Energy dissipation and dynamic response in adaptive molecular circuits

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. A more complete approach to the problem requires a statistical mechanical reformulation in terms of discrete chemical states and transition rates governed by free energies. 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. They further obtained a relation among energy dissipation, adaptation speed and adaptation error through model calculation and suggested that it may hold generally.

However, adaptation is only one aspect of the bacterial chemo-sensing system. Its transient response to ligand concentration fluctuations with high gain is at least as important. Therefore, it would be quite surprising if the operational cost of the sensory network is solely for reducing the adaptation error. In fact, the energy dissipation is present even when there is no change in the extracelllar ligand concentration. We therefore propose to re-analyze the stochastic model of G. Lan et al. to gain a better understanding of the origin of the observed relationship. The simplicity of the model allows a rigorous treatment using methods of statistical mechanics. The model also possesses several desirable analytic properties which make it an attractive testing ground to demystify various general results on energy dissipation and linear response in nonequilibrium states in the literature. We believe the detailed model study will contribute to the “Hamiltonian formulation” of molecular network dynamics that goes beyond the rate equation approach, thereby bringing physics closer to biology.