Investigation of Cooperative Modes for Collective Molecules Using Grid-Based Principal Component Analysis

A grid-based principal component analysis method (GBPCA) has been developed and implemented to investigate the modes of collective molecules present in the cube in the grid system from their trajectories using molecular dynamics (MD) simulation. This method is applied to the simulations of water, methane, and hydrated proteins. In the cases of single molecules, GBPCA demonstrates that while individual molecules interact with other molecules and move randomly, the collective molecules nevertheless produce cooperative principal component (PC) modes. Notably, these PC modes of the collective molecules formed vorticial or symmetrical structures, with some resembling torus-like structures. Such structures were observed not only in simulations with models that reproduced real molecules, such as water or methane, but also in simulations with artificial molecules that were modified to interact weakly or only repulsively. On the contrary, molecules without any interactions did not exhibit the cooperative PC modes that lead to the formation of specific structures. These results imply that when molecules subject to intermolecular forces are located in a space in which they can interact with one another, the PC modes of the collective molecules will form vorticial and torus-like structures. In the cases of hydrated proteins, the results reveal that the collective molecules in the protein and water molecules showed cooperative PC modes, forming vorticial or torus-like structures, as in the cases of the water or methane molecules. The PC modes of the water molecules close to the protein were influenced by the protein motion and indicated cooperative modes with the protein. Moreover, proteins with the same folds had similar PC mode structures. Besides, the PC modes of the proteins composed of multiple domains appeared independently in the protein domain. Hence, it can be understood that the cooperative motions of the collective molecules of the protein and surrounding water molecules contribute strongly to the protein's structure and function. These results are expected to help our understanding of the dynamics of molecules in the liquid state.