Abstract
Lipids play key roles in Biology. Mechanical properties of the lipid bilayer influence their neighbouring membrane proteins, however it is unknown whether different membrane protein properties have the same dependence on membrane mechanics, or whether mechanics are tuned to specific protein processes of the protein. We study the influence of lipid lateral pressure and electrostatic effects on the in vitro reconstitution, folding, stability and function of a representative of the ubiquitous major facilitator transporter superfamily, lactose permease. Increasing the outward chain lateral pressure in the bilayer, through addition of lamellar phosphatidylethanolamine lipids, lowers lactose permease folding and reconstitution yields but stabilises the folded state. The presence of phosphatidylethanolamine is however required for correct folding and function. An increase in headgroup negative charge through the addition of phosphatidylglycerol lipids favours protein reconstitution but is detrimental to topology and function. Overall the in vitro folding, reconstitution, topology, stability and function of lactose permease are found to have different dependences on bilayer composition. A regime of lipid composition is found where all properties are favoured, even if suboptimal. This lays ground rules for rational control of membrane proteins in nanotechnology and synthetic biology by manipulating global bilayer properties to tune membrane protein behaviour.
Introduction
The interaction of proteins and lipids in membranes is central to cellular function. Whilst proteins are key players in regulating transport and communication across membranes, the lipids are not just passive bystanders that provide an impermeable layer, but are also active participants in membrane reactions1,2. Certain lipids, such as inositol phospholipids, operate in terms of chemically specificity3, whilst others interact directly with membrane proteins as in the case of cardiolipin with cytochrome oxidase4,5. Annular lipids, which are proposed to surround proteins in membranes, have also attracted attention6,7. However, there is another, relatively unexplored lipid mechanism, in which global properties of the lipid bilayer regulate protein behavior. The mechanical and charge properties of the bilayer affect membrane protein folding, stability, topology and function8–13.
Many different lipids are found in biology, providing a means to maintain the fluid bilayer that is crucial to membrane integrity and function. Manipulating lipid compositions in vitro proffers the chance to probe the influence of such global bilayer properties on membrane proteins. A range of distinct but interdependent global properties are involved; including stored curvature elastic stress, lipid monolayer curvature, lipid lateral pressure, bending rigidity, area expansion modulus, hydrophobic thickness and headgroup charge14,15.
Phosphatidylcholine (PC) lipids (e.g. L-α-1,2-dioleoylphosphatidylcholine, DOPC) form monolayers with relatively flat interface with water that tend to form fluid, lamellar (bilayer) phases. In contrast, phosphatidylethanolamine (PE) lipids like L-α-1,2-dioleoylphosphatidylethanolamine (DOPE) have very different properties. The ethanolamine headgroup contains a primary amine that can form both intra- and inter-lipid hydrogen bonds, which increases the transition temperatures and significantly alters the hydration at the water:lipid interface. The intermolecular forces and reduced size of the headgroup compared with PC lipids also contributes to a greater desire to curve towards an aqueous phase and form inverted hexagonal (non-lamellar) phases16–18. Addition of DOPE to a DOPC bilayer increases the monolayer curvature and the stored curvature elastic stress of the PC/PE bilayer. An effect of introducing PE lipids into a PC bilayer is to redistribute the lateral pressure; resulting in a decrease in the headgroup region and an increase in the chain region19. This alteration of lateral pressure by PE and the proposed resultant effects on proteins has previously been discussed20–22. Anionic lipids are also a major component of biological membranes with headgroups such as phosphatidylserine (PS) and phosphatidylglycerol (PG) common. Similarly to DOPC, 1,2-dioleoyl-glycero-3-phosphoglycerol (DOPG) forms a fluid lamellar bilayer in physiological conditions, and the addition of DOPE increases the monolayer curvature23 with predicted corresponding effects on the lateral pressure profile.
Correct folding is an essential process for any protein. The folding feat has been extensively explored for water soluble proteins, but there is considerable less known for membrane proteins, especially in lipid membranes. It has previously shown that lipid composition affects protein folding, topology and function and we have postulated that different membrane protein properties, such as insertion, folding, stability and function are likely to be favoured by different membrane lateral pressures24–26. Increasing the amount of PE lipids in a PC bilayer has been found to increase the stability of the KcsA potassium channel11 and activation energy for insertion of a transmembrane helix have been found to increase with increasing PE27. This increase in activation energy was assigned to the difficulty of inserting a helix across the bilayer when the pressure in the lipid chain region is higher. Similarly increasing the PE content of bilayers decreased the folding yield of bacteriorhodopsin, which was inserted into PC/PE bilayers from a partially denatured state28. The results pointed to the increased chain pressure hindering insertion of a folding protein across the bilayer. These studies however are on model peptides/proteins, with bacteriorhodopsin being an unusually stable protein, and the results on lipid effects on folding have not been generalised in any systematic manner.
In parallel to our studies on lipid influence of membrane protein folding, we have also been advancing mechanistic folding work to families of larger, flexible membrane proteins, including the vast ubiquitous major facilitator superfamily (MFS) of transporters. The transporters are relatively large with predominantly helical, dynamic structures that are usually arranged in, two, 6-helical domains. We have shown that the MFS galactose and lactose transporters (GalP and LacY) can be folded from a partially denatured state in urea into lipid bilayer vesicles29,30. Moreover, we found a dependence of folding yield for the MFS galactose transporter, GalP, where the folding yield increased with PE to give optimal recovery of secondary structure with 0.6 DOPE (mole fraction) present in DOPE/DOPC lipid vesicles. Higher PE content reduced the yield of folded protein29.
