Linear aggregation of proteins on the membrane as a prelude to membrane remodeling
Edited by Michael L. Klein, Temple University, Philadelphia, PA, and approved November 7, 2013 (received for review June 4, 2013)
Significance
The remodeling of lipid membranes accompanies many cellular processes, such as the formation of organelles, division, trafficking, and signaling. Although many proteins have been implicated to play roles in these processes, their vast complexity precluded the profound understanding of how they occur at the molecular level. The most notable membrane remodelers are proteins containing one of several types of Bin/amphiphysin/Rvs (BAR) domains. They adhere and insert into the membrane to sculpt it into different shapes. Our work demonstrates that N-BAR proteins arrange into string-like aggregates and meshes that generate the initial curvature on the membrane. Our observation on the self-assembly of proteins elucidates the way these proteins may interact rapidly to participate in complex cellular machineries.
Abstract
Adhesion and insertion of curvature-mediating proteins can induce dramatic structural changes in cell membranes, allowing them to participate in several key cellular tasks. The way proteins interact to generate curvature remains largely unclear, especially at early stages of membrane remodeling. Using a coarse-grained model of Bin/amphiphysin/Rvs domain with an N-terminal helix (N-BAR) interacting with flat membranes and vesicles, we demonstrate that at low protein surface densities, binding of N-BAR domain proteins to the membrane is followed by a linear aggregation and the formation of meshes on the surface. In this process, the proteins assemble at the base of emerging membrane buds. Our work shows that beyond a more straightforward scaffolding mechanism at high bound densities, the interplay of anisotropic interactions and the local stress imposed by the N-BAR proteins results in deep invaginations and endocytic vesicular bud-like deformations, an order of magnitude larger than the size of the individual protein. Our results imply that by virtue of this mechanism, cell membranes may achieve rapid local increases in protein concentration.
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Lipid membranes protect cells and their organelles and serve as mechanical support for proteins involved in signal transduction and cellular trafficking (1). Owing to the way lipids are assembled into bilayers of mesoscopic length and molecular width, membranes behave as elastic and highly dynamic molecular sheets. Their innate multiscale nature is further evident in the local interplay between proteins and lipids, which results in large-scale membrane remodeling characterized by an impressive array of morphologies (2). These properties allow biological membranes to take part in several important cellular processes, as their restructuring is key to enabling communication between cells, formation of organelles, trafficking, division, and cell migration (1).
The interactions between individual proteins and lipid molecules alone are insufficient to remodel flat membrane sheets to an appreciable extent, implying that the experimentally observed membrane remodeling is a result of the concerted action of multiple proteins (3) in ways mechanistically differing from the mode of action of a single protein. Considering the multiple timescales required to capture protein dynamics as the membrane deformations are induced, as well as the difficulty in separating individual events of the remodeling process, this mechanism remains largely unclear. It previously was demonstrated that the binding of curvature-inducing nanoparticles may form tubular and vesicular structures, in which particles interact with one another solely via curvature (3–6). Furthermore, analytical theory predicts that anisotropic inclusions may induce budding on the membrane surface (7). However, the way proteins assemble on the membrane and how their oligomerization couples to both local and long-wavelength transformations of biological membranes remain open questions. The most notable membrane remodelers are those containing several types of BAR (Bin/amphiphysin/Rvs) domains (8). They share structural similarities but promote curvatures of different magnitude and direction, consequently participating in distinct biochemical pathways. Adhesion and insertion of BAR domains into the membrane leaflet induces bending and tubulation, and helps promote vesiculations (9–13). It is becoming increasingly apparent that these proteins do more than simply imprint their shape on the membrane surface; rather, membrane remodeling is a result of a collective effort among many proteins. Recent cryo-electron microscopic reconstruction revealed a high structural organization among BARs on membrane tubules under very high protein surface densities (14), and showed a required lateral alignment of amphipathic helices for the stabilization of membrane tubes. At the same time, fluorescence experiments suggest protein crowding also may be responsible for membrane remodeling resulting in the same membrane structures as with the binding of N-BAR domains (15).
