A Comparison of the Slow Dynamics in the Protein Ubiquitin Predicted by the LE4PD, PCA, and tICA from a Long Equilibrium Molecular Dynamics Simulation*

The Langevin Equation for Protein Dynamics (LE4PD) is a coarse-grained diffusive method to model protein dynamics, accounting for hydrodynamic effects and mode-dependent free-energy barriers. The LE4PD has been used to quantify the dynamics of proteins on timescales ranging from the picosecond to tens of nanoseconds. Here, we connect the slow dynamics predicted by the LE4PD to that predicted by principal component analysis (PCA) and time-lagged component analysis (tICA). An analytic connection between the LE4PD and PCA is made, while the comparison between the LE4PD and tICA is qualitative. Performing this comparison for a microsecond molecular dynamics trajectory of the protein ubiquitin, we find all three methods predict slow dynamics in three main regions of the protein (the Lys11 and 50 s loops and C-terminal tail), but the decomposition of the dynamics can differ significantly. The tICA finds the slowest motions are due to fluctuations in the 50 s loop, a result supported by the LE4PD once free-energy barriers are included in the analysis. We also find that inclusion of free-energy barriers and hydrodynamic interactions affects greatly the predicted LE4PD dynamics when compared to PCA.