Conformational changes (i.e., dynamic transitions between pairs of conformational states) play important roles in many chemical and biological processes. Constructing the Markov state model (MSM) from extensive molecular dynamics (MD) simulations is an effective approach to dissect the mechanism of conformational changes. When combined with transition path theory (TPT), MSM can be applied to elucidate the ensemble of kinetic pathways connecting pairs of conformational states. However, the application of TPT to analyze complex conformational changes often results in a vast number of kinetic pathways with comparable fluxes. This obstacle is particularly pronounced in heterogeneous self-assembly and aggregation processes. The large number of kinetic pathways makes it challenging to comprehend the molecular mechanisms underlying conformational changes of interest. To address this challenge, we have developed a path classification algorithm named latent-space path clustering (LPC) that efficiently lumps parallel kinetic pathways into distinct metastable path channels, making them easier to comprehend. In our algorithm, MD conformations are first projected onto a low-dimensional space containing a small set of collective variables (CVs) by time-structure-based independent component analysis (tICA) with kinetic mapping. Then, MSM and TPT are constructed to obtain the ensemble of pathways, and a deep learning architecture named the variational autoencoder (VAE) is used to learn the spatial distributions of kinetic pathways in the continuous CV space. Based on the trained VAE model, the TPT-generated ensemble of kinetic pathways can be embedded into a latent space, where the classification becomes clear. We show that LPC can efficiently and accurately identify the metastable path channels in three systems: a 2D potential, the aggregation of two hydrophobic particles in water, and the folding of the Fip35 WW domain. Using the 2D potential, we further demonstrate that our LPC algorithm outperforms the previous path-lumping algorithms by making substantially fewer incorrect assignments of individual pathways to four path channels. We expect that LPC can be widely applied to identify the dominant kinetic pathways underlying complex conformational changes.

Uncovering slow collective variables (CVs) of self-assembly dynamics is important to elucidate its numerous kinetic assembly pathways and drive the design of novel structures for advanced materials through the bottom-up approach. However, identifying the CVs for self-assembly presents several challenges. First, self-assembly systems often consist of identical monomers and the feature representations should be invariant to permutations and rotational symmetries. Physical coordinates, such as aggregate size, lack the high-resolution detail, while common geometric coordinates like pairwise distances are hindered by the permutation and rotational symmetry challenge. Second, self-assembly is usually a downhill process, and the trajectories often suffer from insufficient sampling of backward transitions that correspond to the dissociation of self-assembled structures. Popular dimensionality reduction methods, like tICA, impose detailed balance constraints, potentially obscuring the true dynamics of self-assembly. In this work, we employ GraphVAMPnets which combines graph neural networks with variational approach for Markovian process (VAMP) theory to identify the slow CVs of the self-assembly processes. First, GraphVAMPnets bears the advantages of graph neural networks, in which the graph embeddings can represent self-assembly structures in a high-resolution while being invariant to permutations and rotational symmetries. Second, it is built upon VAMP theory that studies Markov processes without forcing detailed balance constraint, which addresses the out-of-equilibrium challenge in self-assembly process. We demonstrate GraphVAMPnets for identifying slow CVs of self-assembly kinetics in two systems: aggregation of two hydrophobic molecules and self-assembly of patchy particles. We expect that our GraphVAMPnets can be widely to applied to molecular self-assembly.

Fragment-based drug design plays an important role in the drug discovery process by reducing the complex small-molecule space into a more manageable fragment space. We leverage the power of deep learning to design ChemPLAN-Net; a model that incorporates the pairwise association of physicochemical features of both the protein drug targets and the inhibitor and learns from thousands of protein co-crystal structures in the PDB database to predict previously unseen inhibitor fragments. Our novel protocol handles the computationally challenging multi-label, multi-class problem, by defining a fragment database and using an iterative feature-pair binary classification approach. By training ChemPLAN-Net on available co-crystal structures of the protease protein family, excluding HIV-1 protease as a target, we are able to outperform fragment docking and recover the target's inhibitor fragments found in co-crystal structures or identified by in-vitro cell assays.