How Membrane Geometry Regulates Protein Sorting Independently of Mean Curvature.

Biological membranes have distinct geometries that confer specific functions. However, the molecular mechanisms underlying the phenomenological geometry/function correlations remain elusive. We studied the effect of membrane geometry on the localization of membrane-bound proteins. Quantitative comparative experiments between the two most abundant cellular membrane geometries, spherical and cylindrical, revealed that geometry regulates the spatial segregation of proteins. The measured geometry-driven segregation reached 50-fold for membranes of the same mean curvature, demonstrating a crucial and hitherto unaccounted contribution by Gaussian curvature. Molecular-field theory calculations elucidated the underlying physical and molecular mechanisms. Our results reveal that distinct membrane geometries have specific physicochemical properties and thus establish a ubiquitous mechanistic foundation for unravelling the conserved correlations between biological function and membrane polymorphism.

Introduction

The geometry of biological membranes are highly conserved, suggesting they are crucial for cell biology (Figure a).[1−5] One of the most important functions of membrane geometry is believed to be the regulation of protein sorting and trafficking.[6−10] However, to the best of our knowledge, currently there are no experimental data, simulations, or theory actually supporting this putative function of membrane geometry, since past investigations have focused on how protein sorting is influenced by membrane curvature.[11−14] Historically, studies of membrane geometry have been impeded by experimental difficulties[6] and discouraged by well-accepted theoretical models[15,16] and simulations[13] predicting that all membrane geometries with the same mean curvature should exhibit the same physicochemical and protein-sorting properties (see also note (17)). Here, we study how membrane geometry regulates protein sorting, independently of mean curvature, for three key families of membrane-binding domains (MBDs). Quantitative comparative experiments between the two most abundant cellular membrane geometries[4] (spherical and cylindrical) reveal that, contrary to predictions,[13] geometry can regulate protein sorting independently of mean curvature. We document geometry-mediated sorting of up to 5000%, surpassing some of the most extreme reports of curvature-mediated sorting.[12,13,18,19] Molecular-field theory calculations revealed the physical and molecular mechanisms underlying membrane geometry mediated protein sorting. These results also revealed the crucial importance of Gaussian curvature, thus prompting the revision of existing theoretical descriptions of membranes that assume it to be negligible. More broadly, our findings demonstrate that membrane geometry, independently of mean curvature, regulates the physicochemical properties of membranes. We thus anticipate geometry-specific regulation of many other membrane-associated processes including the localization, structure, and function of transmembrane proteins.

Figure 1

High-throughput assay of protein binding on membranes with controlled spherical and cylindrical geometries. (a) Biological membranes have distinct geometries that modulate their physical and molecular properties in ways that are not fully understood. Local geometry on a 2D surface in 3D space can be defined by the two principle curvatures (c1 and c2), or the mean and Gaussian curvature (H and K, respectively defined as the sum and the product of the principle curvatures). (b) Scheme of the four membrane binding domains we investigated. Left to right: α-synuclein (with the helical wheels depicting the amphipathic structure of the two helices), annexinB12 (with the helical wheel representing the amphipathic structure of one of the helix monomers), the N-Ras lipidation (tN-Ras), the C2AB domain of synaptotagmin1. (c) Illustrations of the two membrane binding assays. Reconstituted lipid vesicles and tubes were supported on a passivated glass slide at dilute densities. This allowed us to image them individually using fluorescence microscopy. (d) Typical images of individual membrane tubes (top) or single vesicles (bottom) ordered here by increasing intensity/diameter (left to right). Particle intensities were converted to diameter as described and validated in refs (15, 16, 26, 28, and 29). A typical sample displayed ∼1012 cm–2 particles of randomly different diameters allowing us to screen with high-throughput protein binding on spherical and cylindrical membranes of different mean and Gaussian curvature.

Results and Discussion

To broaden the scope of this investigation, we studied geometry-mediated protein sorting for representative members of three different major classes of MBDs which have been reported to be sensors of membrane curvature: the amphipathic helix containing proteins alpha synuclein (α-Syn) and AnnexinB12 (Anx),[20] the minimal anchor of the lipidated protein N-Ras (tN-Ras),[12] and the C2AB domain of synaptotagmin 1 (Syt)[21] (Figure b and Methods). We performed all experiments with purified proteins binding on lipid bilayers that were reconstituted either in the form of vesicles or tubes (spherical or cylindrical geometry) (Figure c). As we have shown previously,[12,14,22] the reduced molecular complexity of this system allows us to assign precisely membrane geometry and perform quantitative comparisons between experiments and molecular-field theory calculations, which ultimately can reveal the physical and molecular mechanisms underlying our observations.

