Investigating causality between principal components in protein dynamics

Principal component analysis (PCA) is widely used to characterize collective protein motions from molecular dynamics (MD) simulations. While PCA identifies the dominant modes of structural fluctuation, it does not reveal whether different principal components (PCs) causally influence each other. Here, we investigate this question using a recently introduced causal-discovery framework [V. D. Tatto et al., Proc. Natl. Acad. Sci. U. S. A. 121, e2317256121 (2024)], which allows us to infer putative causal asymmetries between high-dimensional time series. We apply this approach to long-timescale MD trajectories of two proteins. By analyzing relationships among PCs, we construct directed networks describing how PCs influence one another across time scales. These directional relationships, whose existence is a necessary condition for the presence of a causal link, are not captured by conventional covariance-based analyses and provide information that is complementary to PCA and time-lagged independent component analysis. Our results suggest that our causal inference approach can uncover previously hidden aspects of the dynamical organization of protein motions and offer a new perspective on this very popular class of collective variables.