Mechanisms of negative membrane curvature sensing and generation by ESCRT III subunit Snf7

Abstract

Certain proteins have the propensity to bind to negatively curved membranes and generate negative membrane curvature. The mechanism of action of these proteins is much less studied and understood than those that sense and generate positive curvature. In this work, we use implicit membrane modeling to explore the mechanism of an important negative curvature sensing and generating protein: the main ESCRT III subunit Snf7. We find that Snf7 monomers alone can sense negative curvature and that curvature sensitivity increases for dimers and trimers. We have observed spontaneous bending of Snf7 oligomers into circular structures with preferred radius of ~20 nm. The preferred curvature of Snf7 filaments is further confirmed by the simulations of preformed spirals on a cylindrical membrane surface. Snf7 filaments cannot bind with the same interface to flat and curved membranes. We find that even when a filament has the preferred radius, it is always less stable on the flat membrane surface than on the interior cylindrical membrane surface. This provides an additional energy for membrane bending which has not been considered in the spiral spring model. Furthermore, the rings on the cylindrical spirals are bridged together by helix 4 and hence are extra stabilized compared to the spirals on the flat membrane surface.

1. INTRODUCTION

Membrane remodeling in living organisms is implicated in a large number of cellular processes and controls various key cellular functions.1, 2, 3, 4, 5, 6, 7, 8 Two main mechanisms of membrane remodeling are amphipathic helix insertion and scaffolding.9, 10, 11 Amphipathic helices are thought to deform the membrane by a wedging mechanism whereby hydrophobic residue insertion into the membrane provides an asymmetric stress to the membrane bilayer, leading to its deformation.12, 13, 14 This mechanism generates positive membrane curvature. In the scaffolding mechanism, proteins with specific shape and curvature bind to the membrane surface and bend the membrane according to the curvature of themselves or their oligomers. This mechanism can generate positive or negative membrane curvature.15, 16, 17, 18 A third mechanism of membrane deformation that generates positive curvature is protein–protein crowding. When proteins adsorb on the membrane surface at sufficiently high density, steric repulsion between them generates lateral pressure which leads to membrane deformation.19, 20, 21, 22, 23 Intrinsically disordered proteins, which have been recognized as potent membrane curvature generators, presumably operate through the crowding mechanism.24, 25 Integral membrane proteins and lipid composition can also generate membrane curvature.26 Some proteins show a binding preference for some specific membrane curvature and hence act as curvature sensors. Some examples include ArfGap1, α synuclein, septin, spoV, and so forth.27, 28, 29, 30, 31

Membrane curvature generation and sensing are thermodynamically linked and are often studied together. Experimental tools like fluorescence imaging and microscopy, transmission EM and cryo‐EM have provided valuable insights in this field.32, 33, 34, 35, 36, 37, 38, 39, 40, 41 However, a molecular‐level understanding is still missing. The study of negative curvature sensing and generating peptides poses some additional challenges, as the same experimental set up for positive membrane curvature might not work for negative curvature.42 Curvature sensing behavior can be measured experimentally by pulling out tubes from Giant unilamellar Vesicles (GUVs) exposed to a protein solution43 using optical tweezers or by conducting protein binding assays on different size vesicles (flotation assay method44, 45, 46 or single liposome curvatures [SLiC] assay).47 However, inward tubes cannot be drawn by optical tweezers and trapping proteins inside vesicles to study their negative curvature sensing behavior is difficult. Computationally intensive all‐atom and coarse‐grained simulations have focused mostly on positive curvature generating peptides, such as BAR domains48, 49, 50, 51, 52 with only a few examining the negative curvature generating I‐BARs.53, 54, 55 Curvature sensing using a buckled membrane has been developed56, 57 but this method is not convenient for large proteins or a large number of proteins and the results are mostly qualitative.

The Endosomal Sorting Complex Required for Transport (ESCRT) is a membrane remodeling and scission machinery which regulates various cellular activities like multivesicular body (MVB) biogenesis, viral budding, cytokinesis, etc.58, 59, 60 ESCRTs are multi‐component protein complexes, categorized as ESCRT‐0, ESCRT‐I, ESCRT‐II, ESCRT‐III, VPS4 complex and Bro1.61, 62 The yeast sucrose nonfermenting protein 7 (Snf7) and analogous proteins in other eukaryotes63 are the most populous subunits in ESCRT‐III.64 The core domain of Snf7 consists of 140 residues with four α‐helices.65 In its activated form, the second and third helices fuse together and form an extended helix. The C‐terminal domain on the other hand is largely unstructured and contains a short α5 helix. This helix is involved in auto‐inhibition by interacting with the core domain.66 A number of membrane binding experiments and mutation studies suggested Snf7 binds only to negatively charged membranes with an interface that has positively charged residues. Hence, electrostatic interaction is the major driving force for membrane binding. The substitution of positively charged residues by negatively charged ones in helix 1 halted membrane binding by just 10%67 but charge inversion on helix 2 and helix 3 drastically changed cargo sorting. The N‐terminal amphipathic helix was also found to have a prominent role in membrane binding. Deletion of this helix resulted in decreased efficiency of cargo sorting to the vacuole as much as 87%.67

