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

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