Geometrical Membrane Curvature As an Allosteric Regulator of Membrane Protein Structure and Function

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Biophysical Journal Volume 106 January 2014 201–209 201

Geometrical Membrane Curvature as an Allosteric Regulator of Membrane Protein Structure and Function

Asger Tonnesen,†‡§ Sune M. Christensen,†‡§ Vadym Tkach,†‡§ and Dimitrios Stamou†‡§* †Bionanotechnology and Nanomedicine Laboratory, Department of Chemistry, ‡Nano-Science Center, and §Lundbeck Foundation Center for Biomembranes in Nanomedicine, University of Copenhagen, Copenhagen, Denmark

ABSTRACT Transmembrane proteins are embedded in cellular membranes of varied lipid composition and geometrical curvature. Here, we studied for the ﬁrst time the allosteric effect of geometrical membrane curvature on transmembrane protein structure and function. We used single-channel optical analysis of the prototypic transmembrane b-barrel a-hemolysin (a-HL) reconstituted on immobilized single small unilamellar liposomes of different diameter and therefore curvature. Our data demonstrate that physiologically abundant geometrical membrane curvatures can enforce a dramatic allosteric regulation (1000-fold inhibition) of a-HL permeability. High membrane curvatures (1/diameter ~1/40 nm1) compressed the effective pore diameter of a-HL from 14.2 5 0.8 A˚ to 11.4 5 0.6 A˚ . This reduction in effective pore area (~40%) when combined with the area compressibility of a-HL revealed an effective membrane tension of ~50 mN/m and a curvature-imposed protein deformation energy of ~7 kBT. Such substantial energies have been shown to conformationally activate, or unfold, b-barrel and a-helical transmembrane proteins, suggesting that membrane curvature could likely regulate allosterically the structure and function of transmembrane proteins in general.

