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Adaptive Moment Closure for Parameter Inference of Biochemical Reaction Networks [chapter]

Sergiy Bogomolov, Thomas A. Henzinger, Andreas Podelski, Jakob Ruess, Christian Schilling
2015 Lecture Notes in Computer Science  
The parameter inference methods that tend to scale best in the dimension of the CTMC are based on so-called moment closure approximations.  ...  model parameters are inferred from real measured data.  ...  In this paper, we propose an approach for parameter inference based on moment closure that is complemented by stochastic simulation.  ... 
doi:10.1007/978-3-319-23401-4_8 fatcat:fhvrznqssfdmndx4mvlxllnrqa

Moment-based inference predicts bimodality in transient gene expression

C. Zechner, J. Ruess, P. Krenn, S. Pelet, M. Peter, J. Lygeros, H. Koeppl
2012 Proceedings of the National Academy of Sciences of the United States of America  
., if they are bimodal. extrinsic variability | high-osmolarity glycerol pathway | moment dynamics | parameter inference | stochastic kinetic models B uilding predictive computational models of intracellular  ...  Here we introduce a moment-based inference scheme for calibrating stochastic models with heterogeneous single-cell measurements.  ...  The work of J.R. and J.L. was supported in part by SystemsX.ch under the project YeastX and by the European Commission under the project MoVeS.  ... 
doi:10.1073/pnas.1200161109 pmid:22566653 pmcid:PMC3361437 fatcat:egkzjrx3p5fmdncg2tqpgfmu2e

Adaptive moment closure for parameter inference of biochemical reaction networks

Christian Schilling, Sergiy Bogomolov, Thomas A. Henzinger, Andreas Podelski, Jakob Ruess
2016 Biosystems (Amsterdam. Print)  
The parameter inference methods that tend to scale best in the dimension of the CTMC are based on so-called moment closure approximations.  ...  Here, we propose a moment-based parameter inference method that automatically chooses the most appropriate moment closure method.  ...  Acknowledgments This work is based on the CMSB 2015 paper "Adaptive moment closure for parameter inference of biochemical reaction networks" (Bogomolov et al., 2015)  ... 
doi:10.1016/j.biosystems.2016.07.005 pmid:27461396 fatcat:ijnlhenre5eehgf27ql34vmfja

CERENA: ChEmical REaction Network Analyzer—A Toolbox for the Simulation and Analysis of Stochastic Chemical Kinetics

Atefeh Kazeroonian, Fabian Fröhlich, Andreas Raue, Fabian J. Theis, Jan Hasenauer, Dennis Salahub
2016 PLoS ONE  
In this manuscript we introduced CERENA, a toolbox for the analysis of stochastic chemical kinetics using Approximations of the Chemical Master Equation solution statistics.  ...  The analysis of these stochastic chemical kinetics is important for understanding cell-to-cell variability and its functional implications, but it is also challenging.  ...  The parameters of differential equations can efficiently be inferred using gradient-based optimization methods [17] .  ... 
doi:10.1371/journal.pone.0146732 pmid:26807911 pmcid:PMC4726759 fatcat:ikkfefujmngopbwjftfr6gkbcu

Diagnostics for assessing the linear noise and moment closure approximations

Colin S. Gillespie, Andrew Golightly
2016 Statistical Applications in Genetics and Molecular Biology  
In particular, we leverage the normality assumption of the linear noise and moment closure approximations.  ...  By constructing an efficient space filling design over the parameter region of interest, we present a number of useful diagnostic tools that aids modellers in assessing whether the approximation is suitable  ...  Within the context of stochastic kinetic models, both the moment closure and LNA approaches can be seen as GP emulators.  ... 
doi:10.1515/sagmb-2014-0071 pmid:27682714 fatcat:7e2bl7marrb77jhe4z2u7dbxxa

Diagnostics for assessing the linear noise and moment closure approximations [article]

Colin S. Gillespie, Andrew Golightly
2016 arXiv   pre-print
In particular, we leverage the normality assumption of the linear noise and moment closure approximations.  ...  By constructing an efficient space filling design over the parameter region of interest, we present a number of useful diagnostic tools that aids modellers in assessing whether the approximation is suitable  ...  Within the context of stochastic kinetic models, both the moment closure and LNA approaches can be seen as GP emulators.  ... 
arXiv:1409.1096v2 fatcat:t6j4d4vjffanbdkmoui3nqxixm

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

Pavel Loskot, Komlan Atitey, Lyudmila Mihaylova
2019 Frontiers in Genetics  
The most common models of BRNs in literature involve differential equations, Markov processes, mass action kinetics, and state space representations whereas the most common tasks are the parameter inference  ...  Over the past decade, the interest in parameter and state estimation in models of (bio-) chemical reaction networks (BRNs) grew considerably.  ...  A multivariate moment closure method is developed in Lakatos et al. (2015) to describe the non-linear dynamics of stochastic kinetics.  ... 
doi:10.3389/fgene.2019.00549 pmid:31258548 pmcid:PMC6588029 fatcat:moxooil5argjhgcb6bpv7zz2gu

