In many biological applications, where the force spectroscopy mode is involved in the cell elasticity measurements, the commonly applied cantilevers have the spring constant in the range of 0.01-0.1 N/m and the typical loading force value does not exceed 30 nN . In this range both glass and mica surfaces can be used as hard, non-deformable samples. When cells are probed, the resulting cantilever deflections are much smaller, indicating that the probing tip indents the cell. Depending on the magnitude of the indentation depth, distinct properties can be studied, revealing heterogenic structure of cell interior (Fig. 4.14).
Figure 4.14 The idea behind the depth-sensing analysis that delivers the information on heterogeneity in the cell interior structure. (a) For small deformations the mechanical response of the cell is dominated by the actin cytoskeleton, while (b) in case of larger deformations, the overall stiffness of a whole cell is obtained.
As an example, the comparison between two cell types will be provided here . Fibroblasts are the cells characterized by highly organized internal structure with well-differentiated both actin and microtubule cytoskeleton (Fig. 4.15a). Actin filaments are dispersed within the entire cell but they are mostly concentrated in the cortex layer beneath the cell membrane. They are organized into two groups: (i) stress fibers visible as a long and thick fibers and (ii) short actin filaments whose presence is barely detected under the fluorescent microscope. Microtubules extend from location close to cell nucleus toward membrane. The length of these cytoskeletal elements can reach even more than 100 microns. The incubation of fibroblasts with 5 pg/ml cytochalasin D leads to depolymerization of actin filaments and, as a consequence, to more homogenous spatial distribution of actin filaments (no stress fibers visible, Fig. 4.15b).
Figure 4.15 The structure of (a) a single fibroblasts visualized using fluorescence microscopy (green—F-actin stained with phalloidin labeled with Alexa Fluor 488, red—microtubules labeled using two-step procedure involving antibody against в-tubulin followed by the secondary antibody labeled with Alexa Fluor-555, and blue—cell nucleus stained with Hoechst dye); (b) Actin cytoskeleton of living fibroblasts after incubation with 5 pg/ml cytochalasin D for 10 minutes at room temperature; (c) Surface topography of a single erythrocyte recorded using atomic force microscopy, accompanied by a scheme of its cytoskeleton being a network in which edges are spectrin filaments interconnected through various proteins (actin, protein 4.1, tropomyosin, etc.).
Erythrocytes are more homogenous as compared to fibroblasts (Fig. 4.15c). There is no nucleus and the cytoskeleton is composed of a filamentous meshwork of proteins that forms a membrane skeleton along the entire cytoplasmic surface of the membrane.
The cytoskeletal filaments are composed of spectrin, forming long, flexible heterodimers through the lateral association of a and b spectrins linked to junctional complexes composed of F- actin, protein 4.1, and actin-binding proteins (like tropomyosin or tropomodulin).
By the depth-dependent analysis of mechanical properties, the effect of cytoskeletal structure and organization on cellular elasticity can be explored. Figure 4.16 present the dependence of the average Young’s modulus calculated as a function of indentation depth for fibroblasts (red circles), erythrocytes (blue squares), and fibroblasts treated with cytochalasin D (dark cyan stars), respectively.
Figure 4.16 Elastic modulus plotted as a function of indentation depth for fibroblasts, erythrocytes, and fibroblasts treated with cytochalasin D agent (cytoD, final concentration of 5 pg/ml) leading to depolymerization of actin filaments). Modulus values correspond to indentation depths increasing by 200 nm and are presented as a mean value ± standard deviation, i.e., 4.85 ± 2.03 kPa, 1.38 ± 0.12 kPa, and 2.48 ± 1.49 kPa, for fibroblasts, erythrocytes and fibroblasts treated with cytochalasin D, respectively.
These relationships are fitted with the simple exponential decay function (y = y0 + A • exp(-ind/sj that enables to estimate the decay rate (expressed in pm-1) used to quantify the degree of cytoskeleton organization. The obtained values are 30.0 ± 0.3 pm-1, 38.2 ± 0.3 pm-1, 46.7 ± 0.2 pm-1 for fibroblasts, erythrocytes, and fibroblasts treated with cytochalasin D, respectively. As mentioned previously, the cytoskeleton of fibroblasts is highly heterogeneous while of erythrocytes is highly homogenous. The decay rate increases with homogeneity of the cytoskeleton organization.
