In vivo dynamic AFM mapping of viscoelastic properties of the primary plant cell wall

Plant development is a complex multiscale process out of thermodynamic equilibrium. While sophisticated mathematical models of this process exist, there are only a few studies which provide experimental evidence. At the cellular level, unidirectional plant growth can be described by the viscoelastic Maxwell (MW) model. At the subcellular level more complicated thermodynamic models exist for which experimental proof is missing, due to the lack of suitable experimental methods. Modern approaches in multifrequency AFM enable high resolution viscoelastic mapping for cells and polymers. However, these methods are based on the viscoelastic Kelvin-Voigt model and, therefore, the viscoelastic properties cannot be associated with plant growth. I provide a link between the generalised MW model and the AFM cantilever observables. Then I show that the primary plant cell wall (CW) behaves, at the subcellular level, like a standard linear solid (SLS). I further use the description of the CW as a SLS and the spatial information of the dynamic modulus to determine the characteristic quantities k∞, kM, η, and τ of the SLS with spatial resolution. The application of two eigenmodes suggests that it is possible to extend the approach from the SLS description to reconstruct the relaxation modulus of polymer networks. This is demonstrated by the stiffnessk2 and relaxation time τ2 which are increased and decreased, respectively, compared to the first eigenmode. Finally, using the example of whole living seedlings of the plant Arabidopsis thaliana, I use this theoretical framework to demonstrate, that the viscoelastic properties at a subcellular level can be linked to thermodynamic models of plant growth. I show that these can be derived using the Onsager principle I develop a non-equilibrium approach to describe the time evolution of thermodynamic systems. Moreover, pharmacological and genetic manipulation of young seedlings indicates that these viscoelastic measurements can be used as an analytical tool to characterise CW deficiencies.