Spatially Resolved Nucleated Polymerization: A Free-Boundary Model of Protein Aggregation in Concentrated Solutions

Kinetic models of protein aggregation describe populations by size, not by spatial organization or morphology. We extend Lumry-Eyring nucleated polymerization to a model in which the monomer is a density field and each aggregate is a region bounded by a level set. Growth is a flux condition on the available sites of a surface. Condensation is a reaction between the bonding sites of two surfaces in contact, at a rate set by the bond rate and the contact geometry. The availability of those sites is a field on the interface, and its equilibrium value follows from Wertheim's perturbation theory. The collision efficiency and the Fuchs stability ratio are therefore computed, not fitted. In a well-mixed limit the model's spatial averages satisfy the rate equations term by term; the monomer fraction agrees to eight parts in ten thousand, a difference that arises from equating aggregate size with volume. The condensation kernel's exponent is $0.5806\pm0.0013$ against the $0.600\pm0.010$ fitted to a monoclonal antibody. The computed stability ratio reproduces thirteen of fourteen published conditions at twelve $k_BT$, but only with the bond rate at the top of its range. In a many-body box, aggregates merge at $2.2$ to $3.8$ times the two-body rate.

Source: arXiv:2609.27185v1 - http://arxiv.org/abs/2609.27185v1 PDF: https://arxiv.org/pdf/2609.27185v1 Original Link: http://arxiv.org/abs/2609.27185v1