Atomic force microscopy and electron microscopy have revealed filaments of Snf7 organized in concentric circular structures.68, 69 The “spiral spring” model proposes that the elastic energy of the rings with suboptimal curvature drives membrane invagination.70 However, the molecular structure of these circular oligomers is not yet available. Another important question is whether the proteins bind with the same or different interface to curved and planar membranes. If they bind with the same interface, there must be some rearrangement on going from a concentric circular structure to a spiral structure. There is some experimental evidence that Snf7 is curvature sensing. CHMP4B, a mammalian protein analogous to Snf7, shows six‐ to nine‐fold higher binding to membrane invaginations than to the planar membranes composed of 82% POPE, 15% POPS and 3% PIP2.68 However, it is not clear whether curvature sensitivity is intrinsic to the Snf7 monomers or it arises from its oligomeric structure.

In the present work, we use an implicit membrane model adapted to curved membranes71 to study the binding of Snf7 monomers and oligomers to planar, tubular, and spherical anionic membranes of different curvature. We find that the monomer by itself is curvature sensing but oligomerization also enhances curvature sensitivity. The main driving force for membrane remodeling is not the suboptimal curvature of the planar spirals but the enhanced binding affinity to negatively curved membranes.

2. RESULTS

2.1. Binding configuration, energetics and curvature sensitivity of the Snf7 monomer

The crystal structure of Snf765 is shown in Figure 1 with the putative membrane binding interface highlighted. It can be seen that positively charged Lys or Arg residues are distributed along a convex curvature which would better interact with a negatively curved membrane surface, if the peptide were rigid enough to maintain that structure. This structure corresponds to the open, activated conformation where helices 2 and 3 have joined into one.65 Snf7 peptides cannot bind to the membrane surface in the absence of anionic lipids, suggesting that binding is largely electrostatic.68 Our implicit membrane simulations of the Snf7 monomer also indicated that the peptide does not bind onto a neutral membrane but bind moderately strongly onto 30% anionic membranes. Thus, all results below refer to anionic membranes.

Figure 1.

(a) Structure of the Snf7 core domain. The lower side represents the membrane binding interface. The positively charged residues LYS and ARG are shown in stick representation. (b) The number of residues in different helices

The binding configuration of monomeric snf7 on a flat membrane agrees with expectations from the crystal structure (Figure 2a). The electrostatic contribution of positively charged residues from helix 2/3 to membrane binding is ~4.8 kcal/mol whereas that of helix 1 is ~2.2 kcal/mol (Table S1). This is consistent with mutation experiments where inversion of charges on helix 2/3 affected membrane binding more than those on helix 1.67 Helix 2/3 tilts ~16° from the membrane plane. One end of the protein has a larger concentration of positive charges in comparison to the other, which makes one end interact more strongly than the other. Although the weakly interacting end has three positive charges, there is also substantial repulsion due to nearby negatively charged residues Asp122 and Glu109. This result is consistent with a recent all‐atom simulation,72 where the orientation with helix 2/3 closer to the membrane gave stronger binding.

Figure 2.

Typical binding configuration of Snf7 monomer on a flat membrane (a), inside a spherical membrane of 30 nm radius (b) and with N‐terminal on a flat membrane (c). All figures are after 20 ns simulation

The binding energies of the Snf7 monomer on the inner and outer surfaces of spherical membranes of different radii are presented in Table 1. Inside the 10 nm sphere, Snf7 changed back to the inactivated conformation where the long 2–3 helix breaks into separate helices. In Table 1, it can be seen that Snf7 prefers negative curvature from radii 30 nm to 50 nm. This result is consistent with AFM and other experimental results that show a curvature preference of ~25 nm.69 The binding energies on the exterior surface are about 1 kcal/mol smaller than those for the interior surface. Of course, for very large sphere, there is no distinction between outer and inner spherical surface as expected.

Table 1.

Binding energies (kcal/mol) of Snf7 monomer on spherical membranes of different curvatures

Radii	10 nm	20 nm	30 nm	40 nm	50 nm	60 nm	150 nm	α b
Outside	−4.5 ± 1.0	−4.2 ± 0.7	−4.4 ± 0.8	−4.1 ± 0.9	−4.2 ± 0.9	−4.0 ± 1.0	−4.7 ± 0.7	−0.45 ± 0.31
Inside	a	−4.6 ± 0.1	−5.1 ± 0.3	−4.9 ± 0.5	−5.2 ± 0.3	−4.5 ± 0.7	−4.6 ± 0.1	0.55 ± 0.35

^aProtein changes to “closed” conformation.

^b30–150 nm radii are considered for the calculation of α.

