The kinetics of multicenter macromolecule growth along a template

A previously developed kinetic theory of polymer replication on linear, effectively single stranded templates is extended to the case of several simultaneously growing chains. The basic assumptions are diffusion of monomer to the template and subsequent reaction of two monomers on adjacent sites competing with monomer desorption. The role of the initiating enzyme in the replication process is formally represented by a first order arrival in time. In this model we distinguish between the different states in which a template may exist at a given instant. These are defined by the number of growing centers and the proximity of the independently propagating chains. Two cases are considered, corresponding to whether coupling of adjacent chains is permitted or not. We give particular emphasis to the two-center case and numerical calculations are carried out, assuming the first center to be initiated at one end of the template. The solutions for conversion, average molecular weight and dispersion are expressed ultimately in terms of incomplete gamma functions. The special properties of these functions for large values of the arguments simplify the calculations and lead to results valid for conversions less than about 90%. A comparison with the previous single center kinetics indicates a significant effect of the addition of a second growing chain. However, the molecular weight dispersions in these two models are very similar. The only significant difference is the slower approach to the final homogeneity with increasing conversion in the latter case. This suggests that experimental discrimination between one and two chain replication by direct analysis of the dispersion is not feasible except for relatively large conversions.