Adaptation is a crucial biological function possessed by many sensory systems. In this paper, we show that the fluctuation-dissipation theorem (FDT) serves as an ideal mathematical tool to study adaptation. With the aid of the nonequilibrium FDT developed by Seifert and Speck [Europhys. Lett. 89, 10007 (2010)], we demonstrate the nonequilibrium nature of adaptation in bacterial chemotaxis. We further show that nonequilibrium is a necessary condition for adaptation even beyond the linear response regime using the spectral theory of generator matrices. In particular, the results of this paper are irrelevant to the specific functional forms of the model parameters. This suggests that the nonequilibrium nature of adaptation is a topological property, rather than a geometric property, of the underlying biochemical reaction network.

• Received 27 December 2016

DOI:https://doi.org/10.1103/PhysRevE.95.042116