To obtain a quantitative measure of curvature sensitivity, we calculated the parameter α defined by the equation below71:

$$\mathrm{\Delta }G°=\text{constant}+\alpha \times \mathrm{RT}\times \ln r$$ (1)

Since in most of our cases the maximal binding were at 30 nm radius, α was calculated from the data of 30–150 nm radii. The results are tabulated in the last column of Table 1. It can be seen that α is negative for the outside surface of sphere, indicating that the protein is repelled by positive curvature. The positive curvature sensitivity parameter of 0.55 for the interior surface shows a clear preference for negative curvature.

An additional, indirect way of assessing curvature sensitivity of the peptides is by determining the binding orientation on a cylindrical membrane. If the peptide prefers a curved surface, it tends to orient away from the axis of the tube. Hence, Snf7 monomers were simulated on cylindrical membranes of different curvatures, initially placed perpendicular or parallel to the tube axis. The average angles over the last 0.5 ns of a 10‐ns simulation are presented in Table 2. In the 10 nm tube, the peptide either changed to inactivated form or remained largely parallel to the tube axis. In the 20‐nm cylinder, it tends to make a ~70° angle to the tube axis regardless of the initial orientation. At 30 and 40 nm radii, the peptide tends to remain more or less perpendicular to the tube axis, indicating this is the curvature range to which the peptide prefers to bind. In radii 50 nm and above, the peptide does not show any directionality, indicating that the peptide is not sensitive above that curvature. The orientations are depicted in Figure S3.

Table 2.

The average angle between the tubular axis and the long molecular axis of Snf7 monomers inside a tubular membrane surface

	10 nm	20 nm	30 nm	40 nm	50 nm
Initial_parallel (θ = 0ο)	19 ± 5	68 ± 4	93 ± 4	80 ± 3	9 ± 4
Initial_perpendicular (θ = 90ο)	a	69 ± 4	81 ± 5	71 ± 4	52 ± 4

Note: The simulations were carried out for 10 ns and averages were calculated over the last 0.5 ns.

^aProtein changes to “closed” conformation.

Although the binding energies above show some clear trends, there is substantial statistical uncertainty in the calculations. The large fluctuations in binding energies resulted from different orientations of the α4 helix in different runs. The α4 helix is largely negatively charged but randomly interacts with the main helix which affects the binding energy with the membrane. The main function of α4 helix is to bridge two Snf7 filaments rather than membrane binding.65 Hence, to reduce the statistical uncertainty, we simulated the Snf7 monomers in the absence of the α4 helix. This construct is named “truncated Snf7.” The binding energies of the truncated Snf7 monomers on the spherical surface are presented in Table 3. They are larger than for the full peptides because of the removal of negatively charged residues. The deletion of the α4 helix does not change the curvature sensitivity pattern but improves the statistical uncertainty. The results indicate maximal binding at 30 nm, after which binding energies start to fall, slightly between 30 and 50 nm and more substantially after that. This gives about four‐fold stronger binding to the negative curvature in comparison to the flat membrane. This value is close to the experimental finding.68 Similarly, the curvature sensing parameter α increases from 0.55 to 0.81 upon truncation of helix 4.

Table 3.

Binding energies (kcal/mol) of truncated‐Snf7 monomer, dimer, and trimer on the interior surface of spheres and cylinders

	20 nm	30 nm	40 nm	50 nm	60 nm	150 nm	Flat	α a
Monomer_sphere	−5.6 ± 0.3	−6.0 ± 0.1	−5.5 ± 0.1	−5.9 ± 0.0	−5.8 ± 0.1	−5.1 ± 0.3	−5.2 ± 0.2	0.81 ± 0.31
Monomer_cylinder	−5.9 ± 0.1	−5.7 ± 0.2	−5.6 ± 0.1	−5.8 ± 0.1	−5.5 ± 0.6	−5.5 ± 0.1		0.33 ± 0.13
Dimer_sphere	−8.2 ± 0.3	−8.1 ± 0.2	−8.1 ± 0.2	−7.5 ± 0.6	−7.3 ± 0.4	−7.0 ± 0.4	−7.1 ± 0.6	1.23 ± 0.35
Dimer_cylinder	−7.9 ± 0.1	−7.8 ± 0.1	−7.8 ± 0.3	−7.8 ± 0.3	−7.7 ± 0.1	−7.2 ± 0.2		0.72 ± 0.14
Trimer_sphere	−9.2 ± 0.7	−9.9 ± 0.6	−9.5 ± 1.0	−9.6 ± 0.6	−8.8 ± 0.2	−8.3 ± 0.7	−8.0 ± 0.6	1.74 ± 0.32
Trimer_cylinder	−9.9 ± 0.1	−9.5 ± 0.3	−9.1 ± 0.1	−8.6 ± 0.6	−8.4 ± 0.8	−8.6 ± 0.9		0.89 ± 0.52

^a30–150 nm radii are considered for the calculation of α.

