A general moment expansion method for stochastic kinetic models.

@article{Ale2013AGM,
  title={A general moment expansion method for stochastic kinetic models.},
  author={Angelique Ale and Paul D. W. Kirk and Michael P. H. Stumpf},
  journal={The Journal of chemical physics},
  year={2013},
  volume={138 17},
  pages={
          174101
        }
}
Moment approximation methods are gaining increasing attention for their use in the approximation of the stochastic kinetics of chemical reaction systems. In this paper we derive a general moment expansion method for any type of propensities and which allows expansion up to any number of moments. For some chemical reaction systems, more than two moments are necessary to describe the dynamic properties of the system, which the linear noise approximation is unable to provide. Moreover, also for… 
View on PubMed
aip.scitation.org
69 Citations
Highly Influential Citations
5
Background Citations
22
Methods Citations
21
Results Citations
2

Figures and Tables from this paper

69 Citations

A moment-convergence method for stochastic analysis of biochemical reaction networks.
TLDR
Convergent moments are introduced (defined in mathematics as the coefficients in the Taylor expansion of the probability-generating function at some point) to overcome the drawback of moment-closure methods for stochastic chemical kinetics.
Distribution Approximations for the Chemical Master Equation: Comparison of the Method of Moments and the System Size Expansion
TLDR
Two approaches for approximating the underlying probability distributions of the CME are studied, based on an integration of the statistical moments and the reconstruction of the distribution based on the maximum entropy principle.
Multivariate moment closure techniques for stochastic kinetic models.
TLDR
A set of multivariate moment-closures is developed that allows us to describe the stochastic dynamics of nonlinear systems, and is used in the context of two models that have proved challenging to the previous attempts at approximating stoChastic dynamics: oscillations in p53 and Hes1.
Comparison of different moment-closure approximations for stochastic chemical kinetics.
TLDR
The results suggest that the normal MA is favourable over the other studied MAs, and the new software package MOCA is described, which enables the automated numerical analysis of various MA methods in a graphical user interface and which was used to perform the comparative analysis presented in this paper.
Model Reconstruction for Moment-based Stochastic Chemical Kinetics
TLDR
This work proposes an analysis framework in which a number of moments of the process are integrated instead of the state probabilities, which results in a very efficient simulation of the time evolution of theprocess.
Validity conditions for moment closure approximations in stochastic chemical kinetics.
TLDR
It is shown that for bistable and oscillatory chemical systems with deterministic initial conditions, the solution of the MA equations can be interpreted as a valid approximation to the true moments of the chemical master equation, only when the steady-state mean molecule numbers obtained from thechemical master equation fall within a certain finite range.
Model Reconstruction for Moment-Based Stochastic Chemical Kinetics
TLDR
This work proposes an analysis framework in which a number of moments of the process are integrated instead of the state probabilities, which results in a very efficient simulation of the time evolution of theprocess.
Tighter bounds on transient moments of stochastic chemical systems
TLDR
A new hierarchy of convex necessary moment conditions crucially reflecting the temporal causality and other regularity conditions that are inherent to the moment trajectories associated with stochastic processes described by the Chemical Master Equation is presented.
Reconstruction of Multimodal Distributions for Hybrid Moment-based Chemical Kinetics, Supporting Information
The stochastic dynamics of biochemical reaction networks can be accurately described by discrete-state Markov processes where each chemical reaction corresponds to a state transition of the process.…
Generalized method of moments for estimating parameters of stochastic reaction networks
TLDR
A generalized method of moments approach for inferring the parameters of reaction networks based on a sophisticated matching of the statistical moments of the corresponding stochastic model and the sample moments of population snapshot data is proposed.
...
...

References

SHOWING 1-10 OF 45 REFERENCES
Approximate Moment Dynamics for Chemically Reacting Systems
TLDR
Comparisons reveal that this moment closure technique based on derivative-matching provides more accurate estimates of the moment dynamics, especially when the population size is small, and it is shown that the accuracy of the proposed moment closure scheme can be arbitrarily increased by incurring additional computational effort.
A study of the accuracy of moment-closure approximations for stochastic chemical kinetics.
  • R. Grima
  • Mathematics
    The Journal of chemical physics
  • 2012
TLDR
This article uses the system-size expansion, a systematic method of solving the chemical master equation for monostable reaction systems, to calculate in the limit of large reaction volumes, the first- and second-order corrections to the mean concentration prediction of the rate equations and thefirst-order correction to the variance and covariance predictions of the linear-noise approximation.
A moment closure method for stochastic reaction networks.
TLDR
A moment closure method for stochastically modeled chemical or biochemical reaction networks that derives the dynamics of means and all central moments from a chemical master equation and estimates the errors in the means and central moments generated by the approximation method.
Lognormal Moment Closures for Biochemical Reactions
TLDR
Striking features of these moment closure functions are that they are independent of the reaction parameters (reaction rates and stoichiometry) and moreover the dependence of higher-order moment on lower order ones is consistent with the population being jointly lognormally distributed.
Analytical Derivation of Moment Equations in Stochastic Chemical Kinetics.
Moment estimation for chemically reacting systems by extended Kalman filtering.
TLDR
The initial motivation for the method was improving over the performance of stochastic simulation and moment closure methods, and it is demonstrated that it can be used in an experimental setting to estimate moments of species that cannot be measured directly from time course measurements of the moments of other species.
A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions
Mass fluctuation kinetics: capturing stochastic effects in systems of chemical reactions through coupled mean-variance computations.
TLDR
The authors describe here the derivation and application of what they term the mass fluctuation kinetics (MFK), a set of deterministic equations to track the means, variances, and covariances of the concentrations of the chemical species in the system.
Stochastic analysis of complex reaction networks using binomial moment equations.
  • B. BarzelO. Biham
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2012
TLDR
The aim of this paper is to present a complete derivation of the binomial moment equations, and to demonstrate the applicability of the moment equations for a representative set of example networks, in which stochastic effects play an important role.
Moment-closure approximations for mass-action models.
TLDR
A general expression for the marginal- and joint-moment equations for a large class of stochastic population models is presented and the generalisation of the moment equations allows this approximation to be applied easily to a wide range of models.
...
...