Exponential sensitivity by a nonequilibrium cooperativity mechanism

Sensitivity to a small perturbation is a basic observable in statistical physics, as well as an important figure of merit for many living processes, including chemical sensing, signal transduction, and morphogenesis. At thermodynamic equilibrium, the basic biophysical mechanism for sensitivity is cooperative binding, for which it can be shown that the Hill coefficient, a sensitivity measure, cannot exceed the number of binding sites. This bound is a manifestation of equilibrium laws relating sensitivity to system structure and spontaneous fluctuations, but living things can violate these laws by expending energy. In search of the ultimate limits to sensitivity, we uncover a remarkable nonequilibrium cooperative binding mechanism—nested hysteresis—with sensitivity exponential in the number of binding sites. We show that this dramatic improvement over equilibrium is, in a precise sense, the best possible. Nested hysteresis could in principle be realized in the complex, energy-expending gene regulatory systems of eukaryotes, and has implications for our understanding of the function of biomolecular condensates.