title: First assembly times and equilibration in stochastic coagulation-fragmentation.
abstract: We develop a fully stochastic theory for coagulation and fragmentation (CF) in a finite system with a maximum cluster size constraint. The process is modeled using a high-dimensional master equation for the probabilities of cluster configurations. For certain realizations of total mass and maximum cluster sizes, we find exact analytical results for the expected equilibrium cluster distributions. If coagulation is fast relative to fragmentation and if the total system mass is indivisible by the mass of the largest allowed cluster, we find a mean cluster-size distribution that is strikingly broader than that predicted by the corresponding mass-action equations. Combinations of total mass and maximum cluster size under which equilibration is accelerated, eluding late-stage coarsening, are also delineated. Finally, we compute the mean time it takes particles to first assemble into a maximum-sized cluster. Through careful state-space enumeration, the scaling of mean assembly times is derived for all combinations of total mass and maximum cluster size. We find that CF accelerates assembly relative to monomer kinetic only in special cases. All of our results hold in the infinite system limit and can be only derived from a high-dimensional discrete stochastic model, highlighting how classical mass-action models of self-assembly can fail.
authors.affiliation: Department of Biomathematics, UCLA, Los Angeles, California 90095-1766, USA.
authors.forename: Maria R
authors.initials: MR
authors.lastname: D'Orsogna
authors.affiliation: Institute for Computational and Engineering Sciences, University of Texas, Austin, Texas 78712-1229, USA.
authors.forename: Qi
authors.initials: Q
authors.lastname: Lei
authors.affiliation: Department of Biomathematics, UCLA, Los Angeles, California 90095-1766, USA.
authors.forename: Tom
authors.initials: T
authors.lastname: Chou
mesh_terms: D007700:Kinetics; D008962:Models, Theoretical; D013269:Stochastic Processes