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Programming Discrete Distributions with Chemical Reaction Networks

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DNA Computing and Molecular Programming (DNA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9818))

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Abstract

We explore the range of probabilistic behaviours that can be engineered with Chemical Reaction Networks (CRNs). We show that at steady state CRNs are able to “program” any distribution with finite support in \(\mathbb {N}^m\), with \(m \ge 1\). Moreover, any distribution with countable infinite support can be approximated with arbitrarily small error under the \(L^1\) norm. We also give optimized schemes for special distributions, including the uniform distribution. Finally, we formulate a calculus to compute on distributions that is complete for finite support distributions, and can be compiled to a restricted class of CRNs that at steady state realize those distributions.

This research is supported by a Royal Society Research Professorship and ERC AdG VERIWARE.

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Notes

  1. 1.

    The reaction rate k depends on the volume V. However, as the volume is fixed, in our notation V is embedded inside k.

  2. 2.

    Note that this is a stricter requirement than those in [9], where output species are produced monotonically, but they are allowed to act as catalysts in some reactions. We cannot allow that because catalyst species influence the value of the propensity rate of a reaction and so the probability that it fires.

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Author information

Authors and Affiliations

  1. Microsoft Research, Cambridge, UK

    Luca Cardelli

  2. Department of Computer Science, University of Oxford, Oxford, UK

    Luca Cardelli, Marta Kwiatkowska & Luca Laurenti

Authors
  1. Luca Cardelli
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  2. Marta Kwiatkowska
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  3. Luca Laurenti
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Corresponding author

Correspondence to Luca Laurenti .

Editor information

Editors and Affiliations

  1. ESPCI, Laboratoire Gulliver UMR 7083, Paris, France

    Yannick Rondelez

  2. Centre de Recherche Inria de Paris, Paris, France

    Damien Woods

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Cardelli, L., Kwiatkowska, M., Laurenti, L. (2016). Programming Discrete Distributions with Chemical Reaction Networks. In: Rondelez, Y., Woods, D. (eds) DNA Computing and Molecular Programming. DNA 2016. Lecture Notes in Computer Science(), vol 9818. Springer, Cham. https://doi.org/10.1007/978-3-319-43994-5_3

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  • DOI: https://doi.org/10.1007/978-3-319-43994-5_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-43993-8

  • Online ISBN: 978-3-319-43994-5

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