Recovery of Equilibrium Free Energy from Nonequilibrium Thermodynamics with Mechanosensitive Ion Channels in E. coli

Dissipation during the Gating Cycle of the Bacterial Mechanosensitive Ion Channel Approaches the Landauer Limit

The Landauer principle sets a thermodynamic bound of kBT ln 2 on the energetic cost of erasing each bit of information. It holds for any memory device, regardless of its physical implementation. It was recently shown that carefully built artificial devices can attain this bound. In contrast, biological computation-like processes, e.g., DNA replication, transcription and translation use an order of magnitude more than their Landauer minimum. Here, we show that reaching the Landauer bound is nevertheless possible with biological devices. This is achieved using a mechanosensitive channel of small conductance (MscS) from E. coli as a memory bit. MscS is a fast-acting osmolyte release valve adjusting turgor pressure inside the cell. Our patch-clamp experiments and data analysis demonstrate that under a slow switching regime, the heat dissipation in the course of tension-driven gating transitions in MscS closely approaches its Landauer limit. We discuss the biological implications of this physical trait.

Temperature dependent mechanical unfolding and refolding of a protein studied by thermo-regulated optical tweezers

Temperature is a useful system variable to gather kinetic and thermodynamic information from proteins. Usually, free energy and the associated entropic and enthalpic contributions are obtained by quantifying the conformational equilibrium based on melting experiments performed in bulk conditions. Such experiments are suitable only for those small single-domain proteins whose side reactions of irreversible aggregation are unlikely to occur. Here, we avoid aggregation by pulling single-protein molecules in a thermo-regulated optical tweezers. Thus, we are able to explore the temperature dependence of the thermodynamic and kinetic parameters of MJ0366 from Methanocaldococcus jannaschii at the single-molecule level. By performing force-ramp experiments between 2°C and 40°C, we found that MJ0366 has a nonlinear dependence of free energy with temperature and a specific heat change of 2.3 ± 1.2 kcal/mol∗K. These thermodynamic parameters are compatible with a two-state unfolding/refolding mechanism for MJ0366. However, the kinetics measured as a function of the temperature show a complex behavior, suggesting a three-state folding mechanism comprising a high-energy intermediate state. The combination of two perturbations, temperature and force, reveals a high-energy species in the folding mechanism of MJ0366 not detected in force-ramp experiments at constant temperature.

Reformulating nonequilibrium steady states and generalized Hopfield discrimination

Despite substantial progress in nonequilibrium physics, steady-state (s.s.) probabilities remain intractable to analysis. For a Markov process, s.s. probabilities can be expressed in terms of transition rates using the graph-theoretic matrix-tree theorem (MTT). The MTT reveals that, away from equilibrium, s.s. probabilities become globally dependent on all rates, with expressions growing exponentially in the system size. This overwhelming complexity and lack of thermodynamic interpretation have greatly impeded analysis. Here we show that s.s. probabilities are proportional to the average of exp(-S(P)), where S(P) is the entropy generated along minimal paths P in the graph, and the average is taken over a probability distribution on spanning trees. Assuming Arrhenius rates, this "arboreal" distribution becomes Boltzmann-like, with the energy of a tree being its total edge barrier energy. This reformulation offers a thermodynamic interpretation that smoothly generalizes equilibrium statistical mechanics and reorganizes the expression complexity: the number of distinct minimal-path entropies depends not on graph size but on the entropy production index, a measure of nonequilibrium complexity. We demonstrate the power of this reformulation by extending Hopfield's analysis of discrimination by kinetic proofreading to any graph with index 1. We derive a general formula for the error ratio and use it to show how local energy dissipation can yield optimal discrimination through global synergy.

Homeostatic and adaptive energetics: Nonequilibrium fluctuations beyond detailed balance in voltage-gated ion channels

Stochastic thermodynamics has largely succeeded in characterizing both equilibrium and far-from-equilibrium phenomena. Yet many opportunities remain for application to mesoscopic complex systems-especially biological ones-whose effective dynamics often violate detailed balance and whose microscopic degrees of freedom are often unknown or intractable. After reviewing excess and housekeeping energetics-the adaptive and homeostatic components of a system's dissipation-we extend stochastic thermodynamics with a trajectory class fluctuation theorem for nonequilibrium steady-state, nondetailed-balanced complex systems. We then take up the neurobiological examples of voltage-gated sodium and potassium ion channels to apply and illustrate the theory, elucidating their nonequilibrium behavior under a biophysically plausible action potential drive. These results uncover challenges for future experiments and highlight the progress possible understanding the thermodynamics of complex systems-without exhaustive knowledge of every underlying degree of freedom.