The non-equilibrium and energetic cost of sensory adaptation

Abstract

Biological sensory systems respond to external signals in short time and adapt to permanent environmental changes over a longer timescale to maintain high sensitivity in widely varying environments. In this work we have shown how all adaptation dynamics are intrinsically non‐equilibrium and free energy is dissipated. We show that the dissipated energy is utilized to maintain adaptation accuracy. A universal relation between the energy dissipation and the optimum adaptation accuracy is established by both a general continuum model and a discrete model i n the specific case of the well‐known E. coli chemo‐sensory adaptation. Our study suggests that cellular level adaptations are fueled by hydrolysis of high energy biomolecules, such as ATP. The relevance of this work lies on linking the functionality of a biological system (sensory adaptation) with a concept rooted in statistical physics (energy dissipation), by a mathematical law. This has been made possible by identifying a general sensory system with a non‐equilibrium steady state (a stationary state in which the probability current is not zero, but its divergence is, see figure), and then numerically and analytically solving the Fokker‐Planck and Master Equations which describe the sensory adaptive system. The application of our general results to the case of E. Coli has shed light on why this system uses the high energy SAM molecule to perform adaptation, since using the more common ATP would not suffice to obtain the required adaptation accuracy.