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Spyridon Sovatzoglou1 Andrew Fleming2 Jamie Hobbs1

1, The University of Sheffield, Sheffield, South Yorkshire, United Kingdom
2, The University of Sheffield, Sheffield, South Yorkshire, United Kingdom

Nano-indentation experiments and their subsequent analysis can provide useful insights into materials' mechanical properties. Moreover, in living cells, knowledge of mechanical properties can lead to improved understanding of function. Despite impressive progress in the field, it is not always possible to acquire adequate information for the characterization of complex biological systems. Real biological samples are often highly heterogeneous and dynamic, and thus nanoindentation experiments must be interpreted carefully under contact mechanics theory1. Here we use the plant leaf as a model complex biological material structure. Plant cells have a thick wall that maintains shape, prevents cell disruption under the action of high osmotic pressure, and plays a vital role in the varied functions of different plant tissues. We focus on the leaf surface and particularly stomata, specialized cells involved in gas and moisture exchange, which are designed to open or close under varying internal pressure.
Beginning from the observation that not all the force curves of a “force-volume” map can be treated universally under the same theoretical model, an automated approach was generated for the analysis of multiple force curves. In the approach presented here, apart from the calculation of Young’s modulus for the whole map, we present three important features for an improved insight into the complexity of cell mechanics. Firstly, a “contact mechanics model” map suggests the appropriate model to be used for the calculation of modulus of each force curve of the map (depending on adhesion, hysteresis cycle and fitting constants α,β and in P=α*hβ). Secondly, a “yield point” map shows the points of the scan where the elastic limit has been exceeded along the indentation depth. Thirdly, a “modulus tomography” movie is generated, from which a possible change of modulus value along fractions of indentation depth, for a non-yield-point force curve, can reveal bad fitting of the experimental data under the current theoretical models (β=3/2 & 2) for non-adhesive/non-plastic contact. Finally, a map of the fitting residuals is presented to provide an immediate insight into the areas of the data that cannot be treated with confidence.
We have applied this approach to the spatial variation of Young’s modulus over the surface of the plant cell wall, and how this feature couples to the structure and the biological function of the cell. We have observed an unexpected stiffening of the polar regions of the cell2, in-line with the mechanical role of this region during the opening and closing of stomata, providing new insights into the mechanics of the cell’s function.

References
[1] Kuznetsova et al. Micron, Volume 38, Issue 8, 2007, 824-833
[2] Carter, Ross et al. Current Biology, Volume 27, Issue 19, 2017, 2974 - 2983.e2

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