Nucleation-conversion-polymerization reactions of biological macromolecules with prenucleation clusters

The self-assembly of biomolecules, such as peptides and proteins, into filaments is conventionally understood as a nucleated polymerization reaction. However, detailed analysis of experimental observation has revealed recently that nucleation pathways generate growth-competent nuclei via a cascade of metastable intermediate species, which are omitted in conventional models of filamentous growth based on classical nucleation theory. Here we take an analytical approach to generalizing the classical theory of nucleated polymerization to include the formation of these prenucleation clusters, providing a quantitative general classification of the behavior exhibited by these nucleation-conversion-polymerization reactions. A phase diagram is constructed, and analytical predictions are derived for key experimental observables. Using this approach, we delineate the characteristic time scales that determine the nature of biopolymer growth phenomena.