Visualizing the trajectories, it becomes clear that binding onto a flat membrane is not optimal. One end of the peptide (usually the 1–2 turn) interacts with the membrane and the other faces up. This supports the idea that Snf7 binds to the flat membrane mainly with the help of the amphipathic N‐terminal helix (omitted in most of our calculations). The binding configurations on flat and spherical membranes are shown in Figure 2a,b, respectively. It can be seen that the Snf7 monomer fits to a negative curvature better than to the flat membrane. On the flat membrane trajectory, the peptide makes large excursions away from the membrane, especially the C‐terminal part. These excursions are smaller on concave surfaces. On negatively curved membranes, the peptide binds in the way expected from the crystal structure.

It is also interesting to analyze the structural flexibility of Snf7 monomers in our simulations. The angle between the two long helices is presented in Table S2. This angle, which is 164° in the crystal structure, fluctuates only between 161 and 162° at different curvatures. This indicates that Snf7 monomer maintains its overall shape regardless of curvature. The RMSD and RMSF values in our simulations are presented in Tables S4 and S3. Although no definite trends can be seen for both RMSD and RMSF with respect to curvature, the values are comparatively larger for lower curvatures or for the flat membrane surface.

2.2. Simulation of Snf7 with the N‐terminal α‐helix

The above simulations were conducted without the first 18 N‐terminal residues that are missing from the crystal structure. To see how the N‐terminal region interacts with the membrane, residues 1–11 were constructed as an α‐helix and residues 12–17 were constructed as unstructured using the CHARMM program. The binding configuration of this construct on a flat membrane is similar to that without the N‐terminal helix (Figure 2c). The tilt angle of helix 2 with the membrane plane was 19 ± 4°, similar to the system without N‐terminal helix, which was 16 ± 1°. In the simulations, the N‐terminal helix is very flexible and interacts transiently with both the membrane and the rest of the protein. Specifically, it tends to get tucked under helix 2–3, rather than being alone on the membrane surface. This interaction, which is stabilized by various hydrogen bonds, may be exaggerated by the implicit solvent model. Upon inclusion of the N‐terminal helix, the membrane binding energy increases from −5.2 ± 0.2 to −6.4 ± 0.3 kcal/mol kcal/mol, consistent with the experimental finding that it contributes to membrane binding affinity.67 This increase is modest and does not involve insertion into the membrane of bulky hydrophobic residues, which would be expected to generate positive curvature.67

2.3. Binding configuration and energetics of lower Snf7 oligomers on the membrane surface

Curvature sensitivity could also arise from the shape of oligomers. Thus, we studied the binding of dimers and trimers on cylindrical and spherical membrane surfaces with radii from 20 to 150 nm. The initial structures of dimer and trimer were generated from the packing observed in the crystal structure. The Snf7 dimers and trimers were very stable and maintained their structure throughout the simulations. The binding energies of dimers on spherical surfaces (Table 3) are highest in the region between 20 and 40 nm and start to drop as curvature decreases. This result parallels that for the Snf7 monomer and confirms that the optimal curvature is between 20 and 40 nm. The binding configurations are shown in Figure 3. The binding energies of the dimer on the cylindrical surface (Table 3) and less curvature sensitive than in spherical membrane but binding is also maximal in the range between 20 and 60 nm. Additionally, some of the Snf7 dimers simulated on cylindrical and spherical membrane with 20 nm radius undergo deactivation with extended helix break down. The binding energies of the dimers are not twice that of the monomers because some of the charged residues are involved in dimer stabilization and become unavailable for electrostatic interaction with the membrane.

Figure 3.

Binding configurations of Snf7 dimer inside a spherical membrane of 20 nm radius after 20 ns simulation. (a) Both monomers interacting equally with the membrane. (b) One monomer interacting more strongly than the other

The binding energies of the trimer are also presented in Table 3. It can be seen that the curvature sensitivity is enhanced for the trimeric form. The binding energy is optimal for the 30 nm sphere and falls from 30 nm to 150 nm radii. The binding energy on the flat membrane differs by ~2 kcal/mol from the optimal binding. In the cylindrical membrane, maximum binding is also observed from 20 to 30 nm. The curvature sensitivity parameter α (last column of Table 3) increases from 0.81 to 1.23 and finally to 1.74 on going from monomer to trimer on spheres. The cylindrical surface showed a smaller change upon oligomerization. In a cylindrical membrane, the peptide can find its preferred curvature by optimizing its tilt angle along the tube axis. The choice is not available on spherical membranes. The higher curvature sensitivity of oligomers might be due to that fact that dimers and trimers are more rigid than monomers and the oligomer tends to attain the curved shape that supports the negative curvature.

Figures 3 and 4 shows the binding configurations of the dimer and trimer on the flat and negatively curved surfaces. Analysis shows that the dimer or trimer can bind to the membrane with two different interfaces. In the predominant configuration, all monomers on the dimer or trimer interact more or less equally to the membrane. In the second configuration, one of the monomers interacts more strongly than the others with the membrane surface.

Figure 4.

