Machine learning methods provide a general framework for automatically finding and representing the essential characteristics of simulation data. This task is particularly crucial in enhanced sampling simulations. There we seek a few generalized degrees of freedom, referred to as collective variables (CVs), to represent and drive the sampling of the free energy landscape. In theory, these CVs should separate different metastable states and correspond to the slow degrees of freedom of the studied physical process. To this aim, we propose a new method that we call multiscale reweighted stochastic embedding (MRSE). Our work builds upon a parametric version of stochastic neighbor embedding. The technique automatically learns CVs that map a high-dimensional feature space to a low-dimensional latent space via a deep neural network. We introduce several new advancements to stochastic neighbor embedding methods that make MRSE especially suitable for enhanced sampling simulations: (1) weight-tempered random sampling as a landmark selection scheme to obtain training data sets that strike a balance between equilibrium representation and capturing important metastable states lying higher in free energy; (2) a multiscale representation of the high-dimensional feature space via a Gaussian mixture probability model; and (3) a reweighting procedure to account for training data from a biased probability distribution. We show that MRSE constructs low-dimensional CVs that can correctly characterize the different metastable states in three model systems: the Müller-Brown potential, alanine dipeptide, and alanine tetrapeptide.

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In this work we propose an application of a nonlinear dimensionality reduction method to represent the high-dimensional configuration space of the ligand-protein dissociation process in a manner facilitating interpretation. Rugged ligand expulsion paths are mapped into 2-dimensional space. The mapping retains the main structural changes occurring during the dissociation. The topological similarity of the reduced paths may be easily studied using the Fréchet distances, and we show that this measure facilitates machine learning classification of the diffusion pathways. Further, low-dimensional configuration space allows for identification of residues active in transport during the ligand diffusion from a protein. The utility of this approach is illustrated by examination of the configuration space of cytochrome P450cam involved in expulsing camphor by means of enhanced all-atom molecular dynamics simulations. The expulsion trajectories are sampled and constructed on-the-fly during molecular dynamics simulations using the recently developed memetic algorithms [ Rydzewski, J.; Nowak, W. J. Chem. Phys. 2015 , 143 ( 12 ), 124101 ]. We show that the memetic algorithms are effective for enforcing the ligand diffusion and cavity exploration in the P450cam-camphor complex. Furthermore, we demonstrate that machine learning techniques are helpful in inspecting ligand diffusion landscapes and provide useful tools to examine structural changes accompanying rare events.