Moment fitting for parameter inference in repeatedly and partially observed stochastic biological models.

The inference of reaction rate parameters in biochemical network models from time series concentration data is a central task in computational systems biology. Under the assumption of well mixed conditions the network dynamics are typically described by the chemical master equation, the Fokker Planc...

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Autor principal:	Philipp Kügler
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2012
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/e707a230802d41ad823d89d967a16704
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spelling	oai:doaj.org-article:e707a230802d41ad823d89d967a167042021-11-18T07:09:04ZMoment fitting for parameter inference in repeatedly and partially observed stochastic biological models.1932-620310.1371/journal.pone.0043001https://doaj.org/article/e707a230802d41ad823d89d967a167042012-01-01T00:00:00Zhttps://www.ncbi.nlm.nih.gov/pmc/articles/pmid/22900079/?tool=EBIhttps://doaj.org/toc/1932-6203The inference of reaction rate parameters in biochemical network models from time series concentration data is a central task in computational systems biology. Under the assumption of well mixed conditions the network dynamics are typically described by the chemical master equation, the Fokker Planck equation, the linear noise approximation or the macroscopic rate equation. The inverse problem of estimating the parameters of the underlying network model can be approached in deterministic and stochastic ways, and available methods often compare individual or mean concentration traces obtained from experiments with theoretical model predictions when maximizing likelihoods, minimizing regularized least squares functionals, approximating posterior distributions or sequentially processing the data. In this article we assume that the biological reaction network can be observed at least partially and repeatedly over time such that sample moments of species molecule numbers for various time points can be calculated from the data. 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. For inferring the reaction rate parameters we suggest to not only compare the sample mean with the theoretical mean prediction but also to take the residual of higher order moments explicitly into account. Cost functions that involve residuals of higher order moments may form landscapes in the parameter space that have more pronounced curvatures at the minimizer and hence may weaken or even overcome parameter sloppiness and uncertainty. As a consequence both deterministic and stochastic parameter inference algorithms may be improved with respect to accuracy and efficiency. 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.Philipp KüglerPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 7, Iss 8, p e43001 (2012)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Philipp Kügler Moment fitting for parameter inference in repeatedly and partially observed stochastic biological models.
description	The inference of reaction rate parameters in biochemical network models from time series concentration data is a central task in computational systems biology. Under the assumption of well mixed conditions the network dynamics are typically described by the chemical master equation, the Fokker Planck equation, the linear noise approximation or the macroscopic rate equation. The inverse problem of estimating the parameters of the underlying network model can be approached in deterministic and stochastic ways, and available methods often compare individual or mean concentration traces obtained from experiments with theoretical model predictions when maximizing likelihoods, minimizing regularized least squares functionals, approximating posterior distributions or sequentially processing the data. In this article we assume that the biological reaction network can be observed at least partially and repeatedly over time such that sample moments of species molecule numbers for various time points can be calculated from the data. 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. For inferring the reaction rate parameters we suggest to not only compare the sample mean with the theoretical mean prediction but also to take the residual of higher order moments explicitly into account. Cost functions that involve residuals of higher order moments may form landscapes in the parameter space that have more pronounced curvatures at the minimizer and hence may weaken or even overcome parameter sloppiness and uncertainty. As a consequence both deterministic and stochastic parameter inference algorithms may be improved with respect to accuracy and efficiency. 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.
format	article
author	Philipp Kügler
author_facet	Philipp Kügler
author_sort	Philipp Kügler
title	Moment fitting for parameter inference in repeatedly and partially observed stochastic biological models.
title_short	Moment fitting for parameter inference in repeatedly and partially observed stochastic biological models.
title_full	Moment fitting for parameter inference in repeatedly and partially observed stochastic biological models.
title_fullStr	Moment fitting for parameter inference in repeatedly and partially observed stochastic biological models.
title_full_unstemmed	Moment fitting for parameter inference in repeatedly and partially observed stochastic biological models.
title_sort	moment fitting for parameter inference in repeatedly and partially observed stochastic biological models.
publisher	Public Library of Science (PLoS)
publishDate	2012
url	https://doaj.org/article/e707a230802d41ad823d89d967a16704
work_keys_str_mv	AT philippkugler momentfittingforparameterinferenceinrepeatedlyandpartiallyobservedstochasticbiologicalmodels
_version_	1718423887616671744

Moment fitting for parameter inference in repeatedly and partially observed stochastic biological models.

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