Binding configurations of Snf7 trimer with the flat membrane surface (a) and with a sphere of 30 nm radius (b) after 20 ns simulation

2.4. Modeling of higher oligomers on the membrane surface

Based on the packing observed in the crystal structure, 12–100 Snf7 monomers were arranged on a straight line (Figure 5a) and simulated on the flat membrane surface. Initially, planar restraints were used to keep the monomers flat on the membrane surface. Within 5–10 ns, all oligomers curled up to make a circular structure in which helix 4 faced to the exterior of the circle. This is expected as it is rich in negatively charged residues and tends to decrease its electrostatic repulsion. The radii of curvature of the circular structures were dependent on the number of monomers taken in the initial structure. For example, the system with 48 monomers made a circular structure consisting of 42 monomers and average radius 20 nm. After making a full circle, it started to make a concentric structure inside (Figure 5b–d). The 80‐monomer system started to curl up from both of its ends making two circular structures with average radius 12 nm. The 100‐monomer system gave one circular structure near one end with average radius about 14 nm. In reality, oligomerization and bending occur simultaneously in a stepwise manner, whereas in our simulation a preformed oligomer was allowed to bend. To obtain the true intrinsic curvature of the oligomers, we simulated 16 monomers, a number insufficient to make a full circle. This oligomer gave a curved structure with radius ~20 nm. This preferred radius in our simulation is about 5–7 nm lower than that determined experimentally.69 The discrepancy might be due to the absence of N‐terminal region in our simulation or model inaccuracies.

Figure 5.

Structure of Snf7 48mer on a flat membrane surface after different simulation times (with planar restraints). For the initial structure only a part is shown

The monomers in the circular structures interact with each other via hydrophobic interactions and salt bridges. Specifically, Lys21, Arg25, Lys36, Lys69 make salt bridges with negatively charged residues Glu85, Glu88, Glu95, Glu102, and Glu109 in a neighboring monomer. Interaction between the monomers is further enhanced by the hydrophobic interaction of Ile117, Met114, Leu121, Leu99 with Met87, Ile94 and Leu101 of neighboring monomers. Positively charged residues Lys60, Lys64, Lys68 and Lys71 contribute strongly to membrane binding. The protein–protein interface in the filament in our simulations shows a strong hydrogen bond interaction between —C=O group of Lys 57 and Arg52 and less frequently with Arg41 (Figure S6). This interaction is absent in the crystal structure and might be responsible for the curved structure.

Two simulations performed without the planar restraint and with 64 or 24 monomers also gave circular structures. The one with 64 monomers had radius about 24 nm (Figure 6). The structure formed a full circle and after that one end faced up indicating a tendency to make a spiral structure if the length was longer. In these circular structures, each long axis of the Snf7 monomers tilted 78 ± 30° from the membrane plane, similar to the monomer (Figure 2).

Figure 6.

The structure of a circular filament with ~24 nm radius obtained from the simulation of 64 monomers of single chain lattice without planar restraint. The top surface is the membrane binding interface and membrane binding charged residues are shown in ball and stick model

A straight chain lattice containing a large number of monomers was also simulated in 20, 30, and 50‐nm cylindrical membranes. In all of these, the Snf7 oligomer also tended to curl up but did not form a complete spiral around the tube axis (Figure S4). An energetic analysis carried out on the system containing 24 monomers is presented in Tables 4 and 5. It can be seen that the oligomer is more stable on the cylindrical membranes than on the flat membrane by more than ~200 kcal/mol. The binding energy is also higher on the cylindrical membrane surface by ~10 kcal/mol. The decomposition of total energy indicates that the stability of the oligomer on the cylindrical surface is contributed from greater amount of van der Waals and electrostatic interactions which is coming from both inter‐ and intra‐peptide interactions.

Table 4.

Energetics of oligomer with 24 monomers simulated on cylindrical and flat membrane surfaces without planar restraint

	Cylindrical, 20 nm	Flat
Total energy	−73,471.0 ± 170.0	−73,265.8 ± 180
Binding energy	−79.1 ± 3.1	−69.3 ± 2.7

Table 5.

Decomposition of total energies of oligomer with 24 monomers simulated on cylindrical and flat membrane surfaces

	Van der Waals	Electrostatic	ASP
Total energy
20 nm	−22,298.9 ± 123.0	−47,663.1 ± 100.0	−29,600.3 ± 92.3
Flat	−21,983.7 ± 105.1	−47,590.1 ± 97.4	−29,834.0 ± 82.1
Interpeptide interaction
20 nm	−285.7 ± 28.8	−121.9 ± 19.1	236.8 ± 24.0
Flat	−283.1 ± 29.3	−121.5 ± 20.9	225.7 ± 25.1
Intrapeptide interaction
20 nm	−767.9 ± 24.9	−1913.4 ± 21.5	1,101.5 ± 17.6
Flat	−766.8 ± 25.5	−1913.1 ± 22.2	1,100.6 ± 19.6

2.5. Simulation of preformed spirals on cylindrical and flat membrane surface

Obtaining a regular spiral along the tube from an initial straight filament was not possible in our simulations. Therefore, we constructed and simulated Snf7 spirals on a flat membrane and inside tubes of radii 10, 22, and 32 nm. The preformed flat spiral is shown in Figure 7a. Within 2–3 ns of the simulation, the circular spiral changed into more or less polygonal shapes (Figure 7b). The oligomers formed on the lipid‐coated mica sheet were found to have similar structures.69 In these spirals, helix 4 bridges only a few points of the neighboring rings. This structure was run with a planar restraint which was released after 4 ns.

