Statistical Mechanics of a Cat's Cradle

TL;DR

This paper models the cytoskeleton as a network of tensioned strings, revealing phase transitions and heterogeneity in mechanical properties through analytical and simulation methods.

Contribution

It introduces a self-consistent phonon theory for buckling networks, predicting phase transitions and heterogeneity in cytoskeletal models, validated by simulations.

Findings

Identifies phase transitions in buckling networks.

Predicts rigidity onset and bond extension fractions.

Shows agreement between theory and simulations.

Abstract

It is believed that, much like a cat's cradle, the cytoskeleton can be thought of as a network of strings under tension. We show that both regular and random bond-disordered networks having bonds that buckle upon compression exhibit a variety of phase transitions as a function of temperature and extension. The results of self-consistent phonon calculations for the regular networks agree very well with computer simulations at finite temperature. The analytic theory also yields a rigidity onset (mechanical percolation) and the fraction of extended bonds for random networks. There is very good agreement with the simulations by Delaney et al. (Europhys. Lett. 2005). The mean field theory reveals a nontranslationally invariant phase with self-generated heterogeneity of tautness, representing ``antiferroelasticity''.