The dynamics of shapes of vesicle membranes with time dependent spontaneous curvature

We study the time evolution of the shape of a vesicle membrane under time-dependent spontaneous curvature by means of phase-field model. We introduce the variation in time of the spontaneous curvature via a second field which represents the concentration of a substance that anchors with the lipid bilayer thus changing the local curvature and producing constriction. This constriction is mediated by the action on the membrane of an structure resembling the role of a Z ring. Our phase-field model is able to reproduce a number of different shapes that have been experimentally observed. Different shapes are associated with different constraints imposed upon the model regarding conservation of membrane area. In particular, we show that if area is conserved our model reproduces the so-called L-form shape. By contrast, if the area of the membrane is allowed to grow, our model reproduces the formation of a septum in the vicinity of the constriction. Furthermore, we propose a new term in the free energy which allows the membrane to evolve towards eventual pinching.

Exploration of cell division times during bacterial cytokinesis

Filamenting temperature-sensitive mutant Z (FtsZ), an essential cell division protein in bacteria, has recently emerged as an important and exploitable antibacterial target. The perturbation of FtsZ assembly is found to have an effect on cell cytokinesis and cell survival. Cell division time is an important physical parameter in cell cytokinesis. Here, the theoretical framework that has been developed by combining a phase field model for rod-shaped cells with a kinetic description for FtsZ ring maintenance is extended to explore cell division times during bacterial cytokinesis. The cell division times of around 72 s in the numerical studies have the same magnitude as the division time of several minutes observed physiologically. The dependence of the cell division time on parameters such as the initial state of rod-shaped cells and various kinetic rates of FtsZ assembly dynamics is thoroughly investigated. The theoretical analysis of the relations between the cell division time and these parameters is found to coincide well with the numerical calculated results.

Phase-field modelling of the dynamics of Z-ring formation in liposomes: Onset of constriction and coarsening

We propose a model for the dynamics of the formation of rings of FtsZ on tubular liposomes which produce constriction on the corresponding membrane. Our phase-field model is based on a simple bending energy that captures the dynamics of the interplay between the protein and the membrane. The short-time regime is analyzed by a linear dispersion relation, with which we are able to predict the number of rings per unit length on a tubular liposome. We study numerically the long-time dynamics of the system in the non-linear regime where we observe coarsening of Z-rings on tubular liposomes. In particular, our numerical results show that, during the coarsening process, the number of Z-rings decreases as the radius of tubular liposome increases. This is consistent with the experimental observation that the separation between rings is proportional to the radius of the liposome. Our model predicts that the mechanism for the increased rate of coarsening in liposomes of larger radius is a consequence of the increased interface energy.

Effects of various kinetic rates of FtsZ filaments on bacterial cytokinesis

Cell morphodynamics during bacterial cytokinesis is extensively investigated by a combination of phase field model for rod-shaped cells and a kinetic description for FtsZ ring maintenance.