Stochastic Models of Self-Assembly of Linear Chains

The article investigates a stochastic model of self-assembly of linear chains, these being arbitrarily long sequences of pairwise linked elements, of which only $n$ are different. Under the assumption that the elements can combine in arbitrary order, descriptions of the self-assembly process by concentrations of chains and links are introduced. It is shown that, under one condition on the intensity of formation and rupture of links between elements, the concentration dependencies of the chain can be found recursively in terms of the solutions of a system containing $n^2$ nonlinear differential equations. Examples are given.