Figure 7.

The starting structure of a flat spiral of Snf7 filament (a), the structure after 2 ns simulation with planar restraint (b), the structure after 6 ns free simulation without restraint (c)

The spiral oligomers (starting structure for 22 nm in Figure 8a) were entirely stable throughout the 20‐ns simulation, except for the 10‐nm tube, where the Snf7 filaments show distortion at some points. In addition, the rings of this spiral become looser increasing the pitch of the helix. This indicates that the 10 nm tube may be too high curvature for Snf7 filaments. At 22‐nm radius, adjacent spiral rings come closer and bridge one another by helix 4 (Figure 8b). The spirals seem to be very stable and no other obvious changes were detected. Although the spiral filament is stable in the 32‐nm tube, it looks wavier (Figure S5). Hence, our preformed spiral simulations gave some indication about the preferred curvature of Snf7 filaments which are consistent with the results reported in the literature.69 On the cylindrical surface, the neighboring rings on the spiral are stabilized by the interaction of helix 4 of one ring with the long helix of adjacent ring. The same type of electrostatic interaction has been recently confirmed in the hetero‐polymer of Snf7 with the ESCRTIII subunit Vps24.73 The energetic properties of these preformed spirals are reported in Table 6. It can be seen that the spirals on the cylindrical surface are more stable by ~7 kcal/mol per monomer. The very slight decrease in binding energy on the cylindrical membrane surface might be due to the electrostatic bridge between the helix 4 and the main helix which increases the overall stability of the spiral but that subsequently reduces the electrostatic interaction with the membrane.

Figure 8.

The starting structure of a cylindrical spiral of Snf7 filament with radius 22 nm (a) and the final structure after 20 ns free simulation (b)

Table 6.

Energetics of preformed spirals on the flat and cylindrical membrane surfaces with 200 monomers

	Flat	Cylindrical, 22 nm
Binding energy/monomer	−3.0 ± 0.8	−2.9 ± 0.04
Total energy/monomer	−3,055 ± 6	−3,062 ± 9

Note: The calculations are done from last 0.5 ns of 8 ns simulations.

It is interesting to examine whether spiral Snf7 filaments have the same binding interface on the cylindrical and planar membrane surfaces. Analysis of the binding interface on the cylindrical membrane shows that Lys60, Lys64, Lys68, Lys69, Lys71 interact with the membrane. The monomers are arranged on the cylindrical spiral in such a way that the long axis of each monomer remains perpendicular to the plane of the curvature. This structure would provide the maximal binding to the inside cylindrical membrane surface for each individual monomer. The structure of the circular filament on the flat membrane surface obtained from the free simulation is shown in Figure 6. It can be seen that each monomer got aligned in such a way that their long axis lies on a plane perpendicular to the membrane plane and each helix 4 sits on top of the ring. Hence, the binding interface of the filament on the flat membrane is different from that on the cylindrical membrane. In this binding interface, the charged residues lie at different depths of the membrane z‐axis and cannot effectively interact with the membrane surface. Hence, even if the circular filament has the preferred curvature, it is always less stable on the flat membrane surface than on a cylindrical membrane surface.

3. DISCUSSION

Membrane remodeling by the ESCRT III machinery has been studied intensively over the last two decades but an understanding at the molecular level is lacking. Here, we have examined the membrane bending and curvature sensing mechanism of the ESCRT III subunit Snf7 using implicit membrane modeling. Our study revealed that Snf7 monomers prefer negative membrane curvature, but undergo deactivation below 20 nm radius. In addition, oligomerization increases the curvature sensitivity. The binding constant for the monomer to optimal negative curvature is 4.13 fold that of planar membrane. The same value for dimer and trimer is determined as 6.7 and 25.5, respectively. This value is a little smaller than the experimentally determined one.68 PIP2 clustering on the membrane, which is absent in our simulation, might cause increased preference for negative curvature. The clustering PIP2 and its dependence on curvature have been studied by MD simulations.54, 74 The curvature sensing parameter α also increases from 0.81 to 1.23 and 1.74 from monomer to dimer to trimer, respectively, which further provides support for increased sensitivity.

Recently, Mandal et al.72 performed all‐atom simulations of snf7 to obtain structural details of lower oligomers on the membrane surface and a higher oligomer in solution. The average distances between the neighboring helix 1 or helix 2 were found to be ~3 nm. This value ranges from 2.8 to 3.1 nm in our circular filaments. Despite the similarities, there are also some differences in our results. Mandal et al. observe positive curvature in their atomistic membranes and propose an alternative mechanism by which negative curvature could result. These differences should be explored in future work.

