Direct Measurement of Cell Wall Stress Stiffening and Turgor Pressure in Live Bacterial Cells

We study intact and bulging Escherichia coli cells using atomic force microscopy to separate the contributions of the cell wall and turgor pressure to the overall cell stiffness. We find strong evidence of power-law stress stiffening in the E. coli cell wall, with an exponent of $1.22\pm 0.12$, such that the wall is significantly stiffer in intact cells ($E=23\pm 8\mathrm{MPa}$ and $49\pm 20\mathrm{MPa}$ in the axial and circumferential directions) than in unpressurized sacculi. These measurements also indicate that the turgor pressure in living cells E. coli is $29\pm 3\mathrm{kPa}$.

Figure 1

(a) Schematic cartoon illustrating the bulging E. coli and AFM stiffness measurement. The magnified region shows the details of the inner membrane (IM), peptidoglycan (PG) network and the outermembrane (OM). (b) Typical force-indentation traces obtained by indenting a cell and bulge. (c) Cytoplasmic GFP (green) is able to occupy both the cell and bulge interiors, indicating the ability of protein–sized objects to transverse the pore. (d) A membrane stain (FM4-64, red) labels the outer membrane. (e) Overlay of the cytoplasmic EGFP and membrane stain. Scale bar is $1\mu \mathrm{m}$. (f) Cell stiffness shows little variation before the bulging event (arrow) at which point it drops suddenly.

Figure 2

Model of a fluidic membrane bulge under a force $F$ exerted by a conical indenter. (a) The total deformation of the bulge consists of a global deformation, $h_{\mathrm{global}}$, a local dent $h_{\mathrm{dent}}$ and the contact height $h_{\mathrm{cone}}$. The dashed line is a sphere of radius equal to the bulge waist. (b) The dimensionless force-indentation relation is nearly linear. Inset: dimensionless stiffness vs indentation.

Figure 3

Bulging cell radius $R_c$ and indentation stiffness $k_c$ are plotted against cell turgor pressure $P$. Data from 72 bulged cells are binned in 10 logarithmically spaced bins using weights from the relative error estimates of the individual indentation traces and fluorescent images (blue crosses). Data from 42 nonbulged cells are plotted as black open squares. Red lines indicate the best fit of the stress-stiffening model along with 68% confidence intervals.

Figure 4

Simulated value of reduced cell indentation stiffness $k_c/P{R}_c$ against the reduced inflation magnitude $P{R}_c/E_{\perp }t$ for different orthotropic ratios of the stretching elasticity in the axial direction to the circumferential directions, $E_{\parallel }/E_{\perp }$. (inset) The result of a single simulation. One quadrant of the indented cylinder is shown, with color labeling the displacement in the indentation direction. The black wire frame shows the undeformed, unpressurized capsule.