Go N
Department of Chemistry, Faculty of Science, Kyoto University, Japan.
Biophys Chem. 1990 Jan;35(1):105-12. doi: 10.1016/0301-4622(90)80065-f.
An exact theorem is proved and its implication is discussed. The theorem states that, if a large molecule, typically biological macromolecules such as proteins, undergoes small-amplitude conformational fluctuations around its native conformation in such a way that within the range of conformational fluctuations at thermal equilibrium the conformational energy surface can be approximated by a multidimensional parabola, then the mass-weighted mean-square displacement of constituent atoms is given by the sum of the contributions from each normal mode of conformational vibration, which in turn is proportional to the inverse of the square of its frequency. This theorem provides a firm theoretical basis for the fact hitherto empirically recognized in the conformational dynamics of, for instance, native proteins that very-low-frequency normal modes make dominant contributions to the conformational fluctuations at thermal equilibrium. Discussion is given on the implication of this theorem, especially on the importance of the concept of the low-frequency normal modes, even in the case where the basic assumption of the harmonicity of the energy surface does not hold.
证明了一个精确的定理并讨论了其含义。该定理指出，如果一个大分子，典型的如蛋白质等生物大分子，在其天然构象周围进行小幅度的构象波动，使得在热平衡时构象波动范围内的构象能量表面可以用多维抛物线近似，那么组成原子的质量加权均方位移由构象振动的每个正常模式的贡献之和给出，而这又与其频率平方的倒数成正比。该定理为迄今在例如天然蛋白质的构象动力学中凭经验认识到的一个事实提供了坚实的理论基础，即非常低频的正常模式对热平衡时的构象波动起主要作用。讨论了该定理的含义，特别是低频正常模式概念的重要性，即使在能量表面的谐波性基本假设不成立的情况下。
