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.
In Gopalkrishnan @cite_2 , one of the present authors has proposed a molecular scheme to do Maximum Likelihood Estimation in Log-Linear models. The reaction networks employed in that work are essentially identical to the reaction networks employed in this work, modulo some minor technical differences. In that paper, the reaction networks were used to obtain M-projections (or reverse I-projections), and thereby to solve for Maximum Likelihood Estimators. In this paper, we obtain E-projections, and sample from conditional distributions. The results in that paper were purely at the level of deterministic mass-action kinetics. The results in this paper obtain at the level of stochastic behavior.
@cite_2
1184690218
We propose a novel molecular computing scheme for statistical inference. We focus on the much-studied statistical inference problem of computing maximum likelihood estimators for log-linear models. Our scheme takes log-linear models to reaction systems, and the observed data to initial conditions, so that the corresponding equilibrium of each reaction system encodes the corresponding maximum likelihood estimator. The main idea is to exploit the coincidence between thermodynamic entropy and statistical entropy. We map a Maximum Entropy characterization of the maximum likelihood estimator onto a Maximum Entropy characterization of the equilibrium concentrations for the reaction system. This allows for an efficient encoding of the problem, and reveals that reaction networks are superbly suited to statistical inference tasks. Such a scheme may also provide a template to understanding how in vivo biochemical signaling pathways integrate extensive information about their environment and history.