Energy dissipation in an adaptive molecular circuit. (21st July 2015)

• Record Type: Journal Article
• Authors: Wang, Shou-Wen; Lan, Yueheng; Tang, Lei-Han
• Is Part Of: Journal of statistical mechanics. (2015:Jul.)
• Publication Date: 2015-07-21
• Subjects: 11 -- 10 -- 4; 11/020 -- 10/400 -- 10/440 -- 4/203; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2015/00/P07025
• Languages: English
• ISSNs: 1742-5468

Abstract

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, Lan et al (2012 Nat. Phys .8 422–8) performed a detailed analysis of a stochastic model for the Escherichia 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.