  Mini-proteins and peptides manifest dynamic conformational fluctuation and
involve mutual interconversion among metastable states. A robust mapping of the
conformational landscape underlying mini-proteins and peptides often requires
low-dimensional projection of the conformational ensemble along optimized
collective variables. However, the traditional choice for the collective
variable (CV) is often limited by user-intuition and prior knowledge about the
system, which lacks a rigorous assessment of their optimality over other
candidate CVs. To address this issue, we propose a generic approach in which we
first choose the possible combinations of inter-residue Calpha-distances within
a given macromolecule as a set of input CVs. Subsequently we derive a
non-linear combination of latent-space embedded collective variables via
auto-encoding the unbiased MD simulation trajectories within the framework of
feed-forward neural network. We demonstrate the ability of the derived latent
space variables in elucidating the conformational landscape in three
hierarchically complex systems. When the conformational dynamics is resolved
along the latent space CVs, it identifies key metastable states of a
bead-in-a-spring polymer. The combination of the adopted dimensionally
reduction technique with a Markov state model, built on the derived latent
space, efficiently projects the free energy landscape of GB1 beta-hairpin,
revealing multiple spatially well-resolved and kinetically well-separated
metastable conformations. A quantitative comparison based on variational
approach to Markov Process of the auto encoder-derived latent-space CVs with
the ones obtained PCA or TICA confirms the optimality of the former. Finally,
as a practical application, we demonstrate that the auto-encoder derived CVs
successfully predict the reinforced folding of Trp-cage mini-protein in an
aqueous osmolyte solution.
