Bending forces plastically deform growing bacterial cell walls

Abstract

Cell walls define a cell's shape in bacteria. The walls are rigid to resist large internal pressures, but remarkably plastic to adapt to a wide range of external forces and geometric constraints. Currently, it is unknown how bacteria maintain their shape. In this paper, we develop experimental and theoretical approaches and show that mechanical stresses regulate bacterial cell wall growth. By applying a precisely controllable hydrodynamic force to growing rod-shaped Escherichia coli and Bacillus subtilis cells, we demonstrate that the cells can exhibit two fundamentally different modes of deformation. The cells behave like elastic rods when subjected to transient forces, but deform plastically when significant cell wall synthesis occurs while the force is applied. The deformed cells always recover their shape. The experimental results are in quantitative agreement with the predictions of the theory of dislocation-mediated growth. In particular, we find that a single dimensionless parameter, which depends on a combination of independently measured physical properties of the cell, can describe the cell's responses under various experimental conditions. These findings provide insight into how living cells robustly maintain their shape under varying physical environments.

Keywords: cell shape; defects; dislocation; elasticity; peptidoglycan.

Fig. 1.

Illustration of the experimental approach. Single E. coli or B. subtilis cells are inserted into microchannels 25 μm in length. The cross-section of the microchannels is square (∼1.2 μm × 1.2 μm) and the cells fit snuggly. Cell division is blocked to induce filamentation. The cells were grown typically up to 50 μm during measurements. Controlled hydrodynamic forces are exerted on the cells by the viscous drag of the growth media (Supporting Information).

Fig. 2.

Cells are deformed elastically by pulse-like forces. (A) Microscopy images of the E. coli cell from Movie S1 taken at different stages of the experiment. The cell initially grows straight out of the microchannel. We applied pulse-like flow to the straight cell repeatedly every several minutes (Upper). This resulted in completely reversible deformations (two examples are shown, Lower Left and Lower Right). (B) The tip positions (x, y) of the cell from multiple experiments are compared with the theoretical predictions of the linear elasticity theory (Supporting Information). An actual cell shape is superimposed on one of the theoretical curves.

Fig. 3.

Decoupling the two fundamental modes of deformation. (A, Lower) At t = 0–16 min, an E. coli cell is growing in the presence of a constant flow for a period comparable to the cell division time. The deformation represents the sum of elastic and plastic modes (Movie S2). At t = 17 min, as the flow is abruptly turned off, the elastic mode vanishes and the cell partly recoils. The residual deformation reflects the cumulative effect of force transduction, which resulted in differential growth of the cell wall. At 17 min, in the absence of the flow, the cell straightens gradually as it grows. (A, Upper) The length of the cell increases exponentially despite the large deflections induced by the external mechanical forces—the mass-doubling time does not change appreciably during the experiment and is comparable to that of nonfilamentous cells. (B) Scatter plot of the experimental results for the tip position as time progresses through the snap-back experiment from A.

Fig. 4.

Illustration of the differential growth driven by coupling between mechanical stress and cell wall synthesis. (A) Tensile (stretching) stress increases the processive motion speed of strand elongation machinery. Compressive stress has the opposite effect. Black arrows indicate the trajectories of activated dislocations. (B) Similarly, tensile stress will lower the activation energy for insertion of a new glycan strand, and compressive stress will increase it. (C) Asymmetric insertion of dislocations is enhanced by the large aspect ratio of the filamentous bacteria, leading to the large observed angular deflections.

Fig. 5.

Relative importance of elastic vs. plastic modes. The snap-back of the cell upon switching off the flow (Fig. 3), parameterized in terms of the slope of the tip position, as measured for 66 cells (33 E. coli and 33 B. subtilis) in differing growth conditions [see the key in the figure for growth media, temperature, and flow rate (1× being the maximal flow rate)]. For each snap-back, we quantified its magnitude by measuring the deflection angle ϕ of the tip before and after the snap-back. The snap-back angle is approximately proportional to the initial angle of deflection when the angles are small, confirming the prediction of the dislocation-mediated growth theory (Supporting Information). The ∼1/2 slope shows that the contributions by the two fundamental modes of deformation (elastic vs. plastic) are comparable with one another, regardless of the temperatures and growth conditions. Error bars are propagated from the uncertainty in calculating cell tip and channel end positions during image analysis.