Single Cell Wall Nonlinear Mechanics Revealed by a Multiscale Analysis of AFM Force-Indentation Curves

Abstract

Individual plant cells are rather complex mechanical objects. Despite the fact that their wall mechanical strength may be weakened by comparison with their original tissue template, they nevertheless retain some generic properties of the mother tissue, namely the viscoelasticity and the shape of their walls, which are driven by their internal hydrostatic turgor pressure. This viscoelastic behavior, which affects the power-law response of these cells when indented by an atomic force cantilever with a pyramidal tip, is also very sensitive to the culture media. To our knowledge, we develop here an original analyzing method, based on a multiscale decomposition of force-indentation curves, that reveals and quantifies for the first time the nonlinearity of the mechanical response of living single plant cells upon mechanical deformation. Further comparing the nonlinear strain responses of these isolated cells in three different media, we reveal an alteration of their linear bending elastic regime in both hyper- and hypotonic conditions.

A minimal rupture cascade model for living cell plasticity

“…Then the cantilever was withdrawn from the sample at the same constant speed (−V 0 ) back to its starting position (figures 1(c) and (d)). From these indentation experiments, the cell shear relaxation modulus G(Z) was estimated as the second-order derivative of the FIC (see equation (B13) in appendix B) [36,39]. From the approach and retract FICs, the initial G i and global G g shear moduli, and the dissipation loss D l were retrieved (see figure S1 is available online at stacks.iop.org/NJP/20/053057/mmedia and supplemental material 11 ).…”

“…A key issue in the analysis of FICs is the determination of Z c for very soft materials, like living cells. To master this practical signal-to-noise issue, we used a wavelet-based decomposition of the FICs and their derivatives [36,39] that likely achieved some compromise between a too strong smoothing of the force derivative that would wipe out the non-contact to contact transition, and a too mild smoothing of the force that would suffer from a noise estimation of the contact points (see figures S2 and S3 (see footnote 11)). Once the cell is deformed by the cantilever, Z>Z c , Z−Z c reads as the sum of two terms, respectively the cell indentation h and the ratio of the force F and the cantilever spring constant k [77]:…”

“…Classical analysis of force-indentation curves (FICs) aims at estimating an elastic modulus by fitting the curves with linear elastic models [37,38]. Here, in contrast, we engineer a wavelet-based multi-scale method [36,39] to identify singularities in the FICs that likely correspond to rupture events in the CSK. Our study provides compelling evidence of the existence of two distinct populations of avalanche rupture events, that we identify to ductile (corresponding to weakly cross-linked filaments) and brittle (corresponding to tightly cross-linked filaments) failures.…”

Bio-tribology of plant cell walls: measuring the interactive forces between cell wall components

“…This differs from cell wall fragments because it considers the cell geometry, which is particularly important for understanding the relationship between turgor pressure and wall stress (this is critical for cell wall extension and will be discussed in a separate section below). Mechanical measurement of isolated single cells have been achieved using compression testing by micromanipulation with a cylindrical probe 72 or pyramidal tip 73,74 , as shown in Figure 2.11. Digiuni et al 73 and Bonilla et al 74 show that individual plant cells behave in a viscoelastic manner that is driven by their internal hydrostatic turgor pressure.…”

“…Mechanical measurement of isolated single cells have been achieved using compression testing by micromanipulation with a cylindrical probe 72 or pyramidal tip 73,74 , as shown in Figure 2.11. Digiuni et al 73 and Bonilla et al 74 show that individual plant cells behave in a viscoelastic manner that is driven by their internal hydrostatic turgor pressure. Wang et al 72 also show a time-dependent mechanical response where water plays a significant role that is dependent on the deformation rate.…”