Model Reconstruction for Moment-Based Stochastic Chemical Kinetics

Andreychenko, Alexander; Mikeev, Linar; Wolf, Verena

doi:10.1145/2699712

Cited by 27 publications

(31 citation statements)

References 51 publications

(82 reference statements)

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“…numerical methods. The maximum entropy method for the construction of the marginal distributions of single species has recently been used in combination with moment closure methods and the system size expansion in [136,137]. Figure 7 shows the result for one example system.…”

Section: Construction Of Distributions From Momentsmentioning

confidence: 99%

Approximation and inference methods for stochastic biochemical kinetics—a tutorial review

Schnoerr

Sanguinetti

Grima

2017

J. Phys. A: Math. Theor.

320

413

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Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the Chemical Master Equation. Despite its simple structure, no analytic solutions to the Chemical Master Equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics.

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Section: Construction Of Distributions From Momentsmentioning

confidence: 99%

Approximation and inference methods for stochastic biochemical kinetics—a tutorial review

Schnoerr

Sanguinetti

Grima

2017

J. Phys. A: Math. Theor.

320

413

View full text Add to dashboard Cite

show abstract

“…In the sequel we describe how to obtain the one-dimensional marginal probability distributions of a reaction network when we use the moments up to order K. We mostly follow Andreychenko et al [17] and simply write X (and x) for any random vector (and state) of at most N S molecular populations at some fixed time instant t. Given a sequence of K + 1 non-central moments 1 E X k = µ (k) , k = 0, 1, . .…”

Section: Maximum Entropy Distribution Reconstructionmentioning

confidence: 99%

Distribution Approximations for the Chemical Master Equation: Comparison of the Method of Moments and the System Size Expansion

Andreychenko

Bortolussi

Grima

et al. 2017

Modeling Cellular Systems

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The stochastic nature of chemical reactions involving randomly fluctuating population sizes has lead to a growing research interest in discrete-state stochastic models and their analysis. A widely-used approach is the description of the temporal evolution of the system in terms of a chemical master equation (CME). In this paper we study two approaches for approximating the underlying probability distributions of the CME. The first approach is based on an integration of the statistical moments and the reconstruction of the distribution based on the maximum entropy principle. The second approach relies on an analytical approximation of the probability distribution of the CME using the system size expansion, considering higher-order terms than the linear noise approximation. We consider gene expression networks with unimodal and multimodal protein distributions to compare the accuracy of the two approaches. We find that both methods provide accurate approximations to the distributions of the CME while having different benefits and limitations in applications.

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“…Note that the maximum entropy approach has been successfully applied to reconstruct distributions based on moments in many areas, e.g. physics [20], stochastic chemical kinetics [21], and performance analysis [22].…”

Section: E[mentioning

confidence: 99%

Moment-based availability prediction for bike-sharing systems

Feng

Hillston

Reijsbergen

2017

Performance Evaluation

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We study the problem of predicting the future availability of bikes in a bike station through the moment analysis of a PCTMC model with time-dependent rates. Given a target station for prediction, the moments of the number of available bikes in the station at a future time can be derived by a set of moment equations with an initial setup given by the snapshot of the current state of all stations in the system. A directed contribution graph is constructed, and a contribution propagation method is proposed to prune the PCTMC so that it only contains stations which have significant contribution to the journey flows to the target station. Once the moments have been derived, the underlying probability distribution of the available number of bikes is reconstructed through the maximum entropy approach. We illustrate our approach on Santander Cycles, the bike-sharing system in London. The model is parameterised using historical data from Santander Cycles. Experimental results show that our model outperforms a time-inhomogeneous Markov queueing model with respect to several performance metrics for bike availability prediction.

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Model Reconstruction for Moment-Based Stochastic Chemical Kinetics

Cited by 27 publications

References 51 publications

Approximation and inference methods for stochastic biochemical kinetics—a tutorial review

Approximation and inference methods for stochastic biochemical kinetics—a tutorial review

Distribution Approximations for the Chemical Master Equation: Comparison of the Method of Moments and the System Size Expansion

Moment-based availability prediction for bike-sharing systems

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