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Sensitivity, robustness, and identifiability in stochastic chemical kinetics models.

ABSTRACT: We present a novel and simple method to numerically calculate Fisher information matrices for stochastic chemical kinetics models. The linear noise approximation is used to derive model equations and a likelihood function that leads to an efficient computational algorithm. Our approach reduces the problem of calculating the Fisher information matrix to solving a set of ordinary differential equations. This is the first method to compute Fisher information for stochastic chemical kinetics models without the need for Monte Carlo simulations. This methodology is then used to study sensitivity, robustness, and parameter identifiability in stochastic chemical kinetics models. We show that significant differences exist between stochastic and deterministic models as well as between stochastic models with time-series and time-point measurements. We demonstrate that these discrepancies arise from the variability in molecule numbers, correlations between species, and temporal correlations and show how this approach can be used in the analysis and design of experiments probing stochastic processes at the cellular level. The algorithm has been implemented as a Matlab package and is available from the authors upon request.

SUBMITTER: Komorowski M

PROVIDER: S-EPMC3102369 | biostudies-literature | 2011 May

REPOSITORIES: biostudies-literature

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Publications

Sensitivity, robustness, and identifiability in stochastic chemical kinetics models.

Komorowski Michał M Costa Maria J MJ Rand David A DA Stumpf Michael P H MP

Proceedings of the National Academy of Sciences of the United States of America 20110506 21

We present a novel and simple method to numerically calculate Fisher information matrices for stochastic chemical kinetics models. The linear noise approximation is used to derive model equations and a likelihood function that leads to an efficient computational algorithm. Our approach reduces the problem of calculating the Fisher information matrix to solving a set of ordinary differential equations. This is the first method to compute Fisher information for stochastic chemical kinetics models ...[more]

PMID: 21551095

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Project description:The master probability equation captures the dynamic behavior of a variety of stochastic phenomena that can be modeled as Markov processes. Analytical solutions to the master equation are hard to come by though because they require the enumeration of all possible states and the determination of the transition probabilities between any two states. These two tasks quickly become intractable for all but the simplest of systems. Instead of determining how the probability distribution changes in time, we can express the master probability distribution as a function of its moments, and, we can then write transient equations for the probability distribution moments. In 1949, Moyal defined the derivative, or jump, moments of the master probability distribution. These are measures of the rate of change in the probability distribution moment values, i.e. what the impact is of any given transition between states on the moment values. In this paper we present a general scheme for deriving analytical moment equations for any N-dimensional Markov process as a function of the jump moments. Importantly, we propose a scheme to derive analytical expressions for the jump moments for any N-dimensional Markov process. To better illustrate the concepts, we focus on stochastic chemical kinetics models for which we derive analytical relations for jump moments of arbitrary order. Chemical kinetics models are widely used to capture the dynamic behavior of biological systems. The elements in the jump moment expressions are a function of the stoichiometric matrix and the reaction propensities, i.e the probabilistic reaction rates. We use two toy examples, a linear and a non-linear set of reactions, to demonstrate the applicability and limitations of the scheme. Finally, we provide an estimate on the minimum number of moments necessary to obtain statistical significant data that would uniquely determine the dynamics of the underlying stochastic chemical kinetic system. The first two moments only provide limited information, especially when complex, non-linear dynamics are involved.

Dataset Information

Sensitivity, robustness, and identifiability in stochastic chemical kinetics models.

Publications

Sensitivity, robustness, and identifiability in stochastic chemical kinetics models.

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