RESUMEN

The models used to calculate Young's moduli from atomic force microscopy (AFM) force curves consider the shape of the indentation. It is then assumed that the geometry of the indentation is identical to the geometry of the indenter, which has been verified for hard materials (E > 1 MPa). Based on this assumption, the force curves calculated by these models, for the same object with a given Young's modulus, are different if the indenter geometry is different. On the contrary, we observe experimentally that the force curves recorded on soft living cells, with pyramidal, spherical, or tipless indenters, are almost similar. This indicates that this basic assumption on the indentation geometry does not work for soft materials (E of the order of 5 kPa or less). This means that, in this case, the shape of the indentation is therefore different from the shape of the indenter. Indentation of living cells by AFM is not what we thought!

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RESUMEN

When testing soft biological samples using the Atomic Force Microscopy (AFM) nanoindentation method, the force-indentation data is usually fitted to the equations provided by Hertzian mechanics. Nevertheless, a significant question remains up to date; is this a correct approach from a mathematical perspective? Biological materials are heterogeneous, so 'what do we calculate' when using a classic fitting approach? In this paper, conclusive answers to the abovementioned questions are provided. In addition, a new tool for the nanomechanical characterization of biological samples, the depth-dependent mechanical properties maps, is introduced.

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Atomic Force Microscopy nanoindentation method is a powerful technique that can be used for the nano-mechanical characterization of bio-samples. Significant scientific efforts have been performed during the last two decades to accurately determine the Young's modulus of collagen fibrils at the nanoscale, as it has been proven that mechanical alterations of collagen are related to various pathological conditions. Different contact mechanics models have been proposed for processing the force-indentation data based on assumptions regarding the shape of the indenter and collagen fibrils and on the elastic or elastic-plastic contact assumption. However, the results reported in the literature do not always agree; for example, the Young's modulus values for dry collagen fibrils expand from 0.9 to 11.5 GPa. The most significant parameters for the broad range of values are related to the heterogeneous structure of the fibrils, the water content within the fibrils, the data processing errors, and the uncertainties in the calibration of the probe. An extensive discussion regarding the models arising from contact mechanics and the results provided in the literature is presented, while new approaches with respect to future research are proposed.

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A generalized double-Hertz (D-H) model has been proposed to consider the adhesive contact between an elastic cylinder and an elastic half space under inclined forces. The normal traction is exactly the same as that in the conventional D-H model. The shear traction of finite value is distributed into a slipping zone and a non-slipping zone. In the slipping zone, the shear traction is proportional to the compressive pressure. With the model, adhesive contact behaviour between cylinders has been numerically illustrated. The shear-induced peeling has been demonstrated. The value of the ratio for shear traction to normal traction larger than friction coefficient has been found in part of the non-slipping zone. Those altogether are consistent with experiments.

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Mechanical properties of hydrogel particles are of importance for their interactions with cells or tissue, apart from their relevance to other applications. While so far the majority of works aiming at tuning particle mechanics relied on chemical cross-linking, we report a novel approach using inwards interweaving self-assembly of poly(allylamine) (PA) and poly(styrenesulfonic acid) (PSSA) on agarose gel beads. Using this technique, shell thicknesses up to tens of micrometers can be achieved from single-polymer incubations and accurately controlled by varying the polymer concentration or incubation period. We quantified the changes in mechanical properties of hydrogel core-shell particles. The effective elastic modulus of core-shell particles was determined from force spectroscopy measurements using the colloidal probe-AFM (CP-AFM) technique. By varying the shell thickness between 10 and 24 µm, the elastic modulus of particles can be tuned in the range of 10-190 kPa and further increased by increasing the layer number. Through fluorescence quantitative measurements, the polymeric shell density was found to increase together with shell thickness and layer number, hence establishing a positive correlation between elastic modulus and shell density of core-shell particles. This is a valuable method for constructing multidensity or single-density shells of tunable thickness and is particularly important in mechanobiology as studies have reported enhanced cellular uptake of particles in the low-kilopascal range (<140 kPa). We anticipate that our results will provide the first steps toward the rational design of core-shell particles for the separation of biomolecules or systemic study of stiffness-dependent cellular uptake.

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