||FtsZ can exist in one of multiple states: inactivated monomer, activated monomer (GTP bound), nucleated (dimer of two activated FtsZ molecules), elongated polymer of three or more GTP bound FtsZ molecules.
The FtsZ molecules can move to states of higher and lower polymerization at rates obtained from Chen et al., 2005 and Surovtsev et al. 2008.
The maximum polymer length is a fittable parameter.
FtsZ polymerization is modeled using a set of differential equations modified from that described in Surovtsev et al. 2008, involving the activation, nucleation, and elongation of FtsZ polymers. The main modifications were that the equations were simplified to not include annealing and cyclization of ftsZ polymers.
This results in a distribution of filament lengths at each time step. Our simple model of cytokinesis takes in filaments of only 1 single length. Therefore, as an approximation, we assume that all FtsZ molecules in a polymer state of greater than or equal to 3 monomers can participate in the FtsZ ring. Using the total number of polymerized monomers, we determine the maximum number of full length filaments that can be formed.
Surovtsev, I.V., Morgan, J.J., Lindahl, P.A. (2008). Kinetic Modelling of the Assembly, Dynamic Steady State, and Contraction of the FtsZ Ring in Prokaryotic Cytokinesis. Plos CB 4: 1-19.
Chen, Y., Bjornson, K., Redick, S.D., Erickson, H.P. (2005). A rapid fluorescence assay for ftsZ assembly indicates cooperative assembly with a dimer nucleus. Biophysical journal 88: 505-514.
Li, Z., Trimble, M.J., Brun, Y.V., Jensen, G.J. (2007). The structure of FtsZ filaments in vivo suggests a force-generating role in cell division. EMBO 26: 4694-4708.
Anderson, D.E., Gueiros-Filho, F.J., Erickson, H.P. (2004). Assembly Dynamics of FtsZ Rings in Bacillus subtilis and Escherichia coli and Effects of FtsZ-Regulating Proteins. Journal of Bacteriology 186: 5775-5781.