Identifying the leading dynamics of ubiquitin: a comparison between the tICA and the LE4PD slow fluctuations in amino acids' position

Abstract

Molecular Dynamics (MD) simulations of proteins implicitly contain the information connecting the atomistic molecular structure and proteins' biologically relevant motion, where large-scale fluctuations are deemed to guide folding and function. In the complex multiscale processes described by MD trajectories it is difficult to identify, separate, and study those large-scale fluctuations. This problem can be formulated as the need to identify a small number of collective variables that guide the slow kinetic processes. Among the methods used to study the slow, leading processes in proteins' dynamics, the time-lagged independent component analysis, or tICA, has been extensively used. Recently, we developed a Langevin coarse-grained approach for the dynamics of proteins, called the Langevin Equation for Protein Dynamics or LE4PD. This approach partitions the protein's MD dynamics into uncorrelated, wavelength-dependent, diffusive modes, and it associates to each mode a free-energy map. In the free energy maps, we measure the spatial extension and the time evolution of the mode-dependent, slow dynamical fluctuations, using the string method and a Markov state model. The theory identifies the slow collective variables in the rescaled LE4PD normal modes. Here, we compare the tICA modes' predictions with the collective LE4PD modes. We observe that the two methods consistently identify the nature and extension of the slowest fluctuation processes. The tICA separates the slow, leading processes in a smaller number of modes than the LE4PD does. However, LE4PD provides time-dependent information and a formal connection to the physics of the kinetic processes missing in the pure statistical analysis of tICA.