# Micro-mechanical approaches to characterize tip growth: Insights into root hair elasto-viscoplastic properties

## TL;DR

This paper introduces new methods to study the mechanical properties of root hairs in plants, revealing insights into their growth and stiffness.

## Contribution

The paper presents two novel mechanical setups to measure the elasto-viscoplastic properties of single root hairs in Arabidopsis thaliana.

## Key findings

- The critical buckling force measurement aligns with previous estimates of the root hair's Young’s modulus.
- The axial stiffness of root hairs is primarily influenced by turgor pressure and tip compression.
- The new cantilever setup confirms earlier findings and provides an independent method for stiffness estimation.

## Abstract

Root hairs are outgrowths of the epidermal cells of plant roots. They increase the root's exchange surface with the soil and provide it with good anchorage in the soil. Root hairs are an emblematic model of apical growth, a process also used by yeasts and hyphae to invade their environment. From a mechanical perspective, the root hair is considered as an elastic cylinder under pressure, closed by a dome that behaves like a yield fluid. We introduce here two innovative mechanical setups and protocols to characterize the mechanical properties of single growing root hairs in Arabidopsis thaliana. In the first setup, root hairs grow against an elastic obstacle until buckling. By measuring the critical buckling force, we determine the surface modulus and estimate the Young’s modulus of the cell wall, which aligns with previous measurements. Using a 1D elasto-viscoplastic model of root hair growth, we assess the excess pressure beyond the yield threshold (the driver of tip growth) and estimate the axial stiffness of the root hair, reflecting its elastic resistance to compression. For the second protocol, we designed a setup where a single root hair grows against a cantilever with variable stiffness, a technique adapted from our earlier work on rigidity sensing by animal cells. This method provides an independent estimate of the root hair's axial stiffness, confirming our initial findings and suggesting that this stiffness primarily involves tip compression and depends mainly on turgor pressure, at least within the low deformation regime explored.

The online version contains supplementary material available at 10.1140/epje/s10189-025-00546-8.