Employing artificial neural networks to find 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 require constructing accurate low-dimensional representations of the transition pathways. In this work, we study the self-assembly of two single-stranded DNA (ssDNA) fragments into a ring-like structure, considering two cases with either symmetric or asymmetric ssDNA base sequences. We perform a time-lagged independent component analysis (TICA) for these systems, and demonstrate how autoencoder architectures based on unsupervised neural networks can be employed to reliably expose transition pathways and to provide a suitable low-dimensional representation. We find that the assembly occurs as a two-step process through distinct half-bound states, which are correctly identified by the TICA representation and the neural net. We use the representations to construct a Markov State Model for predicting the four molecular conformations and their transitions. Our work opens up new avenues for the computational modeling of multi-step and hierarchical self-assembly, which has proven challenging so far.