Dimerization of model polymer chains under nonequilibrium conditions

Dimerization and subsequent aggregation of polymers and biopolymers often occur under nonequilibrium conditions. When the initial state of the polymer is not collapsed, or the final folded native state, the dynamics of dimerization can follow a course sensitive to both the initial conditions and the conformational dynamics. Here, we study the dimerization process by using computer simulations and analytical theory, where the two monomeric polymer chains are in the elongated state and are initially placed at a separation distance, d0. Subsequent dynamics lead to the concurrent processes of collapse, dimerization, and/or escape. We employ Langevin dynamics simulations with a coarse-grained model of the polymer to capture certain aspects of the dimerization process. At separations d0 much shorter than the length of the monomeric polymer, the dimerization could happen fast and irreversibly from the partly extended polymer state itself. At an initial separation larger than a critical distance, dc, the polymer collapse precedes dimerization, and a significant number of single polymers do not dimerize within the time scale of simulations. To quantify these competitions, we introduce several time-dependent order parameters, namely, (i) the time-dependent radius of gyration RG(t) of individual polymers describing the conformational state of the polymer, (ii) a center-to-center of mass distance parameter RMM, and (iii) a time dependent overlap function Q(t) between the two monomeric polymers, mimicking the contact order parameter popular in protein folding. In order to better quantify the findings, we perform a theoretical analysis to capture the stochastic processes of collapse and dimerization by using the dynamical disorder model.