INTRODUCTION Transmembrane proteins are embedded in cellular mem- b-barrel bacterial exotoxin a-hemolysin (a-HL) (13,14), in branes that locally differ in their lipid composition and their liposomes with symmetric leaflet lipid composition of shape, or geometrical curvature (henceforth curvature). The zero spontaneous curvature. The wealth of knowledge avail- term curvature describes here the geometrical shape of a able on a-HL (13,14) allowed us to handle a-HL as a mem- membrane that has been imposed by an external force, e.g., brane-force probe to experimentally quantify for the first by a protein coat. Thus, curvature describes a nonequilibrium time to our knowledge membrane force and energy as a state and is distinct from the intrinsic spontaneous curvature function of membrane curvature. of a membrane, which favors equilibrium shapes and is zero In vivo, membranes of different curvature typically differ for membranes of symmetric leaflet composition. also in their lipid and protein composition (8,10). To decon- The lipid composition of cellular membranes has been volve the regulatory effects of biochemical composition long established as a critical effector of the structure and from curvature, we performed experiments in vitro, at a fixed function of transmembrane proteins via both indirect phys- lipid composition and over a range of physiologically impor- ical effects and direct chemical interactions; and in that tant membrane curvatures (1/500–1/50 nm1). a-HL is one of sense the lipid bilayer acts as an allosteric regulator (1–6). the best characterized members of a family of transmembrane However, there is currently no evidence to demonstrate b-barrel proteins found in the mitochondria and chloroplasts whether, under constant lipid composition, changes in mem- of eukaryotic cells and the outer membranes of Gram-nega- brane curvature that occur, e.g., during endo- or exocytosis, tive bacteria (14,15). We used this prototypical b-barrel to is missing can play an equally important regulatory role for quantify the magnitude of intrabilayer forces exerted by transmembrane proteins (7). Most studies to date have membrane curvature on an imbedded protein, and thus eval- instead focused on the ability of membrane curvature to uate whether such ubiquitous membrane mechanical effects regulate the localization of membrane-binding domains are likely to regulate allosterically the structure and function (8–11) and lipids (12). We therefore investigated here the of transmembrane proteins in general. By the very nature of direct allosteric effect of membrane curvature on the struc- a-HL, membrane insertion is unidirectional because of the ture and function of a transmembrane protein, the prototypic bulky charged extracellular globular domain on each mono- mer that cannot pass through the membrane (14,16). The most powerful method to measure the permeability Submitted August 28, 2013, and accepted for publication November 12, of pore- and channel-forming proteins at the single-mole- 2013. cule level is through electrical recordings of ion conduc- *Correspondence: [email protected] tance (17). However, neither patch-clamp technique (17) Sune M. Christensen’s present addresses are Howard Hughes Medical Insti- nor black lipid membrane techniques (16) can perform tute, Department of Chemistry, University of California Berkeley, Berkeley, experiments with membranes bent to curvatures of 1/50– CA 94720, and Physical Biosciences Division, Lawrence Berkeley National 1/100 nm1 (18), which abound in eukaryotic membranes Laboratory, Berkeley, CA 94720. (e.g., in endocytotic buds, caveolae, synaptic or trafficking Editor: Tobias Baumgart. Ó 2014 by the Biophysical Society 0006-3495/14/01/0201/9 $2.00 http://dx.doi.org/10.1016/j.bpj.2013.11.023 202 Tonnesen et al. vesicles, curved regions of the golgi or the endoplasmic formation on single vesicles. To exclude rare traces showing reticulum, etc. (19,20)). sequential stepwise insertion of two a-HL pores/liposome, To probe the effects of physiologically occurring mem- we selected only transport events displaying monoexpo- brane curvatures on the permeability of a-HL, we performed nential decays according to theory (Eq. 2). Furthermore, to optical single-channel recordings (21) in conjunction with exclude transport from multilamellar liposomes, traces a high-throughput membrane curvature assay (22–24) (see were accepted only if they reached background intensity, Fig. 1 and Materials and Methods). which indicated fully emptied liposomes. The transport To experimentally probe the solute transport activity of rate of Alexa488 (k) was then used to quantify the perme- a-HL (see Fig. 3 A), we prepared liposomes of diameters ability (P) of a single a-HL pore, according to P ¼ kV 40–500 nm (see Fig. 3) with fluorophore-labeled lipids (Eq. 3), where V is the liposome volume (21). As seen from (DHPE-Atto633) in their membrane loaded with a water- the raw intensity traces (see Fig. 3 D), bleaching of Alexa488 soluble fluorophore (Alexa488) in their lumen (25). The was negligible on the timescale of the transport events. liposomes were tethered on a biofunctional surface at dilute densities (see Fig. 3 B). We used confocal fluorescence microscopy (see Materials and Methods) to image ar- MATERIALS AND METHODS rays of thousands of single, surface-tethered, intact (25), and Materials nondeformed (24), nanoscale proteoliposomes of different 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1-palmitoyl- diameters (D) and membrane curvatures (1/D)(22,23). 0 2-oleoyl-sn-glycero-3-phospho-1 -rac-glycerol sodium salt (POPG), and Insertion of a heptameric a-HL pore in any of the immobi- 1,2.dioeoyl-sn-glycero-3-phosphoethanolamine-N-(cap biotinyl) sodium lized liposomes induced passive transport of Alexa488 down salt (DOPE-cap-biotin) were purchased from Avanti Polar Lipids (Alabaster, its concentration gradient (21) and a concomitant reduction AL). Neutravidin and Alexa488 hydrazide were purchased from Life of fluorescence intensity over time (see Fig. 3, C and D). Technologies (Naerum, Denmark). Atto633-1,2-dihexadecanoyl-sn-glyc- To ensure that we were measuring transport events origi- ero-3-phosphoethanolamine (DHPE-Atto633) and Atto633-1,2.dioeoyl-sn- glycero-3-phosphoethanolamine (DOPE-Atto633) were purchased from nating from single a-HL pores, we diluted the concentration Atto-Tec (Siegen, Germany). Poly(L-lysine) (20 kDa)-graft[3.5]-poly of a-HL to the point where we observed rare stochastic pore (ethylene glycol) (2 kDa) (PLL-PEG) and PLL-PEG-biotin (PLL-PEG (2)/ PEG(3.4)-biotin (18%)) were purchased from Susos (Du¨bendorf, Switzerland). Dimethylsiloxane (DMSO) and a-HL from Staphylococcus aureus were all purchased from Sigma (Broendby, Denmark). Single-channel optical recording assay -hemolysin Preparation of liposomes and a-HL pore insertion

