标题： 曲率物理与蛋白质折叠：数学类比 显示英文标题

标题： Physics of Caustics and Protein Folding: Mathematical Parallels

摘要： 蛋白质折叠的能量来源于多个来源，总体能量并不大。 尽管能量景观和其他方法取得了许多具体成功，但似乎仍有一些缺失的指导因素，解释来自不同小来源的能量如何驱动复杂分子到一个独特状态。 我们探讨了缺失因素可能在于几何学的可能性。 将折叠与其他物理现象进行比较，并结合对分子的分析建模，使我们同时分析了光学焦散形成的物理原理和折叠行为。 折叠和焦散的物理原理表面上看起来非常不同，但存在几个强烈的相似之处。 这种比较强调了数学上的相似性，并且也指出了差异。 自20世纪70年代以来，光学焦散的物理原理已经通过突变理论发展到非常高的数学复杂程度。 这种对突变理论的定量应用以前尚未应用于折叠，也没有识别或利用与光学的相似之处。 焦散和折叠之间潜在的物理联系是一种在二面角和$\Psi$中发现的非恒定波速的扭转波，在分子的分析模型中找到。 无论我们是否正确识别了潜在的联系，焦散形成和折叠之间的类比都很强，物理学中的相似之处（和差异）是有用的。 显示英文摘要

摘要： The energy for protein folding arises from multiple sources and is not large in total. In spite of the many specific successes of energy landscape and other approaches, there still seems to be some missing guiding factor that explains how energy from diverse small sources can drive a complex molecule to a unique state. We explore the possibility that the missing factor is in the geometry. A comparison of folding with other physical phenomena, together with analytic modeling of a molecule, led us to analyze the physics of optical caustic formation and of folding behavior side-by-side. The physics of folding and caustics is ostensibly very different but there are several strong parallels. This comparison emphasizes the mathematical similarity and also identifies differences. Since the 1970's, the physics of optical caustics has been developed to a very high degree of mathematical sophistication using catastrophe theory. That kind of quantitative application of catastrophe theory has not previously been applied to folding nor have the points of similarity with optics been identified or exploited. A putative underlying physical link between caustics and folding is a torsion wave of non-constant wave speed, propagating on the dihedral angles and $\Psi$ found in an analytical model of the molecule. Regardless of whether we have correctly identified an underlying link, the analogy between caustic formation and folding is strong and the parallels (and differences) in the physics are useful.