Data‐driven coordinate discovery and causal inference in molecular simulations

Molecular simulations generate high-dimensional trajectories in which the mechanistically relevant features are buried across widely separated time scales ranging from collective structural motions that govern, for example, protein fluctuations to electronic transitions induced by light absorption in photochemistry. While such simulations capture the underlying atomic and electronic dynamics in fine detail, the cause-and-effect relationships that drive these types of processes remain poorly understood and emerge only through targeted analysis. This thesis develops and applies data-driven, information-theoretic tools to this extraction problem, using distances between molecular configurations and the information they carry as the central objects of analysis. The work spans two complementary directions: the excited-state photophysics of biomolecules that display novel photochemistry, and the causal structure between different degrees of freedom that can be extracted from equilibrium molecular dynamics. We first study the intrinsic, non-aromatic fluorescence of L-cysteine crystals, showing through a synergy of experiments and excited-state simulations, that a change in the solvent used during crystallization from light to heavy water, alters the crystal packing and hydrogen-bonding network. This in turn, constrains the thiol and amine motions responsible for non-radiative decay, and thereby enhances emission. Motivated by the difficulty of identifying such decay-driving motions, we then introduce an unsupervised machine learning framework based on the Differentiable Information Imbalance that ranks nuclear degrees of freedom by their ability to predict electronic observables, and extracts compact, interpretable coordinates that explain the non-radiative decay processes across a wide range of photochemical systems. In the second part of the thesis, we turn to causal inference in molecular systems. Using the aforementioned Information Imbalance method, we establish the conditions under which directed putative causal links emerge between collective variables at equilibrium, relating them to asymmetries in information content and to a separation of relaxation time scales. We further elucidate how one can quantify genuine causal links using interventional experiments. Finally, we apply this causal inference framework to the collective dynamics of folded proteins, uncovering directed causal relationships between the leading principal components (PCs) of two proteins, Ubiquitin and NTL9. In both of these cases we observe that the leading PC has a causal link towards the lower-variance PCs, although the nature of this link and its correlation with spatial delocalization of the PCs varies between the two systems considered. Together, these studies show that using our causal inference measure built on distances rather than on probability densities, one can infer interpretable, and highly non-trivial causal relationships in molecular systems.