Alexa 488 For single a-HL pore recordings, two kinds of liposomes were prepared. DHPE-Atto 633 Liposomes referred to as POPC/POPG were composed of POPC/POPG/ DHPE-Atto633/DOPE-cap-biotin (93.5:5:1:0.5). Liposomes were prepared as described previously (26). Briefly, lipids stored in chloroform were mixed in a chosen composition and dried under a nitrogen flow for D 20 min followed by 40 min in vacuum. The created dried thin lipid film was rehydrated with 1 mM Alexa488 hydrazide in buffer A (100 mM NaCl and 10 mM HEPES, pH 7.4) (2 g/L), incubated at 37C for 12 h to create a broad distribution of liposome diameters, and then freeze-thawed 20 times to maximize the percentage of unilamellar liposomes of all diameters to ~95% (25,27). The 1 mM Alexa488 in the bulk was removed by dialysis, leaving 1 mM Alexa488 inside liposomes, which was expected to produce a negligible osmotic pressure difference, thus ensuring that there was no osmotic induced membrane stretching or additional surface tension. Liposomes referred to as DOPE-inserted (see Fig. 5) were surface-immobilized POPC/POPG liposomes on which DOPE-Atto633 (200 nM) was added 4 min before adding a-HL. This resulted in insertion of the FIGURE 1 Optical recording of single-channel permeability as a func- DOPE-Atto633 only to the outer lipid monolayer. DOPE-Atto633 was tion of membrane curvature. Nanoscale liposomes tethered via biotin-neu- dissolved in DMSO (99% v/v), ensuring a final concentration of DMSO travidin on a passivated surface at a density dilute enough to be imaged with of %0.5% in the microscope chamber, as described in Hatzakis et al. confocal fluorescence microscopy on an individual basis. A fluorescently (23). In all cases, a-HL was solubilized in buffer A and added to the immo- labeled lipid (DHPE-Atto633) homogenously incorporated in the mem- bilized liposomes to a final concentration of 4.5 mM. brane provided accurate quantification of liposome diameter and therefore membrane curvature (Fig. 2). The broad range of randomly occurring liposome diameters (40–500 nm) allowed us to characterize the effect of Functionalizing surfaces and immobilization of membrane curvature in a high-throughput manner. Insertion of a-hemolysin liposomes (a-HL) into liposomes caused passive transport of a water-soluble fluorophore (Alexa488) trapped in their lumen, allowing us to record the perme- Surfaces used for a-HL pore recordings were prepared as described ability of single a-HL pores as a function of membrane curvature. previously (26–28). Ultraclean glass slides (thickness 170 5 10 mm)

Biophysical Journal 106(1) 201–209 Membrane Shape Regulates Protein Function 203 were plasma-etched for 2 min, mounted in the microscope chamber, of ~7% as described previously in Kunding et al. (27). In brief, the and incubated for 30 min with a mixture of 1 g/L PLL-PEG and PLL- integrated intensity of a single liposome (IM) is proportional to the number PEG-biotin (dissolved in 15 mM HEPES at pH 5.6) at a ratio of of ﬂuorescently labeled lipids in the liposome membrane and thereby to

1000:80. Unbound polymers were washed away with buffer A and the the liposome surface area (Aves). The diameter (D) with 7% error, dD,is surfaces were incubated with 0.1 g/L neutravidin (dissolved in 15 mM consequently related to IM by the proportionality factor Ccal according HEPES) for 10 min followed by extensive washing with buffer A. The to Eq. 1: pffiffiffiffiffi density of immobilized liposomes was controlled by recording liposome 2 binding in real time after adding 4 mL of 0.05 g/L liposomes to a chamber IMfAves ¼ p D 0D ¼ Ccal IM; dD ¼ 0:07D (1) with a total volume of 80 mL buffer. Unbound liposomes were removed by washing when the surface density reached ~500 liposomes/51 51 mm2 Ccal was quantified by the use of a calibration sample where the liposomes region. were extruded 20 times through two 50 nm polycarbonate filters (Millipore, Billerica, MA) that produced a narrow size distribution. The calibration sample was first examined by dynamic light scattering (ALV-5000 Corre- Confocal laser scanning microscopy lator equipped with a 633 nm laser line) followed by confocal microscopy using identical imagining conditions as for a normal sample. The mean in- Images were acquired on a Leica TCS-SP5 inverted confocal microscope tegrated liposome intensity of the imaged calibration sample was correlated setup using an HCX PL APO 100 magnification, 1.4 NA oil immersion to the mean radius obtained by dynamic light scattering. Once the calibra- objective (Leica, Wetzlar, Germany). For the single a-HL pore recordings, tion factor was known, all integrated liposome intensities were converted to the lumen dye (Alexa488) and the membrane label (DHPE-Atto633) were physical size. excited with 488 nm and 633 nm laser lines, respectively. Images of mem- The amount of intercalated DOPE-Atto633 (mol%) in the outer lipid brane label intensities were acquired in the range 645–750 nm using photo- membrane leaflet of individual liposomes was quantified as the percentage multiplier tube detection and acoustic optical beam splitter technology. change of integrated intensity before and after the intercalation using the Membrane images were acquired at a resolution of 1024 1024 pixels, 2 initial intensity from DHPE-Atto633 of 1.0 mol% as a reference (see each pixel corresponding to 50.5 50.5 nm , and a bit depth of 16, with Fig. 5 A). a line-scan speed of 100 Hz in the bidirectional mode, pinhole 1.5, and Lumen intensities (Alexa488) of liposomes were colocalized with four line averages. their membrane intensities (Atto633) and region of interest integrated Lumen dye intensities were selected with a bandpass filter ET 525/50 in sequential frames providing a time trace of each transport event. (Chroma Technology, Brattleboro, VT) and detected with an Avalanche To ensure that we monitored transport events originating from perfect photodiode (Perkin Elmer, Waltham, MA). Lumen images for transport pore formation of single a-HL pores, we selected pores that 1), showed traces were acquired with a temporal resolution of 147 ms/image at a res- 2 monoexponential decays, and 2), reached zero (background) intensity olution of 256 256 pixels, each pixel corresponding to 202 202 nm , according to permeability theory (Eq. 2). It is important to note that and a bit depth of 8, with a line-scan speed of 1000 Hz in the bidirectional transport to zero intensity also ensured that we were investigating unila- mode, pinhole 1.5, and four line averages. mellar vesicles. Of a total of 861 POPC/POPG liposomes, ~46% (396) showed transport within the timeframe of the experiment, of which Analysis of single liposome diameter and a-HL ~55% (218) satisfied the above two criteria and were included in the analysis. pore transport events

