# Buckling Soft Tensegrities: Fickle Elasticity and Configurational Switching in Living Cells

## TL;DR

This paper extends tensegrity models of cell cytoskeletons by incorporating flexible, bendable struts and nonlinear elasticity, revealing complex behaviors like energy storage, shape modulation, and configurational switching in living cells.

## Contribution

It introduces a novel tensegrity model with flexible, nonlinear elastic components, challenging the traditional rigid-strut assumption in cell mechanics modeling.

## Key findings

- Demonstrates that flexible, nonlinear tensegrity models can replicate cellular behaviors.
- Shows cells can modulate elasticity and shape via pre-stress and instability.
- Reveals counterintuitive mechanical behaviors relevant to cell function.

## Abstract

Tensegrity structures are special architectures made by floating compressed struts kept together by a continuous system of tensed cables. The multiplicity of shapes that tensegrity structures can assume and their intrinsic capability to be deployable and assembled, so storing (and releasing) elastic energy, have motivated their success as paradigm -pioneeringly proposed by Donald E. Ingber- to explain some underlying mechanisms regulating dynamics of living cells. The interlaced structure of the cell cytoskeleton, constituted by actin and intermediate filaments and microtubules which continuously change their spatial organization and pre-stresses through polymerization/depolymerization, seems to steer migration, adhesion and cell division by obeying the tensegrity construct. Even though rough calculations lead to estimate discrepancies when comparing axial stiffness of actin filaments and microtubules and recent works have shown bent microtubules, no one has yet tried to remove the hypothesis of rigid struts in tensegrities when used to idealize the cytoskeleton mechanics. With reference to the 30-element tensegrity cell paradigm, we introduce both compressibility and bendability of the struts and rewrite the theory to take into account nonlinear elasticity of both tendons and bars, so abandoning the classical linear stress-strain assumptions. By relaxing the hypothesis of rigidity of the struts, we demonstrate that some quantitative confirmations and many extreme and somehow counterintuitive mechanical behaviors actually exploited by cells for storing/releasing energy, resisting to applied loads and deforming by modulating their overall elasticity and shape through pre-stress changes and instability-guided configurational switching, can be all theoretically found.