A Unified Model for Treadmilling and Nucleation of Single-Stranded FtsZ Protofilaments

Bacterial cell division is tightly coupled to the dynamic behavior of FtsZ, a tubulin homolog. Recent experimental work in vitro and in vivo has attributed FtsZ's assembly dynamics to treadmilling, in which subunits add to the bottom and dissociate from the top of protofilaments. However, the molecular mechanisms producing treadmilling have yet to be characterized and quantified. We have developed a Monte Carlo model for FtsZ assembly that explains treadmilling, and also explains assembly nucleation by the same mechanisms. A key element of the model is a conformational change from R (relaxed), which is highly favored for monomers, to T (tense), which is favored for subunits in a protofilament. This model was created in MATLAB. Kinetic parameters were converted to probabilities of execution during a single, small time step. These were used to stochastically determine FtsZ dynamics. Our model is able to accurately describe the results of several in vitro and in vivo studies for a variety of FtsZ flavors. With standard conditions, the model FtsZ polymerized and produced protofilaments that treadmilled at 23 nm/s, hydrolyzed GTP at 3.6-3.7 GTP min^-1 FtsZ^-1, and had an average length of 30-40 subunits, all similar to experimental results. Adding a bottom capper resulted in shorter protofilaments and higher GTPase, similar to the effect of the known bottom capper protein MciZ. The model could match nucleation kinetics of several flavors of FtsZ using the same parameters as treadmilling and varying only the R to T transition of monomers.