Intrinsic computation of a Monod-Wyman-Changeux molecule

Abstract

Causal states are minimal sufficient statistics of prediction of a stochastic process, their coding cost is called statistical complexity, and the implied causal structure yields a sense of the process' "intrinsic computation". We discuss how statistical complexity changes with slight variations on a biologically-motivated dynamical model, that of a Monod-Wyman-Changeux molecule. Perturbations to nonexistent transitions cause statistical complexity to jump from finite to infinite, while perturbations to existent transitions cause relatively slight variations in the statistical complexity. The same is not true for excess entropy, the mutual information between past and future. We discuss the implications of this for the relationship between intrinsic and useful computation of biological sensory systems.