Membrane Sculpting by F-BAR domains
Figure 1: Side and top views of a N-BAR and F-BAR domain dimer colored by monomer, in cartoon and vdW representations.
It remains unclear how membrane curvature depends on the type of F-BAR domain lattice arrangement. Two further open questions are: How do individual F-BAR domains interact with a membrane to form local curvature? What dynamics is involved in membrane curvature formation by F-BAR domain lattices?
The F-BAR domain binds and curves a membrane via scaffolding
Figure 2: Lipid membrane interaction with the wild type F-BAR (WT) domain (WT1) and F-BAR domain with positive charges on residues along the inner leaflet abolished (NC). WT binds to the membrane in 30 ns and generates a 28 nm radius of curvature within 100 ns. In the case of NC, the F-BAR domain does not bind to the membrane over 80 ns and the membrane remains flat. Membrane lipids are colored in grey; F-BAR proteins are colored in blue and orange to distinguish the monomers.
In simulation WT1, the wild type F-BAR domain binds to the membrane within 30 ns, at which moment most positively charged residues are in close contact with the negative charges on DOPS headgroups; at this point the membrane curvature gradually increases to reach a maximum within 100 ns. Several positively charged residues are found to form close contacts with negatively charged DOPS headgroups. Two clusters of positively charged residues, cluster 1 (residues Lys27, Lys30, Lys33, Lys110, Arg113, Lys114, Arg121, Arg122) located at the center of the F-BAR domain and represented by Lys114 and Lys33, and cluster 2 (residues Lys132, Arg139, Lys140, Arg146, Lys150) represented by Lys132 and located at the side helices of the F-BAR domain, are found to form extensive contacts with DOPS headgroups in the course of the simulation. Indeed, clusters 1 and 2 are important for binding and membrane curvature formation; mutation of the residues mentioned can abolish lattice formation (Frost et al., Cell, 132:807 (2008)); most of the stated residues are conserved in both their sequence and structural context across different species and different F-BAR domains.
Theoretical description of the membrane sculpting process
Binding of the F-BAR domain to the membrane leads to a match between shapes of F-BAR domain and membrane. The resulting membrane curvature depends on the balance of two forces, one resisting protein shape changes and the other resisting membrane curvature changes. The bending energy of an F-BAR domain dimer attached to the membrane surface (or any other attached rod-like protein) can be described through
The intrinsic curvature of the protein was determined as the mean curvature of the protein, namely Cp = 0.0283 nm-1, corresponding to a radius of curvature of 35.3 nm. The root-mean square fluctuation of the curvature of the protein was determined from its standard deviation from the average protein curvature and was found to be ΔCp = 0.0062 nm-1. The membrane bending modulus Kl had been measured, through experiments and simulations, to be 20 kBT. The radius of curvature of an F-BAR dimer on top of a lipid patch is then estimated to be 45.1 nm. This value compares well with the radius of curvature monitored during the last 100 ns of simulation WT1, which is 48.1 nm.
With the parameters stated above, one can estimate the total binding energy of WT1 F-BAR dimer and membrane patch at equilibrium to be 2.30 kBT, with the bending energy of F-BAR dimer and of membrane patch contributing 0.74 kBT and 1.56 kBT, respectively. The average membrane curvature during the early (i.e., phase 1) period 38-40 ns is 0.12 nm-1 and amounts to the highest membrane curvature during the binding phase. During this period the total energy of the F-BAR-membrane system, the bending energy of the F-BAR dimer and of the membrane patch are 3.99 kBT, 3.47 kBT and 0.52 kBT, respectively. During the later (i.e., phase 2) period 78-80 ns the average membrane curvature is 0.20 nm-1 and amounts to the highest membrane curvature during the membrane bending phase. During this period the total energy of the F-BAR-membrane system, the bending energy of the F-BAR dimer and of the membrane patch are 2.34 kBT, 0.90 kBT and 1.44 kBT, respectively. Therefore, the total energy that is stored in the protein conformational change during membrane binding and membrane bending phases is (3.47 - 0.90) kBT = 2.57 kBT.
