Microrheology of human lung epithelial cells measured by atomic force microscopy

Abstract

Lung epithelial cells are subjected to large cyclic forces from breathing. However, their response to dynamic stresses is poorly defined. We measured the complex shear modulus (G(*)(omega)) of human alveolar (A549) and bronchial (BEAS-2B) epithelial cells over three frequency decades (0.1-100 Hz) and at different loading forces (0.1-0.9 nN) with atomic force microscopy. G(*)(omega) was computed by correcting force-indentation oscillatory data for the tip-cell contact geometry and for the hydrodynamic viscous drag. Both cell types displayed similar viscoelastic properties. The storage modulus G'(omega) increased with frequency following a power law with exponent approximately 0.2. The loss modulus G"(omega) was approximately 2/3 lower and increased similarly to G'(omega) up to approximately 10 Hz, but exhibited a steeper rise at higher frequencies. The cells showed a weak force dependence of G'(omega) and G"(omega). G(*)(omega) conformed to the power-law model with a structural damping coefficient of approximately 0.3, indicating a coupling of elastic and dissipative processes within the cell. Power-law behavior implies a continuum distribution of stress relaxation time constants. This complex dynamics is consistent with the rheology of soft glassy materials close to a glass transition, thereby suggesting that structural disorder and metastability may be fundamental features of cell architecture.

FIGURE 1

Illustration of the experimental process. The solid and dashed lines show an example of a force-displacement (F-z) curve recorded in the central region of an A549 cell before sinusoidal oscillation measurements. The F-z curve shows the force measured while the piezotranslator was extended (solid line) toward the cell and retracted (dashed line) at constant velocity (6 μm/s). This curve exhibits hysteresis indicative of viscoelasticity. The retracted limb shows unspecific adhesion before the tip-cell contact was lost (F < 0). The arrow indicates the estimated contact point (z_c). The complex shear modulus was computed from low amplitude (50 nm) sinusoidal oscillations (0.1–100 Hz) taken at different operating points (∼0.1–0.9 nN).

FIGURE 2

Fourier components at the oscillation frequency, corrected for the viscous drag, of force-indentation (F-δ) loops measured at different frequencies at mean operating force F_o ∼ 0.53 nN and indentation depth δ_o ∼ 760 nm. The loops became steeper and exhibited larger hysteresis as frequency increased. Data were obtained in the same cell as in Fig. 1.

FIGURE 3

Frequency dependence of the storage modulus G′ (filled symbols) and the loss modulus G″ (open symbols) measured on A549 cells (N = 12) and on BEAS-2B cells (N = 7) at different oscillation frequencies. Data are mean ± SE. Solid lines are the fit of the power-law structural damping model (Eq. 8) (r² = 0.95 and 0.99 for A549 and BEAS-2B, respectively). The fitted power-law exponent (α) was 0.22 for A549 and 0.20 for BEAS-2B. The Newtonian coefficient of the model (μ) was 1.68 and 2.69 Pa·s for A549 and BEAS-2B cells, respectively.

FIGURE 4

Frequency dependence of the loss tangent G″/G′ (filled symbols) measured on A549 and BEAS-2B cells. Data are mean ± SE. Solid line is the loss tangent obtained from the fit of the structural damping model (Eq. 8). The measured loss modulus corrected for the fitted Newtonian viscosity ((G″ − ωμ)/G′) (open symbols) conformed very well to the fitted constant hysteresivity of the model (η = tan(απ/2)) (dashed line). The value of η was 0.36 and 0.33 for A549 and BEAS-2B cells, respectively.