Major questions remain concerning the mechanism of protein–lipid interaction in membrane remodeling. In the mechanism of clathrin-mediated endocytosis, different BARs are thought to be recruited at different times, assembling at the early stages, coating the emerging tubule, and participating in membrane fission (16, 17). Considering that deletion of many of these proteins often shows only moderate consequences on the membrane morphology, it reinforces the argument that the remodeling is a result of robust interactions between proteins and the surface of the membrane. Protein-induced membrane remodeling is an intriguing problem from both structural and biophysical standpoints, so a computational approach connecting the underlying physics to the observed behavior may help reveal a more complete scope of the mechanism. Our recently developed coarse-grained (CG) models of N-BAR domain proteins (14, 18, 19) and of lipid bilayers (20) form the basis for the present work. The forces between CG lipids are derived from their underlying atomic interactions, using the multiscale coarse-graining method (21, 22), which minimizes the number of adjustable ad hoc parameters. Distinct from previous work, in which either a single protein or dense N-BAR lattices were studied theoretically and experimentally (14, 23–26), simulating the N-BAR protein behavior at low and intermediate surface densities provides microscopic insights into the transient structures during the membrane restructuring at physiologically relevant concentrations. This is especially important in light of recent experimental work revealing the difference in mechanics of membrane bending under low- and high-density regimes of N-BAR proteins (27) and showed that N-BAR’s mode of action needs to be studied with precise control of the bound protein density. In this work, we demonstrate a self-assembly behavior of N-BAR proteins on the membrane and quantify the relationship between the protein concentration and the resulting membrane morphology.
Results
We simulated a CG N-BAR domain interacting with constant stress and infinite (i.e., periodically replicated) bilayer sheets from low to high bound protein densities. At low bound densities (<10%), our simulations show striking behavior of the N-BAR proteins during the initial stages of membrane remodeling. The self-assembly of proteins is marked by a linear aggregation of protein molecules on the surface of the membrane. The process starts with the adhered individual proteins initiating changes in the local curvature, whereby the recruitment of more proteins is facilitated. They then form linear aggregates, finally resulting in morphological transitions of the bilayer. The protein recruitment clearly was evident from a simulation at very low protein surface density (4% coverage), in which a lone N-BAR molecule explores the surface of the membrane until it firmly joins a preformed aggregate made up of three proteins (Fig. 1). Structurally, the N-BAR proteins induce invaginations parallel to their longitudinal axes, giving rise to spherical caps of positive curvature, with the proteins firmly gathering at the neck of these shallow buds (Fig. 1 and Fig. S1), in line with inferences drawn from experimental work (17). Contrary to the prevailing picture of BARs on membranes, in our simulations the proteins initially aggregate in the areas of negative Gaussian curvature, i.e., in troughs. The crescent shape (28) of BARs and the way they coat tubules (14) are what has motivated the perception of them populating positively curved membrane regions. Although single N-BAR proteins were observed in the present simulations to readily explore convex areas of the membrane, it appears that the quasi-linear aggregates have very different curvature proclivities at early stages of membrane remodeling.
Fig. 1.
At intermediate densities (10%–20% coverage), the longer aggregates help form and fully coat the base of the membrane bud, with a radius of 20–50 nm (Fig. 1). Apparently, increased protein density induces percolation, with linear aggregates crossing and forming meshes, which control the radius of the emerging bud. Moreover, unlike previous experimental and theoretical reports, in which the adhesion of spherical and cylindrical particles caused a concave membrane deformation and, therefore, negatively curved vesiculation similar in order of magnitude to the adhered particles (3, 5, 29, 30), we observe budding on the same side of the protein. Our qualitative observations on the budding behavior, as well as our quantitative results (in terms of bud radii), are consistent with in vivo and in vitro experiments of curvature-inducing proteins (9, 27, 28, 31, 32).
