Non-equilibrium Fluctuations and Cooperativity in Single-Molecule Dynamics: Going Beyond FluctuationTheorems and Large Deviation Theory: Thermodynamically consistent renewal networks for driven single-molecule dynamics with memory

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Conformational changes are essential for the function of proteins, nucleic acids, and larger molecular nanomachines. The so-called large-amplitude collective motions can beunderstood as transitions between transient ensembles of characteristic geometrical large-scale structures persisting over longer periods of time, which correspond to attractors in a high-dimensional potential. While approaching a hopping process on the longest time-scales conformational transitions generally display a temporally complex multi-scale structure. Understanding conformational transitions remains a grand challenge, as they involve many degrees of freedom and span ten to fifteen orders in time and typically also evolve via various pathways with many intermediates. Biomacromolecular systems, in particular biological nanomachines, driven irreversibly by an external force are even more challenging, especially from the point of view of the thermodynamics that requires to correctly account for the dissipation.Atomistic molecular dynamics (MD) simulations could in principle provide a detailed insightinto conformational dynamics but cannot overcome the broad time-scale problem. As a result transition-network approaches emerged as alternatives, which aim at a Markov jump process description on a reduced state-space that on the longest time-scales agrees with the exact dynamics. This always introduces constraints on the spatio-temporal resolution in order to ensure that the resulting dynamics is still Markovian. In addition, the Markov-jump restriction is doomed to fail for potentials with extended diffusive transition regions, which require too many states to be practically useful. The latter are in fact typical for intrinsically disordered proteins (IDPs) and were also associated with protein mis-folding. Transition regions between metastable states are often flat even in the case of structured proteins. Similar effects arise in the presence of strong external driving that may destabilize metastable states. This poses an obvious need for relaxing the Markov-jump assumption.Our overreaching goal is therefore to shift the paradigm from Markov towards the weakerrenewal assumption, and to rigorously formulate and implement a thermodynamically consistent renewal network approach for modeling driven conformational dynamics of biopolymers. This will relax the unnecessarily stringent assumption on Markovian jumps and will hence allow for multi-scale dynamics on the reduced state-space with a much higher temporal resolution thus enabling the study of strongly driven systems as well as systems whose underlying potential is characterized by extended diffusive transition regions.