Employing Artificial Neural Networks to Identify Reaction Coordinates and Pathways for Self-Assembly

Capturing the autonomous self-assembly of molecular building blocks in computer simulations is a persistent challenge, requiring to model complex interactions and to access long time scales. Advanced sampling methods allow to bridge these time scales but typically need accurate low-dimensional representations of the transition pathways. In this work, we demonstrate for the self-assembly of two single-stranded DNA fragments into a ring-like structure how autoencoder neural networks can be employed to reliably provide a suitable low-dimensional representation and to expose transition pathways: The assembly proceeds through a two-step process with two distinct half-bound states, which are correctly identified by the neural net. We exploit this latent space representation to construct a Markov state model for predicting the four molecular conformations and their transition rates. We present a detailed comparison with two other low-dimensional representations based on empirically determined order parameters and a time-lagged independent component analysis (TICA). Our work opens up new avenues for the computational modeling of multistep and hierarchical self-assembly, which has proven challenging so far.