Multivariate moment closure techniques for stochastic kinetic models

Eszter Lakatos, Angelique Ale, Paul D. W. Kirk, Michael P. H. Stumpf
2015 Journal of Chemical Physics  
Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems.  ...  We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics  ...  We adjusted initial conditions and parameters to fit the above stochastic model assuming an average system size of 9.24 · 10 5 (based on the 1540 µm 3 average volume of HeLa cells) and also lowered molecular  ... 
doi:10.1063/1.4929837 pmid:26342359 fatcat:doyt7wkc7jc4hl2cd3syi4tfpq

Generalized method of moments for estimating parameters of stochastic reaction networks

Alexander Lück, Verena Wolf
2016 BMC Systems Biology  
We propose 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  ...  The proposed parameter estimation method exploits recently developed moment-based approximations and provides estimators with desirable statistical properties when a large number of samples is available  ...  Methods Stochastic chemical kinetics Our inference approach relies on a Markov modeling approach that follows Gillespie's theory of stochastic chemical kinetics.  ... 
doi:10.1186/s12918-016-0342-8 pmid:27769280 pmcid:PMC5073941 fatcat:uismfqeyxjfntdlop4tb73l6fi

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

David Schnoerr, Guido Sanguinetti, Ramon Grima
2017 Journal of Physics A: Mathematical and Theoretical  
In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics.  ...  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  ...  In summary, we have presented an introduction to modelling, approximation and inference methods for stochastic chemical kinetics based on the chemical master equation.  ... 
doi:10.1088/1751-8121/aa54d9 fatcat:bdds2szh5zhlpc6j3kesftujgi

Comprehensive review of models and methods for inferences in bio-chemical reaction networks [article]

Pavel Loskot and Komlan Atitey and Lyudmila Mihaylova
2019 arXiv   pre-print
The aim of this review paper is to explore developments of past decade to understand what BRN models are commonly used in literature, and for what inference tasks and inference methods.  ...  Over past decade, the interest in parameter and state estimation in models of (bio-)chemical reaction networks (BRNs) grew considerably.  ...  Multivariate moment closure method is developed in (Lakatos et al., 2015) to describe nonlinear dynamics of stochastic kinetics.  ... 
arXiv:1902.05828v1 fatcat:sjb4jm53a5h3jf2swbiz7vk6hu

A general moment expansion method for stochastic kinetic models

Angelique Ale, Paul Kirk, Michael P. H. Stumpf
2013 Journal of Chemical Physics  
Moment approximation methods are gaining increasing attention for their use in the approximation of the stochastic kinetics of chemical reaction systems.  ...  We demonstrate the method using a dimerisation reaction, Michaelis-Menten kinetics and a model of an oscillating p53 system.  ...  Other analyses have employed approximate Bayesian computation schemes 42 , and used moment-based inference employing the mean and variance to infer parameters of a bimodal system 43 .  ... 
doi:10.1063/1.4802475 pmid:23656108 fatcat:mygtx5kjzjcu3kqlvhxwwahskm

A data-integrated method for analyzing stochastic biochemical networks

Michael W. Chevalier, Hana El-Samad
2011 Journal of Chemical Physics  
the kinetic rate constants of stochastic network models and subsequent analysis of their dynamics.  ...  By coupling this moment-closure method with a parameter search procedure, we further demonstrate how a model's kinetic parameters can be iteratively determined in order to fit measured distribution data  ...  To achieve this, we develop a practical data-based methodology for truncating moment equations in the stochastic formulation of biological network models.  ... 
doi:10.1063/1.3664126 pmid:22149782 pmcid:PMC3324259 fatcat:xca7tzjhfjelfel7bc6av77sja

Model reduction for stochastic CaMKII reaction kinetics in synapses by graph-constrained correlation dynamics

Todd Johnson, Tom Bartol, Terrence Sejnowski, Eric Mjolsness
2015 Physical Biology  
A stochastic reaction network model of Ca(2+) dynamics in synapses (Pepke et al PLoS Comput.  ...  Data from numerically intensive simulations is used to train a reduced model that, out of sample, correctly predicts the evolution of interaction parameters characterizing the instantaneous probability  ...  Additional model reductions for stochastic chemical kinetics, other than moment closure methods, include the classic strategy of using separation of time scales to eliminate fast degrees of freedom as  ... 
doi:10.1088/1478-3975/12/4/045005 pmid:26086598 pmcid:PMC4489159 fatcat:bpqivawfdzchtaoza3rb3cezmu

Moment Fitting for Parameter Inference in Repeatedly and Partially Observed Stochastic Biological Models

Philipp Kügler, Jérémie Bourdon
2012 PLoS ONE  
We demonstrate the potential of moment fitting for parameter inference by means of illustrative stochastic biological models from the literature and address topics for future research.  ...  Based on the chemical master equation we furthermore derive closed systems of parameter dependent nonlinear ordinary differential equations that predict the time evolution of the statistical moments.  ...  Acknowledgments I have developed the moment fitting concept presented in this paper during my visiting fellowship at the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK and kindly acknowledge  ... 
doi:10.1371/journal.pone.0043001 pmid:22900079 pmcid:PMC3416831 fatcat:jhxqfikhqnajho6jmz7jcrbtca
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