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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.
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Romain Yvinec, Maria R. d'Orsogna, Tom Chou. First passage times in homogeneous nucleation and self-assembly. Journal of Chemical Physics, American Institute of Physics, 2012, 137 (24), pp.1-18. ⟨10.1063/1.4772598⟩. ⟨hal-02649185⟩

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