The ability of protein chains to spontaneously form their spatial structures is a long-standing puzzle in molecular biology. Experimentally measured folding times of single-domain globular proteins range from microseconds to hours: the difference (10–11 orders of magnitude) is the same as that between the life span of a mosquito and the age of the universe. This review describes physical theories of rates of overcoming the free-energy barrier separating the natively folded (N) and unfolded (U) states of protein chains in both directions: “U-to-N” and “N-to-U”. In the theory of protein folding rates a special role is played by the point of thermodynamic (and kinetic) equilibrium between the native and unfolded state of the chain; here, the theory obtains the simplest form. Paradoxically, a theoretical estimate of the folding time is easier to get from consideration of protein unfolding (the “N-to-U” transition) rather than folding, because it is easier to outline a good unfolding pathway of any structure than a good folding pathway that leads to the stable fold, which is yet unknown to the folding protein chain. And since the rates of direct and reverse reactions are equal at the equilibrium point (as follows from the physical “detailed balance” principle), the estimated folding time can be derived from the estimated unfolding time. Theoretical analysis of the “N-to-U” transition outlines the range of protein folding rates in a good agreement with experiment. Theoretical analysis of folding (the “U-to-N” transition), performed at the level of formation and assembly of protein secondary structures, outlines the upper limit of protein folding times (i.e., of the time of search for the most stable fold). Both theories come to essentially the same results; this is not a surprise, because they describe overcoming one and the same free-energy barrier, although the way to the top of this barrier from the side of the unfolded state is very different from the way from the side of the native state; and both theories agree with experiment. In addition, they predict the maximal size of protein domains that fold under solely thermodynamic (rather than kinetic) control and explain the observed maximal size of the “foldable” protein domains.

蛋白质链自发形成其空间结构的能力是分子生物学中一个长期存在的难题。实验测得的单域球状蛋白的折叠时间从微秒到几小时不等：差异（10-11个数量级）与蚊子的寿命和宇宙年龄之间的差异相同。这篇综述描述了在两个方向上克服蛋白质链的天然折叠（N）和未折叠（U）状态的自由能垒的速率的物理理论：“ U-to-N”和“ N-to-U”。在蛋白质折叠速率理论中，链的天然状态和未折叠状态之间的热力学（和动力学）平衡点起着特殊的作用。在这里，理论获得了最简单的形式。矛盾的是，折叠时间的理论估计值比蛋白质的折叠（“ N到U”过渡）更容易考虑，而不是折叠，因为与任何具有良好折叠效果的折叠路径相比，勾勒出任何结构的良好折叠路径都比较容易。导致稳定的折叠，而折叠蛋白链尚不知道。并且由于在平衡点上正反应和逆反应的速率相等（如从物理“详细平衡”原理中得出的结论），因此可以从估计的展开时间中得出估计的折叠时间。从“ N到U”过渡的理论分析概述了蛋白质折叠速率的范围，与实验非常吻合。在蛋白质二级结构的形成和组装水平上进行折叠（从“ U到N”过渡）的理论分析，概述了蛋白质折叠时间（即搜索最稳定折叠时间的上限）的上限。两种理论得出的结果基本相同。这并不奇怪，因为它们描述了克服一个相同的自由能壁垒的方法，尽管从展开状态的一侧到该壁垒的顶部的方式与从原始状态的一侧的方式非常不同。两种理论都与实验相吻合。此外，他们预测了仅在热力学（而非动力学）控制下折叠的蛋白质结构域的最大大小，并解释了观察到的“可折叠”蛋白质结构域的最大大小。因为它们描述了克服一个相同的自由能壁垒的方法，尽管从展开状态的一侧到达该壁垒顶部的方式与从原始状态的一侧非常不同；两种理论都与实验相吻合。此外，他们预测了仅在热力学（而非动力学）控制下折叠的蛋白质结构域的最大大小，并解释了观察到的“可折叠”蛋白质结构域的最大大小。因为它们描述了克服一个相同的自由能壁垒的方法，尽管从展开状态的一侧到达该壁垒顶部的方式与从原始状态的一侧非常不同；两种理论都与实验相吻合。此外，他们预测了仅在热力学（而非动力学）控制下折叠的蛋白质结构域的最大大小，并解释了观察到的“可折叠”蛋白质结构域的最大大小。