The consensus mechanics of cultured mammalian cells

Abstract

Although understanding cells' responses to mechanical stimuli is seen as increasingly important for understanding cell biology, how to best measure, interpret, and model cells' mechanical properties remains unclear. We determine the frequency-dependent shear modulus of cultured mammalian cells by using four different methods, both unique and well established. This approach clarifies the effects of cytoskeletal heterogeneity, ATP-dependent processes, and cell regional variations on the interpretation of such measurements. Our results clearly indicate two qualitatively similar, but distinct, mechanical responses, corresponding to the cortical and intracellular networks, each having an unusual, weak power-law form at low frequency. The two frequency-dependent responses we observe are remarkably similar to those reported for a variety of cultured mammalian cells measured with different techniques, suggesting it is a useful consensus description. Finally, we discuss possible physical explanations for the observed mechanical response.

Fig. 1.

Sketch of our four cell rheology techniques. From top to bottom, MTC measures the rocking motion of 4.5-μm-diameter tracers, adhered to the apical cell surface by integrins, in response to a sinusoidal magnetic torque. TPM measures the correlation of the random motion of pairs of endogenous tracers to infer the Brownian fluctuations of the intervening network. LTM measures the translational Brownian motion of the MTC tracers either phagocytosed into the cell interior or on the apical surface.

Fig. 2.

Typical data from our four methods on ATP-depleted TC7 epithelial cells (curves). (A) Shear modulus (normalized such that |G*(ω/2π = 5 Hz)| = 1) reported for ATP-depleted cells (closed symbols) compared with untreated cells (open symbols). (B) MSD reported by TPM, scaled to a 4.5-μm tracer. (C) Passive MSDs for phagocytosed 4.5-μm tracers. (D) Passive MSDs for external, integrin-adhered 4.5-μm tracers.

Fig. 3.

Normalized shear modulus for ATP-depleted cells collapse onto two master curves (offset by 2× for clarity). As discussed in the text, the upper curve is the TPM-like response, and the lower is the MTC-like response. The small black points are from single tracer external bead LTM trajectories, which can correspond to either curve. The squares are cell-averaged internal (phagocytosed) LTM data (n = 41), triangles are a typical single-cell MTC response, and open circles are cell-averaged TPM (n = 7). Dashed lines are best fits of Eq. 1 to data (upper curve: β₁ = 0.26, A = 0.51, B = 0.020; lower curve: β₂ = 0.17, A = 0.66, B = 0.009; both normalized at 10 rad/s). High-frequency line has slope 0.75.

Fig. 4.

Summary of literature shear moduli versus frequency, offset vertically for clarity. From top to bottom: mechanical measurements from cell creep (magnetic pulling) (13) (a), uniaxial rheometry (14) (b), atomic force microscopy (15) (c), LTM in the lamellae (6) (d), cell creep (magnetic bead twisting) (16) (e), MTC (8) (f), and optical tweezers (17) (g). All data are well fit to a sum of power laws (Eq. 2). Interestingly, magnetic pulling and uniaxial rheometry (a and b) results have fit slopes of 0.29 and 0.26 (comparable to our intracellular curve), respectively, whereas others (c–g) have slope of 0.16–0.18 (comparable to our cortical curve).

Fig. 5.

Comparison of ATP-depleted (filled symbols) and untreated TC7 cells (open symbols). (A) Typical external LTM data for tracers showing typical cortical (Upper) and intracellular (Lower) responses. The curves are offset by a factor of 4 and aligned at the shortest time point. (B) Averaged MSDs for internalized tracers by LTM; n = 23 cells (ATP−), n = 21 (control, ATP+). (C) Averaged MSDs reported by TPM (scaled to a 4.5-μm tracer); n = 7 (ATP−), n = 20 (control, ATP+). (D) The shear modulus (in Pa) at ω = 1000 rad/s. Error bars are log-normal standard errors.