Machine Learning Based Dimensionality Reduction Facilitates Ligand Diffusion Paths Assessment: A Case of Cytochrome P450cam

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.