Spatially Resolved Nucleated Polymerization: A Free-Boundary Model of Protein Aggregation in Concentrated Solutions
Abstract
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±0.0013 against the 0.600±0.010 fitted to a monoclonal antibody. The computed stability ratio reproduces thirteen of fourteen published conditions at twelve kBT, 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.
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BibTeX
@misc{mistani2026spatially,
title = {{Spatially Resolved Nucleated Polymerization: A Free-Boundary Model of Protein Aggregation in Concentrated Solutions}},
author = {Pouria A. Mistani},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27185},
eprint = {2609.27185},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27185},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Spatially Resolved Nucleated Polymerization: A Free-Boundary Model of Protein Aggregation in Concentrated Solutions
AU - Pouria A. Mistani
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27185
UR - https://arxiv.org/abs/2609.27185
AB - 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±0.0013 against the 0.600±0.010 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.
ER -