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Stochastic Chemical Reaction Networks for Robustly Approximating Arbitrary Probability Distributions

Cappelletti, Daniele and Ortiz-Muñoz, Andrés and Anderson, David F. and Winfree, Erik (2020) Stochastic Chemical Reaction Networks for Robustly Approximating Arbitrary Probability Distributions. Theoretical Computer Science, 801 . pp. 64-95. ISSN 0304-3975.

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We show that discrete distributions on the d-dimensional non-negative integer lattice can be approximated arbitrarily well via the marginals of stationary distributions for various classes of stochastic chemical reaction networks. We begin by providing a class of detailed balanced networks and prove that they can approximate any discrete distribution to any desired accuracy. However, these detailed balanced constructions rely on the ability to initialize a system precisely, and are therefore susceptible to perturbations in the initial conditions. We therefore provide another construction based on the ability to approximate point mass distributions and prove that this construction is capable of approximating arbitrary discrete distributions for any choice of initial condition. In particular, the developed models are ergodic, so their limit distributions are robust to a finite number of perturbations over time in the counts of molecules.

Item Type:Article
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URLURL TypeDescription Paper
Winfree, Erik0000-0002-5899-7523
Additional Information:© 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license ( Received 6 November 2018, Revised 12 June 2019, Accepted 8 August 2019, Available online 29 August 2019. The current structure of the project was conceived when the four authors participated in the BIRS 5-day Workshop “Mathematical Analysis of Biological Interaction Networks.” Parts of the proofs for the present work were then completed while two of the authors were taking part in the AIM SQuaRE workshop “Dynamical properties of deterministic and stochastic models of reaction networks.” We thank the Banff International Research Station and the American Institute of Mathematics for making this possible. Anderson gratefully acknowledges support via the Army Research Office through grant W911NF-18-1-0324. Winfree gratefully acknowledges support via the National Science Foundation “Expedition in Computing” grant CCF-1317694. Cappelletti has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme grant agreement No. 743269 (CyberGenetics project). This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1745301. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Funding AgencyGrant Number
Army Research Office (ARO)W911NF-18-1-0324
European Research Council (ERC)743269
NSF Graduate Research FellowshipDGE-1745301
Subject Keywords:Stochastic chemical reaction networks; Approximation; Arbitrary distributions; Detailed balance; Robustness; Molecular computing
Record Number:CaltechAUTHORS:20190619-141711510
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Official Citation:Daniele Cappelletti, Andrés Ortiz-Muñoz, David F. Anderson, Erik Winfree, Stochastic chemical reaction networks for robustly approximating arbitrary probability distributions, Theoretical Computer Science, Volume 801, 2020, Pages 64-95, ISSN 0304-3975, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:96572
Deposited By: Tony Diaz
Deposited On:19 Jun 2019 21:27
Last Modified:02 Dec 2019 17:16

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