Lipid composition also influences the transport activity and topology of the MFS lactose transporter LacY in vitro and in vivo 31,32. In the absence of the dominant E. coli membrane lipid, PE, the N domain of LacY is flipped into an inverse topology, upside down in the membrane compared to the C domain33–36. This has been assigned primarily to a charge effect across the membrane. The transport activity of LacY has been shown to be affected by the surrounding lipid composition both in modified E. coli strains in vivo and in vitro reconstituted protein31,32. Previous folding work using chemical denaturants in a detergent micelle system has demonstrated that LacY can be reversibly folded in a similar manner and with a similar free energy of folding as GalP30. Additionally, there are 3D structures available of LacY in a variety of conformations37,38. Together this suggests that LacY is an excellent candidate protein for a more systematic study of lipid-membrane protein interactions.
Here, we test our hypotheses that lipid bilayer properties have different effects on different membrane protein properties, and begin to generalise previous results on the influence of lateral pressure on membrane proteins to an archetypal member of one of the largest transporter families. We investigate the influence of DOPE and 1,2-dioleoyl-glycero-3-phosphoglycerol (DOPG) on LacY folding, stability and function. Specifically we address: a) the efficiency of reconstitution into lipid bilayers, of LacY purified from native membranes as a folded state in detergent micelles, b) the stability of the reconstituted LacY, c) the domain topology of LacY reconstituted into bilayers, d) the transport function of reconstituted LacY and e) the folding yield of LacY, folded from a urea denatured state into bilayers. In all cases, we use a three component lipid system based on a non-native lipid DOPC to provide a basic bilayer. DOPG is incorporated as this is a native E. coli lipid that forms bilayers but introduces negative charge into the headgroup region. Additionally we add DOPE, which is the dominant headgroup in LacY’s native E. coli membranes. We explore the full range of compositions of this 3 component DOPC/DOPG/DOPE lipid system to give a comprehensive picture of the dependence of different membrane protein parameters that are critical to function, using DOPE content as a proxy for chain lateral pressure and DOPG content for negative charge.
Results
Liposomes were prepared with mixtures of the neutral lipid DOPC, the anionic lipid DOPG and the non-lamellar lipid DOPE, comprised of a range of 0–1 mole fraction DOPC and DOPG and 0–0.7 mole fraction DOPE in intervals of 0.1. Higher fractions of DOPE were not used as Large Unilamellar Vesicles (LUVs) could not be formed with those compositions. These tertiary mixtures can be visualised as a triangle (e.g. Fig. 1C) where moving in the direction of the DOPG axis point represents an increase in membrane surface charge and moving in the direction of the DOPE axis point corresponds to an increase in bilayer rigidity and lateral pressure within the core of the bilayer. Purified LacY in n-dodecyl-β-D-maltopyranoside (DDM) detergent was reconstituted into these liposomes as previously described39. Vesicles were first pre-saturated with the detergent n-octyl-β-D-glucopyranoside (OG), before addition of the protein and incubated to allow insertion into the bilayer. The excess detergent was then removed by multiple exchanges with :Bio-BeadsTM. It is important that as much detergent as possible is removed to minimise its impact on the bilayer, and the high critical micellar concentration (CMC) of OG facilitates this. The amount of residual detergent can be measured using a colorimetric assay40, with a typical result giving a final concentration of approximately 1 detergent molecule per 800–1000 lipid molecules in the bilayer (see Supplementary Figure 3). The reconstitution efficiency, secondary structure, topology, transport and stability of the protein was assessed across the full range of lipid compositions. Protein secondary structure was determined by circular dichroism (CD). The proteoliposomes of reconstituted LacY have a high background absorbance, such that CD spectra obtained in a conventional in-house machine have limited range, down to approximately 215 nm. Therefore in order to obtain full spectra allowing for deconvolution of secondary structure, samples were run using synchrotron radiation circular dichroism (SRCD). SRCD beamlines have a higher light intensity and improved signal/noise through the far UV, which enables the collection of more data from difficult samples, including down to 190 nm in lipids, thus giving a sufficient spectrum to estimate secondary structure content. Thus for example the SRCD spectrum of reconstituted LacY in a binary mixture of DOPC and DOPG of 0.8 and 0.2 mole fractions respectively (0.8/0.2 DOPC/DOPG) (Fig. 1A) gives an α-helical content of 75%, similar to that observed in the 3D crystal structure. The total protein concentration in the liposomes post-reconstitution was measured by the Markwell-Lowry assay41 and the reconstitution efficiency calculated as a percentage of originally added protein. LacY has a high reconstitution efficiency of >75% in DOPC/DOPE vesicles with DOPE mole fractions up to 0.5 but as the amount of non-lamellar DOPE is increased above 0.5 mole fraction the efficiency starts to decrease (Fig. 1B). Expanding the analysis across all possible lipid mixes shows that PE is a dominant factor influencing reconstitution efficiency, although high concentration of DOPG did promote reconstitution to between 90–100% (Fig. 1D, coded green). Values for reconstitution efficiency at the full range of lipid compositions studied are given in Supplementary Table 1.
Stability
LacY is significantly stabilised when reconstituted into a bilayer environment compared to the detergent micelles the protein used for purification. LacY in DDM micelles is susceptible to denaturation by urea, with far UV SRCD indicating that a third of the secondary structure is lost in 8 M urea (Figure S1A and30). In contrast, the protein is stable to urea denaturation in liposomes, with no change in secondary structure occurring in 8M urea (as shown by the spectra for 0.8/0.2 mole ratio DOPC/DOPG in Figure S1B). Thermal stability was assessed by circular dichroism, monitoring the loss of secondary structure during heating. It was not possible to gain enough beamtime for SRCD with appropriate temperature control to obtain full spectra so measurements were made on our specially adapted Aviv commercial machine. Since the complete spectra (characteristic of helical structure) could not be obtained for liposome samples, the signal intensity at 222 nm was monitored with temperature. As LacY is almost entirely helical in structure, the change at 222 nm is a reasonable proxy for loss of secondary structure and comparative stability. The thermal stability was compared for LacY in DDM and reconstituted into different PC/PE/PG lipid mixtures. For mixes of PC and PE, thermal denaturation curves could be fitted to a sigmoidal equation to give a melting midpoint, Tm, for comparison. LacY in DDM loses almost all of its structure when heated to 80 °C and has a low Tm at 53 °C, whereas protein reconstituted into DOPC/DOPE (0.4/0.6) mixtures only loses about half the secondary structure and has a higher Tm of 74 °C (Fig. 2A). Increasing the PE content results in a small increase in Tm compared to DOPC alone, with the Tm being 67 °C in DOPC, 70 °C with 0.2 mole fraction DOPE present, 71 °C with 0.4 DOPE and 74 °C with 0.6 DOPE present. These values are still somewhat below that observed with protein reconstituted into native E. coli lipid extracts, where the Tm was 81 °C (Fig. 2A).