The nanoscopic vesicles and tubes were labeled fluorescently and supported on a passivated surface, which allowed us to image them individually with quantitative fluorescence microscopy[14,23] (see Figure c,d, Methods). As we have shown previously, this approach enabled us to extract the radius (r) and the principal curvature (c = 1/r) of single membrane particles,[12,14,23,24] circumventing bias introduced by ensemble-averaging.[23] All MBDs were labeled on single accessible cysteines with Alexa-488 (see Methods) and incubated with membranes at concentrations that, as we have shown previously,[12,14,20] were too low to induce changes in membrane curvature. Combining the quantitative two-color measurements of fluorescence from both the membrane and the protein provided us with an accurate measure of protein densities for thousands of individual spherical and cylindrical membranes across a continuous range of curvatures that spanned 1/20 nm–1 to 1/200 nm–1 (Figure and Supplementary Figures 2 and 3). As expected, and as we have shown previously,[12] negative controls (including binding streptavidin (Strep) to biotinylated lipids and premixing two fluorescently labeled lipids) did not show any curvature-dependent sorting for either geometry (Supplementary Figures 4 and 5).

Figure 2

Quantitative side-by-side comparison of protein binding on spherical and cylindrical membranes of different diameters. (a–f) Open symbols, membrane-bound protein density measured on tubes (a, c, e) and vesicles (b, d, f) of different diameter. Top to bottom: tN-Ras, Syt, Anx. Protein density on the largest measured diameters is normalized to 1. Data demonstrate higher sorting by spherical as compared to cylindrical curvature in all cases. Solid lines, error-weighted fits to the data. Solid black markers, molecular-field theory calculations of the equilibrium membrane-bound protein density are in excellent agreement with the experimental data. n ≥ 3, where hereafter n is the number of independent experiments per condition. (g) Relative sorting ratio is the fold increase in protein density when decreasing the membrane diameter by a factor of 10. The negative control, Strep (blue), as expected did not show any curvature-dependent bound-density increase on either cylindrical or spherical membrane geometries. Geometry discrimination ratio varied from 2-fold to 40-fold. Using a two-tailed Student’s t test, the significance of the sorting difference between tubes and vesicles was evaluated, finding p values of p = 0.7 for Strep, p = 0.02 for tN-Ras, p = 0.0003 for Syt, and p = 0.003 for Anx. Error bars represent the standard error of the mean (SEM).

Figure a–g and Supplementary Figure 4 show that tN-Ras, Syt, Anx, and α-Syn can all sense (i.e., preferentially bind to) membranes of high curvature, as shown previously.[12,20,21] To quantify the MBD sorting potency, we fitted the data shown in Figure a–f and Supplementary Figure 4 to obtain the relative sorting ratio (R), defined as the ratio of the MBD density between a 40 nm and a 400 nm diameter liposome or a 40 nm and a 400 nm diameter tube (see Methods).[12] In addition to the sensing curvature, our data demonstrate quantitatively that these MBDs can discriminate membrane geometry, and we calculated the geometry discrimination efficiency as the ratio between Rves and Rtube for each MBD. Strikingly, different MBDs exhibit a dramatically different geometry discrimination efficiency, which ranges from 2-fold to 40-fold (Figure g; Supplementary Tables 1 and 2; Methods).[12]

The experimental finding that MBDs can discriminate membrane geometry is highly surprising since it contradicts existing theoretical descriptions of membranes for the following reasons (see also Supporting Information). The local curvature is mathematically determined by the mean and Gaussian curvature of a given geometry (H = (c1 + c2)/2 and K = c1 × c2 (see Figure a and Supplementary Figure 6).[4] However, the contribution from the Gaussian term has often been estimated to be negligible (see refs (15 and 16) and note (17)). On this basis, MBD sorting in our experiments is predicted to be identical on different geometries that have the same mean curvature.[13,15,16]

We experimentally tested this theoretical prediction by examining the ratio of MBD sorting by spheres with a given radius and cylinders with half that radius, whereby both membrane geometries have the same mean curvature. Interestingly, our experiments revealed the existence of dramatic deviations from unity (up to 50-fold) (Figure a and Supplementary Figure 7) demonstrating directly sensing of membrane geometry and Gaussian curvature, independently of mean curvature. In the following, we present the physical reasons and the molecular mechanisms that underlie the deviations between experiment and past theoretical predictions, and comprise the basis for geometry discrimination by MBDs independently of mean curvature.

