Free energy differences are a central quantity of interest in physics, chemistry, and biology. We develop design principles that improve the precision and accuracy of free energy estimators, which have potential applications to screening for targeted drug discovery. Specifically, by exploiting the connection between the work statistics of time-reversed protocol pairs, we develop near-equilibrium approximations for moments of the excess work and analyze the dominant contributions to the precision and accuracy of standard nonequilibrium free-energy estimators. Within linear response, minimum-dissipation protocols follow the geodesics of the Riemannian metric induced by the Stokes friction tensor. We find that the next-order contribution arises from the rank-3 supra-Stokes tensor that skews the geometric structure such that minimum-dissipation protocols follow the geodesics of a generalized cubic Finsler metric. Thus, near equilibrium, the supra-Stokes tensor determines the leading-order contribution to the bias of bidirectional free-energy estimators.
Driven barrier crossings are pervasive in optical-trapping experiments and steered molecular-dynamics simulations. Despite the high fidelity of control, the freedom in the choice of driving protocol is rarely exploited to improve efficiency. We design protocols that reduce dissipation for rapidly driven barrier crossing under two-dimensional control of a harmonic trapping potential, controlling both trap center and stiffness. For fast driving, the minimum-dissipation protocol jumps halfway between the control-parameter endpoints. For slow driving, the minimum-dissipation protocol generically slows down and tightens the trap as it crosses the barrier, resulting in both significant energy savings and increased flux compared to naive and one-dimensional protocols (that only change trap center). Combining fast and slow results, we design protocols that improve performance at all speeds.
Entropic segregation of chain ends to the surface of a monodisperse polymer melt and its effect on surface tension are examined using self-consistent field theory (SCFT). In order to assess the dependence on chain stiffness, the SCFT is solved for worm-like chains. Our focus is still on relatively flexible polymers, where the persistence length of the polymer, p , is comparable to the width of the surface profile, ξ, but still much smaller than the total contour length of the polymer, c. Even this small degree of rigidity causes a substantial increase in the level of segregation, relative to that of totally flexible Gaussian chains. Nevertheless, the long-range depletion that balances the surface excess still exhibits the same universal shape derived for Gaussian chains. Furthermore, the excess continues to reduce the surface tension by one unit of k B T per chain end, which results in the usual N −1 reduction in surface tension observed by experiments. This enhanced segregation will also extend to polydisperse melts, causing the molecular-weight distribution at the surface to shift towards smaller N n relative to the bulk. This provides a partial explanation for recent quantitative differences between experiments and SCFT calculations for flexible polymers.
Cell-cell communication is often achieved by diffusible signaling molecules that bind membranebound receptors. A common class of such receptors are G-protein coupled receptors, where extracellular binding induces changes in the membrane affinity near the receptor for certain diffusible cytosolic proteins, effectively altering their chemical potential. We analyze the minimum-dissipation schedules for dynamically changing chemical potential to induce steady-state changes in protein copy-number distributions, and illustrate with analytic solutions for linear chemical reaction networks. Protocols that change chemical potential on biologically relevant timescales are experimentally accessible using optogenetic manipulations, and our framework provides non-trivial predictions about functional dynamical cell-cell interactions.
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