LacY reconstituted into bilayers containing DOPG results in changes in the CD spectrum that were not observed in DOPC or DOPE. The spectrum in solely DOPG was more similar to that in DDM micelles, than that in mixes of DOPC/DOPG with mole fractions of DOPG < 0.2; in particular a different 210/222 nm band intensity ratio was observed for DOPG alone versus DOPC/DOPG (Fig. 2C,D). These differences in far UV CD spectra for helical proteins in lipids have been correlated with the differing hydrophobic environment of transmembrane versus soluble domains42. The change in LacY fold at high DOPG could suggest a more exposed structure. Therefore monitoring the 222 nm band is no longer a good indication of purely helical reduction when DOPG is present, and although a large reduction in the intensity of this band occurred upon heating in DOPC/DOPG liposomes it did not fit to a simple sigmoidal equation (Figure S1C).
Topology
LacY is known to form structures with an inverted N-terminal domain in vitro in liposomes lacking PE or containing PG or cardiolipin, where the first six transmembrane helices have a reversed orientation and the seventh helix is expelled entirely from the bilayer. Despite this structural rearrangement, the partially inverted LacY is still capable of facilitating transport across the bilayer43. The topology of reconstituted LacY was determined with a single cysteine mutant, S146C, in which the wild-type cysteine residues were replaced by various small aliphatic residues that allow the retention of activity as previously described in44. The single Cys is introduced at position 146 in the long loop between the N- and C-terminal domains. In the correct domain topology this loop is exposed on the outside of the liposomes and can be labelled, whilst if the N-domain is inverted before site 146 it is inside the liposome and cannot be labelled by a membrane impermeable reagent (Fig. 3A). S146C LacY was reconstituted into the different lipid mixes. The maleimide-PEG-biotin label is membrane impermeable and reacts with cysteine residues. The proteoliposomes were incubated with the label, then the reaction stopped by the addition of β-mercaptoethanol and the vesicles dissolved in 2% (w/v) n-octyl-β-D-glucopyranosideside (OG). The extent of labelling was compared to that when the liposomes were dissolved before labelling. The protein was separated by SDS-PAGE and stained with fluorescein-avidin. This modified avidin protein binds to the biotinylated LacY, allowing for easy in-gel quantification. The percentage of labelled protein before liposome solubilisation in OG was compared to the total amount labelled after solubilisation to give a measure of how much LacY is in the correct topology. In DOPC/DOPE mixtures S146C was found to be available to labelling, indicating high levels of correct topology, eg of ~80% in DOPC liposomes (Figs 3 and S3). Increasing the amount of charged lipid, DOPG with DOPC or DOPE present resulted in lower labelling of S146C, indicating an inverted topology as the headgroup charge increases, with <20% of the protein having the correct topology with DOPG mole fractions above 0.6 (Fig. 3). To ensure the changes in labelling were as a result of internal structural rearrangements and not from a total inversion of the protein during reconstitution, labelling was also performed at another site – S401C – on the C-terminal domain. This labelled with at least 75% efficiency at all lipid compositions measured, demonstrating only the N-domain was changing in structure.
Folding
In line with previous work on LacY and GalP29,30, LacY was unfolded from DDM micelles to a partially denatured state in 8M urea then refolded into liposomes. The urea denatured protein was diluted into liposomes and incubated for 30 mins. SRCD spectra were collected to assess recovery of α-helical structure after residual urea was removed by dialysis. LacY folded into 0.5/0.5 DOPE/DOPG vesicles recovered the correct secondary structure with both the intensity of the CD bands and the 210/222 ratio being equivalent to that of a reconstituted LacY sample (e.g. Fig. 4A). As previously predicted from studies on lipid composition effects on folding, increasing the DOPE content in DOPC vesicles reduced the amount of helical structure recovered, with a reduced intensity of 222 nm band as DOPE mole fractions increased from 0.2 to 0.6 (Fig. 4B plus example spectra in 4A). However some DOPE was required to attain maximum folding of LacY, with low yields of helix recovered with DOPE mole fractions < 0.2 and in DOPC alone. An approximation of refolding yield could also be determined by separating refolded proteoliposomes from misfolded protein by a sucrose flotation and measuring the total protein content of the liposomes, though this method does not distinguish between the normal and inverted topologies. This showed that DOPG was better than DOPC at supporting folding, with a reduction in folded LacY only occurring with high DOPE present (Fig. 4C). This is similar to findings from GalP that DOPC bilayers have lower folding yields and some DOPE being required for optimal recovery of the folded state24. The dependence of GalP is slightly different to LacY, with the highest yields of recovered helical structure occurring at higher DOPE mole fractions of 0.5–0.6 for GalP, but 0.2–0.4 for LacY (compare Fig. S5 29 and Fig. 4B).
