Comparing open and closed molecular self-assembly

¹ Laboratoire de Physique, Ecole Normale Supérieure de Lyon, Université de Lyon and CNRS 46 Allée d'Italie, 69364 Lyon Cedex 07, France
² Laboratoire de Physique Statistique, Ecole Normale Supérieure, Université Pierre et Marie Curie, Université Paris Diderot and CNRS - 24 Rue Lhomond, 75005 Paris, France

Received: 22 November 2013
Accepted: 20 January 2014

Abstract

We study theoretically in the present work the self-assembly of molecules in an open system, which is fed by monomers and depleted in partial or complete clusters. Such a scenario is likely to occur for example in the context of viral self-assembly. We provide a general formula for the mean-field size distribution which is valid both at equilibrium in a closed system, and in the stationary state in an open system. This allows us to explore in a simple way out-of-equilibrium features for self-assembly and compare them to equilibrium properties. In particular, we identify a region of parameter space for which the out-of-equilibrium size distribution in the presence of external fluxes is equal to the equilibrium size distribution in the absence of external fluxes, up to a constant renormalization factor. The range of validity of this result and its consequences are discussed.