Challenges in Inferring the Directionality of Active Molecular Processes from Single-Molecule Fluorescence Resonance Energy Transfer Trajectories

Estimator of entropy production for partially accessible Markov networks based on the observation of blurred transitions

A central task in stochastic thermodynamics is the estimation of entropy production for partially accessible Markov networks. We establish an effective transition-based description for such networks with transitions that are not distinguishable and therefore blurred for an external observer. We demonstrate that, in contrast to a description based on fully resolved transitions, this effective description is typically non-Markovian at any point in time. Starting from an information-theoretic bound, we derive an operationally accessible entropy estimator for this observation scenario. We illustrate the operational relevance and the quality of this entropy estimator with a numerical analysis of various representative examples.

Milestoning estimators of dissipation in systems observed at a coarse resolution

Many nonequilibrium, active processes are observed at a coarse-grained level, where different microscopic configurations are projected onto the same observable state. Such "lumped" observables display memory, and in many cases, the irreversible character of the underlying microscopic dynamics becomes blurred, e.g., when the projection hides dissipative cycles. As a result, the observations appear less irreversible, and it is very challenging to infer the degree of broken time-reversal symmetry. Here we show, contrary to intuition, that by ignoring parts of the already coarse-grained state space we may-via a process called milestoning-improve entropy-production estimates. We present diverse examples where milestoning systematically renders observations "closer to underlying microscopic dynamics" and thereby improves thermodynamic inference from lumped data assuming a given range of memory, and we hypothesize that this effect is quite general. Moreover, whereas the correct general physical definition of time reversal in the presence of memory remains unknown, we here show by means of physically relevant examples that at least for semi-Markov processes of first and second order, waiting-time contributions arising from adopting a naive Markovian definition of time reversal generally must be discarded.

Emergence of Memory in Equilibrium versus Nonequilibrium Systems

Experiments often probe observables that correspond to low-dimensional projections of high-dimensional dynamics. In such situations distinct microscopic configurations become lumped into the same observable state. It is well known that correlations between the observable and the hidden degrees of freedom give rise to memory effects. However, how and under which conditions these correlations emerge remain poorly understood. Here we shed light on two fundamentally different scenarios of the emergence of memory in minimal stationary systems, where observed and hidden degrees of freedom either evolve cooperatively or are coupled by a hidden nonequilibrium current. In the reversible setting the strongest memory manifests when the timescales of hidden and observed dynamics overlap, whereas, strikingly, in the driven setting maximal memory emerges under a clear timescale separation. Our results hint at the possibility of fundamental differences in the way memory emerges in equilibrium versus driven systems that may be utilized as a "diagnostic" of the underlying hidden transport mechanism.

Cochaperones convey the energy of ATP hydrolysis for directional action of Hsp90

The molecular chaperone and heat shock protein Hsp90 is part of many protein complexes in eukaryotic cells. Together with its cochaperones, Hsp90 is responsible for the maturation of hundreds of clients. Although having been investigated for decades, it still is largely unknown which components are necessary for a functional complex and how the energy of ATP hydrolysis is used to enable cyclic operation. Here we use single-molecule FRET to show how cochaperones introduce directionality into Hsp90's conformational changes during its interaction with the client kinase Ste11. Three cochaperones are needed to couple ATP turnover to these conformational changes. All three are therefore essential for a functional cyclic operation, which requires coupling to an energy source. Finally, our findings show how the formation of sub-complexes in equilibrium followed by a directed selection of the functional complex can be the most energy efficient pathway for kinase maturation.

Waiting Time Distributions in Hybrid Models of Motor-Bead Assays: A Concept and Tool for Inference

In single-molecule experiments, the dynamics of molecular motors are often observed indirectly by measuring the trajectory of an attached bead in a motor-bead assay. In this work, we propose a method to extract the step size and stalling force for a molecular motor without relying on external control parameters. We discuss this method for a generic hybrid model that describes bead and motor via continuous and discrete degrees of freedom, respectively. Our deductions are solely based on the observation of waiting times and transition statistics of the observable bead trajectory. Thus, the method is non-invasive, operationally accessible in experiments and can, in principle, be applied to any model describing the dynamics of molecular motors. We briefly discuss the relation of our results to recent advances in stochastic thermodynamics on inference from observable transitions. Our results are confirmed by extensive numerical simulations for parameters values of an experimentally realized F1-ATPase assay.