Coarse-grained model
Our nanoscale ESCRT-III filament model is built of beads connected by springs. The minimal unit required to construct a chiral filament that preserves its flat spiral shape was found to be a triplet of beads, where the beads of neighbouring triplets are interconnected as shown in Fig. 1a. Filament geometry is controlled by bond lengths linking neighbouring triplets (Fig. 1a), while rigidity, measured by filament persistence, is controlled by bond strength between the triplets. Since building units and bond lengths between neighbouring units are equal, the target geometry of such a filament is a closed ring of radius R. Though some ESCRT-III filaments are observed as rings [1, 18–20], the effects of volume-exclusion will force longer filaments to form spirals with the adoption of non-preferred curvatures causing a build-up of tension in the filament. The membrane is described using a coarse-grained one particle thick membrane model that reproduces the fluidity and correct mechanical properties of biological membranes [21]. As a check, we confirmed that the main results hold when using a three-bead-per-lipid membrane model that explicitly accounts for the existence of the bilayer structure [22] (Additional file 1: Figure S5). Finally, the membrane-filament interface is modelled using a short-range attractive potential between two beads of the triplet (coloured in blue) and the membrane beads. This potential describes the adsorption of the filament onto the membrane, including screened charge-driven adsorption. Further details of the model are described the Additional file 1: Supplementary Information [23–28].
Single filament geometry cannot deform membranes
Pre-assembled planar ESCRT-III spirals (Fig. 1b) were placed on an equilibrated flat membrane, and their behaviour followed over time as tension in the system was allowed to relax (Fig. 1c). Since the outer arms of the spiral are stretched beyond the preferred filament curvature, while the inner arms are compressed, the filament will attempt to reach mechanical equilibrium by contracting its outer and expanding its inner filament arms, as previously suggested [14, 18]. This leads to the formation of dense spirals, since the filament cannot overlap with itself. If the modelled filament was allowed to overlap with itself, it would take on a ring shape of the target curvature (Additional File 1: Figure S3). Remarkably, for any tested spiral geometry or level of stored tension, spirals remained effectively flat on the membrane (Additional file 2: Video 1), even when all three beads of the filament triplets were allowed to bind to the membrane. Thus, under our model, a tense filament that only possesses in-membrane-plane curvature is not sufficient to drive membrane deformation. In line with this, in vitro experiments have reported ESCRT-III spirals can grow to several hundred nanometers in radius [18, 29], without deforming the membrane on which they sit [1, 30].
Additional file 2: A polymer spiral in the flat state does not lead to a significant membrane deformation. The filament density increases, but its membrane-attracted face remains trapped in the same 2D plane (see also Fig. 1c).
Filament geometry changes
ESCRT-III filaments have also been observed in a variety of 3D shapes, such as helices and cones [1, 16, 19, 30–34], indicating that ESCRT-III filaments can assume alternative target geometries. To account for this, we allowed our filaments to switch between two well-defined categories of geometrical states. In the first category, the target geometry is a ring that has its membrane binding site lying in a 2D plane, leading to the formation of spirals when bound to a membrane. In the second, the target geometry switches to a ring with its membrane binding site globally rotated outwards assuming a tilt angle τ (Fig. 2a). As a result, the membrane attachment site now sits on a 3D cone/tubule surface, which causes the filament take on a 3D helical shape (Fig. 2a). We suggest that this internal filament tilt, which has not been taken into account in previous models [14–16], drives membrane deformation. When a planar spiral-shaped filament is placed on a flat membrane and the target geometry is switched through-out the filament to a ŞtiltedŤ state, the relaxation of the filament induces a membrane buckle. This deformation develops away from the cytoplasm and grows in time to a fixed depth (Fig. 2b, Additional file 3: Video 2).
Additional file 3: Switching from the flat to the tilted a ring rotated by a tilt angle τ (τ=60∘) creates downward membrane deformations, away from the cytoplasm (see also Fig. 2b).
This works as follows. The membrane deformation is initiated by the filament internal tilt which transforms the filament-membrane attraction site from a 2D plane to a 3D conical surface with aperture θ=90∘−τ. This initiates an out-of-plane membrane deformation, which frees the filament from being trapped in a 2D plane, allowing the filament arms to move in 3D and relax closer to their desired radius R. While doing so, the outer filament arms push the inner arms down into the buckle, deepening the deformation. Because this is achieved via volume exclusion, tension in the filament only makes an indirect contribution to membrane deformation by encouraging the filament to enter the buckle (see Additional file 1: Figure S3 and Additional file 4: Video 3 and Additional file 5: Video 4 for control experiments). The resulting filament assumes a tightly coiled helical geometry, even though the filament does not possess a preferred target pitch.
Additional file 4: Self-overlapping filament spiral in the flat state ends up in a flat ring conformation (see also Figure S3).
Additional file 5: Self-overlapping filament spiral in the tilted state ends up in a tilted ring conformation (see also Figure S3).
While helical filaments will attempt to relax into a state in which neighbouring rings are stacked and tilted by τ, the wrapping of membrane about each separate ring of the spiral in the tilted state is not energetically favourable. The trade-off deformation is therefore a cone. Only for filament’s internal tilt of τ=90∘ do we observe tubule formation (Fig. 3a).