Accurate curvature calculations, based on the local maximum entropy approach (33), confirm that as the protein density is increased 20 times, there is an approximately threefold increase in the root-mean-squared mean curvature per lipid and a more dramatic 45-fold increase in the (positive) Gaussian curvature per lipid (Fig. 2). This result indicates that the membrane becomes progressively more curved and that morphologically it transforms into a dome of positive curvature. The linear aggregation of the N-BAR proteins is what drives the vesiculation-like budding behavior, and hence such a mechanism may potentially contribute to curvature generation in cells. Interestingly, an analysis of the curvature in the vicinity of the proteins reveals that their aggregation is a driving factor of the morphological change, as it significantly alters the magnitude and the nature of local curvature. The curvature profile for a nonaggregated protein (Fig. 2 and Fig. S2) shows a maximum of absolute curvature of 0.018 nm−1 corresponding to a shallow radius of curvature (r ∼ 60 nm), at a distance 6 nm away from the protein’s center of mass (protein’s edges). In aggregates, the curvature maximum is an order of magnitude higher, 0.103–0.163 nm−1 (r = 6–9 nm). This value is in striking agreement with values of intrinsic curvature induced by N-BAR proteins in the same density regime predicted with fluorescence microscopy (27). Our result demonstrates that local curvatures in aggregates are comparable with the size of the protein but are coupled to emerging buds of at least an order of magnitude larger length scales.
Fig. 2.
Additionally, the areas around the protein show an intriguing pattern of alternating positive and negative Gaussian curvatures, which follows the line of aggregates, with maxima at n = 6 nm, 3n, 5n and minima at 2n, 4n, etc. (Fig. 2), where n equals the half-length of the protein. These “pinches” of Gaussian curvature are a consequence of aggregation, with the magnitudes of maxima and minima increasing with the number of proteins in the aggregate (Fig. 2 and Fig. S2). In all, we find that the anisotropic curvature interactions between the N-BAR protein and the membrane, and the local saddle-like deformations caused by linear aggregation, are prerequisites in inducing positively curved remodeling. Such morphology was observed in experiments with N-BAR–coated vesicles (9), whereas conversely, concave (opposite) vesiculation was reported with isotropically curving particles interacting with the membrane in both experiments and in theory (3, 5, 29, 34). Our observations also are in direct accordance with a theoretical prediction that anisotropic inclusions in membranes undergo attractive interactions, which ultimately drive their linear assembly (7).
A closer inspection of the structural properties of protein aggregates revealed that the protein aggregates deviate from linearity by 20°–30° for very low density and 10°–20° for intermediate density (Fig. 2 and Table S1). This result indicates that as the chain grows, it becomes more static. Furthermore, there is a decrease in the radius of gyration of protein aggregates with the increased protein density. At the same time, it appears that with the larger chain, the probability of forming perpendicular protein dimers increases (from 0% to 20%). Both of these results are evidence of the formation of meshes on the membrane surface at bound densities of ∼20%.
Next, we tested the importance of the orientation of N-terminal helices on the membrane-remodeling capabilities of the protein. Structural and computational studies have revealed that the N-terminal helices in membrane tubule protein coats likely are perpendicular to both axes of the protein (Fig. 1), oriented in opposite directions (14). The way they are oriented on flat membranes at lower bound densities, especially at the assembly stage, remains unclear. To test the influence of helix orientation on self-assembly of N-BARs, we created a CG model with N-terminal helices placed underneath the protein’s arch. During the course of the simulation, similar to the assembly described in the main article, N-BAR proteins rapidly form linear aggregates and meshes, promoting the formation of a membrane bud (Fig. S3). The result implies that at the assembly stage, the orientation of the amphipathic helix does not compromise the anisotropy of the interactions between the protein and the membrane.
Endocytosis ends with a vesicle pinching off the bilayer, and although the role of insertion of protein helices in inducing bending recently was challenged by experiments (15), they likely are key in scission (9). The process is thought to alter the area of the membrane leaflet and introduce stress upon inclusion. Experimentally measuring the local stresses in the membrane would be extremely challenging (35). We used the stress tensor and the principal curvatures to calculate the lateral pressure per lipid in the true tangential plane of the bilayer. The results show that at the initial stages of membrane remodeling, the proteins already have a marked effect on the stress profile in their vicinity. There is a sharp minimum of 100 bar lower than the bulk constant pressure, located at a distance 0.5n from the center of mass of each protein belonging to an aggregate (Fig. 2). This observation is in line with analytically predicted stiffening of the membrane caused by linear aggregates forming on curved surfaces (36). Interestingly, the difference in pressure (and thus implicitly membrane tension) is independent of the size of the aggregate, at least up to a maximum observed size. The pressure minimum is even deeper for the lone protein (240 bar below average), suggesting that by aggregation, adhesion interactions prevail over topological changes in the binding layer. This result supports a previous prediction (26) that the formation of aggregates is necessary to alleviate excessive stress applied by a single BAR protein and that their collective behavior is more complicated than a simple addition of physical parameters observed for a single protein molecule. Furthermore, we do not observe fluctuations in the stress profile anywhere on the forming bud, except within 10 nm of each protein. Taken together, the quasi-linear N-BAR aggregates may be viewed as analogues of plate stiffeners in engineering that help stabilize the membrane-reshaping apparatus, e.g., in endocytosis.