Figure 3

Molecular-field theory reveals the physical and molecular mechanisms underlying membrane geometry discrimination. (a) Experimentally measured membrane-bound protein density ratio for vesicle of radius r and a tube of radius r/2 plotted against vesicle diameter. This demonstrates protein sorting independently of mean curvature. Error bars represents SEM. (b) Theoretically calculated ΔP (here integrated solely over the outer leaflet) and ΔA ratios for a vesicle of radius r and a tube of radius r/2 plotted against vesicle diameter. (c) Theoretically calculated interaction energy terms for Syt; excluded volume (red circles), hydrophobic interactions (blue squares), electrostatic interaction (black triangles), and internal degrees of freedom (green triangles) plotted as ratios for a vesicle of radius r and a tube of radius r/2 against vesicle diameter. (d) Color map of the Gaussian curvature energy discrimination factor showing how the specific residues of the C2A domain contribute to geometry discrimination as a function of the physicochemical nature and spatial distribution of the chemical groups. Deviations from unity in panels a–c demonstrate effects mediated by Gaussian curvature.

We have previously used molecular-field theory calculations[25] to successfully describe the sorting of tN-Ras by vesicles of different diameters and therefore mean curvature.[12] Here, we greatly extended this theoretical framework to explicitly include hydrophobic and electrostatic interactions, in addition to excluded volume considerations, to characterize geometry discrimination by MBDs (see Supporting Information). Our analysis was confined to Anx, Syt, and tN-Ras, because we lacked quantitative experimental data on geometry discrimination for α-Syn because its binding on tubular membranes was below the detection limit (Supplementary Figure 4c). For tN-Ras, we did not use any free parameters in the calculations, while for Syt and Anx the insertion depth in the bilayer was the only free parameter (Supplementary Figure 7). As shown in Figure , theory and experimental data were in quantitative agreement for all three MBDs (compare black data points and colored solid lines respectively).

Next, we exploited the theoretical model to delineate the physical properties of the membrane that enable curvature sensing and geometry discrimination. Curvature is thought to affect membrane properties by modulating lipid packing, which in turn translates to and can be quantified as changes (a) in area per lipid (ΔAlipid) and (b) in the integrated lateral pressure profile (ΔP). The lateral pressure profile is the local difference between the transverse and normal components of the pressure tensor. This interfacial property is typically used to connect the local inhomogeneous environment between two fluid phases with the surface tension. It turns out that this property is closely related to quantitatively predicting how different MBDs will sense curvature. The connections can be seen by comparing equation (XVII) with equation (XXI) in the Supporting Information. Knowing how the lateral pressure profile changes for a given bilayer allows you to make accurate predictions of MBD curvature sensing if you know the molecular specifics of the MDB in question. As shown in equation (XVII) in the Supporting Information, the lateral pressure profile has contributions from electrostatics, the hydrophobic interactions, and excluded volume interactions. By tracking changes in the lateral pressure profile of the membrane due to curving the bilayer into varying shapes without the presence of proteins, we can get a sense of how the membrane’s physical properties depend on geometry. The difference in the lateral pressure for a sphere of radius r and a cylinder of radius r/2, with r = 100 nm and r = 40 nm, is shown in Supplementary Figure 7b. The plot demonstrates that the influence of Gaussian curvature is distributed relatively evenly throughout the thickness of the bilayer, and that the higher the curvature of the bilayer, the greater is the effect of Gaussian curvature on the lateral pressure profile. In Figure b, we plot the ratio of the difference in the curved versus planar integrated lateral pressure for the entire exterior leaflet, ΔP, between a sphere of radius r and a cylinder of radius r/2. The ΔP ratio displays an ∼10% increase for r = 75 nm and up to about 50% for r = 20 nm. Since the change in ΔP is an important predictor for curvature sensing membrane-binding proteins, this suggests that Gaussian curvature has a major role in protein recruitment. Note again ΔP is the lateral pressure difference between a sphere of radius r and a cylinder of radius r/2 integrated across the exterior leaflet, so the larger the value of ΔP in this context, then the greater the curvature discrimination as seen for a generic MBD in equation XXI of the Supporting Information.

