Programming Discrete Distributions with Chemical Reaction Networks

TL;DR

This paper demonstrates that Chemical Reaction Networks can be engineered to produce any finite or countably infinite distribution at steady state, providing methods for approximation, optimization, and computation on distributions.

Contribution

It establishes that CRNs can program any finite support distribution and approximate countably infinite distributions, introducing a calculus for distribution computation.

Findings

CRNs can realize any finite support distribution at steady state.

CRNs can approximate distributions with countable infinite support arbitrarily closely.

Optimized schemes are provided for specific distributions like the uniform distribution.

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 $m \geq 1$. 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.