The effective binding energy of peripheral membrane proteins on the membrane depends strongly on various chemical and mechanical properties, such as ionic strength of the solvent, the charge of vesicles, surface curvature, and the net charge in the protein’s binding region (13, 37). We tested how the binding affinity affects the self-assembly of N-BAR domains. For that purpose, we “mutated” the N-BAR domain by altering the interaction strength between the sites representing the amphipathic helices and the head groups of lipids. We found that at ∼20% surface density, the minimum interaction strength required for linear aggregation of the protein on the surface is 1 kcal/mol per interacting CG site. Below this value, the proteins randomly sample the membrane surface and, consequently, do not induce appreciable curvature. On the other hand, in simulations in which the interaction strength exceeded 2.5 kcal/mol, the topology and the fluidity of the bilayer were disrupted, resulting in tearing and crumpling of the membrane surface (Fig. 3). Based on free-energy simulations and the umbrella sampling method (Fig. S4), it appears that the optimal binding free energy of the N-BAR domain for the observation of linear aggregation is between −4.6 and −11.6 kcal/mol. These predictions are in agreement with binding affinity measurements for amphiphysin (∼−10 kcal/mol), an N-BAR protein known to induce budding and tubulation (27). Moreover, our results may explain why the reversal of charge in the amphipathic helix of a whole series of N-BAR proteins resulted in the absence of tubulation, despite binding to the membrane (38). Mutations of this type would decrease the adhesion energy of the protein significantly, precluding its insertion into the bilayer and the aggregation as we observe.
Fig. 3.
To demonstrate that the linear aggregation phenomenon observed on flat membrane sheets translates to closed membranes and thus to experimentally realizable systems, we carried out simulations of N-BAR proteins bound to an optically resolvable lipid vesicle, 300 nm in diameter (Fig. 4). This is a formidable simulation system, as it comprises more than 3 million particles, which, if including the solvent, would correspond to more than a billion atoms. Such a simulation system complements optical microscopy, providing detailed structural and mechanical insights into restructuring processes at molecular resolution. The vesicle simulation at low protein coverage revealed the same protein assembly and membrane morphology as those of the bilayer sheets. Initially, proteins adhere to the surface of the vesicle. Shortly afterward, they assemble into linear aggregates that form a net of invaginations on the vesicle. Even at sparse densities (<10%), we observed significant aggregation in only a few million CG simulation time steps (Fig. 4, Movie S1, and Fig. S5). The length of the forming aggregates in the low-density regime (7%) increased during the course of the simulation time, up to an average of 38 nm, with the longest aggregates measuring more than 80 nm in length. At intermediate density (20%), equivalent to sheet simulations, there is percolation of the proteins on the vesicle, resulting in a chain length average of 34 nm and a narrower length distribution (Fig. 4). In these simulations, the proteins join to form meshes at an average angle of 108° in the junction. Again, N-BAR proteins form both parallel and perpendicular dimers with a much higher probability of forming parallel dimers (88%). Finally, the invaginations induce a series of shallow buds emerging from the vesicle, with radii on the order of 30–50 nm (Fig. 4), as seen in budding and vesiculation experiments with membrane-curving proteins (9).
Fig. 4.
