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

构象变化对于蛋白质、核酸和更大分子纳米机器的功能是必不可少的。所谓的大振幅集体运动可以理解为特征几何大尺度结构在较长时间内持续存在的瞬态系综之间的过渡，对应于高维势中的吸引子。当在最长时间尺度上接近跳跃过程时，构象转变通常显示时间复杂的多尺度结构。理解构象转变仍然是一个巨大的挑战，因为它们涉及许多自由度，在时间上跨越10到15个顺序，并且通常也通过具有许多中间体的各种途径进化。生物大分子系统，特别是生物纳米机器，由外力不可逆地驱动，甚至更具挑战性，特别是从热力学的角度来看，需要正确考虑耗散.原子分子动力学（MD）模拟可以在原则上提供详细的insightinto构象动力学，但不能克服广泛的时间尺度问题.因此，过渡网络的方法出现的替代品，其目的是在一个减少的状态空间，在最长的时间尺度上同意确切的动态马尔可夫跳跃过程的描述。这总是对时空分辨率引入约束，以确保所得到的动态仍然是马尔可夫的。此外，马尔可夫跳跃限制是注定要失败的潜力与扩展扩散过渡区，这需要太多的国家是实际有用的。后者实际上是典型的内在无序蛋白（IDP），也与蛋白质错误折叠。亚稳态之间的过渡区通常是平坦的，即使在结构蛋白质的情况下。类似的效应出现在强外部驱动的存在下，可能会破坏亚稳态。这就提出了一个明显的需要放宽马尔可夫跳跃的假设，因此，我们的过度的目标是转移范式从马尔可夫对weakerrenewal假设，并严格制定和实施一个物理上一致的更新网络方法建模驱动的构象动力学的生物聚合物。这将放松不必要的严格假设马尔可夫跳跃，因此将允许多尺度动力学的减少状态空间具有更高的时间分辨率，从而使研究强驱动系统以及系统的潜在特点是扩展的扩散过渡区。

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.