We extracted membrane and lumen intensities from fluorescence images using software written in Igor Pro Ver. 5.01 (Wavemetrics, Lake THEORY Oswego, OR). The software identified liposomes as membrane label inten- a sities (Atto633) above a user-defined threshold. Each of the identified lipo- Quantification of single -HL transport rates some intensities was integrated inside a scalable region of interest twice as We calculated the permeability of the single a-HL large as the liposome and subsequently background-subtracted. Diameters of imaged fluorescent liposomes (Fig. 2) were determined to a precision pores formed in liposomes of different curvatures (Fig. 3 E, and see Fig. 5 B) according to the methods of Hemmler et al. (21). Briefly, those authors calculated and AB25 POPC/POPG experimentally validated that the pore permeability (P), Liposome N = 218 20 in units of volume/time, is the product of the apparent transport rate (k) of the solute (Eq. 2) and the volume 15 confining the solute (V). In our case, V was calculated D 10 via the experimentally measured liposome size, described in Materials and Methods. For each single pore transport Liposomes (#) 5 event, k was extracted with an error dk by fitting the Lipid labels 0 kinetics of solute intensity reduction with an exponential D = C ·√I cal M 100 200 300 400 500 function: Diameter (nm) IðtÞ¼I0 expðktÞ (2) FIGURE 2 Size calibration of single liposomes. (A) The liposome diameter, D, is related to the intensity of the fluorescently labeled membrane lipids, IM, through a calibration factor, Ccal, according to Eq. 1. (B) Distri- The permeability of each single pore with error dP was then bution of POPC/POPG liposome diameters obtained in the a-HL experi- calculated as ments (Fig. 3). The number of liposomes/condition that exhibited qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > 2 2 monoexponential transport was typically 200, and covered a diameter P ¼ kV; dP ¼ ðV dkÞ þðk dVÞ (3) range of 40–500 nm. To see this figure in color, go online.

Biophysical Journal 106(1) 201–209 204 Tonnesen et al.

A D FIGURE 3 Membrane curvature changes significantly the pore radius and permeability of the Diameter 146 nm α-HL 200 Diameter 88 nm transmembrane protein a-HL as a consequence Mono exponential fit of membrane tension. (A) Schematic illustration 150 of the hypothesis to scale. (B) Zoom of representa- Alexa 488 tive ﬂuorescence images showing POPC/POPG Membrane Lumen 100 100

B DHPE-Atto633 Alexa488 Intensity (A.U.) (9:1 molar ratio) liposomes labeled ﬂuorescently 80 in their membrane and in their lumen. Scale 60 50 40 bars, 5 mm. (C) Cropped micrographs of two 0 Liposomes 20 representative time sequences show transport Norm. Intensity Alexa488 (%) 0 0 600 700 800 900 1000 events after single pore formation in two Time (s) liposomes with diameters of 146 nm (blue) and

Alexa488 leakage events Snapshots Intensity (A.U.) 50 88 nm (red). Temporal resolution 147 ms. (D) C Diameter Diameter 146 nm 88 nm 25 Fitting the normalized raw lumen intensity traces

