The dynamic structure of protein molecules based on coupling among normal modes

本研究旨在从简正波的线性运动扩展到非线性范围的观点出发，以蛋白质分子各简正波方向上的初始速度，用分子动力学系统地研究蛋白质的复杂运动。在简正波分析中，由于描述分子三维结构的变量数量减少，因此经常使用像二面角这样的内部坐标。分子动力学程序(FEDER/3)也采用二面角坐标系，对同源蛋白434Cro和434阻遏蛋白和P22c2阻遏蛋白沿200 cm^~(-1)~(-1)&gt~(-1)以下约300个简正模式进行了全方向的分子动力学计算。当每个模式的温度为300K(整个分子约为0.7K)时，以高于40 cm^~(-1)~(-1)的模式启动的运动导致了具有预期频率的简谐振荡。在较高的温度下，观察到一个模中的能量被耗散到其他模，在这些模中，能量有向大致对应于二次谐波的模移动的趋势。在以低于40 cm^-1的模式初始化的动力学中，在300K也观察到三级结构转移到能量最小值附近，而不是在进行简正模式分析的能量最小值附近。然而，从几个不同的简正波开始的轨迹中的低能状态的能量最小化收敛到相同的能量最小值。也就是说，本征结构附近的能量极小值并不是很多，例如434Cro，在300K和1500K能够转移的能量极小值分别为7个和32个。实验证明，即使在复杂的蛋白质多维结构空间中，利用该算法也可以系统地寻找天然结构附近的能量极小值。

This research aims to investigate complicated motions of a protein systematically by the molecular dynamics with the initial velocity in the direction of each normal mode of a protein molecule from the viewpoint that linear movement of normal modes is extended to the nonlinear range. In normal mode analyses, since the number of variables describing the three-dimensional structure of a molecule decreased, internal coordinates like dihedral angles were often used. The dihedral angle coordinate system was also used for the program of molecular dynamics (FEDER/3) which we have developed.Molecular dynamics were performed in all the directions along about 300 normal modes lower than 200cm^<-1>, respectively for 434Cro and 434 repressor, and P22c2 repressor, which are homologous proteins. When the temperature per each mode was 300K (about 0.7 K for the whole molecule), the movement initialized with a mode faster than 40cm^<-1> resulted in harmonic oscillation with the fiequency expected from the mode. In higher temperature it was observed that the energy in a mode was dissipated to other modes, in which the energy had a tendency to move to modes roughly corresponding to the second harmonic. In the dynamics initialized with a mode slower than 40cm^<-1>, it was observed also in 300K that the tertiary structure was transferred to that around an energy minimum other than the energy minimum where the normal mode analysis was done. Energy minimization from low-energy states in the trajectories, which started from several different normal modes, however converged to the same energy minimum. That is, the number of energy minima near the native structure was not so many, for example of 434Cro, ones which were able to be transferred at 300K and at 1500K were seven and 32, respectively. It was proved that using this protocol the energy minima near the native structure can be systematically explored even in complicated multidimensional structural space of a protein.