Theoretical Prediction of Disrupted Min Oscillation in Flattened Escherichia coli

Abstract

The dynamics of the Min-protein system help Escherichia coli regulate the process of cell division by identifying the center of the cell. While this system exhibits robust bipolar oscillations in wild-type cell shapes, recent experiments have shown that when the cells are mechanically deformed into wide, flattened out, irregular shapes, the spatial regularity of these oscillations breaks down. We employ widely used stochastic and deterministic models of the Min system to simulate cells with flattened shapes. The deterministic model predicts strong bipolar oscillations, in contradiction with the experimentally observed behavior, while the stochastic model, which is based on the same reaction-diffusion equations, predicts more spatially irregular oscillations. We further report simulations of flattened but more symmetric shapes, which suggest that the flattening and lateral expansion may contribute as much to the irregular oscillation behavior as the asymmetry of the cell shapes.

Multistability and dynamic transitions of intracellular Min protein patterns

“…In addition, some pattern transitions were observed during instances of drastic switching of cell axes that are associated with a low aspect ratio of the cell shapes (Fig G and Video EV5), similar to examples shown previously (Corbin et al , ; Männik et al , ). This phenomenon was explained previously by invoking theoretical predictions that low aspect ratios should lead to a transient coupling between longitudinal and transverse modes (Halatek & Frey, ) and Min patterns in these shapes are more sensitive to stochastic perturbations (Fange & Elf, ; Schulte et al , ). The above scenarios show that pattern multistability can emerge through adaptation of persistent Min oscillations during different modes of cell growth.…”

“…In the present paper, our study of the Min oscillations throughout the growth history of the cells revealed a remarkable persistence in the face of boundary changes induced by cell growth. This phenomenon could not be deduced from previous studies on the Min system, which showed various degrees of fluctuations in cells with certain degrees of asymmetry and enlargement (Corbin et al , ; Fange & Elf, ; Varma et al , ; Männik et al , ; Hoffmann & Schwarz, ; Schulte et al , ). Indeed, although Min oscillations do fluctuate in our experimental settings, they rarely undergo drastic switches even during periods of growth that increase the cell volume by up to 20‐fold.…”

The mechanism of MinD stability modulation by MinE in Min protein dynamics

“…Most mathematical models of MinDE dynamics are based on a subset of the reactions described above, and generally their aim has been to recapitulate behaviors of the Min system in vivo. They have successfully demonstrated oscillatory behaviors particular to short cells [12,34], mid-sized cells [35][36][37][38][39][40], long cells [34,36,38,[40][41][42], dividing cells [40,[42][43][44], aberrant cellular geometries [16,34,[45][46][47][48], and MinE mutants [49,50]. Several mathematical models have recapitulated behaviors of the Min system in vitro, including traveling waves [21,51] and spiral waves [21,34] on supported lipid bilayers and patterning on geometrically confined membranes [52] and micropatterned substrates [53].…”

The mechanism of MinD stability modulation by MinE in Min protein dynamics

“…Most mathematical models of MinDE dynamics are based on a subset of the reactions described above, and generally their aim has been to recapitulate behaviors of the Min system in vivo. They have successfully demonstrated oscillatory behaviors particular to short cells [12,4], mid-sized cells [16,34,29,43,51], long cells [34,26,33,47,4,51], dividing cells [47,44,10,51], aberrant cellular geometries [27,11,13,4,48,41], and MinE mutants [8,2]. Several mathematical models have recapitulated behaviors of the Min system in vitro, including traveling waves [32,37] and spiral waves [32,4] on supported lipid bilayers and patterning on geometrically confined membranes [42] and micropatterned substrates [15].…”