Time (s) ~ 601 ~ 601.5 ~ 840 ~ 845 ~ 850 ~ 855 0 from the two liposomes in C allowed accurate quantification of the exponential transport rates, 1 1 Membrane Tension (mN/m) 5 5 80 0.488 0.016 s and 0.094 0.004 s , respec- EF POPC/POPG 8.0 Pore radius -1 y = a·Db tively. Bleaching of Alexa488 was negligible on 10 Fit 1 Membrane Tension /s) 3 7.5 Theoretical Tension 60 the timescale of transport. Complete transport -2 demonstrates that the liposomes are unilamellar. 10 7.0 40 (E) Increased membrane curvature reduces the -3 10 6.5 pore permeability of a-HL by four orders of 20 -4 magnitude. Here, single-pore permeability data Pore Radius (Å) 6.0 10 ¼ Permeability (µm (N 218) are fitted with a power function (pink -5 5.5 0 10 line) for clarity, where the thickness of the fit 50 100 200 300 500 0 100 200 300 400 500 reflects its uncertainty. (F) Increasing membrane Diameter (nm) Diameter (nm) curvature reduces the pore radius (black crosses) of a-HL due to the increasing tension in the membrane. Pore radii were binned using weighted averaging. The two independent calculations of bilayer tension using either the change in pore radius (red crosses) or the change in lipid packing (dashed pink line), are in good agreement. Pore radii and tension data are calculated using a cylinder model of the a-HL pore. Error bars represent the mean 5 SD.

2 1 a-HL pore model and calculation of effective Alexa488 with Di ¼ 400 mm s (31,32). Furthermore, single pore radii we neglected the role of charges of Alexa488 and of the pore interior, because the preference of a-HL for conducting To calculate the effective pore radius (r)ofa-HL (Fig. 3 F, negative relative to positive charges is only 10% (33). black crosses) from the quantified permeability of the single pores shown in Fig. 3 E, we used an analytical description of the pore permeability (Eq. 4) developed in Deen (29) Calculation of membrane tension using the pore and Peters (30), which takes into account hindrance of deformation solute diffusion in the pore by a transport probability factor, To be able to determine the tension (g) of a curved mem- 4(r). Briefly, the permeability of a pore is described by its brane, needed to impose the observed pore deformation effective interior cross-sectional area (A), its pore length (Fig. 3 F, black crosses), we first estimated the compress- (L), and the diffusion constant (D ) of the transported solute i ibility of the a-HL pore. Because in a lipid bilayer trans- in bulk. In our case, the diffusion of the solute Alexa488 membrane proteins experience pressures only in the plane with radius a inside the a-HL pore was hindered as the r of the membrane, we could not use literature values of vol- of the compressed pore approached a. The probability fac- ume compressibility, but had to estimate the area compress- tor, 4(r), described the pore area excluded by the solute it- ibility, k . The fluctuation-dissipation relation from self and in the limits r ¼ a and r >> a took the values A thermodynamics (Eq. 5) was applied to estimate the k of 4(r) ¼ 0 and 4(r) ¼ 1, respectively. To link P and r,we A the transmembrane b-barrel of the a-HL pore by using the assumed the interior of the homoheptameric pore to be cir- fluctuations of the cross-sectional area of the pore’s interior: cular along the z axis with a pore radius r: A2 A 2 N 1 d A h i h i A h i D A D A a 2 D r2 a 2 kA ¼ ¼ (5) P ¼ i ðrÞ¼ i 1 ¼ i p 1 hAi RT hAi dg L 4 L r L r (4) This relation has been previously used to calculate area compressibilities of various membranes from the areal fluc- To calculate the r of a-HL (Fig. 3 F, black crosses, and tuations obtained in simulated lipid bilayers (34,35) and has Fig. 4) from the quantified P, we used L ¼ 10 nm as been validated experimentally (36). For the a-HL pore, we measured in its crystal structure (13) and a ¼ 0.56 nm of estimated the average compressibility of the pore section

Biophysical Journal 106(1) 201–209 Membrane Shape Regulates Protein Function 205

A 40 in good agreement with the variation/ﬂuctuation in NaCl POPC/POPG conductance of 6.8% obtained by electrical conductance N = 218 measurements (37). 30 µ = 7.4 SD = 1.8 To calculate the bilayer tension (Fig. 3 F, red crosses) 20 SE = 0.1 needed for the observed deformation, we combined the estimated KA,p value with our observation of the changed pore

