Dataset Information

Piecewise parameter estimation for stochastic models in COPASI.

ABSTRACT:

Motivation

Computational modeling is widely used for deepening the understanding of biological processes. Parameterizing models to experimental data needs computationally efficient techniques for parameter estimation. Challenges for parameter estimation include in general the high dimensionality of the parameter space with local minima and in specific for stochastic modeling the intrinsic stochasticity.

Results

We implemented the recently suggested multiple shooting for stochastic systems (MSS) objective function for parameter estimation in stochastic models into COPASI. This MSS objective function can be used for parameter estimation in stochastic models but also shows beneficial properties when used for ordinary differential equation models. The method can be applied with all of COPASI's optimization algorithms, and can be used for SBML models as well.

Availability and implementation

The methodology is available in COPASI as of version 4.15.95 and can be downloaded from http://www.copasi.org

Contact

frank.bergmann@bioquant.uni-heidelberg.de or fbergman@caltech.edu

Supplementary information

Supplementary data are available at Bioinformatics online.

SUBMITTER: Bergmann FT

PROVIDER: S-EPMC6169462 | biostudies-literature | 2016 May

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Piecewise parameter estimation for stochastic models in COPASI.

Bergmann Frank T FT Sahle Sven S Zimmer Christoph C

Bioinformatics (Oxford, England) 20160118 10

<h4>Motivation</h4>Computational modeling is widely used for deepening the understanding of biological processes. Parameterizing models to experimental data needs computationally efficient techniques for parameter estimation. Challenges for parameter estimation include in general the high dimensionality of the parameter space with local minima and in specific for stochastic modeling the intrinsic stochasticity.<h4>Results</h4>We implemented the recently suggested multiple shooting for stochastic ...[more]

PMID: 26787664

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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.

Project description:BackgroundStochastic effects can be important for the behavior of processes involving small population numbers, so the study of stochastic models has become an important topic in the burgeoning field of computational systems biology. However analysis techniques for stochastic models have tended to lag behind their deterministic cousins due to the heavier computational demands of the statistical approaches for fitting the models to experimental data. There is a continuing need for more effective and efficient algorithms. In this article we focus on the parameter inference problem for stochastic kinetic models of biochemical reactions given discrete time-course observations of either some or all of the molecular species.ResultsWe propose an algorithm for inference of kinetic rate parameters based upon maximum likelihood using stochastic gradient descent (SGD). We derive a general formula for the gradient of the likelihood function given discrete time-course observations. The formula applies to any explicit functional form of the kinetic rate laws such as mass-action, Michaelis-Menten, etc. Our algorithm estimates the gradient of the likelihood function by reversible jump Markov chain Monte Carlo sampling (RJMCMC), and then gradient descent method is employed to obtain the maximum likelihood estimation of parameter values. Furthermore, we utilize flux balance analysis and show how to automatically construct reversible jump samplers for arbitrary biochemical reaction models. We provide RJMCMC sampling algorithms for both fully observed and partially observed time-course observation data. Our methods are illustrated with two examples: a birth-death model and an auto-regulatory gene network. We find good agreement of the inferred parameters with the actual parameters in both models.ConclusionsThe SGD method proposed in the paper presents a general framework of inferring parameters for stochastic kinetic models. The method is computationally efficient and is effective for both partially and fully observed systems. Automatic construction of reversible jump samplers and general formulation of the likelihood gradient function makes our method applicable to a wide range of stochastic models. Furthermore our derivations can be useful for other purposes such as using the gradient information for parametric sensitivity analysis or using the reversible jump samplers for full Bayesian inference. The software implementing the algorithms is publicly available at http://cbcl.ics.uci.edu/sgd.

Dataset Information

Piecewise parameter estimation for stochastic models in COPASI.

Motivation

Results

Availability and implementation

Contact

Supplementary information

Publications

Piecewise parameter estimation for stochastic models in COPASI.

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