Lumry-Eyring nucleated-polymerization model of protein aggregation kinetics. 2. Competing growth via condensation and chain polymerization.

The Lumry-Eyring with nucleated polymerization (LENP) model from part 1 (Andrews, J. M.; Roberts, C. J. J. Phys. Chem. B 2007, 111, 7897-7913) is expanded to explicitly account for kinetic contributions from aggregate-aggregate condensation polymerization. Experimentally accessible quantities described by the resulting model include monomer mass fraction (m), weight-average molecular weight (Mw), and ratio of Mw to number-average molecular weight (Mn) as a function of time (t). Analysis of global model behavior illustrates ways to identify which steps in the overall aggregation process are kinetically important on the basis of the qualitative behavior of m, Mw, and Mw/Mn vs t, and on whether bulk phase separation or precipitation occurs. For cases in which all aggregates remain soluble, moment equations are provided that permit straightforward numerical regression of experimental data to give separate time scales or inverse rate coefficients for nucleation and for growth by chain and condensation polymerization. Analysis of simulated data indicates that it may be possible to neglect condensation reactions if only early time data are considered and also highlights difficulties in conclusively distinguishing between alternative mechanisms of condensation, even when kinetics are monitored with both m and Mw.