Transport
LacY activity is strongly influenced by bilayer composition both in cells and in vitro 33,34. LacY is a symporter, where galactoside substrates can be transported in two ways; facilitated diffusion - downhill transport – where the sugar diffuses across the membrane down its concentration gradient, or active transport – uphill transport – where a downwards pH gradient drives substrate translocation, including moving the substrate up its own concentration gradient. A colorimetric assay was used to measure transport rates of LacY reconstituted into liposomes. The enzyme β-galactosidase was incorporated into the interior of the LUVs. This enzyme cleaves the LacY substrate ο-nitrophenol galactoside (ο-NPG) to produce nitrophenol, which can be monitored by changes in absorbance at 410 nm. ο-NPG was added to the outside of the liposomes to trigger transport, with matching internal and external buffers at pH 7.5 to measure rates of downhill facilitated diffusion. Additionally, the external pH was buffered at pH 6.5 to measure active transport driven by the proton gradient. It is important that the pH gradient is maintained for the duration of these assays. This was tested and confirmed by incorporating a pH-sensitive dye inside the liposomes and monitoring any change in fluorescence, and therefore interior pH, during transport (see supplementary Figure S2). LacY reconstituted into 0.2/0.6/0.2 DOPC/DOPE/DOPG lipids showed increased transport in the presence of the pH gradient, with a 7-fold increase in the initial rate,Vo, from 4 nmol/mg/min with no pH gradient across the proteoliposome membrane to 29 nmol/mg/min in the presence of the pH gradient. Thus protein is competent for active transport (Fig. 5B). Across the range of lipid compositions, there was little difference in rates of facilitated diffusion. However, the active transport differed considerably, with both variables being important. At least 0.4 mole fraction DOPE was required for a significant amount of uphill transport. Lipid compositions containing >0.5 mole fraction DOPG were unfavourable, which correlates with the changes in protein topology in those lipid mixes. High concentrations of DOPC also results in lower transport (Fig. 5C).
Discussion
This study confirms the premise that lipid bilayer global properties, notably electrostatic and elastic, influence different aspects of membrane protein behaviour in different ways. Here, we sought empirical correlations with membrane protein properties over a range of lipid compositions that are known to alter electrostatic charge in the headgroup region and the lateral pressure profile of the lipid bilayer. In line with our predictions, membrane protein reconstitution, folding, topology and function exhibit different dependencies on lipid composition in DOPC/DOPE/DOPG mixtures, which in turn are likely to reflect different dependencies on headgroup charge and other lipid bilayer mechanical properties.
Reconstitution and folding of LacY in lipid vesicles exhibit similar dependencies on DOPE content with the efficiency of both processes decreasing when the DOPE mole fraction is >0.5 in DOPE/DOPC/DOPG vesicles (see Figs 1 and 4). Reconstitution involves the transfer of LacY from detergent micelles into the vesicles, with the vesicle pre-treated with detergent that partitions into the vesicles to facilitate this transfer. In spite of this pre-saturation by detergent, high levels of DOPE appear to hinder reconstitution, which involves inserting the folded protein across the bilayer. Similarly, in line with previous work27, high PE concentration hinders insertion across the bilayer when LacY is folded from a urea-denatured state (with no detergent present). Reconstitution and folding differ at low DOPE, as some DOPE is needed for folding but not reconstitution. Differences are also seen in the dependence on DOPG. The latter has little influence on folding from urea, however high amounts of DOPG favour reconstitution, with yields increasing from ~75% to ~90–100% with mole fractions of >0.5 DOPG in bilayers of the tri-component bilayer mixtures studied here (Fig. 1C).
Some DOPE needs to be present in the bilayer for LacY to refold efficiently from urea. This is in line with our earlier work on the related MFS protein, GalP where low PE is unfavourable for folding29. As observed for LacY, the folding yield of GalP increases with DOPE before reaching complete recovery of folded protein, after which at higher PE the yield decreases. The proportion of PE needed to give optimal recovery of LacY is lower than GalP: highest refolding yields occur for LacY at 0.2–0.4 mole fraction DOPE (in DOPE/DOPC bilayers) and at 0.5–0.6 mole fraction DOPE for GalP.
The influence of DOPG and DOPE on several properties of reconstituted LacY was investigated. In line with the notion that an increased chain lateral pressure increases protein stability, thermal stability of LacY appeared to increase slightly with higher DOPE mole fractions. With regard to correct topology, this was observed in accordance with previous findings33. Topology is maintained in DOPC/DOPE mixtures, but the presence of charged DOPG above 0.4 mole fraction results in an inverted topology. Correlating with this is an absence of the ability to transport with DOPG present (as previously noted45), which therefore results from the inverted topology being unable to support active transport. Active, uphill, transport is the key biological function of LacY, as this allows the bacterium to utilise the proton gradient across the plasma membrane to import and concentrate galactoside substrates within the cell, and is only possible within a much narrower range of lipid compositions than transport by facilitated diffusion. The inversion in topology has previously been shown to be induced by the lipid environment and ascribed to a charge balance effect35. As previously noted DOPE aids active transport activity of LacY45. In summary, our results show that increased DOPG favours in vitro insertion and reconstitution yield, but is detrimental to topology and function once the protein is in the bilayer. Equally PE affects different aspects of membrane protein behaviour differently. PE is required for stability, topology and active transport as well as refolding from urea, but too high PE content limits folding/reconstitution yields. There is thus a region of lipid composition in the DOPC/DOPE/DOPG systems where all LacY properties studied are favourable, but not necessarily optimised (see Fig. 6).
Some of this variation in protein structure and function can be rationally explained by the changes in the physical properties of the bilayer. A membrane with high PE content has an increased bending rigidity, increased lateral pressure through the central hydrophobic region of the bilayer and extensive hydrogen bonding in the headgroup region19,20,46–50. It has been shown here to increase the stability of LacY, an effect that has also been observed with other proteins of very different structures11,51, and can likely be generalised more broadly to other membrane proteins. Similarly the decrease in yield of folded protein, both from reconstitution and folding, at the highest PE concentrations may arise from an increased lateral pressure in the core of the bilayer. It has previously been shown that the activation energy for inserting a helix across a bilayer increases with increased lipid chain pressure27. It has also been shown that the in vitro folding yield and kinetics of bacteriorhodopsin correlated with lipid chain lateral pressure in PC/PE mixtures8,52. There seems to be a requirement for intermediate concentrations of PE for efficient folding of LacY and GalP. The MFS transporters are relatively large and flexible, with two 6-helical domains, and it may be that a certain chain pressure needs to be exerted on the two domains to attain a folded state. The optimum PE concentration is somewhat different for GalP and LacY. This could be related to the N-terminal flexibility of LacY which enables the structural inversion, or just a difference in the balance of various aspects of the folding process. With further work on this, including kinetic measurements, it should be possible to isolate the differential impact of insertion and folding in the bilayer on the final folded protein yield.
