Whole cell mechanics of contractile fibroblasts: relations between effective cellular and extracellular matrix moduli

Abstract

While much is known about the subcellular structures responsible for the mechanical functioning of a contractile fibroblast, debate exists about how these components combine to endow a cell with its form and mechanical function. We present an analysis of mechanical characterization experiments performed on bio-artificial tissue constructs, which we believe serve as a more realistic testing environment than two-dimensional cell culture. These model tissues capture many features of real tissues with the advantage that they can be engineered to model different physiological and pathological characteristics. We study here a model tissue consisting of reconstituted type I collagen and varying concentrations of activated contractile fibroblasts that is relevant to modelling different stages of wound healing. We applied this system to assess how cell and extracellular matrix (ECM) mechanics vary with cell concentration. Short-term and long-term moduli of the ECM were estimated through analytical and numerical analysis of two-phase elastic solids containing cell-shaped voids. The relative properties of cells were then deduced from the results of numerical analyses of two-phase elastic solids containing mechanically isotropic cells of varying modulus. With increasing cell concentration, the short-term and long-term tangent moduli of the reconstituted collagen ECM increased sharply from a baseline value, while those of the cells decreased monotonically.

Figure 1.

Logarithmic relaxation curves following stretches of a ring-shaped tissue construct specimen to strains of 2% and 8%. Specimens were stretched rapidly by a gravity loading (over 10–15 ms) first to a nominal strain of ε=0.02 (filled circles), and then, after a 3600 s relaxation period, to a nominal strain of ε=0.08 (open circles).

Figure 2.

Representative FE discretizations of cells within FE meshes of tissue constructs containing (a) a low cell concentration and (b) a high cell concentration, in which the same number of cells is now confined to a smaller volume.

Figure 3.

FE simulations of the ratio of tissue elastic modulus, E_t, to ECM modulus, E_m, for m≤1. Error bars represent the standard deviation of four FE simulations and dashed lines correspond to the two-parameter fitting function (equation (4.2)).

Figure 4.

FE simulations (filled circles) of the ratio of tissue elastic modulus, E_t, to ECM modulus, E_m, for (a) m=10, (b) m=100 and (c) m=1000. Error bars indicate the standard deviations of four FE simulations, solid lines correspond to the three-point bounds for overlapping spheres, dashed lines represent two-point bounds and dotted lines show the estimates for the elastic modulus. Shaded portion, Hashin–Shtrikman bounds.

Figure 5.

(a) Short-term (10 ms post-stretch) and (b) long-term (3600 s post-stretch) moduli of ECM (triangles) and cells (circles) in a tissue construct, calculated from experiments. The trend lines for entire tissue constructs (dash-dotted lines) and deoxycholate-treated constructs (dotted lines) are curve fits; the trend lines for ECM (solid lines) and cellular (dashed lines) moduli are derived mathematically from the curve fits for entire tissue constructs and deoxycholate-treated constructs.