Abstract
We explore the range of probabilistic behaviours that can be engineered with Chemical Reaction Networks (CRNs). We give methods to “program” CRNs so that their steady state is chosen from some desired target distribution that has 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.
Highlights
Individual cells and viruses operate in a noisy environment and molecular interactions are inherently stochastic
We explore the range of probabilistic behaviours that can be engineered with Chemical Reaction Networks (CRNs)
We formulate a calculus that is complete for finite support distributions, which can be compiled to a restricted class of CRNs that at steady state compute those distributions
Summary
Individual cells and viruses operate in a noisy environment and molecular interactions are inherently stochastic. We formulate a calculus that is complete for finite support distributions, which can be compiled to a restricted class of CRNs that at steady state compute those distributions. Our results are of interest for a variety of scenarios in systems and synthetic biology They can be used to program a biased stochastic coin or a uniform distribution, enabling implementation of randomized algorithms and protocols in CRNs. Preliminary version of this work appeared as Cardelli et al (2016a). A first attempt to model distributions with CRNs can be found in Fett et al (2007), where the problem of producing a single distribution is studied Their circuits are approximated and cannot be composed to compute operations on distributions
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