It is well known that Snf7 forms circular structures on the rigid flat membrane surface. AFM provided the image of such circular filaments but the resolution was not high enough to see the molecular details.69 Such a detailed molecular picture is provided by the present simulations, which predict a preferred radius of Snf7 filaments of about ~22 nm. The average diameter of the filaments was about ~4 nm, consistent with experimental findings.69 In each circular structure on the flat membrane surface, each monomer's principal axis makes an angle of ~78° to the plane of the membrane, leading to inefficient interaction with the flat membrane.

Membrane deformation by Snf7 has been explained in terms of the spiral spring theory.70 The spiral springs get formed on the membrane surface by stepwise oligomerization of Snf7 monomers in which the inner rings are highly compressed and the outer rings are less curved than the optimal curvature. These springs finally release energy by buckling inside the membrane. One issue with this picture is that the spirals should interact using a different interface with the flat and the cylindrical membrane surface. The oligomerization interface between monomers is highly unlikely to change on going from flat membrane to cylindrical membrane as that would require a complete rearrangement of Snf7 filaments. Similarly, the charged residues on the Snf7 filaments reside mainly on one surface (Figure 1). For maximal binding, it should bind with the same interface on both flat and cylindrical membrane surface. Our free simulation of Snf7 filaments on the flat membrane surface showed that it does not bind in the same way to flat and cylindrical membrane surfaces. Due to the tilting of each monomer by roughly 78°, the binding is less favorable on the flat membrane surface. Hence, each circular structure on the flat membrane surface is less stable in comparison to the cylindrical membrane surface even if the curvature is the preferred one. This component of energy would provide an additional energy for membrane bending that is not accounted for in the spiral spring mechanism. The simulations of the preformed spirals on the cylindrical membrane surface show that Snf7 tends to have a circular structure of preferred curvature ~22 nm. Energetic analysis shows that the flat spirals are less stable by ~7 kcal/mol per monomer than the cylindrical spirals.

Furthermore, our study confirmed the role of helix four in membrane tubulation. We have shown here that helix 4 bridges the two rings on the cylindrical spiral by largely electrostatic interactions. This interaction is not possible on the flat membrane surface due to the tilting of each monomer with respect to the membrane plane. This explains the experimental finding that helix 4 is necessary for helical oligomer formation. The same type of interaction and its importance for membrane tubulation has recently been highlighted in the Snf7‐Vps24 hetero polymer.73

Although Snf7 alone is capable of undergoing oligomerization and causing membrane bending, membrane remodeling in living organisms involves additional subunits of ESCRT III.75, 76, 77 A key question in this field is the mechanism of abscission, for which various proposals have been made.78 It has now been established that ATP hydrolysis by vps4 is required for membrane scission.79, 80 One possibility is that vps4 unfolds and removes individual Snf7 subunits from filaments, leading to tightening of the spirals and narrowing of the cylindrical membrane neck.81 Our preliminary modeling of spirals on 10‐nm tubes suggested that these spirals have larger helical pitch and over the course of the simulation the pitch tends to increase. Perhaps this could lead to membrane destabilization and scission. This possibility should be examined by further studies.

4. METHODS

4.1. MD simulation

MD simulations were carried out with IMM1_curv,71 an extension of Implicit Membrane Model 1 (IMM1)82 to spherical and cylindrical membranes. IMM1 is itself an extension of Effective Energy Function 1 (EEF1) for water‐soluble proteins.83 In these models, the solvation free energy is considered to be the sum of group contributions

$$\mathrm{\Delta }{G}^{\mathrm{slv}}={\mathrm{\sum }}_i\mathrm{\Delta }{G_i}^{\mathrm{slv}}={\mathrm{\sum }}_i\mathrm{\Delta }{G_i}^{\mathrm{ref}}-{\mathrm{\sum }}_i{\mathrm{\sum }}_{j\ne i}{f}_i\left(r_{\mathit{ij}}\right)V_j$$ (2)

where ΔG _i ^slv is the solvation free energy of atom i and ΔG _i ^ref is the solvation free energy of atom i in a small model compound. The last term describes the loss of solvation due to surrounding groups; f _i is the solvation free energy density of atom i (a Gaussian function of r _ij), r _ij is the distance between atoms i and j, and V _j is the volume of atom j. The dielectric constant is distance‐dependent and the ionic side chains are neutralized to account for the screening effect of the surrounding solvent.

