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Estimation and discrimination of stochastic biochemical circuits from time-lapse microscopy data.

ABSTRACT: The ability of systems and synthetic biologists to observe the dynamics of cellular behavior is hampered by the limitations of the sensors, such as fluorescent proteins, available for use in time-lapse microscopy. In this paper, we propose a generalized solution to the problem of estimating the state of a stochastic chemical reaction network from limited sensor information generated by microscopy. We mathematically derive an observer structure for cells growing under time-lapse microscopy and incorporates the effects of cell division in order to estimate the dynamically-changing state of each cell in the colony. Furthermore, the observer can be used to discrimate between models by treating model indices as states whose values do not change with time. We derive necessary and sufficient conditions that specify when stochastic chemical reaction network models, interpreted as continuous-time Markov chains, can be distinguished from each other under both continual and periodic observation. We validate the performance of the observer on the Thattai-van Oudenaarden model of transcription and translation. The observer structure is most effective when the system model is well-parameterized, suggesting potential applications in synthetic biology where standardized biological parts are available. However, further research is necessary to develop computationally tractable approximations to the exact generalized solution presented here.

SUBMITTER: Thorsley D

PROVIDER: S-EPMC3491022 | biostudies-literature | 2012

REPOSITORIES: biostudies-literature

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Estimation and discrimination of stochastic biochemical circuits from time-lapse microscopy data.

Thorsley David D Klavins Eric E

PloS one 20121106 11

The ability of systems and synthetic biologists to observe the dynamics of cellular behavior is hampered by the limitations of the sensors, such as fluorescent proteins, available for use in time-lapse microscopy. In this paper, we propose a generalized solution to the problem of estimating the state of a stochastic chemical reaction network from limited sensor information generated by microscopy. We mathematically derive an observer structure for cells growing under time-lapse microscopy and in ...[more]

PMID: 23139740

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Project description:BackgroundThe importance of stochasticity in cellular processes having low number of molecules has resulted in the development of stochastic models such as chemical master equation. As in other modelling frameworks, the accompanying rate constants are important for the end-applications like analyzing system properties (e.g. robustness) or predicting the effects of genetic perturbations. Prior knowledge of kinetic constants is usually limited and the model identification routine typically includes parameter estimation from experimental data. Although the subject of parameter estimation is well-established for deterministic models, it is not yet routine for the chemical master equation. In addition, recent advances in measurement technology have made the quantification of genetic substrates possible to single molecular levels. Thus, the purpose of this work is to develop practical and effective methods for estimating kinetic model parameters in the chemical master equation and other stochastic models from single cell and cell population experimental data.ResultsThree parameter estimation methods are proposed based on the maximum likelihood and density function distance, including probability and cumulative density functions. Since stochastic models such as chemical master equations are typically solved using a Monte Carlo approach in which only a finite number of Monte Carlo realizations are computationally practical, specific considerations are given to account for the effect of finite sampling in the histogram binning of the state density functions. Applications to three practical case studies showed that while maximum likelihood method can effectively handle low replicate measurements, the density function distance methods, particularly the cumulative density function distance estimation, are more robust in estimating the parameters with consistently higher accuracy, even for systems showing multimodality.ConclusionsThe parameter estimation methodologies described in this work have provided an effective and practical approach in the estimation of kinetic parameters of stochastic systems from either sparse or dense cell population data. Nevertheless, similar to kinetic parameter estimation in other modelling frameworks, not all parameters can be estimated accurately, which is a common problem arising from the lack of complete parameter identifiability from the available data.

Dataset Information

Estimation and discrimination of stochastic biochemical circuits from time-lapse microscopy data.

Publications

Estimation and discrimination of stochastic biochemical circuits from time-lapse microscopy data.

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