Abstract
Stochastic network dynamics are typically assumed to be memoryless. Involving prolonged dwells interrupted by instantaneous transitions between nodes, such Markov networks stand as a coarse-graining paradigm for chemical reactions, gene expression, molecular machines, spreading of diseases, protein dynamics, diffusion in energy landscapes, epigenetics, and many others. However, as soon as transitions cease to be negligibly short, as often observed in experiments, the dynamics develops a memory. That is, state changes depend not only on the present state but also on the past. Here, we establish the first thermodynamically consistent—dissipation-preserving—mapping of continuous dynamics onto a network, which reveals ingrained dynamical symmetries and an unforeseen kinetic hysteresis. These symmetries impose three independent sources of fluctuations in state-to-state kinetics that determine the “flavor of memory.” The hysteresis between the forward- or backward-in-time coarse graining of continuous trajectories implies a new paradigm for the thermodynamics of active molecular processes in the presence of memory, that is, beyond the assumption of local detailed balance. Our results provide a new understanding of fluctuations in the operation of molecular machines as well as catch bonds involved in cellular adhesion.
- Received 7 April 2021
- Revised 20 August 2021
- Accepted 4 October 2021
DOI:https://doi.org/10.1103/PhysRevX.11.041047
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
In elastic materials, friction is known to cause a phenomenon called hysteresis—more energy is required to stretch a rubber band than is released during unloading. As a result, the rubber band becomes warm. On microscopic scales where thermal fluctuations are important, such as in molecular motors operating far from equilibrium, hysteresis emerges in the form of a broken time-reversal symmetry. Here, we report on a novel form of hysteresis that is of a purely kinetic nature and emerges as soon as a system does not locally equilibrate in metastable states. This gives rise to memory in the observed dynamics; that is, state changes depend on past states.
Kinetic hysteresis arises from the finite duration of transition paths, which are completed transitions between pairs of metastable states. We derive, for the first time, a network theory that preserves the microscopic dissipation and accounts for the finite duration of transition paths. We unravel three ingrained symmetries of the dynamics memory that determine the characteristics of the observed memory. These symmetries reveal hidden, vital information about the dynamics even in the limit where the hysteresis may become negligibly small. We use the theory to explain the counterintuitive “catch-bond” phenomenon, where a larger mechanical load prolongs the lifetime of an adhesion bond.
Our results pave the way toward a deeper understanding of violations of time-reversal symmetry in the presence of memory. In practice, the symmetries unraveled in our work allow for robustly detecting the coexistence of multiple transition pathways in a measured time series without resolving them individually.
