The notion of entropy is shared between statistics and thermodynamics, and is fundamental to both disciplines. This makes statistical problems particularly suitable for reaction network implementations. In this paper we show how to perform a statistical operation known as Information Projection or E projection with stochastic mass-action kinetics. Our scheme encodes desired conditional distributions as the equilibrium distributions of reaction systems. To our knowledge this is a first scheme to exploit the inherent stochasticity of reaction networks for information processing. We apply this to the problem of an artificial cell trying to infer its environment from partial observations.
One previous work which has engaged with stochasticity in reaction networks is by @cite_20 . They give a reaction scheme that takes an arbitrary finite probability distribution and encodes it in the stationary distribution of a reaction system. In comparison, we are taking samples from a marginal distribution and encoding the full distribution in terms of the stationary distribution. Thus our scheme allows us to do conditioning and inference.
@cite_20
2271750763
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 @math , with @math . Moreover, any distribution with countable infinite support can be approximated with arbitrarily small error under the @math 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.