To examine the contribution of Gaussian curvature to the area of exterior leaflet lipid headgroups, we plotted the area of exterior headgroups for a sphere of radius r divided by the area of the exterior headgroups of a cylinder of radius r/2 (Figure b). Equation (X) in the Supporting Information is used to calculate the exterior area with z = 1.3 nm. As seen in equation (X) the difference between A(z = 1.3 nm) for cylinders of size r/2 compared to spheres of size r is the presence of the Gaussian curvature term. The resulting plot depicted in Figure b demonstrates that the Gaussian curvature has almost no measurable effect on the area of the lipid headgroups in the exterior membrane leaflet, since the ratio between the lipid area of spheres and cylinders with radius r and r/2, respectively, never deviates more than 0.5% from 1.

The area per molecule is a two-dimensional property that is determined at a single well-defined distance above the midplane of the bilayer. Any property that is purely two-dimensional will not show a considerable dependence on Gaussian curvature. As another example of the weak dependence of two-dimensional properties on Gaussian curvature, the change in lateral pressure at any selected single height above the midplane does not show a sizable dependence on Gaussian curvature as seen in Supplementary Figure 7b. However; when you integrate the change in lateral pressure over the entire outer leaflet of the bilayer, then you do see a measurable dependence on Gaussian curvature. It can be seen in equation XXI in the Supporting Information that it is this integrated (three-dimensional) property that is important in determining the curvature sensing of the MBDs. Thus, we want to highlight the error in making curvature sensing predictions of MBDs while only using two-dimensional properties and neglecting the effects of Gaussian curvature. In Figure b, we plot the ratio of changes in these two physical parameters for spheres with a given radius and cylinders with half that radius (Supplementary Figure 7). The data reveal that the ratio of change in the area per lipid does not scale with Gaussian curvature and cannot thus form the basis for the observed geometry discrimination. On the contrary, the ratio of change in ΔP shows significant deviation from unity with decreasing radii, thus revealing a pronounced dependency on Gaussian curvature. This allowed us to identify ΔP as a physical membrane parameter that underlies geometry discrimination. We note that integration over the entire thickness of the outer leaflet is critical for revealing these effects because the contribution of Gaussian curvature to observable membrane properties is negligible for a two-dimensional surface, i.e., for a membrane where the thickness is assumed to be equal to zero (see Supporting Information).

To reveal the molecular mechanism underlying membrane geometry specific protein sorting, we turned to how the relative densities of the MBDs are calculated as a function of curvature in the molecular theory. The relative density calculation for the MBDs can be written as a product of four terms that highlight a specific free energy contribution:

Each of the four terms is discussed in detail for each of the MBDs in the Supporting Information (Supplementary Figure 7f). In short, the excluded volume interaction is a repulsive term that quantifies the packing of the MBD volume into the outer leaflet of the bilayer, the electrostatic contribution can be attractive or repulsive depending on the charge distribution on the MBD, the hydrophobic interaction is attractive and quantifies the free energy benefit of having the distribution of hydrophobic groups along the MBD buried into the fatty-acid tails of the lipids, and the internal energy quantifies the number of gauche ± dihedral bonds along the chain of the MBD. These energy terms combined reveal how geometry can affect membrane–protein interactions at the molecular and atomic level.

Figure c isolates the contribution of Gaussian curvature to geometry discrimination and reveals that it is dominated by the product of two terms, the excluded volume and the hydrophobic interaction. Electrostatics and internal degrees of freedom do not contribute significantly in geometry discrimination for membranes with a low content of charged lipids. Indeed, as shown by the good correlation in Supplementary Figure 7g, the former two terms alone prove sufficient in predicting the geometry discrimination we measured for tN-Ras, Anx, and Syt.

Importantly, the synergy between coupled attractive and repulsive molecular interactions that enables the discrimination of different geometries is modulated by protein-specific parameters. To showcase this, we calculated the Gaussian curvature energy discrimination factor (I(r)Vol × Hyd) for the product of the two most important energy terms excluded volume and hydrophobic interactions:

This factor is used in Figure d for Syt, allowing us to visualize the specific contribution of individual amino acids to geometry discrimination, depending on their volume (size and shape), hydrophobicity, and penetration depth in the membrane. These results illustrate how geometry discrimination by proteins can be tailored at the atomic level presumably to accommodate specific biological functions.

The experimentally validated theoretical description of the system is also valuable because it allows us to make qualified quantitative predictions about conditions currently beyond the reach of direct experimental observation. As an illustrative example, we choose here the lipidated tN-Ras motif because the intracellular movement of N-Ras is primarily mediated by vesicular trafficking and because its localization to the plasma membrane is reported to coincide with highly curved spherical structures called caveolae.[26]Supplementary Figure 8 provides a quantitative prediction of how the equilibrium N-Ras localization would be upregulated (∼7-fold) solely by the geometrical transformations involved in vesicle budding or caveolae formation (see Supporting Information). Note than in contrast to perfect spheres or cylinders, the complex shapes of real biological membranes comprise a spectrum of different local geometries. The predicted nanoscopic equilibrium protein density patterns depicted in Supplementary Figure 8 result from the combined influence of both mean and Gaussian curvature on local membrane properties.