Binding and close adhesion of the F-BAR domain to the membrane require shape complementarity between protein and membrane. In case that both protein and membrane shapes are radially symmetric, i.e., the centerline of either one obeys in the x, z-plane the equation x2 + z2 = R2, shape complementarity leads to membrane curvature 1/R. If the F-BAR domains are forming on top of the initially planar membrane a lattice oriented (with the protein major axes) along the x-axis then the planar membrane coils into a tube with its long axes pointing along the y-axis.
However, in case that the F-BAR domain does not assume a radial shape, shape complementarity results in an interesting variation. To demonstrate this we assume that the F-BAR domain prefers either intrinsically or through the effect of adhesion to the membrane an ellipsoidal shape governed by the equation (x/a)2 + (y/b)2 = 1 where a and b are the major and minor axis of the ellipse. In this case a membrane tube along the y-axis does not permit close adhesion as the radially symmetric membrane and the ellipsoidal F-BAR domain don't match exactly. However, a tube tilted by an angle β relative to the y-axis permits a perfect match of protein and membrane shape. To see this we note that, according to a well known result of geometry, the tilted tube is cut by the x, z-plane along an ellipsoid. One can convince oneself readily that this ellipse has a short axis b = R and a long axis a = R/cosβ. One can then conclude that for the assumed ellipsoidally shaped F-BAR domains (characterized by long axis a and short axis b), forming a lattice oriented along the x-axis on an initially planar membrane, a tube of curvature 1/R results with direction along an angle β relative to the y-axis, where β is given by
Membrane curvature generated by F-BAR domain lattices
In a series of SBCG simulations, we examined how the F-BAR domain density affects membrane curvature. As Figure 4 shows, of the F-BAR domain lattices with five different densities, the one with 10 dimers per 1000 nm2 achieves highest curvature; lattices with lower densities achieve much lower curvature. This result is expected since the denser the lattices are, the more the F-BAR domains can act on the same area of lipid. However, membrane curvature becomes also reduced when the F-BAR domain density gets too high, due to neighboring F-BAR domains hindering each others' access to the membrane. This hinderance of neighboring domains increases as domain density increases. The F-BAR domain density generating the narrowest tubules, as seen in cryo-EM (Frost et al., Cell, 132:807 (2008)), is 8 to 10 dimers per 1000 nm2.
Figure 3: Membrane curvature induced by lattices of F-BAR domains. Dependence of membrane curvature on F-BAR domain density (A), lattices of different angle (B), inter-dimer distance (C) and staggered or aligned arrangement of F-BAR domains (D).
The observed tilt angle β = 8o between y-axis and tube axis suggests that the actual shape of the F-BAR domain membrane adhesion surface is ellipsoidal with axes a = 1.01 R and b = R, i.e., the widening of the F-BAR domain shape is very small, but significant enough to induce an observable reorientation of the tube axis. To understand how a deviation from circular shape as reflected by a = 1.01 R can be significant one should note that the lattice of F-BAR domains averages over the shape effect of many proteins such that even minor effects add up to the tube axis tilt.
Membrane tubulation by F-BAR domain lattices
Figure 4: Membrane tubulation by lattices of F-BAR domains. (A) Initial conformation of lattices of F-BAR domains on the membrane in a SBCG representation. (B) Membrane tube formation with lattices of F-BAR domains. Shown are snapshots of membrane structures during the 350 μs simulation. Membrane lipids are shown in green; individual F-BAR domains are differentiated by color.
Equilibrated F-BAR domain pdb structure from WT1 simulation at 200 ns FBAR.pdb, 723k
Please cite this website and the following publication when using this structure.
Membrane Sculpting by F-BAR domains, http://www.ks.uiuc.edu/Research/FBAR.
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