A two-step biopolymer nucleation model shows a nonequilibrium critical point

The Journal of Chemical Physics
Alexander I. P. TaylorRosemary A. Staniforth

Abstract

Biopolymer self-assembly pathways are complicated by the ability of their monomeric subunits to adopt different conformational states. This means nucleation often involves a two-step mechanism where the monomers first condense to form a metastable intermediate, which then converts to a stable polymer by conformational rearrangement of constituent monomers. Nucleation intermediates play a causative role in amyloid diseases such as Alzheimer's and Parkinson's. While existing mathematical models neglect the conversion dynamics, experiments show that conversion events frequently occur on comparable timescales to the condensation of intermediates and growth of mature polymers and thus cannot be ignored. We present a model that explicitly accounts for simultaneous assembly and conversion. To describe conversion, we propose an experimentally motivated initiation-propagation mechanism in which the stable phase arises locally within the intermediate and then spreads by nearest-neighbor interactions, in a manner analogous to one-dimensional Glauber dynamics. Our analysis shows that the competing timescales of assembly and conversion result in a nonequilibrium critical point, separating a regime where intermediates are kinetically unstabl...Continue Reading

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