Conclusion

Biological membranes have distinct geometries, which appear to be highly conserved. This suggests distinct membrane geometries are endowed with distinct properties; however, validation of the molecular mechanisms behind this phenomenological correlation proved elusive. The work presented here establishes a ubiquitous mechanistic foundation for assigning distinct physicochemical properties to distinct membrane geometries by revealing the importance of Gaussian curvature in addition to mean curvature. We anticipate that the methods and findings presented herein apart from advancing our understanding of protein sorting will contribute broadly in elucidating the reasons that render cellular membrane geometry/polymorphism a conserved phenotype.

Methods

Lipids and Membrane-Binding Domains

In both the single vesicle and tube assay, we employed vesicles prepared as previously described[12] from a mixture of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), 1,2-dioleoyl-sn-glycero-3-phosphatidylserine (DOPS), 1,2-dioleoyl-sn-glycero-3-phosphatidylethanolamine-N-(cap biotinyl) (DOPE-biotin), and 1,1′-dioctadecyl-3,3,3′,3′-tetramethylindodicarbocyanine perchlorate (DiD); DOPC:DOPS:DOPE-biotin:DiD 89.6:10:0.2:0.2 all in mol %. MBD synthesis, purification, and handling are described for tN-Ras and Syt below and previously for Anx and α-Syn.[20] The four MBDs were labeled with Alexa488. All experiments were performed in a 10 mM Hepes, 95 mM NaCl, pH 7.4 buffer. We added 1 μM tN-Ras, 0.5 μM Syt (1 mM Ca2+), 0.1 μM Anx, 0.1 μM α-Syn, or 0.1 μM Strep, in both assays, and waited 30 min before acquiring images to ensure that binding had equilibrated. All proteins were kept on ice prior to addition.

No unexpected or unusually high safety hazards were encountered.

tN-Ras Peptide Synthesis

All solvents and reagents used for peptide synthesis were of analytical reagent grade and were obtained from Sigma-Aldrich (Denmark), IRIS Biotech GmbH (Germany), or Invitrogen (Denmark).

Purification was accomplished by preparative RP-HPLC (FeF Daiso C4 column (Køge, Denmark), 300 Å, 5 μm particles, 21.2 × 250 mm) using the following solvent system: solvent A, water containing 0.1% TFA; solvent B, acetonitrile containing 0.1% TFA. B gradient elution (0–3 min 10%, 3–5 min 10–80%, 5–19 min 80%, 19–20 min 80–100%, 20–33 100%) was applied at a flow rate of 15 mL min–1, and column effluent was monitored by UV absorbance at 215 nm.

Identification and quantification were carried out by LC-MS (Dionex UltiMate 3000 with Chromeleon 6.80SP3 software, MSQ Plus Mass Spectrometer, Thermo) using the eluent system A–B (solvent A, water containing 0.1% formic acid; solvent B, acetonitrile containing 0.1% formic acid). The eluent system A–B was applied on a C4 analytical column (Phenomenex Jupiter C4 column, 300 Å, 5 μm, 4.6 × 150 mm) where the B gradient elution (0–2 min 5–10%, 2–4 min 10–80%, 4–12 min 80%, 12–13 min 80–100%, 13–17 min 100%) was applied at a flow rate of 1.0 mL min–1.

MIC-Gly-Cys(HD)-Met-Gly-Leu-Pro-Cys(Far)-NHCH2CH2NH2 No. 1

Fmoc-Cys(Far)-OH was synthesized as described by Lumbierres et al.[27] and Fmoc-Cys(HD)–OH was synthesized as described by Triola et al.[28]