Other aspects of the bilayer properties are less well understood. Although the topology inversion of LacY in high PG bilayers is relatively specific to this and some other similar proteins12,53, the “positive-inside” rule for membrane proteins is commonly observed, where an imbalance of positively charged amino acids on either side of the bilayer are important for directing the topology of membrane proteins54. It is therefore likely that large changes in bilayer charge could affect the structure and/or topology of other proteins in different ways. It can also be noted that the PC/PE and PG/PE axes are different for different properties of LacY. Although DOPG/DOPE bilayers show a similar increasing monolayer curvature with increased PE, the headgroup likely effects the lateral pressure profile in addition to the direct charge effect. More complete data on the mechanical properties of bilayers composed of these lipid mixes and especially the tertiary mixes we use here would allow further analysis of which aspects of the bilayer properties drive which protein characteristics.
It is widely accepted that lipid composition affects membrane protein function. Here, we provide a more comprehensive, systematic study giving insight into the origin of the lipid effects. Many investigations in vitro do not routinely check a wide range of lipid types and composition, and thus if the chosen lipid composition for study is suboptimal, this will influence results and the conclusions drawn regarding membrane protein function and other properties. Nonetheless, several studies do screen across lipids. Lipid influence has been ascribed to specific chemical interactions55, lipid binding pockets on the protein4, the influence of an annular shell of lipids56, hydrophobic mismatch15, charge effects as well as non-lamellar lipid properties. We provide evidence that global mechanical properties modulate different membrane protein properties in different ways. The fact that different membrane protein parameters are optimised by poising membrane mechanics at different points could be used exploited in vivo in different membranes. For example we can conjecture that the endoplasmic reticulum membrane may facilitate initial folding but a plasma membrane favours final fold and functional motions. Methods however need to be developed to probe this in cellular membranes to assess whether this is the case. In many instances membranes are likely to be poised so that all relevant protein properties are favourable. For example it has been shown that bacteria Acholeplasma laidlawii and E. coli maintain the physical state of their membranes close to a bilayer–nonbilayer phase transition, and hence if synthesis of a particular lipid is prevented, they compensate by producing another lipid with similar phase behaviour57,58.
Our systematic study of the influence of bilayer properties on various characteristics of LacY provides further evidence for the notion of lateral pressure influencing key membrane protein parameters. Furthermore, we show the dependence on lateral pressure across a range of bilayer headgroup charge. The predictive aspects that are emerging in this area, aid synthetic biology and nanotechnology applications of membrane proteins by beginning to lay down rules for designing efficient lipid systems that are optimised for the efficient insertion of functional proteins.
Methods
Materials
Lipds were purchased from Avanti Polar Lipids Inc and detergents from Anatrace. Unless otherwise stated, all other chemicals were purchased from Sigma Aldrich.
Protein expression and purification
LacY was overexpressed and purified in E. coli as previously described30. Briefly, BL21-AI (Invitrogen) cells were transformed with the lacy gene cloned in the pET28 plasmid (Novagen) with a C-terminal 10-histidine tag, grown in LB media to an OD600 of 0.8 then expression was induced with 1 mM IPTG and 0.1% (w/v) arabinose and growth continued until saturation. The cells were harvested, passed through a microfluidiser (Constant Systems) and the membranes isolated by centrifugation for 30 mins at 100,000 × g. Membrane proteins were solubilised for 2 hours in 50 mM sodium phosphate, 100 mM NaCl, 10% (v/v) glycerol, 20 mM imidazole, 2 mM B-mercaptoethanol, pH 7.4 with 2% (w/v) DDM. Solubilised LacY was bound to a 1ml Histrap column (GE Healthcare) and washed with buffer containing 75 mM imidazole and 0.05% (w/v) DDM. Purified protein was eluted with 500 mM imidazole and exchanged into a final buffer of 50 mM sodium phosphate, 10% (v/v) glycerol, 1 mM B-mercaptoethanol, 0.05% DDM pH 7.4 on a 5 ml Hitrap desalting column (GE Healthcare).
Liposome preparation and reconstitution
LacY proteoliposomes were prepared as previously described39. DOPC, DOPE and DOPG were dissolved at 50 mg/ml in cyclohexane, combined in the desired molar ratio, frozen in liquid nitrogen then dried overnight under vacuum. The lipid film was rehydrated to 10 mg/ml in 50 mM sodium phosphate pH 7.4 and stirred for 30 mins. Large unilamellar vesicles were made by extrusion (Avanti Mini-extruder) by passing at least 20 times through a filter of first 400 nm pore size, then 100 nm pore. To reconstitute LacY, the LUVs were presaturated with OG 1% (w/v), then protein was added to a final concentration of 0.2 mg/ml (w/v) and incubated for 30 mins. Excess detergent was removed by 3 exchanges of Bio-BeadsTM (BioRad) pre-equilibrated in buffer. Final protein concentration was determined by a Markwell-Lowry assay41 and the reconstitution efficiency calculated as a percentage of protein in the liposome compared to the initial amount of protein added.
Circular dichroism
Circular dichroism spectra were measured at a synchrotron on beamline UV12 at ANKA, Karlsruhe Institute of Technology. The samples were loaded in a 0.2 mm pathlength cell, scans were measured from 270 to 190 nm with 1 nm intervals and an averaging time of 3 s. 4 repeat scans were averaged and a background of empty liposomes subtracted using CDTool software59. Thermal melts were performed on an Aviv 310 CD spectrophotometer in a 1 mm pathlength cell. The CD signal at 222 nm was measured at 2deg intervals from 25deg to 95deg. Spectra were analysed using CDTool and deconvoluted on Dichroweb using CDSSTR with the SMP180 reference set60,61.
