Tight-binding derivation of a discrete-continuous description of mechanochemical coupling in a molecular motor

Virial-like thermodynamic uncertainty relation in the tight-binding regime

We presented a methodology to approximate the entropy production for Brownian motion in a tilted periodic potential. The approximation stems from the well known thermodynamic uncertainty relation. By applying a virial-like expansion, we provided a tighter lower limit solely in terms of the drift velocity and diffusion. The approach presented is systematically analyzed in the tight-binding regime. We also provide a relative simple rule to validate using the tight-binding approach based on drift and diffusion relations rather than energy barriers and forces. We also discuss the implications of our results outside the tight-binding regime.

A model of minimal entropy generation for cytoskeletal transport systems with multiple interacting motors

We study the steady-state rate of entropy generation for multiple interacting particles. The description used is based on the partially asymmetric exclusion process in a lattice with periodic boundary conditions. Our methodology shows that in the steady-state, the rate of entropy generation is directly proportional to the bulk drift and the applied driving force. Since in many cases the driving force is unknown or hard to determine. We circumvent this by deriving a lower bound for the entropy, resulting in an extended thermodynamic uncertainty relation for the asymmetric simple exclusion process. We systematically compared this bound with the actual entropy generation. Thus, we identify the force regimes, and particles' density conditions where the entropy bound derived from this extended thermodynamic uncertainty relation is meaningful.

Thermodynamic uncertainty relations and molecular-scale energy conversion

The thermodynamic uncertainty relation (TUR) is a universal constraint for nonequilibrium steady states that requires the entropy production rate to be greater than the relative magnitude of current fluctuations. It has potentially important implications for the thermodynamic efficiency of molecular-scale energy conversion in both biological and artificial systems. An alternative multidimensional thermodynamic uncertainty relation (MTUR) has also been proposed. In this paper we apply the TUR and the MTUR to a description of molecular-scale energy conversion that explicitly contains the degrees of freedom exchanging energy via a time-independent multidimensional periodic potential. The TUR and the MTUR are found to be universal lower bounds on the entropy generation rate and provide upper bounds on the thermodynamic efficiency. The TUR is found to provide only a weak bound while the MTUR provides a much tighter constraint by taking into account correlations between degrees of freedom. The MTUR is found to provide a tight bound in the near or far from equilibrium regimes but not in the intermediate force regime. Collectively, these results demonstrate that the MTUR is more appropriate than the TUR for energy conversion processes, but that both diverge from the actual entropy generation in certain regimes.

Reconstructing free-energy landscapes for cyclic molecular motors using full multidimensional or partial one-dimensional dynamic information

Diffusion on a free-energy landscape is a fundamental framework for describing molecular motors. In the landscape framework, energy conversion between different forms of energy, e.g., chemical and mechanical, is explicitly described using multidimensional nonseparable potential landscapes. We present a k-space method for reconstructing multidimensional free-energy landscapes from stochastic single-molecule trajectories. For a variety of two-dimensional model potential landscapes, we demonstrate the robustness of the method by reconstructing the landscapes using full dynamic information, i.e., simulated two-dimensional stochastic trajectories. We then consider the case where the stochastic trajectory is known only along one dimension. With this partial dynamic information, the reconstruction of the full two-dimensional landscape is severely limited in the majority of cases. However, we reconstruct effective one-dimensional landscapes for the two-dimensional model potentials. We discuss the interpretation of the one-dimensional landscapes and identify signatures of energy conversion. Finally, we consider the implications of these results for biological molecular motors experiments.

Theory of Nonequilibrium Free Energy Transduction by Molecular Machines

Biomolecular machines are protein complexes that convert between different forms of free energy. They are utilized in nature to accomplish many cellular tasks. As isothermal nonequilibrium stochastic objects at low Reynolds number, they face a distinct set of challenges compared with more familiar human-engineered macroscopic machines. Here we review central questions in their performance as free energy transducers, outline theoretical and modeling approaches to understand these questions, identify both physical limits on their operational characteristics and design principles for improving performance, and discuss emerging areas of research.