Single Pores 10 radius for different membrane curvatures (Fig. 3 F, black crosses). Integrating the standard relation between tension 0 and areal change (Eq. 8) with the assumed pore circularity 6 8 10 12 14 gives tension as a function of pore radius: Pore Radius (Å) dA dg ¼KA;p 0 B A 40 POPC/POPG ¼K ðA=A Þ¼2K ðr=r Þ N = 218 g A;p ln 0 A;p ln 0 (8) sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 30 µ = 3.0 K 2 r 2 SD = 1.3 d A;p d dg ¼ g þ 2KA;p 20 SE = 0.1 KA; p r

Single Pores 10 This implies an increase in bilayer tension of g ¼ 53 5 0 13 mN/m in a highly curved membrane (40 nm) relative 2 4 6 8 to zero tension in a ﬂat membrane (500 nm). Pore Radius Error (%)

FIGURE 4 Single a-HL pores in liposomes. (A) A distribution of calcu- Theoretical calculation of tension in a liposome lated pore radii of single pores formed in POPC/POPG liposomes has a peak at radius ~7 A˚ with a mean 5 SD value of 7.4 5 1.8 A˚ .(B) The We calculated the theoretical tension (gm) as a function of percentage distribution of the pore radius errors of the single pore radii liposome diameter (Eq. 9), thus curvature (Fig. 3 F, dashed shows low errors ranging between 1 and 8%, comparable to the spread red line), using the expansion and compression of the of ~7% obtained by electrical pore conductance measurements (37). outer and inner membrane monolayers (19,35,38) according to the methods of Malinin and Lentz (39), who derived the around the amino acids T145, where the minimal pore corresponding energy term. Briefly, for a liposome with radius is found. A circular shape is a good approximation a mean diameter D, both expansion and compression of of the interior cross-sectional area of the symmetric a-HL the lipid areas in the outer (Aout) and inner (Ain) membrane pore. In that case, kA takes the form of Eq. 6, where it is leaflets, respectively, are derived by employing spheres of seen from the last term that the area compressibility only diameter D þ 2h and D 2h in the first term in (Eq. 9) depends on the radial fluctuations (sr) of the pore: and integrating over the neutral leaflet surfaces of the outer (A ¼ p(D þ 2h)2) and inner (A ¼ p(D 2h)2) hA2ihAi2 N ðAÞ N 2 N out in k ¼ A ¼ var A ¼ sA A membranes (39). A;p hAi RT hAi RT hAi RT dA A 2 d ¼K 0 ¼ K out ð2p r srÞ NA 2 NA gm A;m gm A;m ln ¼ ¼ 4ps (6) A Ain

hp r2i RT r RT 1 = 2 D þ h

¼ 2KA;m (9) ln 1 = 2 D h The area compression modulus of the a-HL pore, KA,p h 1/kA,p, is hereby derived, with its propagated error, as Here, h ¼ 1.8 nm is the distance from the membrane middle RT RT K ¼ ; K ¼ dsr (7) to the neutral surfaces of the leaflets where expansion/ A;p 2 d A;p 2 4psr NA 2psr NA sr compression is decoupled from membrane bending. We used a membrane compression modulus for POPC KA,m ¼ We calculated an average pore compression modulus of 235 mN/m (36). KA,p ¼ 131.2 5 26.4 mN/m using sr ¼ 0.5 A˚ , as reported for T145 in a 50-ns-long all-atom simulation of a preequi- Calculation of membrane curvature deformation librated a-HL pore in a flat DPPC membrane (33). We as- energy signed dsr ¼ 10% error to sr. The fluctuation of the pore structure found in the simulation, sr ¼ 0.5 A˚ , which corre- The energy, E, corresponding to a deformation of a channel sponds to a fluctuation of ~7% for the pore radius at T145 is or a pore like a-HL, is the product of the change in pore

