Anisotropy vs isotropy in living cell indentation with AFM

www.nature.com/scientificreports OPEN Anisotropy vs isotropy in living cell indentation with AFM Yuri M. Efremov1,2, Mirian Velay-Lizancos3, Cory J. Weaver 4,7, Ahmad I. Athamneh2,4, Pablo D. Zavattieri3, Daniel M. Suter2,4,5,6 & Arvind Raman1,2 Received: 23 November 2018 Accepted: 18 March 2019 Published: xx xx xxxx The measurement of local mechanical properties of living cells by nano/micro indentation relies on the foundational assumption of locally isotropic cellular deformation. As a consequence of assumed isotropy, the cell membrane and underlying cytoskeleton are expected to locally deform axisymmetrically when indented by a spherical tip. Here, we directly observe the local geometry of deformation of membrane and cytoskeleton of different living adherent cells during nanoindentation with the integrated Atomic Force (AFM) and spinning disk confocal (SDC) microscope. We show that the presence of the perinuclear actin cap (apical stress fibers), such as those encountered in cells subject to physiological forces, causes a strongly non-axisymmetric membrane deformation during indentation reflecting local mechanical anisotropy. In contrast, axisymmetric membrane deformation reflecting mechanical isotropy was found in cells without actin cap: cancerous cells MDA-MB-231, which naturally lack the actin cap, and NIH 3T3 cells in which the actin cap is disrupted by latrunculin A. Careful studies were undertaken to quantify the effect of the live cell fluorescent stains on the measured mechanical properties. Using finite element computations and the numerical analysis, we explored the capability of one of the simplest anisotropic models – transverse isotropy model with three local mechanical parameters (longitudinal and transverse modulus and planar shear modulus) – to capture the observed non-axisymmetric deformation. These results help identifying which cell types are likely to exhibit non-isotropic properties, how to measure and quantify cellular deformation during AFM indentation using live cell stains and SDC, and suggest modelling guidelines to recover quantitative estimates of the mechanical properties of living cells. Recent developments in fluorescent live-cell imaging and biophysical methods have significantly advanced our understanding of the dynamic biochemical and mechanical processes underlying cellular functions such as cell migration. These cellular functions are intimately related to mechanical properties of live cells such as stiffness and adhesion. Thus, linking cell mechanical properties to specific cellular structures is of high interest to many cell biologists. Atomic Force Microscope (AFM)-based indentation of live cells is one of the most frequently used techniques to assess mechanical properties of cells due to its relative ease of operation, high precision of force measurement, and high spatial resolution1–4. Mathematical models of contact mechanics between the AFM tip and the cell5–11 are required to interpret and quantify data derived from AFM indentation on live cells. Isotropic mechanical response is a common underlying assumption in these models. However, without the visualization of the cell structure and geometry of deformation simultaneously during cell indentation, it is extremely difficult, if not impossible, to verify if many underlying assumptions of the model are actually met. Such simultaneous visualization can help assess how the inhomogeneity of the cell structure affects the indentation; how the underlying cytoskeleton behaves to produce observed cellular mechanical behaviour; and to check the presence of any effects of the indentation on cells, like distant cytoskeletal rearrangements, residual damage or induced mechanoresponse12–24. Here, we integrated the AFM with a spinning disk confocal (SDC) microscope to create an experimental platform for simultaneous analysis of cellular deformation and mechanical properties with high spatio-temporal 1 School of Mechanical Engineering, Purdue University, West Lafayette, Indiana, USA. 2Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana, USA. 3Lyles School of Civil Engineering, Purdue University, West Lafayette, Indiana, USA. 4Department of Biological Sciences, Purdue University, West Lafayette, Indiana, USA. 5Bindley Bioscience Center, Purdue University, West Lafayette, Indiana, USA. 6Purdue Institute for Integrative Neuroscience, West Lafayette, Indiana, USA. 7Present address: University of South Carolina, Department of Biological Sciences, Jones PSC Building, 712 Main Street, room 517, Columbia, SC, 29208, USA. Correspondence and requests for materials should be addressed to D.M.S. (email: ) or A.R. (email: ) Scientific Reports | (2019) 9:5757 | https://doi.org/10.1038/s41598-019-42077-1 1 www.nature.com/scientificreports/ www.nature.com/scientificreports Figure 1. Morphology and mechanical properties of fibroblasts and cancer cells. (a) F-actin (SiR-actin) structure in NIH 3T3 and MDA-MB-231 cells, the height is colour coded with respect to the scaling shown in the colour scale bars. Vertical cross-sections along the marked lines shows that F-actin is mostly localized in the submembranous region (CellMask staining for plasma membrane). Scale bars 10 μm in the horizontal direction and 2 μm in the vertical direction. (b) Box plots of cell height, Young’s relaxation modulus scale factor E1, and power-law exponent α. The differences between all distributions are significant at the p < 0.001 level. resolution15–17,25. With live-cell imaging stains to fluorescently label the F-actin and microtubule cytoskeleton as well as the plasma membrane, we were able to directly observe structural changes during the indentation process with a spherical indenter in NIH 3T3 fibroblasts and MDA-MB-231 epithelial cancer cells. We found a strong correlation between presence of the perinuclear actin cap fibers and cell mechanical properties; highly anisotropic indentation geometry was found in cells with actin cap. To further assess anisotropy in cell mechanical properties, we performed finite element simulations and compared with the experimental surface displacement data. Our observations suggest a significant role of an anisotropic deformability and stiffness in the mechanics of cells. Results Cell viscoelastic properties and the effect of live-cell imaging stains. Live cell imaging requires special fluorescent dyes, some of which were shown to alter properties of their targeted structures and overall cell mechanical properties26–28. Among all stains used, only SiR-actin caused significant cell stiffening (the details are given in Supplementary Information, Section C, Table S1 and Fig. S1). For viscoelastic characterization, the power law rheology model (Eq. 3) was selected because it has been shown to sufficiently describe cell properties in a wide range of indentation times29,30. E1 is the relaxation modulus at t = 1 s (scale factor of the relaxation modulus), characte (...truncated)