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 behavior in general, and relaxation times of cells of multicellular organisms in vivo with nanoscale resolution, 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 τ = 2.2 – 2.7 μs of their cell walls. Our results demonstrate that cell walls, despite their complex molecular composition, display a striking continuity of simple, linear, viscoelastic behavior 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 (milliseconds) are key to understand macroscopic scale dynamics (e.g. growth) as predicted by the physics of polymer dynamics.