Biophysical and Geometric Regulation of Bacterial Cell Morphology

Abstract

Bacterial cell morphology is governed by an interplay of cytoskeletal dynamics, mechanical forces, and stochastic processes. This study investigates size and shape homeostasis in rod-shaped Escherichia coli by integrating high-resolution microscopy, quantitative image analysis, mechanical modeling, and statistical analysis. We quantify the scaling of bacterial morphology in terms of surface area (SA) and volume (V) using quantitative phase contrast microscopy sampling E. coli cells from mid-log culture. We find that the scaling exponent of 𝑆𝐴 ∼ 𝑉𝛾 results in higher-than-geometric scaling 𝛾 > 0.66. Increased variability, especially in cell length in fast growing conditions, further changes the scaling exponent, while the effects of cell width variability are minor. Time series analysis of growing cells show similar SA-V scaling where 𝛾 ∼ 0.8, implying comparable scaling behavior in population and time-resolved measurements. In order to answer the question whether population-level and single-cell time-series data are interchangeable in cell size analysis, we compare time-resolved single-cell trajectories with static population snapshots. We find high values of comparability scores, indicating cell size distributions are ergodic under steady-state growth. The allometric scaling exponent observed can be explained by a model of width increase and saturation which we proceeded to examine in terms of the mechanical basis of size regulation. We analysed de-regulated bulging (blebbing) of cells inhibited for MreB and PBP2 using A22 and cephalexin respectively. We estimate total and turgor pressure to be ∼ 0.56 and 0.15 MPa respectively and the bending rigidity to be ∼ 0.22 MPa 𝜇𝑚3, which were obtained by fitting a shell-mechanics model to cell shape dynamics from both literature and our experiments. Comparing simulations to experiments with treated cells reveal a threshold bending rigidity (< 0.1 MPa 𝜇𝑚3) results in failure of cell size homeostasis and bulging. We combine the model of width growth and compare three phenomenological models of bacterial size control: sizer, adder and timer. These specify that cells either divide at a critical size, or after adding a fixed amount of growth, or at a fixed time interval. By comparing single-cell growth data on agarose pads to simulation predictions that include width saturation, we find that E. coli behaves like a length-sizer but volume-adder, falsifying the conventional length adder model for E. coli. Thus, bacterial cell size homeostasis arises from an interplay of cell length and width regulation. To summarize, these results provide a unified framework linking molecular-scale feedback, me- chanical stability, and statistical properties, offering insight into bacterial size and shape regulation.