Biophysical Journal 106(1) 201–209 206 Tonnesen et al. area, DA, and the applied 2-dimensional pressure (mem- of a-HL, we estimated it from the amplitude in thermal fluc- brane tension), gm,as tuations of the pore structure obtained from an atomic simu- qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi lation of a-HL in an unperturbed planar membrane (Eq. 7). 2 2 We found a tension of ~50 mN/m in highly curved mem- E ¼ gm DA; dE ¼ ðDA dgmÞ þðgm dDAÞ (10) branes that declined toward zero in flatter membranes (Fig. 3 F, red crosses). This finding is in agreement with the idea that an unperturbed planar membrane is tensionless, RESULTS AND DISCUSSION as the symmetric lateral pressure profiles of its two leaflets equalize, whereas membrane curvature enforces an asym- Increasing membrane curvature inhibits single metric pressure profile, produced by the rearrangement of a-HL pore permeability the lipid packing in the two membrane leaflets. This lipid We were then able to plot the permeability from single a-HL packing rearrangement, occurring with increased curva- transport events as a function of liposome diameter (Fig. 3 ture-enhanced lipid compression and pressure in the lipid E). The a-HL pore is structurally extremely stable, which headgroup region of the inner membrane leaflet, but also a suggests that large forces would be required to induce remarkable pressure in the alkyl chain region of the outer detectable changes (16,40). Interestingly, the experiments monolayer, resulted in increased tension (41). These two revealed that membrane curvature reduced pore perme- regions of increased pressure on the a-HL pore imply a ability by nearly four orders of magnitude over the investi- reasonable cylindrical pore model that is concentrically gated range of curvatures. This demonstrates a remarkably compressed upon increased membrane tension. Values of potent allosteric inhibitory effect of membrane curvature pore radius, membrane tension, and the related deformation on the activity of a-HL. energy are effective values and their variations across the membrane and the asymmetry of the membrane are not taken into account in these calculations. The pore model Effective pore radius changes with membrane used neglects a possible dependence of pore area compress- curvature ibility on membrane curvature that most likely would Next, we converted the measured permeability values decrease with increased pore compression and therefore (Fig. 3 E) to absolute effective pore radii, adopting the yield a higher membrane tension than the ~50 mN/m widely used approximation of hindered solute diffusion in- cited above for highly curved membranes. Our findings side a cylindrical pore ((29,30) and Eq. 4). The accurate suggest that activity and deformation of a-HL depended measurements of permeability allowed us to calculate the on the degree of membrane tension imposed by membrane individual effective pore radii with an average weighted curvature. standard deviation (SD) of 0.24 A˚ (Fig. 4). Uncertainties As a cross-validation, we performed an independent spanned 1–8%, which is comparable to the spread in potas- theoretical calculation of the tension present in a mem- sium conductance of 7% obtained by high-resolution elec- brane due to curvature-induced changes in lipid packing trical recordings of a-HL (37). of the outer and inner membrane leaflets. According to For pores formed in liposomes of low curvature (500 nm), other reports in the literature (19,35,38,39), the change in we calculated a mean radius (5 SD) of 7.1 A˚ 5 0.4 A˚ .This lipid packing of a spherical liposome can be calculated as was in good agreement with the average radius of 7 A˚ the expansion and compression of lipid area in the outer measured in the crystal structure (13), and with the experi- and inner layers (Eq. 9), assuming that deformations are mentally measured effective pore radius of 9 A˚ (21), further elastic, and that the compression moduli of the pore and supporting the reliability of our activity measurements and the membrane are constant with curvature. As seen in the quantitative data analysis based on the pore cylinder Fig. 3 F (dashed pink line), the theory was indeed in model. The effective pore radius of a-HL was continuously good quantitative agreement with the tension values calcu- reduced by membrane curvature, down to a mean value of lated independently from pore deformation data (Fig. 3 F, 5.7 A˚ 5 0.3 A˚ for the smallest measured liposome diameter red crosses). of 40 nm (Fig. 3 F, black crosses). Controlling pore permeability by changing Linking pore compression to effective membrane membrane leaflet asymmetry tension To further test the dependence of a-HL pore deformation We next calculated the membrane tension needed to induce on membrane tension, we performed a control experiment the observed conformational change (Fig. 3 F, red crosses) designed to modulate selectively the lipid composi- using the direct relation between membrane tension, pore tion of only the outer membrane leaflet and thereby the compressibility, and pore deformation (Eqs. 5–8). Because curvature-induced asymmetry of the lateral pressure it is not possible to measure directly the area compressibility profile (42). This was achieved by addition of a lipid at