The peptide was prepared by both manual peptide synthesis at room temperature and automated microwave-assisted peptide synthesis (Syro Wave) on 2-Cl Trt PS resin with 9-fluorenylmethyl-oxycarbonyl (Fmoc) for protection of Nα-amino groups. N-Fmoc-ethylenediamine (4 equiv) was anchored to the 2-Cl trityl linker in anhydrous dichloromethane and DIEA (10 equiv) under argon atmosphere overnight at room temperature. The loading was determined by a loading test. Nα-Fmoc amino acids (8.0 equiv) were coupled using N-[(dimethylamino)-1H-1,2,3-triazole[4,5-b]pyridine-1-ylmethylene]-N-methylmethanaminium hexafluorophosphate N-oxide (HATU) (5.8 equiv) as a coupling agent and 1-hydroxy-7-azabenzotrizole (HOAt) (6.0 equiv) as an additive. Fmoc-Cys(Far)-OH, Fmoc-Cys(HD)-OH, and the maleimidocaproic acid were coupled overnight at room temperature. The N-terminal Gly was coupled for 2 h at room temperature. The residual amino acids were coupled for 2 × 10 min at 75 °C. Nα-Fmoc deprotection was performed using piperidine-DMF (1:4) for 3 min followed by piperidine-DMF (1:4) for 17 min at room temperature. The peptides were released from the solid support by treatment with 1% TFA in DCM (trifluoroacetic acid (TFA)-triethylsilane (TES)-dichloromethane (1:1:98)) for 2 h. The TFA solutions were concentrated by nitrogen flow to yield the crude materials. The peptide was purified as described above. Yield: 22.4 mg (0.017 mmol); 22%. MS (ESI) Calculated for C69H118N10O10S3 [M + H]+ 1342.8, found 1343.6.

MIC-Gly-Cys(HD)-Met-Gly-Leu-Pro-Cys(Far)-NHCH2CH2NH-Alexa488 No. 2

Peptide 1 (2.2 mg) was dissolved in anhydrous DMF, and triethylamine (0.43 μL) was added. A solution of 1 mg of Alexa 488 succinimidyl ester (Invitrogen) in 200 μL of anhydrous DMF was added to the peptide solution and stirred overnight. The solvent was concentrated in vacuo and redissolved in H2O–acetonitrile 1:2. The peptide was purified as described in the general section. Yield: 2.4 mg (0.00129 mmol); 82%. MS (ESI) Calculated for C90H130N12O20S5 [M + H]+ 1858.8, found 1860.5 and 931.1, see Supplementary Figure 1).

Syt1 C2AB Expression, Purification, and Labeling

We performed expression, purification, and labeling of the Synaptotagmin1 C2AB fragment (residues 96–421) from pGex4T1 (GE Biosciences) as already published.[29] The sequence of the clone was free of the deleterious mutations described previously.[30] Briefly, we cleaved the GST fusion protein from glutathione agarose, followed by ion exchange and gel-filtration chromatography (Mono S and Superdex 200, GE Biosciences). We examined all proteins by SDS-PAGE for purity (>90%) and then dialyzed them into 20 mM Tris, pH 8.0, 200 mM NaCl, 1 mM DTT. From cysteine-free templates, we generated single cysteine mutations of Syt1 C2AB (T383C) and labeling with Alexa488-maleimide (Invitrogen) was conducted according to published standard protocol[29] (Supplementary Figure 1). Labeling efficiency (assessed by absorbance spectroscopy) was >80%.

The schematic representation in Figure b displays the N-Ras lipidation,[31] the C2AB domain from synaptotagmin1 (PDB: 1BYN),[32] full-length annexinB12, with the helical wheel representing the amphipathic structure of one of the suggested helix monomers[20] and full-length α-synuclein with the helical wheels representing the amphipathic structure of each of the helices (PDB: 1XQ8).

Assays

The single vesicle assay was utilized as previously described.[12,14] The membrane tube assay was prepared from the same vesicles as the ones used for the vesicle assay, to keep the lipid composition identical between the two membrane systems. To prepare an SLB, the freeze/thawed vesicles were extruded 21 times through two polycarbonate filters of 50 nm pore size, using an Avanti hand extruder. Quickly, 80 μL of the vesicle solution was transferred to a plasma etched glass slide mounted in a custom-made microscope chamber. After incubation for 1 h at room temperature, an SLB was formed. Excess lipids were washed away by thoroughly rinsing the surface with 50 mL of buffer. Next, the sample was incubated for 3 h at 40 °C in a cell incubator to induce tube formation. Finally, the samples were left at room temperature for 12 h to allow tube adsorption to the surface.

Measuring the Sorting of Membrane-Binding Domains by Spherical or Cylindrical Membrane Curvature

Both assays relied on confocal laser scanning microscopy, and all samples were examined with a Leica TCS SP5 inverted confocal microscope using an oil immersion objective HCX PL APO CS × 100 (NA 1.4). Detection of Alexa488 labeled MBDs was performed at 495–580 nm (exc. 488 nm); detection of Atto655 labeled vesicles was performed at 640–750 nm (exc. 633 nm). In all cases, sequential imaging was used to avoid cross excitation. Images had a resolution of 2048 × 2048 pixels, with a pixel size of 44.5 nm and a bit depth of 16. Image analysis and data treatment were performed using custom-made routines in Igor Pro (Wavemetrics) and Fiji (ImageJ).

