Preprint Open Access

A finite state projection method for steady-state sensitivity analysis of stochastic reaction networks

Dürrenberger, Patrik; Gupta, Ankit; Khammash, Mustafa


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  <identifier identifierType="URL">https://zenodo.org/record/4839189</identifier>
  <creators>
    <creator>
      <creatorName>Dürrenberger, Patrik</creatorName>
      <givenName>Patrik</givenName>
      <familyName>Dürrenberger</familyName>
      <affiliation>Department of Biosystems Science and Engineering, ETH Zurich, Mattenstrasse 26, 4058 Basel, Switzerland</affiliation>
    </creator>
    <creator>
      <creatorName>Gupta, Ankit</creatorName>
      <givenName>Ankit</givenName>
      <familyName>Gupta</familyName>
      <affiliation>Department of Biosystems Science and Engineering, ETH Zurich, Mattenstrasse 26, 4058 Basel, Switzerland</affiliation>
    </creator>
    <creator>
      <creatorName>Khammash, Mustafa</creatorName>
      <givenName>Mustafa</givenName>
      <familyName>Khammash</familyName>
      <affiliation>Department of Biosystems Science and Engineering, ETH Zurich, Mattenstrasse 26, 4058 Basel, Switzerland</affiliation>
    </creator>
  </creators>
  <titles>
    <title>A finite state projection method for steady-state sensitivity analysis of stochastic reaction networks</title>
  </titles>
  <publisher>Zenodo</publisher>
  <publicationYear>2021</publicationYear>
  <dates>
    <date dateType="Issued">2021-03-01</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Preprint</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/4839189</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.1063/1.5085271</relatedIdentifier>
    <relatedIdentifier relatedIdentifierType="URL" relationType="IsPartOf">https://zenodo.org/communities/cosy-bio</relatedIdentifier>
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  <rightsList>
    <rights rightsURI="https://creativecommons.org/licenses/by/4.0/legalcode">Creative Commons Attribution 4.0 International</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">&lt;p&gt;&lt;strong&gt;Abstract&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;Consider the standard stochastic reaction network model where the dynamics is given by a continuous-time Markov chain over a discrete lattice. For such models, estimation of parameter sensitivities is an important problem, but the existing computational approaches to solve this problem usually require time-consuming Monte Carlo simulations of the reaction dynamics. Therefore, these simulation-based approaches can only be expected to work over finite time-intervals, while it is often of interest in applications to examine the sensitivity values at the steady-state after the Markov chain has relaxed to its stationary distribution. The aim of this paper is to present a computational method for the estimation of steady-state parameter sensitivities, which instead of using simulations relies on the recently developed&amp;nbsp;&lt;em&gt;stationary finite state projection&lt;/em&gt;algorithm [Gupta&amp;nbsp;&lt;em&gt;et al.&lt;/em&gt;, J. Chem. Phys.&amp;nbsp;&lt;strong&gt;147&lt;/strong&gt;, 154101 (2017)] that provides an accurate estimate of the stationary distribution at a fixed set of parameters. We show that sensitivity values at these parameters can be estimated from the solution of a Poisson equation associated with the infinitesimal generator of the Markov chain. We develop an approach to numerically solve the Poisson equation, and this yields an efficient estimator for steady-state parameter sensitivities. We illustrate this method using several examples.&lt;/p&gt;</description>
  </descriptions>
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    <fundingReference>
      <funderName>European Commission</funderName>
      <funderIdentifier funderIdentifierType="Crossref Funder ID">10.13039/501100000780</funderIdentifier>
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      <funderName>European Commission</funderName>
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