Torsion and curvature of FtsZ filaments

Abstract

FtsZ filaments participate in bacterial cell division, but it is still not clear how their dynamic polymerization and shape exert force on the underlying membrane. We present a theoretical description of individual filaments that incorporates information from molecular dynamic simulations. The structure of the crystallized Methanococcus jannaschii FtsZ dimer was used to model a FtsZ pentamer that showed a curvature and a twist. The estimated bending and torsion angles between monomers and their fluctuations were included in the theoretical description. The MD data also permitted positioning the curvature with respect to the protein coordinates and allowed us to explore the effect of the relative orientation of the preferred curvature with respect to the surface plane. We find that maximum tension is attained when filaments are firmly attached and oriented with their curvature perpendicular to the surface and that the twist serves as a valve to release or to tighten the tension exerted by the curved filaments on the membrane. The theoretical model also shows that the presence of torsion can explain the shape distribution of short filaments observed by Atomic Force Microscopy in previously published experiments. New experiments with FtsZ covalently attached to lipid membranes show that the filament on-plane curvature depends on lipid head charge, confirming the predicted monomer orientation effects. This new model underlines the fact that the combination of the three elements, filament curvature, twist and the strength and orientation of its surface attachment, can modulate the force exerted on the membrane during cell division.

Chiral twisting in a bacterial cytoskeletal polymer affects filament size and orientation

“…Although previous models have studied how MreB orientation is related to filament mechanics 23,35 , they have either assumed a non-twisted filament conformation 23 , or neglected the fact that membrane binding only occurs on a specific side of the filament 35 . Another related theoretical model for FtsZ filaments incorporated both twisting and membrane binding, but was limited to long filaments on flat membrane surfaces 36 . Our course-grained model suggests that the interplay between twist and binding may determine the filament lengths and orientation, thus providing an expanded view of MreB mechanics and ultrastructure.…”

Shape Selection of Surface-Bound Helical Filaments: Biopolymers on Curved Membranes

“…Our results show that, for surface bound biopolymers, their elasticity and chirality can combine in non-trivial ways with surface interactions and surface geometry to determine equilibrium morphology. For twisted filaments interacting with a flat surface, we previously showed [16] that there exists a critical interaction strength V ∞ = π 2 4 Kω 2 0 above which the filament exists in an untwisted, strongly bound configuration that maximizes the interaction energy at the for FtsZ [22,23]. From this one may estimate the torsional rigidity as [26] and that reasonable membrane charge densities under physiological conditions could give rise to V el ∼ 1 − 2k B T /nm for actin [16], we anticipate that V net /V ∞ could range from 0.2 to 1.5 for all cases considered.…”

“…Another interesting feature of this novel coupling emerges when we consider that filaments can have spontaneous curvature as well. A transition in the twist state can the be coupled to a reorientation or even the emergence of a plane of spontaneous curvature that can then lead to the exertion of forces [23]. It has been observed with AFM experiments on FtsZ polymerized on mica [27] that they can exist in two states -as long curved filaments or short straight filaments, which could arise from different torsional states in the two populations.…”

Guided by curvature: shaping cells by coupling curved membrane proteins and cytoskeletal forces

“…In bacteria, the condensation of constricting rings (usually of FtsZ proteins) can mark the locations for the recruitment of the cell-wall building machinery [102], which forms the septum that divides the cell or organelle. The FtsZ filaments possess spontaneous curvature [103,104], may induce constrictive forces [105], and therefore both bend the membrane and are affected by its curvature [106]. In mitochondria, such rings serve to recruit the cytoskeleton of the cell, to complete the fission process [107].…”