Energy dissipation in an adaptive molecular circuit

TL;DR

This paper analyzes the energy dissipation and adaptation accuracy in a stochastic model of bacterial sensory networks, revealing a phase transition and exponential error reduction with methylation range, advancing understanding of nonequilibrium biological systems.

Contribution

It provides an exact analytic solution for the nonequilibrium steady state and entropy production in a stochastic adaptation model, extending the ESA trade-off framework.

Findings

Adaptation error decreases exponentially with methylation range.

A nonequilibrium phase transition exists at infinite methylation range.

Exact entropy production rate expression derived for the model.

Abstract

The ability to monitor nutrient and other environmental conditions with high sensitivity is crucial for cell growth and survival. Sensory adaptation allows a cell to recover its sensitivity after a transient response to a shift in the strength of extracellular stimulus. The working principles of adaptation have been established previously based on rate equations which do not consider fluctuations in a thermal environment. Recently, G. Lan et al. (Nature Phys., 8:422-8, 2012) performed a detailed analysis of a stochastic model for the E. coli sensory network. They showed that accurate adaptation is possible only when the system operates in a nonequilibrium steady-state (NESS). They further proposed an energy-speed-accuracy (ESA) trade-off relation. We present here analytic results on the NESS of the model through a mapping to a one-dimensional birth-death process. An exact expression for the entropy production rate is also derived. Based on these results, we are able to discuss the ESA relation in a more general setting. Our study suggests that the adaptation error can be reduced exponentially as the methylation range increases. Finally, we show that a nonequilibrium phase transition exists in the infinite methylation range limit, despite the fact that the model contains only two discrete variables.