Reduced finite-dimensional model of 2D protein cluster formation
File(s)
Published version
Author(s)
Bressloff, Paul C
Chen, Kevin
Type
Journal Article
Abstract
The aggregation or clustering of proteins plays an important role in the formation of postsynaptic domains (PSDs) at excitatory and inhibitory synapses in neurons. PSDs are rich in scaffolding proteins that can transiently trap transmembrane neurotransmitter receptors, allowing them to regulate the strength of synaptic connections during learning and memory. Recently, a two-dimensional diffusion-mediated aggregation model of PSD formation was developed in which the spatial locations of the clusters are determined by a set of fixed anchoring sites. The system is kept out of equilibrium by the recycling of particles between the cell membrane and interior. This results in a nontrivial stationary state consisting of multiple stable protein clusters. In this paper, we use matched asymptotic methods to reduce the underlying reaction-diffusion model with moving interior boundaries to a corresponding finite-dimensional nonlinear system. The latter couples the cluster radii to the spatially averaged protein concentration in the bulk domain. We assume that the diffusivity 𝐷 is 𝑂(1/𝜈), where 𝜈=−1/ln𝜀 and 𝜀 is a small parameter that characterizes the size of the clusters relative to the size of the bulk domain. The reduced dynamical system allows us to explore both the existence and stability of the multicluster stationary state while maintaining the effects of diffusion-mediated interactions between clusters.
Date Issued
2026-09-01
Date Acceptance
2026-07-24
Citation
Physical Review E, 2026, 114 (3)
ISSN
2470-0045
Publisher
American Physical Society (APS)
Journal / Book Title
Physical Review E
Volume
114
Issue
3
Copyright Statement
Published by the American Physical Society Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
License URL
Publication Status
Published
Article Number
034402
Date Publish Online
2026-09-08