Morphology, Growth, and Size Limit of Bacterial Cells

Bacterial cells utilize a living peptidoglycan network (PG) to separate the cell interior from the surroundings. The shape of the cell is controlled by PG synthesis and cytoskeletal proteins that form bundles and filaments underneath the cell wall. The PG layer also resists turgor pressure and protects the cell from osmotic shock. We argue that mechanical influences alter the chemical equilibrium of the reversible PG assembly and determine the cell shape and cell size. Using a mechanochemical approach, we show that the cell shape can be regarded as a steady state of a growing network under the influence of turgor pressure and mechanical stress. Using simple elastic models, we predict the size of common spherical and rodlike bacteria. The influence of cytoskeletal bundles such as crescentin and MreB are discussed within the context of our model.

Figure 1

The bacterial cell wall is a growing network of PG strands. PG subunits are inserted at random points along the cell by enzymes. The network is also under mechanical stress from turgor pressure and cytoskeletal influences. The cartoon shows the reversible assembly reaction where the cell wall area increases from $A$ to $A+dA$. The net energy change of the reaction has a chemical component and a mechanical component [Eq. (1)]. The dotted line is the reaction energy without mechanical contributions, and the solid line includes the mechanical energy.

Figure 2

(a) The free energy of a spherical bacteria as a function of radius $R$. (b) The growth velocity of a spherical bacteria vs bacteria radius. The parameters are $P=0.2\mathrm{MPa}$, $E=50\mathrm{MPa}$, $\nu =0.3$, $h=7\mathrm{nm}$, $ϵ=0.05\mathrm{J}{\mathrm{m}}^{-2}$, and $M=0.01{\mathrm{m}}^2{\mathrm{J}}^{-1}{\mathrm{s}}^{-1}$.

Figure 3

The time evolution of the radius and length of rodlike bacteria with varying initial radius. The inset of (b) is the growth velocity in the axial direction. The parameters are $P=0.2\mathrm{MPa}$, $E=50\mathrm{MPa}$, $\nu =0.3$, $h=7\mathrm{nm}$, $ϵ=0.05\mathrm{J}{\mathrm{m}}^{-2}$, and $M=0.01{\mathrm{m}}^2{\mathrm{J}}^{-1}{\mathrm{s}}^{-1}$. The cell lengths as functions of time in (b) are almost indistinguishable. (b) can be compared with experimental measurements in Ref. 20.

Figure 4

(a) The growth velocity in axial direction for rodlike bacteriavs the steady radius $R_s$. Larger cells grow faster, although the $(R_s,ϵ)\to 0$ limit is unphysical and should not be considered. The parameters are the same as Fig. 3. (b) MreB (red line) can be modeled as an additional mechanical influence on the cell wall. By solving Eq. (5), we observe that the shape of the cell can slowly morph from a sphere to a rod, in agreement with experimental observations.