Nonequilibrium Self-Assembly Time Forecasting by the Stochastic Landscape Method

Many biological systems rely on the ability to self-assembletargetstructures from different molecular building blocks using nonequilibriumdrives, stemming, for example, from chemical potential gradients.The complex interactions between the different components give riseto a rugged energy landscape with a plethora of local minima on thedynamic pathway to the target assembly. Exploring a toy physical modelof multicomponents nonequilibrium self-assembly, we demonstrate thata segmented description of the system dynamics can be used to providepredictions of the first assembly times. We show that for a wide rangeof values of the nonequilibrium drive, a log-normal distribution emergesfor the first assembly time statistics. Based on data segmentationby a Bayesian estimator of abrupt changes (BEAST), we further presenta general data-based algorithmic scheme, namely, the stochastic landscapemethod (SLM), for assembly time predictions. We demonstrate that thisscheme can be implemented for the first assembly time forecast duringa nonequilibrium self-assembly process, with improved prediction powercompared to a nai''ve guess based on the mean remaining timeto the first assembly. Our results can be used to establish a generalquantitative framework for nonequilibrium systems and to improve controlprotocols of nonequilibrium self-assembly processes.