPMC2586632 | biostudies-literature | 2008 Sep

REPOSITORIES: biostudies-literature

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Parameter estimation and determinability analysis applied to Drosophila gap gene circuits.

Ashyraliyev Maksat M Jaeger Johannes J Blom Joke G JG

BMC systems biology 20080925

<h4>Background</h4>Mathematical modeling of real-life processes often requires the estimation of unknown parameters. Once the parameters are found by means of optimization, it is important to assess the quality of the parameter estimates, especially if parameter values are used to draw biological conclusions from the model.<h4>Results</h4>In this paper we describe how the quality of parameter estimates can be analyzed. We apply our methodology to assess parameter determinability for gene circuit ...[more]

PMID: 18817540

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Project description:BACKGROUND: Inverse modelling of gene regulatory networks (GRNs) capable of simulating continuous spatio-temporal biological processes requires accurate data and a good description of the system. If quantitative relations between genes cannot be extracted from direct measurements, an efficient method to estimate the unknown parameters is mandatory. A model that has been proposed to simulate spatio-temporal gene expression patterns is the connectionist model. This method describes the quantitative dynamics of a regulatory network in space. The model parameters are estimated by means of model-fitting algorithms. The gene interactions are identified without making any prior assumptions concerning the network connectivity. As a result, the inverse modelling might lead to multiple circuits showing the same quantitative behaviour and it is not possible to identify one optimal circuit. Consequently, it is important to address the quality of the circuits in terms of model robustness. RESULTS: Here we investigate the sensitivity and robustness of circuits obtained from reverse engineering a model capable of simulating measured gene expression patterns. As a case study we use the early gap gene segmentation mechanism in Drosophila melanogaster. We consider the limitations of the connectionist model used to describe GRN Inferred from spatio-temporal gene expression. We address the problem of circuit discrimination, where the selection criterion within the optimization technique is based of the least square minimization on the error between data and simulated results. CONCLUSION: Parameter sensitivity analysis allows one to discriminate between circuits having significant parameter and qualitative differences but exhibiting the same quantitative pattern. Furthermore, we show that using a stochastic model derived from a deterministic solution, one can introduce fluctuations within the model to analyze the circuits' robustness. Ultimately, we show that there is a close relation between circuit sensitivity and robustness to fluctuation, and that circuit robustness is rather modular than global. The current study shows that reverse engineering of GRNs should not only focus on estimating parameters by minimizing the difference between observation and simulation but also on other model properties. Our study suggests that multi-objective optimization based on robustness and sensitivity analysis has to be considered.

Dataset Information

Parameter estimation and determinability analysis applied to Drosophila gap gene circuits.

Publications

Parameter estimation and determinability analysis applied to Drosophila gap gene circuits.

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