Thermodynamics of Biological Switches

TL;DR

The work addresses how to formulate a First Law for nonequilibrium thermodynamics in biological information processing by partitioning entropy into microscopic $S_m$ and mesoscopic information $I_M$. It introduces a generalized framework where $S = S_m - I_M$ and external energy flux $J$ (e.g., ATP/ADP cycling) drives mesoscopic information processing, yielding a Biological Free Energy $B = U + pV - T S_m$ with $dB = -T\,dI_M + dW$; this formulation demonstrates a nonequilibrium steady state (NESS) for the mesoscopic subsystem, potentially arising before microscopic equilibrium, and shows how $Q = J q$ can characterize total energy input and heat output. The paper shows that $dS = dS_m - dI_M \ge 0$ with entropy production concentrated at the microscopic level, while the mesoscopic system saturates certain information configurations (up to multiple quasistable states) under constraint $dI_M = 0$. This framework generalizes Gibbs free energy to biological switches operating far from equilibrium, clarifying how energy and information couple to regulate cellular processes and offering a path to analyze networks of switches.

Abstract

We derive a formulation of the First Law of nonequilibrium thermodynamics for biological information-processing systems by partitioning entropy in the Second Law into microscopic and mesoscopic components and by assuming that natural selection promotes optimal information processing and transmission. The resulting framework demonstrates how mesoscopic information-based subsystems can attain nonequilibrium steady states (NESS) sustained by external energy and entropy fluxes, such as those generated by ATP/ADP imbalances in vivo. Moreover, mesoscopic systems may reach NESS before microscopic subsystems, leading to ordered structures in entropy flow analogous to eddies in a moving stream.

Figures (1)

• Figure 1: An example of a simple chemical reaction commonly used as a biological switch. Typically, energy input is required to phosphorylate an amino acid. ATP imbalance drives the energy $E_D$ of the dephosphorylated state to the higher energy $E_P$ of the phosphorylated state. The switch lives in a protein matrix that, through conformational changes, alter the energy relations between phosphorylated and dephosphorylated states. Whether a site is phosphorylated or not can determine intracellular response to the switch state.