Large values of standard deviation, observed for smaller indentation depths, are the manifestation of Young’s modulus distributions as it can be seen in Fig. 4.17 showing histograms for two limit values of the indentation depths, namely, 200 nm and 1400 nm. The widest distributions of elastic modulus are observed for small indentation depths (for instance, for 200 nm, Fig. 4.17a,c). Distributions become narrower with the increase of the indentation depth (for example, for 1400 nm, Fig. 4.17b,d). The depth-sensing analysis suggests that the very local AFM measurements of cell’s mechanical properties, carried out at high lateral and force resolution, detect small/minute changes in the organization of cytoskeletal network that can be explained by its filamentous nature.
Figure 4.17 Histograms of the relative values of Young’s modulus obtained for living fibroblasts (red columns), fibroblasts treated with cytochalasin D (dark cyan columns), and erythrocytes (red columns). Typical modulus distributions of a single cell obtained for indentation depths: 200 nm (a) and 1400 nm
(b). Elastic modulus distributions for cell populations obtained analogously (c, d for 200 and 1400 nm, respectively). Force versus indentation curves were fitted assuming that the AFM tip can be represented as a cone. Bin size = 0.5 kPa, n denotes either the number of force curves or cells taken for the analysis. Reprinted with permission from .
The observed heterogeneity in Young's modulus observed at small indentations depths can be explained by several phenomena, including non-homogenous cytoskeleton density, removal of a limited number of filaments composing the network or even disruption of cytoskeletal filaments induced by AFM indentations. The narrowing of histograms as indentation depths increases stems from the fact that for larger indentations the information on cell mechanical properties is gathered from a larger volume. In this limit, elastic modulus should reach constant level at very large indentations, above 1-2 microns. Distributions presented in Fig. 4.17 show also cell-type relationship. Fibroblasts, being the cells with highly differentiated cytoskeleton and heterogeneous organization of filaments, reveal wider distribution of the modulus values. The modulus distribution for erythrocytes is much narrower. The incubation of fibroblasts with cytochalasin D, an agent depolymerizing actin filaments, manifests in the narrowest modulus histogram. This relation is observed both when a single cell or a population of cells are considered (Fig. 4.17).
To quantify the observed changes, a comparative parameter R has been introduced by Pogoda et al. . It is defined as a ratio between the modulus values calculated for two limits of indentation depths: 1200 nm and 200 nm. In the original paper, its value was determined for randomly chosen single cells. Figure 4.18 shows parameter R distribution calculated for all studied cells (still being defined as a ratio E200 and E1200).
In the analysis, histograms corresponding to each studied cell type were created and to each one the Gauss function was fitted in order to get the center position of the distribution denoting the mean value. The comparison of the mean values ± standard deviations for all analyzed cell types is shown in Fig. 4.18b. Depending on the cell type, erythrocytes and fibroblasts, two distinct values of R parameter are observed as it was confirmed by the Student t-test (p < 0.001, at the 0.05 level). The treatment of fibroblasts with the cytochalasin D shows slight increase of the R value, accompanied by a low standard deviation value indicating high degree of homogeneity in elastic properties of cells. The Student t-test showed non-significant difference between non-treated and cytochalasin D treated fibroblasts which became statistically significant when compared with erythrocytes (at the 0.05 level).
Figure 4.18 (a) Exemplary distributions of a parameter R (defined as a ratio E1200 and E200) obtained for erythrocytes, fibroblasts, and fibroblasts treated with cytochalasin D. (b) Mean values of R parameter determined for a given cell sample types. Errors are standard deviations.
The largest difference between elastic modulus values for small and large indentation depths manifests in low R value. More homogenous internal cellular structure shows much smaller variations in the depth-dependent modulus values and thus R takes larger values, with the limit at 1 (when modulus is independent on the indentation depth). This case is observed for fibroblasts and erythrocytes. The treatment of fibroblasts with cytochalasin D increases R value, but still the internal structure inside such cell is far from being homogenous.