Sensitivity and Memory in Physics and Biology

Abstract

Living cells exhibit striking abilities—for example, their astonishing sensitivity to small perturbations, as well as their remarkable memory of transient events and stimuli. Since living things are out-of-equilibrium, the quest to understand how these abilities arise raises very basic problems in nonequilibrium physics. In Part I, I focus on dissipation and its role as a constraint on nonequilibrium behavior.

In Part II, I present a set of simple, universal identities and inequalities constraining the sensitivity properties of nonequilibrium systems. For a large class of perturbations, I find an equilibrium-like expression for sensitivity, whereas for other perturbations, I am able to bound the response in terms of measurable thermodynamic quantities. Applied to biochemical networks, these results extend and unify a patchwork of prior biophysics results on the energetic costs of sharp biochemical switches, accurate sensors, and molecular discrimination—revealing their common origin in the perturbation theory of Markov chains.

In Part III, I turn to the question of how cells remember. In eukaryotes such as ourselves, memory of cell type—nerve, muscle, blood, and so on—is maintained in complex cellular networks whose kinetic details we know incompletely, and which perhaps even involve chemical dynamics coupled to the polymer dynamics of chromatin. I explore a simple biophysical model inspired by a class of these systems—involving the spreading of covalent modifications on chromatin—with the aim of uncovering qualitative features that can imbue them with the capacity for memory. We find that limitation of the modifying enzymes relative to their substrates dramatically stabilizes memory.

Together, these findings highlight the role of the size and architecture in constraining functional behaviors, and begin to suggest the possible form of a future precise, but qualitative, theory relating structure to the functional capacities of nonequilibrium systems.