Intensity Quantification and Size Determination of Diffraction-Limited Tubes

Our high-throughput assay produced numerous tubes of a wide variety of diameters within a single field of view (Supplementary Figure 2a). The strategy used to quantify the density of tN-Ras on the membrane tubes is based on a previously published protocol.[33] This strategy will be applied for all membrane-binding domains studied in this work. We acquired line scans across tubes in both the DiD and tN-Ras channels and normalized the intensity profiles to the intensity of the supported lipid bilayer (SLB). Then, we extracted the integrated tube intensities (IDiD and ItN-Ras) as the area under a Gaussian function fitted to the normalized intensity profiles. To evaluate sorting by membrane curvature on tubes, we need to accurately assign tube diameter. Thus, we exploited that the assay produced tubes both below and above the diffraction limit (Supplementary Figure 2b). For the nondiffraction limited tubes, we could quantify the physical tube diameter as the interpeak distance and extract the integrated intensity by fitting a double Gaussian function to a line scan across the tube (Supplementary Figure 2c). We confirmed that even the largest tubes where fully axially resolved by measuring the full-width at half-maximum of the axial optical slice thickness to be fwhmaxial = 3500 μm, using the method described in Kunding et al.[23] This is important since an accurate determination of the integrated intensity relies on the object being smaller than the confocal volume. Next, we plotted the integrated intensity as a function of tube diameter for seven nondiffraction limited tubes and fitted them with a straight line (Supplementary Figure 2d). The strong correspondence between the data and the straight line fit substantiates that tube diameter scales linearly with integrated intensity. In addition, this strong linear correlation verified that tubes are not significantly deformed, which is pivotal when employing the assay for studying sorting by membrane curvature. A vertical z-scan of a resolved tube supports that there was no apparent collapse of the tube on the SLB (Supplementary Figure 2a, inset). Since previous experimental[24] and theoretical work[34] has shown that membrane deformation preferentially affects tubes of larger diameters, we do not expect any deformation for tube sizes below the optical resolution limit. We used the slope of the fit to convert diffraction limited tube intensities to tube diameter. Using this method, we converted the intensity histogram of 627 tubes acquired under identical imaging conditions to a tube size histogram in nm (Supplementary Figure 2e,f). We evaluated the error as the SEM between three individual measurements on each tube. We plotted a histogram of the errors in Supplementary Figure 2g and found them to be distributed between 0.1% and ∼30%, with the majority (∼75%) being below 10%. The trend is apparent in a plot of the percentage error versus tube diameter for the individual tubes, displaying that it is only for the very smallest tube diameters, that you start to see a minor subset of tubes with larger errors (Supplementary Figure 2h). To evaluate the uncertainty on the calculated densities, we propagated the SEM from the intensity measurements in the two channels. The histogram of the propagated errors for the tN-Ras densities presented in Figure established that the majority of the errors were below 10% (Supplementary Figure 2i).

Molecular Field Theory

We use a highly detailed molecular field theory to determine the physical properties of curved lipid bilayers that are needed to elucidate the molecular mechanics of protein recruitment by cylindrical and spherically curved membrane geometries. In particular, we use the theory to calculate the lateral stress profiles across the membrane, the lipid area per molecule in both leaflets, the electrostatic potential, the distribution of hydrophobic interactions, and the protein density profiles for lipid membranes of cylindrical and spherical geometry. The purpose of using this approach is to easily determine how Gaussian curvature contributes to the thermodynamics of protein binding. The basic concept of the theory is to consider each possible conformation of the lipids and formulate a free energy in terms of the probability of each of those conformations. By summing over each possible conformation, we are explicitly including fluctuations into the calculation. The intramolecular interactions are therefore treated exactly within the model. The intermolecular interactions are only exact within the length scale of a single molecule, so correlations beyond that length scale are only approximate. We are using a field theory that includes the physical conformations of the molecules and fluctuations, and we expect the agreement that we see with the experiments to be due to these improvements over more simplified mean-field theories.

