Folding-unfolding asymmetry and a RetroFold computational algorithm

We treat protein folding as the molecular self-assembly, while unfolding
is viewed as disassembly. Self-assembly and disassembly (fracture) are two
opposite non-equilibrium dynamic processes; however, they cannot be
converted to each other by a simple time variable reversal. Fracture is
typically a much faster process than self-assembly. Self-assembly is often
an exponentially decaying process, since energy relaxes due to
dissipation, while fracture may be a constant rate process as the driving
force is opposed by damping. Typically, protein folding takes two orders
of magnitude longer time than unfolding, and it consumes a lot of
computational resources to model folding. Based on energy dissipation
rates, we suggest a mathematical transformation of variables, which makes
it possible to view self-assembly as time-reversed disassembly, thus
folding can be studied as reversed unfolding. We investigate the molecular
dynamics modeling of folding and unfolding of the short Trp-cage protein.
Folding time constitutes about 800 ns while unfolding (denaturation) takes
only about 5.0 ns, and therefore, fewer computational resources are needed
for its simulation. This “RetroFold” approach can be used for the design
of a novel computation algorithm, which, while approximate, is less
time-consuming than traditional folding algorithms.

我们将蛋白质折叠（protein folding）视为分子自组装（molecular self-assembly），而解折叠（unfolding）则被视作解聚（disassembly）。自组装与解聚（disassembly，即断裂fracture）是两类对立的非平衡动态过程，但二者无法通过简单的时间变量反转实现相互转换。通常断裂过程远快于自组装过程。自组装往往呈指数衰减过程，这是因为能量会因耗散而弛豫；而断裂过程则可视为恒定速率过程，因为驱动力会受到阻尼的对抗。通常蛋白质折叠所需时长是解折叠的两个数量级以上，且折叠建模需要消耗大量计算资源。基于能量耗散速率，本文提出一种变量数学变换方法，可将自组装视为解聚的时间反演过程，进而可通过反向解折叠来研究折叠问题。本研究针对短序列Trp笼蛋白（Trp-cage protein）的折叠与解折叠分子动力学建模展开探究。该蛋白折叠时长约为800纳秒（ns），而解折叠（变性，denaturation）仅需约5.0纳秒，因此其模拟所需计算资源更少。此“RetroFold”方法可用于设计新型计算算法，尽管该算法属于近似方法，但相较于传统折叠算法，其耗时更短。