Biochemical interactions are inherently stochastic: the time for the reactions to fire and which reaction fires next are both random variables. It has been argued that natural systems use stochasticity to perform functions that would be impossible in a deterministic setting. However, the mechanisms used by cells to compute in a noisy environment are not well understood. 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  support in N^m, with m \geq 1. We present an algorithm to systematically program a CRN so that its stochastic semantics at steady state approximates a particular distribution with arbitrarily small error  . We also give optimized schemes for special distributions, including the uniform distribution. Finally, we formulate a calculus  that is complete for finite support distributions, and that can be compiled to a restricted class of CRNs that at steady state realize those distributions . We illustrate the approach on an example of drug resistance in bacteria .
 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 N^m, with m \geq 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 .
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Biochemical interactions are inherently stochastic: the time for the reactions to fire and which reaction fires next are both random variables. It has been argued that natural systems use stochasticity to perform functions that would be impossible in a deterministic setting. However, the mechanisms used by cells to compute in a noisy environment are not well understood.
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finite
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We present an algorithm to systematically program a CRN so that its stochastic semantics at steady state approximates a particular distribution with
Moreover, any distribution with countable infinite support can be approximated with
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under the L^1 norm
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to compute on distributions
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that
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. We illustrate the approach on an example of drug resistance in bacteria