The effect of remodelling and contractility of the actin cytoskeleton on the shear resistance of single cells: a computational and experimental investigation

Abstract

The biomechanisms that govern the response of chondrocytes to mechanical stimuli are poorly understood. In this study, a series of in vitro tests are performed, in which single chondrocytes are subjected to shear deformation by a horizontally moving probe. Dramatically different probe force-indentation curves are obtained for untreated cells and for cells in which the actin cytoskeleton has been disrupted. Untreated cells exhibit a rapid increase in force upon probe contact followed by yielding behaviour. Cells in which the contractile actin cytoskeleton was removed exhibit a linear force-indentation response. In order to investigate the mechanisms underlying this behaviour, a three-dimensional active modelling framework incorporating stress fibre (SF) remodelling and contractility is used to simulate the in vitro tests. Simulations reveal that the characteristic force-indentation curve observed for untreated chondrocytes occurs as a result of two factors: (i) yielding of SFs due to stretching of the cytoplasm near the probe and (ii) dissociation of SFs due to reduced cytoplasm tension at the front of the cell. In contrast, a passive hyperelastic model predicts a linear force-indentation curve similar to that observed for cells in which the actin cytoskeleton has been disrupted. This combined modelling-experimental study offers a novel insight into the role of the active contractility and remodelling of the actin cytoskeleton in the response of chondrocytes to mechanical loading.

Figure 1.

Schematic of cell and probe: (a) prior to indentation; (b) during shear indentation. Experimental image of cell and probe: (c) prior to indentation; (d) during shear indentation (probe and deflection δ are not to scale in (a) and (b)). (Online version in colour.)

Figure 2.

(a) SF formation in response to an exponentially decaying signal C, and generating tension T. (b) Cross-bridge cycling tension–velocity relationship for SFs. The solid curve corresponds to a fully activated SF. The dashed curve corresponds to an SF that has partially dissociated (0 < η > 1). (c) SF dissociation in response to tension reduction. (d) Cut-away view of a three-dimensional cell and nucleus geometry. Insets show SF distribution on two-dimensional sections at two points in the cell cytoplasm for illustrative purposes (note: distribution is actually predicted in three-dimensional space at every integration point in the cell cytoplasm). (e) The active SF and passive components of the model are placed in parallel and summed to give the total stress. (Online version in colour.)

Figure 3.

Experimental probe force–indentation data for: (a) untreated (diamonds, n = 8) and cyto-D (triangles, n = 8) cells; (b) untreated (diamonds, n = 8), acrylamide (squares, n = 8) and colchicine (circles, n = 8) cells. The data points represent the average force and indentation values for the experimental groups (mean ± s.d.). (Online version in colour.)

Figure 4.

Contour plots of the average SF activation levels : (a) at 30 s after signal initiation; (b) at 70 s after signal initiation; (c) at 1000 s after signal initiation. Contour plots of the variance (Π): (d) at 30 s after signal initiation; (e) at 70 s after signal initiation; (f) at 1000 s after signal initiation. A half cell is shown owing to symmetry.

Figure 5.

Contour plots of the average SF activation levels at a probe indentation of: (a) 1.5 µm; (b) 4.7 µm; (c) 10.9 µm. Contour plots of the variance (Π) at a probe indentation of: (d) 1.5 µm; (e) 4.7 µm; (f) 10.9 µm. A half cell is shown owing to symmetry.

Figure 6.

(a) Computational probe force–indentation curves for the active model (solid line; E_cyto = 1.5 kPa, T_max = 0.85 kPa, ); mean experimental untreated cell (diamonds, n = 8) data included for comparison. (b) Computational probe–force indentation curves assuming a passive hyperelastic (solid line) cell cytoplasm. Predictions are shown for three values of cytoplasm stiffness: 1.5, 4 and 8 kPa. (c) Parametric study of the effect of active parameters T_max and on predicted probe force–indentation curves (with E_cyto = 1.5 kPa). Diamonds, untreated cells (n = 8); triangles, cyto-D cells (n = 8). (d) Computational probe force–indentation curve for the active model with reduced cytoplasm stiffness (solid line; E_cyto = 0.03 kPa, T_max = 0.85 kPa, ), and experimental probe force–indentation data (mean ± s.d.) for acrylamide (squares, n = 8) and colchicine (circles, n = 8) treated cells. (Online version in colour.)

Figure 7.

(a) Representative brightfield and fluorescent image (bottom-up view) of a cell before shear deformation, with nuclei (blue) and actin (red) shown at a focal plane near the base. (b) Predicted distribution of the actin cytoskeleton before shear deformation for the active model (E_cyto = 1.5 kPa, T_max = 0.85 kPa, ). (c) Representative brightfield and fluorescent image (bottom-up view) of a cell after shear deformation. (d) Predicted distribution of the actin cytoskeleton following 10.9 µm of probe indentation. The arrow indicates the direction of probe movement.