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

The complex multidimensional energy landscape of biomolecules makes the extraction of suitable non-intuitive collective variables (CVs) which describe their conformational transitions challenging. At present dimensionality reduction approaches and machine learning schemes are employed to obtain reaction coordinates from datasets sampled either from techniques like molecular dynamics (MD) simulations or structural databanks for biomolecules. However, a poor understanding of sampling convergence and completeness of the dataset seriously limits assessment of the quality of the extracted CVs. Here, we build upon statistically rigorous ideas of local equilibration to develop a Mode evolution Metric (MeM) which can extract quantitatively converged CVs from non-equilibrated MD simulations using dimensionality reduction or machine learning approaches. Specifically, we apply MEM to extract converged principal components for transitions in model potential energy landscapes of varying complexities and in solvated alanine dipeptide. Finally, we demonstrate a possible application of MeM in designing efficient biased sampling schemes to construct accurate energy landscape slices which link transitions between two 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 descriptions of associated transitions.