In IMM1 ΔG _i ^ref is made a function of the vertical position,

$$\mathrm{\Delta }{G}^{\mathrm{ref}}\left(z\prime \right)=f\left(z\prime \right)\mathrm{\Delta }{G_i}^{\mathrm{ref},\text{water}}+\left(1-f\left(z\prime \right)\right){\mathrm{\sum }}_i\mathrm{\Delta }{G_i}^{\mathrm{ref};\text{chex}}$$ (3)

where ΔG _i ^ref,water and ΔG _i ^ref;chex are reference solvation free energies of atom i in water and cyclohexane, respectively. The membrane is oriented on the xy plane and z = 0 defines the mid‐plane of the bilayer. The function f(z′) describes the transition from one phase to the other:

$$f\left(z^{\prime }\right)={z^{\prime }}^n/1+{z^{\prime }}^n,\text{where}{z}^{\prime }=\mid z\mid /\left(T/2\right)$$ (4)

where T is the thickness of the hydrophobic core of the membrane. The exponent n controls the steepness of the transition. The dielectric's dependence on vertical position accounts for the strengthening of the electrostatic interactions within the membrane.

IMM1‐curv changes the shape of the hydrophobic region and uses the lateral pressure profile to account for changes in lipid packing. The center of the sphere is placed at the origin and R defines the distance between the origin and the sphere mid‐surface. The equation for z above is modified to z′ = |r − R|/(T/2) where r is the distance of the atom from the origin, given by

$$r=\sqrt{x^2+y^2+z^2}$$ (5)

For a cylinder, the x component is omitted, assuming that the cylindrical axis is along the x‐axis.

The calculations were carried out with the CHARMM package84 version c44a2. The simulations were run at 300 K with a 2‐fs time step and frames were saved every 1 ps. The simulations were run for 20 ns and analyses were carried out over the last 10 ns. Because implicit solvent simulations correspond to much longer timescales than their nominal duration, this time was deemed sufficient to obtain converged result. As a check, extension of two simulations to 40 ns gave similar results (see Table S5). The initial structure of the monomer was obtained from PDB code http://bioinformatics.org/firstglance/fgij//fg.htm?mol=5FD7.65 The packing in that crystal structure was used to construct initial structures of the oligomers. In the IMM1 calculations, the width of the membrane hydrophobic core was set to 25.4 Å and the anionic fraction was set to 30%. For the higher oligomers, 50% anionic membrane was used. As usual, the charge layer was set 3 Å above or below the membrane surface and 0.1 M salt concentration was used. Since membrane binding of the snf7 core is dominated by electrostatic interactions without hydrophobic residue insertion, the present calculations were carried out without the lateral pressure component. Multiple trials were averaged to estimate statistical uncertainty. The binding energies were calculated from the difference in energy of the peptides on the membrane surface and the same conformation in bulk water.

4.2. Approximate analytical solutions of the nonlinear Poisson–Boltzmann (PB) equation for the exterior and interior surfaces of cylinders and spheres

As electrostatic interaction is the major driving force for membrane binding of Snf7, the implicit membrane model should account for these interactions as accurately as possible. The previous IMM1_curv model approximated protein‐membrane electrostatic interactions with the Gouy–Chappman equation, which is strictly valid only for flat surfaces. This approach can be adequate for low curvatures, but becomes less satisfactory when the curvature is high. More importantly, the previous model did not differentiate between the interior and exterior surfaces of a sphere or a cylinder. To represent electrostatic interactions more accurately, we used approximate analytical solutions of the nonlinear PB equation and implemented them into the IMM1_curv model. The solution for the exterior surface of spheres and cylinders was available in the literature.85 Solutions for the interior surfaces were developed in the same spirit. We validated our results by comparing them to numerical solutions. Full description of these approximations is available in Supplementary Material.

AUTHOR CONTRIBUTIONS

Binod Nepal: Investigation; methodology; visualization; writing‐original draft; writing‐review and editing. Aliasghar Sepehri: Investigation; methodology. Themis Lazaridis: Conceptualization; funding acquisition; supervision; writing‐review and editing.

Supporting information

Supplementary Material S1 Approximate solution of the non‐linear PB equation for curved surfaces. Figure S1. Comparison of approximate PB models with numerical solution for inside and outside of sphere. Figure S2. Comparison of approximate PB models with numerical solution for inside and outside of cylinder. Figure S3. The orientation of snf7 monomer along the tube axis of various radii. Figure S4. The final structure of straight chain lattice of Snf7 oligomer simulated for 10 ns inside a 20 nm tube. Figure S5. The starting structure of cylindrical spiral of Snf7 filament with radius 31 nm (a) and the final structure after 8 ns simulation (b). Figure S6. Straight filament (a), curved filament b). C=O·····H3N+ hydrogen bond between Lys57 and Arg52 is highlighted. Table S1. Contribution of positively charged residues to membrane binding in kcal/mol. Table S2. The average angle between two long helices in Snf7 monomer after 20 ns simulation on spherical membrane. Table S3. RMSD values for truncated Snf7 monomers in 20 ns simulations. Table S4. RMSF values for truncated Snf7 monomers in 20 ns simulations. Table S5. Comparison of the results of 20‐ns and 40‐ns simulations for two systems.

Nepal B, Sepehri A, Lazaridis T. Mechanisms of negative membrane curvature sensing and generation by ESCRT III subunit Snf7. Protein Science. 2020;29:1473–1485. 10.1002/pro.3851