Application of time series analysis on molecular dynamics simulations of proteins: a study of different...

Time series analysis is applied on the collective coordinates obtained from principal component analysis of independent molecular dynamics simulations of alpha-amylase inhibitor tendamistat and immunity protein of colicin E7 based on the Calpha coordinates history. Even though the principal component directions obtained for each run are considerably different, the dynamics information obtained from these runs are surprisingly similar in terms of time series models and parameters. There are two main differences in the dynamics of the two proteins: the higher density of low frequencies and the larger step sizes for the interminima motions of colicin E7 than those of alpha-amylase inhibitor, which may be attributed to the higher number of residues of colicin E7 and/or the structural differences of the two proteins. The cumulative density function of the low frequencies in each run conforms to the expectations from the normal mode analysis. When different runs of alpha-amylase inhibitor are projected on the same set of eigenvectors, it is found that principal components obtained from a certain conformational region of a protein has a moderate explanation power in other conformational regions and the local minima are similar to a certain extent, while the height of the energy barriers in between the minima significantly change. As a final remark, time series analysis tools are further exploited in this study with the motive of explaining the equilibrium fluctuations of proteins.