= 31.5 nm, 34.7 nm, and 37.6 nm, respectively, from left to right). (Lower) Twenty percent bound density at 300,000 τ ( = 36.3 nm).Finally, to test the importance of percolation of proteins on the membrane and how the membrane morphologically responds to higher densities, we carried out simulations with bound N-BAR domains up to ∼65% coverage. At ∼50% bound density, there is significant local protein crowding, which induces deep invaginations, encapsulating the proteins and leading to the formation of exocytic (negatively curved) buds, ∼10 nm in diameter (Fig. 5A). These vesicular structures already were reported for simple model systems (3, 29) and indicate that percolation of the protein at intermediate concentrations may be a decisive factor in positively curved budding. Calculations of membrane bending energy (Supporting Information), inferred from curvature calculations, reveal that the energy linearly depends on a protein surface density up to 20%, with a slope of 0.145 kBT per percentage of protein per 200 lipids (an approximate number of lipids in both layers in the vicinity of each protein). After this point, there is saturation (Fig. 5B). In other words, beyond the percolation density—at which, because of steric constraints, linear aggregates become clusters and proteins start crowding—no additional energy is converted into bending. This result reaffirms the notion that the morphological consequences of the membrane are deeply connected to the bound density of the protein and that linear aggregation may be a key mechanism in curvature generation.
Fig. 5.
Discussion
Our study shows that membrane remodeling induced by N-BAR proteins may be driven by quasi-linear aggregation of the proteins. This process induces local saddle-like deformations in the lipid bilayer, leading to the formation of convex buds, similar in shape and size to those observed in experiments. Given how binding of N-BAR domains locally affects the curvature properties of lipids, we may view a membrane coated with proteins as a system of multiple components with different intrinsic curvatures. As such, the minimum free energy is achieved by segregating membrane components with different curvatures (i.e., the lipids in contact with the protein from the bulk lipids) (39, 40), thus causing the aggregation of proteins. In the same way, we may explain the experimentally observed segregation of F-BAR and BAR domains on the membrane (23) as a consequence of the curvature-driven attraction of membrane components. Furthermore, aggregation of proteins creates a stable oligomer to which, through the same process, more N-BAR proteins may be recruited. By using this mechanism, proteins avoid the long timescales of a more random sampling of the membrane surface, such as in searching for curvature defects (19), and thus can accomplish a more rapid local density increase, required for in vivo morphological changes (e.g., in synaptic transmission).
Our results show that linear aggregation and membrane bending are robust processes that may be modulated by the binding energy and the anisotropy of the protein–membrane interactions. This fact helps explain the remodeling activity of epsin proteins (9, 41), which exhibit no apparent special shape, and provides insights into the mechanics of tubulation induced by crowding of proteins and anchored polymers (15, 42). We also demonstrated that regardless of the orientation of their N-terminal helices, the proteins may assemble rapidly to induce membrane buds. Their orientation likely is key in later stages of the tubulation process, in which a precise alignment of N-BAR domains helps in stabilizing long membrane tubes (14, 23). Mutations of charged residues in the protein’s binding region diminish its bilayer anchoring strength, which in turn would reduce the spontaneous curvature induced by the protein. Our simulations show that mutations also preclude their linear assembly and, thus, subsequent curvature generation. It has been reported for a whole series of sorting nexin proteins that altering the net charge in their N-terminal helices results in the absence of tubulation (38). At the same time, it is known that the absence of amphipathic helices does not necessarily deactivate the tubulation activity of the protein (9, 15). Together with our simulations, these results imply that membrane-remodeling activity is a robust process that requires control of the bound surface density and sufficient adhesive strength to promote proper assembly of the protein on the bilayer surface.
Similarly, it was observed in vivo that remodeling of membranes is correlated with the binding strength of BAR domains (28, 31), showing not only that BAR proteins are capable of inducing remodeling, but that this process is correlated with the affinity of the protein to the membrane. Recently, by measuring the amount of N-BAR proteins on the surface of the membrane, quantitative microscopy demonstrated that the mechanical properties of the membrane show density-dependent behavior similar to that seen in our simulations (27). The results of these experiments also imply a cooperative action of proteins, indicating aggregation (43); however, such experiments could not resolve the dynamic behavior of proteins at the molecular level. According to our results, at low surface density the protein can assemble in areas of negative Gaussian curvature, whereas fluorescence experiments (27) show a preference for mean positive curvature. One explanation for this different behavior comes from the fact that the fluorescence observations were made in a system with a nanotube formed by external force, whereas we observe the curvature generated by the protein itself. Therefore, the curvature-sensing behavior seen in the experiments mostly helps us understand the protein behavior at late stages of membrane remodeling. In contrast, our observation of the protein’s preference for Gaussian curvature relates to the formation of the type of curvature found at the necks of buds and vesicles, thus at the start of membrane remodeling. A goal for future research will be to elucidate how the self-assembly and curvature generation leads to the formation of large tubules and to incorporate the different curvature-sensing behaviors of N-BAR proteins at the two stages of remodeling.
