A Mode Evolution Metric to Extract Reaction Coordinates for Biomolecular Conformational Transitions

The complex, multidimensional energy landscape of biomolecules makes the extraction of suitable, nonintuitive collective variables (CVs) that describe their conformational transitions challenging. At present, dimensionality reduction approaches and machine learning (ML) schemes are employed to obtain CVs from molecular dynamics (MD)/Monte Carlo (MC) trajectories or structural databanks for biomolecules. However, minimum sampling conditions to generate reliable CVs that accurately describe the underlying energy landscape remain unclear. Here, we address this issue by developing a <u>M</u>ode <u>e</u>volution Metric (MeM) to extract CVs that can pinpoint new states and describe local transitions in the vicinity of a reference minimum from nonequilibrated MD/MC trajectories. We present a general mathematical formulation of MeM for both statistical dimensionality reduction and machine learning approaches. Application of MeM to MC trajectories of model potential energy landscapes and MD trajectories of solvated alanine dipeptide reveals that the principal components which locate new states in the vicinity of a reference minimum emerge well before the trajectories locally equilibrate between the associated states. Finally, we demonstrate a possible application of MeM in designing efficient biased sampling schemes to construct accurate energy landscape slices that link transitions between states. MeM can help speed up the search for new minima around a biomolecular conformational state and enable the accurate estimation of thermodynamics for states lying on the energy landscape and the description of associated transitions.