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

本研究的目的是利用分子动力学的方法，系统地研究蛋白质分子的复杂运动，从初始速度在蛋白质分子各法向模方向的角度出发，将法向模的线性运动扩展到非线性范围。在正态分析中，由于描述分子三维结构的变量数量减少，因此经常使用二面角等内部坐标。我们开发的分子动力学程序（FEDER/3）也采用了二面角坐标系。对同源蛋白434Cro和434阻遏因子以及P22c2阻遏因子分别沿着低于200cm^<-1>的约300个正常模式在所有方向上进行了分子动力学研究。当每个模式的温度为300K（整个分子约为0.7 K）时，以大于40cm^<-1>的模式初始化的运动导致谐振振荡，其频率与模式预期的频率一致。在较高的温度下，观察到某一模态中的能量耗散到其他模态，其中能量有向与二次谐波大致对应的模态移动的趋势。在慢于40cm^<-1>的模态初始化动力学中，在300K时也观察到三级结构转移到能量最小值附近，而不是进行正态模态分析的能量最小值附近。从几个不同的正态模态开始的轨迹的低能态的能量最小值收敛到相同的能量最小值。也就是说，在原生结构附近的能量极小值并不多，例如434Cro，在300K和1500K下能够转移的能量极小值分别为7个和32个。结果表明，即使在蛋白质复杂的多维结构空间中，利用该方法也能系统地求出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.