Although the formation of linear, instead of isotropic, aggregates may seem less intuitive, it was demonstrated experimentally on simple vesicle models that binding of colloids indeed leads to the formation of linearly adhered particles (6). Free-energy simulations on an equivalent system demonstrated that the joining of a particle to a preformed particle pair has the lowest energy if the binding trajectory is linear (4). We demonstrate that long aggregates (more than twice the average aggregate length) still may form stably. Based on the presence of long aggregates rather than locally meshed structures, we predict no appreciable remodeling at very low bound densities. Instead, linear aggregation most likely serves to increase the local protein concentration. Further binding leads to the formation of protein meshes controlling the size of emerging buds. This result may explain the minimal tube radius found in fluorescence experiments and the observed homogeneous distribution in radii of N-BAR–induced tubules.
Beyond 20% protein surface density, no more energy is converted into bending; rather, clustering of the protein induces budding on the opposite side of the membrane, a type of remodeling observed previously. This behavior shows that the elongation of aggregates is energetically favorable—or, at least in part, is converted into bending—whereas the formation of clusters bound to the membrane does not make a significant additional contribution. Structurally, it also indicates that percolation behavior and relatively high stiffness of protein aggregates most likely are responsible for membrane bending toward the protein, rather than enveloping it into a concave bud. Following budding, the initially formed aggregate may recruit additional proteins to form N-BAR coats and stabilize mature membrane tubules, as observed in cryo-electron microscopy and CG simulations (14). In addition, the binding of N-BAR domains significantly alters the local lateral pressure of the membrane, implying that the lipid bilayer is stiff in the vicinity of the protein. The lower constriction seen in aggregates compared with lone proteins indicates the dominance of adhesion interactions. This observation may explain why F-BARs, known only to adhere to the surface, in addition to more easily sensing shallower deformations, are recruited readily at early stages of endocytosis in vivo. Complementing previous analytical studies, it appears that aggregation is crucial in controlling the mechanical properties of membranes and thus ensuring the physical state required for remodeling. This observation reinforces the notion that the interaction of BAR proteins with the membranes should be studied by keeping in mind crowding effects and the protein’s bound density.
Taken in its entirety, our study agrees well not only with previous analytical predictions, but also with in vitro and in vivo experiments, and it provides a possible molecular mechanism for the initial stages of membrane remodeling. Actually dynamically observing the collective behavior of proteins on the membrane at controlled surface densities would be impossible with current experimental techniques, making our model an invaluable complementary tool for studying membrane remodeling. Based on our results and the available experimental data, we propose that protein–protein interactions at low protein densities as a consequence of anisotropic interactions with the membrane, as well as their interplay with intrinsic membrane curvature, are responsible for the early morphological changes in membrane-remodeling processes. Curvature-mediating proteins essentially are cellular architectural elements that induce and stabilize complex membrane morphologies by stiffening the membrane and inducing local anisotropic curvatures. Endocytosis is a highly complex biological process comprising a multitude of proteins. Our study does not implicate N-BAR proteins as being the initiators of the process in vivo; rather, it provides important insights on how curvature of the membrane leading to buds, tubules, and vesicles may be generated. It also helps in understanding how N-BAR proteins and, by extension, any proteins that would apply similar mechanical effects on the membrane, may be recruited rapidly and participate in membrane remodeling.
Methods
Model Details.
Lipids were modeled with a hybrid coarse-graining strategy (20) that starts with the multiscale coarse-graining procedure (22), in which forces calculated from atomic-resolution simulations are averaged in a variational manner and are supplemented with analytical functions to cover poorly sampled regions of the configurational space. Lipids were coarse-grained into head, body, and tail groups, with the forces between sites calculated from atomic simulations of a 1,2-dilauroyl-sn-glycero-3-phosphocholine bilayer and were used in tabular form, with a 2-nm cutoff. The complete CG lipid interaction parameters may be found in the supporting information of the publication describing the model (20). For the protein, the 26-site N-BAR domain was used, as previously modeled with the heterogeneous elastic network approach (14, 19). The tables of interactions may be found in the supporting information of a previous publication (referred to as the zigzag model) (44). The cutoff for the intraprotein interactions was 3.5 nm. All other interactions were the Lennard-Jones type. A well depth of 1.8 kcal/mol at 1.5 nm between sites representing N-terminal helices and the head group of lipid molecules was used, based on estimation from thermodynamic experiments (27), although a range of 0.3–5.0 kcal/mol was tested (Results). The interaction parameters between other protein sites and the lipid head group were 0.2 kcal/mol at 1.5 nm and 0.24 kcal/mol at 2 nm for all protein–protein interactions (18). In addition, we tested additional N-BAR CG models, carried out supplemental controls, and conducted additional analyses, as discussed in Results and Supporting Information (Figs. S1–S3, S6, and S7).
