Polymerization and bundling kinetics of FtsZ filaments

Abstract

FtsZ is a tubulin homolog essential for prokaryotic cell division. In living bacteria, FtsZ forms a ringlike structure (Z-ring) at the cell midpoint. Cell division coincides with a gradual contraction of the Z-ring, although the detailed molecular structure of the Z-ring is unknown. To reveal the structural properties of FtsZ, an understanding of FtsZ filament and bundle formation is needed. We develop a kinetic model that describes the polymerization and bundling mechanism of FtsZ filaments. The model reveals the energetics of the FtsZ filament formation and the bundling energy between filaments. A weak lateral interaction between filaments is predicted by the model. The model is able to fit the in vitro polymerization kinetics data of another researcher, and explains the cooperativity observed in FtsZ kinetics and the critical concentration in different buffer media. The developed model is also applicable for understanding the kinetics and energetics of other bundling biopolymer filaments.

FIGURE 1

Schematic depictions of three simplified schemes of our kinetic model. (A) The activation step which converts Z to Z* is common to all three schemes. (B) The single-polymer scheme. The activated monomers form single filaments that can elongate, break, and anneal. The number of monomers or the length of the filament is computed in the model. (C) The simple-bundling scheme. The activated monomers can form filaments and bundles with two protofilaments. The lengths of the protofilaments are identical in the bundle; however, the filaments and bundles can break and anneal. (D) The multifilament scheme. The activated monomers can form filaments and bundles, although the model does not contain information about the longitudinal length. This scheme assesses whether bundles with more than two filaments are important during the timescales of the experiments.

FIGURE 2

(A) We propose that FtsZ can form three kinds of bonds, depending on whether one or both longitudinal interfaces are occupied. We denote the longitudinal bond energy of a monomer with a monomer that occurs in a dimer as U_p (top). The bond energy of a monomer at the tip of a filament is U_p + ΔU_t (center). The bond energy of monomers in the middle of a filament is U_p + ΔU_m (bottom). (B) The reaction rates and equilibrium constants are not independent. Here, a filament with four monomers can be formed in two ways. The relationships between the equilibrium constants are explained in the text.

FIGURE 3

Model results for L68W polymerizing in MMK buffer. Four initial concentrations of FtsZ are shown. The symbols are the experimental data of Chen et al. (20); the error bars show the spread of the data points. The solid lines are model results. All three schemes describe the data quite well, although the multifilament scheme is not as good as the single-polymer or the simple-bundling scheme. Average error per data point is 27.23 for the single polymer scheme, 23.01 for the simple-bundling scheme, and 23.77 for the multifilament scheme.

FIGURE 4

Model results for the simple-bundling scheme for L68W in all four buffer conditions. The initial concentrations of the FtsZ are shown. The symbols are the experimental data and the solid lines are the simple-bundling model results. The parameters obtained for these buffer conditions are summarized in Table 2.

FIGURE 5

Model results for the F268C mutant. The fitted short-time data are shown in the upper panels where the solid lines are model results and symbols are data from Chen and Erickson (21). Again the single-polymer and simple-bundling schemes can both explain the short-time data. For longer times (3 min), the length distributions computed from these schemes are different (lower panel). The solid line is the simple-bundling scheme and the dashed line is the single-polymer scheme. The bars are also from data in Chen and Erickson (21). The fitted parameters are shown in Table 3.

FIGURE 6

Distributions of single filaments and bundles obtained from the simple-bundling scheme for L68W in MMK after 3 min of reaction. (A) If the initial FtsZ monomer concentration is 2 μM, our model predicts that single filaments, not bundles, dominate the system. The single filament length is ∼80 nm. (B) If the concentration is >10 μM, bundles are the dominant species. Longer bundles (more than a micron) are stabilized by lateral interactions. This result is more relevant for in vivo conditions where FtsZ concentration in the cell is ∼7 μM.

FIGURE 7

Distributions of single filaments and bundles obtained from the simple-bundling scheme for F268C after 3 min of reaction. A similar behavior as L68W is seen. Although at 2 μM, there are hardly any bundles. At 10 μM, there is significant bundling and the concentration for longest bundles diverge. To fully converge the results with respect to N is computationally difficult. However, the results show that bundles eventually dominate.

FIGURE 8

Cooperativity during FtsZ assembly for L68W. The fluorescence of the polymers (left panel) and the monomer concentration (right panel) as functions of the total protein concentration are plotted for each buffer. These results are obtained from the simple-bundling scheme. All four panels show a clear critical concentration where formation of polymers becomes the more favored. The critical concentrations depend on the buffer and the model results are in accord with experimental data.