Langevin computer simulations of FtsZ filaments: lateral interactions can generate force to drive bacterial cell division

FtsZ is a bacterial protein that forms filaments that play an essential role in midcell constriction during the process of cell division. The shape of individual filaments of different lengths imaged with atomic force microscopy was modeled considering the protein monomers as beads in a chain and a few parameters to represent their effective interactions. The flexural rigidity and persistence length of the filaments were estimated. This latter value was comparable to the filament length, implying that these biological polymers are halfway between the perfectly stiff linear aggregate whose shapes are fully controlled by the angle between the monomers and highly flexible polymers whose shapes follow a random walk model. The lateral interactions between adjacent filaments, also estimated in the modeling, were found to play an essential role in determining the final shape and kinetics of the coiled structures found in longer polymers. The estimated parameters were used to model the behavior of the polymers also on a cylindrical surface. This analysis points to the formation of helical structures that suggest a mechanism for force generation and amplification through the development of FtsZ spirals at the midcell division point