Biophysical Journal 106(1) 201–209 Membrane Shape Regulates Protein Function 207 the exterior of the liposomes, after liposome formation Effective membrane curvature deformation and immobilization. We used a lipid that was labeled energy fluorescently at the headgroup (DOPE-Atto633) for two Our data on increasing pore deformation with membrane reasons: 1), to allow in situ quantification of the absolute curvature, and the independent theoretically calculated mem- amount of incorporation into the outer leaflet of each brane tension, provide a measure of pore-deformation energy single liposome shown in Fig. 5 A, in agreement with (Eq. 10). The quantified pore-deformation energy is zero for a Hatzakis et al. (23); and 2), to minimize flip-flop to the flat membrane (Fig. 6) but increases with membrane curva- inner membrane leaflet during data acquisition, because 1 ture and reaches ~7 kBT (~28.8 pN nm, ~17.4 kJ mol )in Atto633 is a large zwitterionic and hydrophilic moiety. membranes of high curvature (1/40 nm 1). The short time delay from addition of DOPE-Atto633 to Introducing lipids of spontaneous curvature can modulate acquisition of a-HL events, on the order of a few minutes, the strong dependence of energy and tension on membrane further minimized possible flip-flop (see Materials and curvature as verified by adding DOPE-Atto633. In general, Methods). biological lipid membranes are not symmetric in composi- Labeling of DOPE at the headgroup also converted it tion, which introduces a nonzero spontaneous membrane effectively to an inverted cone-shaped amphiphile. This curvature, and it is therefore the mismatch between geomet- shape, which energetically favors the outer monolayer, pre- rical and spontaneous curvature that defines the induced vented its flip-flop to the inner monolayer (19) and favored membrane tension and energy, as described by Helfrich the relaxation of the membrane tension upon incorporation. elastic membrane theory (43). The latter is confirmed in Fig. 5 B, where insertion of labeled DOPE into the outer leaflet resulted indeed in a relaxation of the membrane and a reduction of the mem- CONCLUSION brane-curvature effect on pore permeability by a factor of 5 for the smallest liposomes, thus validating the contrib- It is well established that changes in the lipid composition of uting effect of membrane tension on pore permeability membranes can regulate the localization and structure of and hence pore structure, when compared to POPC/ both membrane-associated and transmembrane proteins POPG liposomes (Fig. 3 E). To further verify how the (2–5). In contrast, geometrical membrane curvature has at- DOPE-Atto633 insertion directly affected the a-HL pore tracted recent attention as a putative regulatory mechanism relative to pores in POPC/POPG liposomes, we calculated that can operate independently of the composition of mem- the relative increase in pore permeability (Fig. 5 C) using branes (8,44). A number of experiments have suggested that the DOPE insertion trend in Fig. 5 A and the permeability for a fixed membrane composition, curvature can regulate fit parameters of Figs. 5 B and 3 E. Hitherto, Fig. 5 C the spatial localization of many soluble proteins possessing shows the x-fold increase in a-HL pore permeability a variety of different membrane-binding domains (8,9) upon DOPE-Atto633 insertion that additionally verifies (including BAR domains (45), amphipathic helices (10), the relaxation of the liposome membrane tension on and lipid anchors (23)), as well as lipid diffusion (46), sort- the pore. ing, and segregation (12). Our data expand significantly the

A B C 8 DOPE inserted 6 DOPE inserted -1 DOPE inserted 10 b p /s) Fit y = a·D 5 Fit y = y + a·D 3 2 6 3 0 -2 y 10 4 0 = 0.06 ± 0.19 4 a =26097 ± 51600 -3 3 p =-2.03 ± 0.44 10 2 2 -4 Inserted (mol%) 10 1 Permeability (µm -5 log

0 10 X fold permeability increase 0 100 200 300 400 500 50 100 200 300 500 0.1 1 10 Diameter (nm) Diameter (nm) Inserted (mol%)

FIGURE 5 Insertion effect of labeled DOPE in single liposomes on a-HL permeability. DOPE-Atto633 inserted exclusively into the outer membrane leaflet (asymmetric insertion) of the preformed and immobilized POPC/POPG liposomes of different membrane curvatures (N ¼ 328). (A) As observed previously (23), the amount of labeled DOPE inserting into liposomes increased as a power function of membrane curvature by a factor of 10 at high curvatures and was quantified as the mol% lipid increase from the change in intensity of Atto633 before to after incubation. (B) Raw single a-HL pore-permeability measurements revealed that asymmetric DOPE insertion relaxed the tension on the single pore imposed by membrane curvature. A comparison of the slope (exponent) b ¼ 1.94 5 0.03 of the fit (blue line) to the slope b ¼ 2.62 5 0.03 for pores formed in POPC/POPG liposomes (Fig. 3 E, red line) confirms a significant reduction of pore permeability by DOPE insertion. The uncertainty in permeability of the fit is represented by the line thickness, which is a prop- agation of a and b and their fit errors. (C) The relative x-fold increase in pore permeability as a function of DOPE insertion on a linear-log plot implies that DOPE insertion releases the membrane tension on the pore. The relative increase was calculated using the DOPE insertion data in A and the permeability fit parameters of B and POPC/POPG (Fig. 3 E). Note the convoluted influence of DOPE insertion density and membrane curvature on pore permeability. Data in A and C were binned using weighted averaging and error is represented as the mean 5 SD. To see this figure in color, go online.

Biophysical Journal 106(1) 201–209 208 Tonnesen et al.

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