On the Stability and Function of Chemical Reaction Networks

The remarkable complexity of living systems emerges from networks of chemical reactions that operate persistently far from equilibrium. These networks sustain stable states despite incessant fluctuations, reorganize in response to changing environments, and process information with extraordinary fidelity. Yet the physical principles that govern their stability and constrain their function remain poorly understood. Unlike equilibrium systems, where free energy provides a unifying organizing principle, nonequilibrium chemical networks lack a comparably general framework. Developing such a framework is a central challenge for modern statistical mechanics. In this talk, I will discuss advances in nonequilibrium theory connecting fluctuations, dissipation, stability, and function. First, I will describe a theory for the stability of reaction - diffusion systems based on the statistical mechanics of rare trajectories. Using instanton approximations and fluctuations around the most probable transition paths, we uncover how nonequilibrium driving and path entropy determine the relative stability of competing states. Second, I will consider biochemical signaling networks and introduce a general dissipation - error bound connecting the energetic cost of driving to the accuracy of responses to time-dependent signals. Together, these results reveal organizing principles that transcend specific molecular mechanisms, with broad implications for chemistry, materials science, and biology.

Speaker: David Limmer, UC Berkeley