Post-Jamming Mechanics of Feedback-Regulated Budding-Cell Packings

TL;DR

This paper develops a mean-field theory to understand the post-jamming mechanics of budding-cell packings, revealing how pressure and unconstrained buds influence rigidity and the transition density.

Contribution

It introduces a novel theoretical framework combining Maxwell count, depletion law, and flux-partition to explain post-jamming behavior in feedback-regulated cell packings.

Findings

Post-jamming coordination is predicted by a modified Maxwell count.

A depletion law describes the crossover density where unconstrained buds are exhausted.

Strong growth feedback can significantly increase rigidity with minimal internal pressure.

Abstract

Budding-cell packings jam before all buds are mechanically constrained. The post-jamming state is therefore set by both the pressure $P$ and the fraction $u$ of buds that remain unconstrained. We develop a mean-field theory for this regime. A modified Maxwell count gives the post-jamming coordination, a depletion law for the unconstrained buds predicts the crossover density $\phi_2$ at which that reservoir is exhausted, and a flux-partition argument explains why strong growth feedback can markedly increase rigidity while generating little internal pressure.