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Synthesizing and Tuning Chemical Reaction Networks with Specified Behaviours

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DNA Computing and Molecular Programming (DNA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9211))

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Abstract

We consider how to generate chemical reaction networks (CRNs) from functional specifications. We propose a two-stage approach that combines synthesis by satisfiability modulo theories and Markov chain Monte Carlo based optimisation. First, we identify candidate CRNs that have the possibility to produce correct computations for a given finite set of inputs. We then optimise the reaction rates of each CRN using a combination of stochastic search techniques applied to the chemical master equation, simultaneously improving the probability of correct behaviour and ruling out spurious solutions. In addition, we use techniques from continuous time Markov chain theory to study the expected termination time for each CRN. We illustrate our approach by identifying CRNs for majority decision-making and division computation, which includes the identification of both known and unknown networks.

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Notes

  1. 1.

    We assume that the reaction volume is 1 to allow for later volume scaling e.g. \(k_x^r/v\) is the propensity for a reaction volume equal to v.

  2. 2.

    We consider terminating computations by enforcing that no reactions are enabled at the state that satisfies \(\phi _F\). Alternative strategies possible within our approach could consider reaching a fix-point (i.e. the firing of any enabled reaction does not cause a transition to a different state), or reaching a cycle along which \(\phi _F\) is satisfied, to guarantee that the correct output is eventually computed and remains unchanged by any subsequent reactions.

  3. 3.

    At present, our uniqueness constraint does not consider other CRN isomorphisms but certain species symmetries are broken by the specification \(\Phi _i\).

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Acknowledgements

We thank Dan Alistarh and Luca Cardelli for helpful discussions on the development and applications of our methodology.

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Authors and Affiliations

  1. Microsoft Research, Cambridge, CB1 2FB, UK

    Neil Dalchau, Niall Murphy, Rasmus Petersen & Boyan Yordanov

Authors
  1. Neil Dalchau
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  2. Niall Murphy
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  3. Rasmus Petersen
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  4. Boyan Yordanov
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Corresponding author

Correspondence to Niall Murphy .

Editor information

Editors and Affiliations

  1. Microsoft Research, Cambridge, United Kingdom

    Andrew Phillips

  2. Wyss Institute, Boston, Massachusetts, USA

    Peng Yin

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Dalchau, N., Murphy, N., Petersen, R., Yordanov, B. (2015). Synthesizing and Tuning Chemical Reaction Networks with Specified Behaviours. In: Phillips, A., Yin, P. (eds) DNA Computing and Molecular Programming. DNA 2015. Lecture Notes in Computer Science(), vol 9211. Springer, Cham. https://doi.org/10.1007/978-3-319-21999-8_2

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  • DOI: https://doi.org/10.1007/978-3-319-21999-8_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21998-1

  • Online ISBN: 978-3-319-21999-8

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