Size limits sensitivity in all kinetic schemes

TL;DR

This paper reveals that the size of a perturbation's support fundamentally limits the sensitivity of kinetic schemes, unifying diverse biological sensitivity mechanisms and introducing a new mechanism with exponential sensitivity.

Contribution

It generalizes the size limit on sensitivity from equilibrium to all kinetic schemes and introduces a nested hysteresis mechanism achieving exponential sensitivity.

Findings

Support size bounds sensitivity in kinetic schemes

Unifies diverse biological sensitivity mechanisms

Proposes a nested hysteresis mechanism with exponential sensitivity

Abstract

Living things benefit from exquisite molecular sensitivity in many of their key processes, including DNA replication, transcription and translation, chemical sensing, and morphogenesis. At thermodynamic equilibrium, the basic biophysical mechanism for sensitivity is cooperative binding, for which it can be shown that the Hill coefficient, a sensitivity measure, cannot exceed the number of binding sites. Generalizing this fact, we find that for any kinetic scheme, at or away from thermodynamic equilibrium, a very simple structural quantity, the size of the support of a perturbation, always limits the effective Hill coefficient. This support bound sheds light on and unifies diverse sensitivity mechanisms, ranging from kinetic proofreading to a nonequilibrium Monod-Wyman-Changeux (MWC) model proposed for the E. coli flagellar motor switch, and represents a simple, precise bridge between experimental observations and the models we write down. In pursuit of mechanisms that saturate the support bound, we find a nonequilibrium binding mechanism, nested hysteresis, with sensitivity exponential in the number of binding sites, with implications for our understanding of models of gene regulation.