Quantifying membrane deformations
The shape of the membrane deformation is determined largely by the filament tilt. This is shown in Fig. 3b, where the depth and the sign of the deformation are found to depend on the tilt angle and the radius of the tilted state. Strikingly, a single model parameter—the tilt angle \(\intercal \)—generates a large variety of observed states ranging from flat spirals, to conical helices of varying aperture and even tubules in both directions.
The depth of the deformation is also influenced by the preferred filament radius (Fig. 3b) and filament rigidity (Fig. 3c). Since all the filaments in our simulations have the same total length, filaments that have larger preferred radii tend to result in shorter helices that give rise to shallower deformations. The persistence length functions here as a measure of the amount of intrinsic tension that the filament possesses. Naturally, filaments with small persistent lengths do not have a strong drive to achieve their target geometry and cannot deform the membrane (Fig. 3c). For increasing filament stiffness, deeper buckles develop, and their shape changes from conical toward tubular. The internal filament energy now dominates over the elastic energy required to bend the membrane, and a tubular deformation that accommodates the preferred filament radius is formed. Finally, to test the possible role of the helical pitch, which is not implemented in our model, we also carried out simulations that included an explicit helical pitch (see Additional file 1: Supplementary Information). Interestingly, we found that this preferred pitch does not influence the resulting deformations and that the filament always remains in a tightly coiled helical state when deforming the membrane (Additional file 1: Figure S4).
The model also provides a simple and intuitive explanation for the origin of the symmetry breaking in the membrane deformation. The buckling direction is determined by the sign of the tilt angle τ, i.e. by the 3D chirality in the filament. We should therefore be able to reverse the buckle direction simply by reversing the filament tilt. As can be seen in Figs. 2c and 3b, by moving the membrane-binding sites to the inside of the filament buckles can be induced in the opposite direction, toward the cytoplasm (Additional file 6: Video 5). In line with this possibility, Cullough et al. reported the formation of both upward and downward buckles of ESCRT-III filaments, depending on the filament composition[3]. Hence, it is possible for ESCRT-III filaments to induce different types of membrane deformation depending on whether they form a helix or an inverted helix.
Additional file 6: Switching from the flat to tilted ring (τ=−40∘) creates upward membrane deformations, toward from the cytoplasm (see also Fig. 2c).
Interestingly, in our model, there is a bias in the system that leads to a preference for downward buckles (as can be seen in Fig. 3b). Simulations for large negative tilt angles (τ=− 80∘ to − 90∘) do not show any deformation, an anomaly that is not mirrored for positive tilt angles. The reason for this bias in the energy landscape is that, for an upward buckle to form, the membrane must adhere to the filament from “the inside” and must adopt a larger curvature than a downward membrane deformation caused by the same amount of filament rotation, rendering upward deformations more costly. In the case of downward deformations, the membrane envelops the filament from the outside, resulting in a smaller curvature, reducing the amount of energy required to deform the membrane. These observations may explain why cytosolic ESCRT-III filaments preferentially deform and cut membranes away from the cytoplasm.
Membrane scission
To explore whether transitions in filament geometry can also drive scission, we introduced a simple generic cargo into the model. This cargo is allowed to weakly adhere to the membrane (see Additional File 1: Supplementary Information for details) so that it remains adsorbed and creates a shallow deformation. The adhesion is, however, too weak to cause substantial cargo wrapping by the membrane and spontaneous budding. We then polymerise a flat ESCRT-III spiral around the cargo. This models the way the ESCRT system is thought to corral cargo in cells [35]. Under these conditions, a switch in filament geometry induced by a transition to a positively tilted state initiates a conical membrane deformation, which traps the cargo at its centre underneath the ESCRT-III helix, as shown in Fig. 4a. In this configuration, the filament stabilises the energetically costly membrane neck. If the filament geometry reverts back to a flat state, this destabilises the neck and causes membrane scission, releasing a membrane bud that carries the cargo particle, while the filament retracts back to the cytoplasm (Additional file 7: Video 6). Thus, transitions between distinct geometrical states can drive ESCRT-III-mediated membrane scission to mimic the role of ESCRT-III in the formation of vesicles.
Additional file 7: A cargo particle is corralled on the membrane by the spiral ESCRT-III polymer in the flat state. The cargo binds to the dark gray receptors in the membrane but cannot bud off on its own. Switching the filament geometry from a flat to a tilted state (τ=60∘) deforms the membrane, while switching back from the tilted to the flat state causes cargo budding where the filament is released back to the cytoplasm (see also Fig. 4a).
The same type of repetitive changes in filament geometry can also sever membranes in situations in which the cargo itself induces substantial membrane deformation, as observed in the case of Gag-driven budding of HIV-1 [36]. Figure 4b shows the scenario in which we used a larger concentration of membrane receptors such that the cargo binds to the membrane strongly enough to cause a substantial membrane deformation, but still not strongly enough to bud off on its own. In this case, the helical filament geometry is needed for the filament to enter the membrane neck, while the change from helical to flat again performs the membrane scission (Additional file 8: Video 7).
Additional file 8: A cargo particle creates deep membrane deformation on its own, due to the high percentage of membrane receptors. Switching the filament geometry from a flat (τ=0∘) to a tilted state (τ=60∘) enables the filament to enter the preformed membrane neck, deepening and stabilising it. Switching back to the flat filament state causes cargo budding where the filament is released back to the cytoplasm (see also Fig. 4b).