Energy dissipation in an adaptive molecular circuit

Shou Wen Wang, Yueheng Lan, Lei Han Tang*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

13 Citations (Scopus)


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.

Original languageEnglish
Article numberP07025
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number7
Publication statusPublished - 1 Jul 2015

Scopus Subject Areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • exact results
  • regulatory networks (theory)
  • signal transduction (theory)
  • stationary states


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