First passage times in homogeneous nucleation and self-assembly

Abstract

Motivated by nucleation and molecular aggregation in physical, chemical and biological settings, we present a thorough analysis of the general problem of stochastic self-assembly of a fixed number of identical particles in a finite volume. We derive the Backward Kolmogorov equation (BKE) for the cluster probability distribution. From the BKE we study the distribution of times it takes for a single maximal cluster to be completed, starting from any initial particle configuration. In the limits of slow and fast self-assembly, we develop analytical approaches to calculate the mean cluster formation time and to estimate the first assembly time distribution. We find, both analytically and numerically, that faster detachment can lead to a shorter mean time to first completion of a maximum-sized cluster. This unexpected effect arises from a redistribution of trajectory weights such that upon increasing the detachment rate, paths that take a shorter time to complete a cluster become more likely.

18 pages, 9 Figures

References in corpus (4)

• First-passage times in complex scale-invariant media
• Stochastic self-assembly of incommensurate clusters
• Coagulation-fragmentation for a finite number of particles and application to telomere clustering in the yeast nucleus
• Coarsening and accelerated equilibration in mass-conserving heterogeneous nucleation

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