Estimating the bending modulus of a FtsZ bacterial-division protein filament

FtsZ, a cytoskeletal protein homologous to tubulin, is the principle constituent of the division ring in bacterial cells. It is known to have force-generating capacity in vitro and has been conjectured to be the source of the constriction force in vivo. Several models have been proposed to explain the generation of force by the Z ring. Here we re-examine data from in vitro experiments in which Z rings formed and constricted inside tubular liposomes, and we carry out image analysis on previously published data with which to better estimate important model parameters that have proven difficult to measure by direct means. We introduce a membrane-energy-based model for the dynamics of multiple Z rings moving and colliding inside a tubular liposome and a fluid model for the drag of a Z ring as it moves through the tube. Using this model, we estimate an effective membrane bending modulus of 500–700   pN  nm. If we assume that FtsZ force generation is driven by hydrolysis into a highly curved conformation, we estimate the FtsZ filament bending modulus to be 310–390   pN  nm². If we assume instead that force is generated by the non-hydrolysis-dependent intermediate curvature conformation, we find that B_f>1400  pN  nm². The former value sits at the lower end of the range of previously estimated values and, if correct, may raise challenges for models that rely on filament bending to generate force.