Topology
LacY with a single cysteine in the large interdomain loop was made by introducing the mutation S146C into a cysteine-free background LacY by Quikchange (Stratagene) site-directed mutagenesis. Reconstituted S146C was labelled with EZ-Link Maleimide-PEG11-Biotin (Pierce) by incubating with 100 uM of the reagent for 1 hour, either before or after solubilising the liposome with 2% (w/v) OG. Labelled protein was separated by SDS-PAGE and detected by staining the gel with 10 uM fluorescein-avidin62. The band densities were measured using ImageJ software63.
Folding
Purified LacY was unfolded by dilution into 50 mM sodium phosphate buffer pH7.4 containing 8M urea and incubated for 5 mins. As previously shown, this results in the protein losing approximately one third of its secondary structure30. This substantially denatured protein was then refolded by diluting tenfold into 10 mg/ml LUVs and incubated for 30 mins. For SRCD spectra, residual urea was removed by dialysis and the proteoliposomes scanned as above in a 0.5 mm pathlength cell. Misfolded protein was separated from inserted protein by sucrose gradient flotation. The liposomes were mixed with 80% (w/v) sucrose in phosphate buffer to give a final concentration of 40% (w/v) sucrose. 400 ul was place at the bottom of a 2.2 ml tube, 1.6 ml 20% (w/v) sucrose was layered over it and a final layer of 200 ul buffer added on top. The gradient was centrifuged for 1 hour at 55,000 rpm in a TLS-55 Beckman rotor. The floated liposomes were removed and the protein concentration determined by Markwell Lowry assay.
Transport
50 μl/ml β-galactosidase was added to the buffer during the rehydration of the lipid films and the vesicles were freeze-thawed 5 times in liquid nitrogen before extrusion to promote the incorporation of the enzyme into the liposomes. External β-galactosidase was separated by sucrose flotation. LacY was then reconstituted as above. Proteoliposomes were diluted 10-fold into phosphate buffer at either pH 7.5 or pH 6.5 and equilibrated for 2 mins. 100 μM of o-nitrophenol galactoside was added, and the production of nitrophenol in the interior of the liposomes, and therefore buffered to pH 7.5, was monitored on a Cary UV-Vis spectrophotometer measuring absorbance at 410 nm. Initial velocities were calculated and compared between samples with and without a pH gradient.
Electronic supplementary material
Acknowledgements
We thank BBSRC (grant F013183/1), the Royal Society (Wolfson Research Merit Award to PJB), the Leverhulme Trust (Research Fellowship RF-2011-559 to PJB) and the ERC (Advanced Grant 294342).
Author Contributions
H.E.F. performed the experiments, H.E.F. and P.J.B. wrote the manuscript.
Competing Interests
The authors declare that they have no competing interests.
Footnotes
Electronic supplementary material
Supplementary information accompanies this paper at 10.1038/s41598-017-13290-7.
Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
References
- 1.Lee AG. How lipids affect the activities of integral membrane proteins. Biochim Biophys Acta. 2004;1666:62–87. doi: 10.1016/j.bbamem.2004.05.012. [DOI] [PubMed] [Google Scholar]
- 2.Engelman DM. Membranes are more mosaic than fluid. Nature. 2005;438:578–580. doi: 10.1038/nature04394. [DOI] [PubMed] [Google Scholar]
- 3.De Craene, J. O., Bertazzi, D. L., Bar, S. & Friant, S. Phosphoinositides, Major Actors in Membrane Trafficking and Lipid Signaling Pathways. Int J Mol Sci18, 10.3390/ijms18030634 (2017). [DOI] [PMC free article] [PubMed]
- 4.Musatov A, Robinson NC. Bound cardiolipin is essential for cytochrome c oxidase proton translocation. Biochimie. 2014;105:159–164. doi: 10.1016/j.biochi.2014.07.005. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 5.Sedlak E, Varhac R, Musatov A, Robinson NC. The kinetic stability of cytochrome C oxidase: effect of bound phospholipid and dimerization. Biophys J. 2014;107:2941–2949. doi: 10.1016/j.bpj.2014.10.055. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 6.Simmonds AC, et al. Annular and non-annular binding sites on the (Ca2+ + Mg2+)-ATPase. Biochim Biophys Acta. 1982;693:398–406. doi: 10.1016/0005-2736(82)90447-3. [DOI] [PubMed] [Google Scholar]
- 7.Reading E, et al. The role of the detergent micelle in preserving the structure of membrane proteins in the gas phase. Angew Chem Int Ed Engl. 2015;54:4577–4581. doi: 10.1002/anie.201411622. [DOI] [PubMed] [Google Scholar]
- 8.Allen SJ, Curran AR, Templer RH, Meijberg W, Booth PJ. Controlling the folding efficiency of an integral membrane protein. J Mol Biol. 2004;342:1293–1304. doi: 10.1016/j.jmb.2004.07.041. [DOI] [PubMed] [Google Scholar]
- 9.Seddon AM, et al. Phosphatidylglycerol lipids enhance folding of an alpha helical membrane protein. J Mol Biol. 2008;380:548–556. doi: 10.1016/j.jmb.2008.05.001. [DOI] [PubMed] [Google Scholar]
- 10.Miller DM, Findlay HE, Ces O, Templer RH, Booth PJ. Light-activated control of protein channel assembly mediated by membrane mechanics. Nanotechnology. 2016;27:494004. doi: 10.1088/0957-4484/27/49/494004. [DOI] [PubMed] [Google Scholar]
