A deep autoencoder framework for discovery of metastable ensembles in biomacromolecules

Biomacromolecules manifest dynamic conformational fluctuation and involve mutual interconversion among metastable states. A robust mapping of their conformational landscape often requires the low-dimensional projection of the conformational ensemble along optimized collective variables (CVs). However, the traditional choice for the CV is often limited by user-intuition and prior knowledge about the system, and this lacks a rigorous assessment of their optimality over other candidate CVs. To address this issue, we propose an approach in which we first choose the possible combinations of inter-residue Cα-distances within a given macromolecule as a set of input CVs. Subsequently, we derive a non-linear combination of latent space embedded CVs via auto-encoding the unbiased molecular dynamics simulation trajectories within the framework of the feed-forward neural network. We demonstrate the ability of the derived latent space variables in elucidating the conformational landscape in four hierarchically complex systems. The latent space CVs identify key metastable states of a bead-in-a-spring polymer. The combination of the adopted dimensional reduction technique with a Markov state model, built on the derived latent space, reveals multiple spatially and kinetically well-resolved metastable conformations for GB1 β-hairpin. A quantitative comparison based on the variational approach-based scoring of the auto-encoder-derived latent space CVs with the ones obtained via independent component analysis (principal component analysis or time-structured independent component analysis) confirms the optimality of the former. As a practical application, the auto-encoder-derived CVs were found to predict the reinforced folding of a Trp-cage mini-protein in aqueous osmolyte solution. Finally, the protocol was able to decipher the conformational heterogeneities involved in a complex metalloenzyme, namely, cytochrome P450.