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

Dürrenberger, Patrik; Gupta, Ankit; Khammash, Mustafa


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    <subfield code="u">Department of Biosystems Science and Engineering, ETH Zurich, Mattenstrasse 26, 4058 Basel, Switzerland</subfield>
    <subfield code="a">Dürrenberger, Patrik</subfield>
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    <subfield code="a">&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;</subfield>
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