Simulation Details.
We created initial configurations by randomly placing N-BAR molecules over the flat equilibrated bilayer sheet, 70 nm in lateral dimension, so that the transversal axis of the protein was parallel to the plane of the membrane (Fig. S1), at a distance of 2–3 nm. All sheet systems contained around 21,000 lipids and were simulated under 10 protein densities (φ): 1% coverage (one protein per simulation box at a ratio of 1:10,500 lipids in one layer), 4% (1:2,630 lipids), 9% (1:1,170 lipids), 18% (1:580 lipids), 20% (1:525 lipids), 26% (1:403 lipids), 34% (1:309 lipids), 40% (1:263 lipids), 54% (1:194 lipids), and 64% (1:164 lipids). The area of N-BAR was taken to be 50 nm2 (9, 27). The bilayer interacted with its periodic images in lateral dimensions. The simulations were carried out under constant NpxyT ensemble, using Nosé–Hoover equations of motion within the molecular dynamics suite LAMMPS (45). The size of the box in x and y dimensions was allowed to change by using a barostat with a coupling constant of 600 τ (τ = 48.89 fs, being the time constant), with no external pressure applied, whereas the side in the z-direction remained constant. The thermostat was set to 300 K, with a coupling constant of 6 τ. After an equilibration period in which the time step and the temperature were slowly increased 1.2 million time steps, production run simulations were carried out 10–30 million integration steps of molecular dynamics simulations at a time step, up to 0.4 τ. Simulations were run in three replicas per protein density, with different initial placements of proteins on the membrane.
The lipid vesicle, 200–300 nm in diameter, was recreated by mapping the CG lipids onto the quasi-particle continuum representation of a sphere (19) to overcome long equilibration periods and by placing them on the outer membrane layer. In one case, the proteins initially were placed bound to the inside of the vesicle (Fig. S5). First, we carried out a constant NVT simulation of the pure lipid vesicle (with the thermostat set at 300 K, with a coupling constant 6 τ; V represents the volume of the simulation box) for 1.5 million CG time steps, after which we placed (i) 1,300 N-BAR molecules (23% coverage, 300-nm vesicle) and (ii) 400 N-BAR molecules (7% coverage, 300-nm vesicle), and (iii) 280 N-BAR molecules (10% coverage, 200-nm vesicle) in the vicinity of the vesicle. The production run was carried out ∼10 million CG time steps.
Acknowledgments
We thank Fernando Fraternali for providing us with the algorithm for curvature calculations, as well as Patricia Bassereau and the members of the Voth group for insightful discussions. We acknowledge the support of the National Institutes of Health (Grant R01-GM063796) and the National Science Foundation for providing computational resources through XSEDE (Grant TG-MCA94P017, supercomputers Kraken and Gordon).
Supporting Information
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Published online: November 27, 2013
Published in issue: December 17, 2013
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Acknowledgments
We thank Fernando Fraternali for providing us with the algorithm for curvature calculations, as well as Patricia Bassereau and the members of the Voth group for insightful discussions. We acknowledge the support of the National Institutes of Health (Grant R01-GM063796) and the National Science Foundation for providing computational resources through XSEDE (Grant TG-MCA94P017, supercomputers Kraken and Gordon).
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This article is a PNAS Direct Submission.
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The authors declare no conflict of interest.
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Linear aggregation of proteins on the membrane as a prelude to membrane remodeling, Proc. Natl. Acad. Sci. U.S.A.
110 (51) 20396-20401,
https://doi.org/10.1073/pnas.1309819110
(2013).
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