Mapping cellular nanoscale viscoelasticity and relaxation times relevant to growth of living Arabidopsis thaliana plants using multifrequency AFM

The shapes of living organisms are formed and maintained by precise control in time and space of growth, which is achieved by dynamically fine-tuning the mechanical (viscous and elastic) properties of their hierarchically built structures from the nanometer up. Most organisms on Earth including plants grow by yield (under pressure) of cell walls (bio-polymeric matrices equivalent to extracellular matrix in animal tissues) whose underlying nanoscale viscoelastic properties remain unknown. Multifrequency atomic force microscopy (AFM) techniques exist that are able to map properties to a small subgroup of linear viscoelastic materials (those obeying the Kelvin-Voigt model), but are not applicable to growing materials, and hence are of limited interest to most biological situations. Here, we extend existing dynamic AFM methods to image linear viscoelastic behaviour in general, and relaxation times of cells of multicellular organisms in vivo with nanoscale resolution (similar to 80 nm pixel size in this study), featuring a simple method to test the validity of the mechanical model used to interpret the data. We use this technique to image cells at the surface of living Arabidopsis thaliana hypocotyls to obtain topographical maps of storage E ' = 120-200 MPa and loss E '' = 46-111 MPa moduli as well as relaxation times tau = 2.2- 2.7 mu s of their cell walls. Our results demonstrate that (taken together with previous studies) cell walls, despite their complex molecular composition, display a striking continuity of simple, linear, viscoelastic behaviour across scales-following almost perfectly the standard linear solid model-with characteristic nanometer scale patterns of relaxation times, elasticity and viscosity, whose values correlate linearly with the speed of macroscopic growth. We show that the time-scales probed by dynamic AFM experiments (microseconds) are key to understand macroscopic scale dynamics (e.g. growth) as predicted by physics of polymer dynamics. Statement of significance In order to persist, biological organisms must grow and construct ordered structures without violating the second law of thermodynamics. This is achieved by constantly creating shapes that both store and dissipate mechanical energy; this process generates the temporal scales that are characteristic of growth patterns at different spatial scales. Understanding the physics of biological growth and shape therefore requires measurement of stored/dissipated energy. In this article, we provide an experimental method and the underlying theory to quantitatively map energy stored, energy dissipated and time response of cells walls in living plants with nanometre resolution using AFM. Our approach allows identifying the models that best describe the mechanical properties of the structures studied and is applicable in any living organism. (c) 2020 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Automated summary

The shapes of living organisms are formed and maintained by precise control in time and space of growth, achieved by dynamically fine-tuning the mechanical properties of their structures. The study demonstrates the continuity of simple, linear, viscoelastic behavior of cell walls across scales, with characteristic nanometer scale patterns of relaxation times, elasticity and viscosity correlating with the speed of macroscopic growth. The approach provides a method to quantitatively map energy stored, dissipated and time response of cell walls in living organisms with nanometer resolution.