The molecular theory uses a free energy functional that is constructed by explicitly writing each of the energetic/entropic contributions and then minimizing the free energy with respect to the free variables. There is only one fitting parameter used in the calculation, and that is the strength of the hydrophobic interactions between CH2 and CH3 groups of the lipids or proteins. Every other physical parameter is obtained from the experimental literature (for more details please see the Supporting Information). We input the physical conformations of the chains, and through free energy minimization we obtain the probability of each of those conformations as a function of the constraints imposed on the system. Through this method, we are able to obtain the molecular level equilibrium physical parameters (such as local lateral stresses, area per molecule, lipid flip-flop between leaflets, and local molecular organization and architecture) that we need to elucidate the fundamental molecular driving forces for protein recruitment. All of the details about the model and the calculation procedures are explained in the Supporting Information.

Independent Method Verifies the Linearity between Integrated Tube Intensity and Tube Diameter

Assuming no curvature dependent sorting of DiD,[35] the integrated tube intensity is theoretically predicted to scale linearly with tube diameter:

To verify this prediction, we employed a well-characterized technique for preparing nanometer sized tubes with accurate tube diameters, i.e., pulling tubes from GUVs. By controlling the GUV aspiration pressure, P, we could obtain the membrane tension fromwhere rp and rGUV is the radius of the micropipette and GUV, respectively. The tube diameter can be accurately determined from the relation .[33] Using a tube pulling setup analogous to the one described by Ramesh et al.[33] with DiD labeled GUVs, we could relate the integrated fluorescent intensity across a tube to the tube diameter obtained from controlling the aspiration pressure (Supplementary Figure 3a,b). This allowed us to plot the integrated tube intensity against tube diameter for tubes of five different diameters (Supplementary Figure 3c). The good agreement between the data and the linear fit in Supplementary Figure 3c verified that tube diameter scales linearly with the integrated tube intensity.

Membrane Tubes Are in Lateral Diffusive Contact with the Supported Lipid Bilayer

To test whether tubes are in diffusive contact with the supported lipid bilayer, we performed FRAP experiments on whole tubes adsorbed to the SLB (Supplementary Figure 5a). We bleached an area containing a diffraction-limited tube and recorded the time dependent intensity recovery of ROIs on the tube or on the SLB next to the tube. As displayed in Supplementary Figure 5b, there is full recovery within minutes for the 10 μm × 20 μm area bleached. To ensure that tube recovery was not due to lipid translocation from the top leaflet of the SLB to the outer leaflet of the tube, we performed an additional control experiment. We allowed vesicles labeled with DiD in the membrane and Alexa488 in the lumen to sediment on the SLB (Supplementary Figure 5a, inset). Upon bleaching of the DiD label, we could track that the vesicle was still present on the SLB using the Alexa488 signal. However, even after 30 min, no recovery of the DiD signal was detected, and thus we conclude that there is no recovery by lipid translocation (Supplementary Figure 5c) and that the recovery stems from the tube being in diffusive contact with the SLB.

The single tube FRAP experiments also strongly indicate that tubes are indeed unilamellar, since we get essentially full recovery after bleaching. Had the tubes been multilamellar, some of the inner leaflet would not have been in contact with the SLB and should thus not have recovered. The unilamellarity of our tubes is in agreement with previous findings for tubes extracted from an SLB.[36,37]

The evidence for diffusive contact between the tube and the SLB signifies that the tube system is connected to a flat membrane reservoir, which the vesicle system is not. However, since the theoretical calculations are performed for both tubular and vesicular systems having no flat membrane reservoirs and show excellent agreement with the experimental findings, we take that the presence of a flat membrane reservoir does not significantly affect the sorting by membrane curvature, but merely ensures a fluid and homogeneous lipid state of the tube membrane.

Statistical Analysis

Quantification of Sorting by Membrane Curvature and Result Summary

To quantify the sorting by membrane curvature, we used error weighted fitting of an offset power function to the MBD density versus tube or vesicle diameter data as previously described:[12]with DMBD being the MBD density, D0 being the offset MBD density value, dves is the tube or vesicle diameter, and α and β are the power and amplitude of the fit, respectively. From the obtained fits, we quantified the relative sorting ratio (R), as the increase in MBD density, when reducing the diameter a factor of 10. R was calculated as the ratio between the density on a 40 nm and a 400 nm liposome:

We use the R value to compare the sorting by membrane curvature of MBDs by cylindrical and spherical curvature. A list of all experiments performed, grouped by MBD, is presented in Supplementary Table 1. For all four MBDs, the two-tailed Student’s t test was used to evaluate (1) the significance of MBD sorting as compared to the negative control Strep and (2) the significance of the sorting difference between tubes and vesicles. The results are displayed in Supplementary Table 2.