Tau creates spatially moving hotspots of amyloid-β secondary nucleation: a reaction-diffusion model
Abstract
Tau-amyloid-β cross-seeding creates a spatial paradox. Bioavailable tau can promote Aβ42 nucleation, thereby increasing local fibril number and catalytic-site burden; yet the same fibrils consume the free Aβ monomer required for homotypic secondary nucleation. The region containing the most tau or fibrillar material therefore need not be the region with the highest secondary-nucleation rate. We test this idea with a reaction-diffusion model that tracks a propagating effective tau catalyst, free Aβ monomer, elongation-competent fibrils, fibril mass, and the catalytic sites exposed to monomer. The model reduces the spatial competition to two quantities: accessible catalytic sites and free monomer. Their balance yields an exact condition for an interior kinetic maximum: the logarithmic decrease in accessible catalytic sites must equal twice the logarithmic increase in free monomer. Two Damkohler numbers then separate the relevant competitions-elongation versus clearance, and elongation versus diffusive redistribution-while a monomer screening length sets the physical scale over which depletion can persist. Independent transport and turnover estimates place this length near 0.44-0.54 mm. Simulations show that tau first raises secondary nucleation near its source; continued fibril growth then produces a monomer-depleted wake, and the maximum shifts to a region with fewer catalytic sites but more available monomer. Oligomer transport and sustained reversible exchange can weaken or eliminate this contrast, whereas growth-history-dependent site density can strengthen it. The robust prediction is therefore a spatial separation among tau burden, fibril-mass growth, and instantaneous Aβ secondary-nucleation activity, rather than a universal hotspot speed.
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BibTeX
@misc{kuznetsov2026creates,
title = {{Tau creates spatially moving hotspots of amyloid-$β$ secondary nucleation: a reaction-diffusion model}},
author = {Andrey V. Kuznetsov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33981},
eprint = {2610.33981},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33981},
}
RIS
TY - UNPB
TI - Tau creates spatially moving hotspots of amyloid-β secondary nucleation: a reaction-diffusion model
AU - Andrey V. Kuznetsov
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.33981
UR - https://arxiv.org/abs/2610.33981
AB - Tau-amyloid-β cross-seeding creates a spatial paradox. Bioavailable tau can promote Aβ42 nucleation, thereby increasing local fibril number and catalytic-site burden; yet the same fibrils consume the free Aβ monomer required for homotypic secondary nucleation. The region containing the most tau or fibrillar material therefore need not be the region with the highest secondary-nucleation rate. We test this idea with a reaction-diffusion model that tracks a propagating effective tau catalyst, free Aβ monomer, elongation-competent fibrils, fibril mass, and the catalytic sites exposed to monomer. The model reduces the spatial competition to two quantities: accessible catalytic sites and free monomer. Their balance yields an exact condition for an interior kinetic maximum: the logarithmic decrease in accessible catalytic sites must equal twice the logarithmic increase in free monomer. Two Damkohler numbers then separate the relevant competitions-elongation versus clearance, and elongation versus diffusive redistribution-while a monomer screening length sets the physical scale over which depletion can persist. Independent transport and turnover estimates place this length near 0.44-0.54 mm. Simulations show that tau first raises secondary nucleation near its source; continued fibril growth then produces a monomer-depleted wake, and the maximum shifts to a region with fewer catalytic sites but more available monomer. Oligomer transport and sustained reversible exchange can weaken or eliminate this contrast, whereas growth-history-dependent site density can strengthen it. The robust prediction is therefore a spatial separation among tau burden, fibril-mass growth, and instantaneous Aβ secondary-nucleation activity, rather than a universal hotspot speed.
ER -