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bioRxiv · 10.1101/2020.02.25.965095

Modelling FtsZ nucleation, hydrolysis and treadmilling activity with Monte Carlo methods

Corbin, L.·Erickson, H. P.
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Abstract

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 FtsZs assembly dynamics to treadmilling, where 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 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 single, small time steps, and 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 28 nm/s, hydrolyzed GTP at 2.8 to 4.2 GTP min-1 FtsZ-1, and had an average length of 25 to 54 subunits, all similar to experimental results. Adding a bottom capper resulted in shorter protofilaments and higher GTPase, similar to the effect of the known the 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. SIGNIFICANCEFtsZ assembly dynamics are now known to be governed by treadmilling, where subunits add to the bottom and dissociate from the top of protofilaments. We have generated a Monte Carlo model of treadmilling based on (a) a conformational transition of FtsZ subunits between two states, and (b) stochastic GTP hydrolysis. Importantly, the nucleation of new protofilaments is explained by the same mechanisms as treadmilling. We have determined kinetic parameters that match a wide range of experimental data. The model is available to users for their own in silico experiments.

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Corbin, L., Erickson, H. P.. 2020-02-25. Modelling FtsZ nucleation, hydrolysis and treadmilling activity with Monte Carlo methods. https://doi.org/10.1101/2020.02.25.965095

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