- 11.van den Brink-van der Laan E, Chupin V, Killian JA, de Kruijff B. Stability of KcsA tetramer depends on membrane lateral pressure. Biochemistry. 2004;43:4240–4250. doi: 10.1021/bi036129d. [DOI] [PubMed] [Google Scholar]
- 12.Zhang W, Campbell HA, King SC, Dowhan W. Phospholipids as determinants of membrane protein topology. Phosphatidylethanolamine is required for the proper topological organization of the gamma-aminobutyric acid permease (GabP) of Escherichia coli. J Biol Chem. 2005;280:26032–26038. doi: 10.1074/jbc.M504929200. [DOI] [PubMed] [Google Scholar]
- 13.Kent C. CTP:phosphocholine cytidylyltransferase. Biochim Biophys Acta. 1997;1348:79–90. doi: 10.1016/S0005-2760(97)00112-4. [DOI] [PubMed] [Google Scholar]
- 14.Findlay HE, Booth PJ. The biological significance of lipid-protein interactions. J Phys Condens Matter. 2006;18:S1281–1291. doi: 10.1088/0953-8984/18/28/S11. [DOI] [PubMed] [Google Scholar]
- 15.Killian JA. Hydrophobic mismatch between proteins and lipids in membranes. Biochim Biophys Acta. 1998;1376:401–415. doi: 10.1016/S0304-4157(98)00017-3. [DOI] [PubMed] [Google Scholar]
- 16.Brown PM, Steers J, Hui SW, Yeagle PL, Silvius JR. Role of head group structure in the phase behavior of amino phospholipids. 2. Lamellar and nonlamellar phases of unsaturated phosphatidylethanolamine analogues. Biochemistry. 1986;25:4259–4267. doi: 10.1021/bi00363a013. [DOI] [PubMed] [Google Scholar]
- 17.Suits F, Pitman MC, Feller SE. Molecular dynamics investigation of the structural properties of phosphatidylethanolamine lipid bilayers. J Chem Phys. 2005;122:244714. doi: 10.1063/1.1899152. [DOI] [PubMed] [Google Scholar]
- 18.Leekumjorn S, Sum AK. Molecular simulation study of structural and dynamic properties of mixed DPPC/DPPE bilayers. Biophys J. 2006;90:3951–3965. doi: 10.1529/biophysj.105.076596. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 19.Ding W, Palaiokostas M, Wang W, Orsi M. Effects of Lipid Composition on Bilayer Membranes Quantified by All-Atom Molecular Dynamics. J Phys Chem B. 2015;119:15263–15274. doi: 10.1021/acs.jpcb.5b06604. [DOI] [PubMed] [Google Scholar]
- 20.Bezrukov SM. Functional consequences of lipid packing stress. Curr Opin Colloid In. 2000;5:237–243. doi: 10.1016/S1359-0294(00)00061-3. [DOI] [Google Scholar]
- 21.Booth PJ, et al. In vitro studies of membrane protein folding. Crit Rev Biochem Mol Biol. 2001;36:501–603. doi: 10.1080/20014091074246. [DOI] [PubMed] [Google Scholar]
- 22.van Dalen A, de Kruijff B. The role of lipids in membrane insertion and translocation of bacterial proteins. Biochim Biophys Acta. 2004;1694:97–109. doi: 10.1016/j.bbamcr.2004.03.007. [DOI] [PubMed] [Google Scholar]
- 23.Alley SH, Ces O, Barahona M, Templer RH. X-ray diffraction measurement of the monolayer spontaneous curvature of dioleoylphosphatidylglycerol. Chem Phys Lipids. 2008;154:64–67. doi: 10.1016/j.chemphyslip.2008.03.007. [DOI] [PubMed] [Google Scholar]
- 24.Lorch M, Booth PJ. Insertion kinetics of a denatured alpha helical membrane protein into phospholipid bilayer vesicles. J Mol Biol. 2004;344:1109–1121. doi: 10.1016/j.jmb.2004.09.090. [DOI] [PubMed] [Google Scholar]
- 25.Booth PJ. Sane in the membrane: designing systems to modulate membrane proteins. Curr Opin Struct Biol. 2005;15:435–440. doi: 10.1016/j.sbi.2005.06.002. [DOI] [PubMed] [Google Scholar]
- 26.Charalambous K, Miller D, Curnow P, Booth PJ. Lipid bilayer composition influences small multidrug transporters. BMC Biochem. 2008;9:31. doi: 10.1186/1471-2091-9-31. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 27.Meijberg W, Booth PJ. The activation energy for insertion of transmembrane alpha-helices is dependent on membrane composition. J Mol Biol. 2002;319:839–853. doi: 10.1016/S0022-2836(02)00342-X. [DOI] [PubMed] [Google Scholar]
- 28.Booth PJ, Templer RH, Curran AR, Allen SJ. Can we identify the forces that drive the folding of integral membrane proteins? Biochem Soc Trans. 2001;29:408–413. doi: 10.1042/bst0290408. [DOI] [PubMed] [Google Scholar]
- 29.Findlay HE, Rutherford NG, Henderson PJ, Booth PJ. Unfolding free energy of a two-domain transmembrane sugar transport protein. Proc Natl Acad Sci USA. 2010;107:18451–18456. doi: 10.1073/pnas.1005729107. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 30.Harris NJ, Findlay HE, Simms J, Liu X, Booth PJ. Relative domain folding and stability of a membrane transport protein. J Mol Biol. 2014;426:1812–1825. doi: 10.1016/j.jmb.2014.01.012. [DOI] [PubMed] [Google Scholar]
- 31.Xie J, Bogdanov M, Heacock P, Dowhan W. Phosphatidylethanolamine and monoglucosyldiacylglycerol are interchangeable in supporting topogenesis and function of the polytopic membrane protein lactose permease. J Biol Chem. 2006;281:19172–19178. doi: 10.1074/jbc.M602565200. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 32.Bogdanov M, Heacock P, Guan Z, Dowhan W. Plasticity of lipid-protein interactions in the function and topogenesis of the membrane protein lactose permease from Escherichia coli. Proc Natl Acad Sci USA. 2010;107:15057–15062. doi: 10.1073/pnas.1006286107. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 33.Wang X, Bogdanov M, Dowhan W. Topology of polytopic membrane protein subdomains is dictated by membrane phospholipid composition. EMBO J. 2002;21:5673–5681. doi: 10.1093/emboj/cdf571. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 34.Bogdanov M, Heacock PN, Dowhan W. A polytopic membrane protein displays a reversible topology dependent on membrane lipid composition. EMBO J. 2002;21:2107–2116. doi: 10.1093/emboj/21.9.2107. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 35.Bogdanov M, Xie J, Heacock P, Dowhan W. To flip or not to flip: lipid-protein charge interactions are a determinant of final membrane protein topology. J Cell Biol. 2008;182:925–935. doi: 10.1083/jcb.200803097. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 36.Vitrac H, MacLean DM, Jayaraman V, Bogdanov M, Dowhan W. Dynamic membrane protein topological switching upon changes in phospholipid environment. Proc Natl Acad Sci USA. 2015;112:13874–13879. doi: 10.1073/pnas.1512994112. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 37.Mirza O, Guan L, Verner G, Iwata S, Kaback HR. Structural evidence for induced fit and a mechanism for sugar/H+ symport in LacY. EMBO J. 2006;25:1177–1183. doi: 10.1038/sj.emboj.7601028. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 38.Jiang X, et al. Crystal structure of a LacY-nanobody complex in a periplasmic-open conformation. Proc Natl Acad Sci USA. 2016;113:12420–12425. doi: 10.1073/pnas.1615414113. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 39.Findlay HE, Booth PJ. Folding alpha-helical membrane proteins into liposomes in vitro and determination of secondary structure. Methods Mol Biol. 2013;1063:117–124. doi: 10.1007/978-1-62703-583-5_6. [DOI] [PubMed] [Google Scholar]
- 40.Taylor KACC. A Modification of the Phenol Sulfuric-Acid Assay for Total Carbohydrates Giving More Comparable Absorbances. Appl Biochem Biotech. 1995;53:207–214. doi: 10.1007/BF02783496. [DOI] [Google Scholar]
- 41.Markwell MA, Haas SM, Tolbert NE, Bieber LL. Protein determination in membrane and lipoprotein samples: manual and automated procedures. Methods Enzymol. 1981;72:296–303. doi: 10.1016/S0076-6879(81)72018-4. [DOI] [PubMed] [Google Scholar]
- 42.Wallace BA, Lees JG, Orry AJ, Lobley A, Janes RW. Analyses of circular dichroism spectra of membrane proteins. Protein Sci. 2003;12:875–884. doi: 10.1110/ps.0229603. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 43.Vitrac H, Bogdanov M, Dowhan W. In vitro reconstitution of lipid-dependent dual topology and postassembly topological switching of a membrane protein. Proc Natl Acad Sci USA. 2013;110:9338–9343. doi: 10.1073/pnas.1304375110. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 44.Kaback HR, Sahin-Toth M, Weinglass AB. The kamikaze approach to membrane transport. Nat Rev Mol Cell Biol. 2001;2:610–620. doi: 10.1038/35085077. [DOI] [PubMed] [Google Scholar]
- 45.Chen CC, Wilson TH. The phospholipid requirement for activity of the lactose carrier of Escherichia coli. J Biol Chem. 1984;259:10150–10158. [PubMed] [Google Scholar]
- 46.Cantor RS. Size distribution of barrel-stave aggregates of membrane peptides: influence of the bilayer lateral pressure profile. Biophys J. 2002;82:2520–2525. doi: 10.1016/S0006-3495(02)75595-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 47.Keller SL, et al. Probability of alamethicin conductance states varies with nonlamellar tendency of bilayer phospholipids. Biophys J. 1993;65:23–27. doi: 10.1016/S0006-3495(93)81040-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 48.Zhan H, Lazaridis T. Inclusion of Lateral Pressure/Curvature Stress Effects in Implicit Membrane Models. Biophysical Journal. 2013;104:643–654. doi: 10.1016/j.bpj.2012.12.022. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 49.Templer, R. H., Castle, S. J., Curran, A. R., Rumbles, G. & Klug, D. R. Sensing isothermal changes in the lateral pressure in model membranes using di-pyrenyl phosphatidylcholine. Faraday Discuss, 41–53; discussion 69–78 (1998). [DOI] [PubMed]
- 50.Costigan SC, Booth PJ, Templer RH. Estimations of lipid bilayer geometry in fluid lamellar phases. Biochim Biophys Acta. 2000;1468:41–54. doi: 10.1016/S0005-2736(00)00220-0. [DOI] [PubMed] [Google Scholar]
- 51.Hong H, Tamm LK. Elastic coupling of integral membrane protein stability to lipid bilayer forces. Proc Natl Acad Sci USA. 2004;101:4065–4070. doi: 10.1073/pnas.0400358101. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 52.Curran AR, Templer RH, Booth PJ. Modulation of folding and assembly of the membrane protein bacteriorhodopsin by intermolecular forces within the lipid bilayer. Biochemistry. 1999;38:9328–9336. doi: 10.1021/bi982322+. [DOI] [PubMed] [Google Scholar]
- 53.Zhang W, Bogdanov M, Pi J, Pittard AJ, Dowhan W. Reversible topological organization within a polytopic membrane protein is governed by a change in membrane phospholipid composition. J Biol Chem. 2003;278:50128–50135. doi: 10.1074/jbc.M309840200. [DOI] [PubMed] [Google Scholar]
- 54.von Heijne G. Control of topology and mode of assembly of a polytopic membrane protein by positively charged residues. Nature. 1989;341:456–458. doi: 10.1038/341456a0. [DOI] [PubMed] [Google Scholar]
- 55.Liu W, et al. Structural Basis for Allosteric Regulation of GPCRs by Sodium Ions. Science. 2012;337:232–236. doi: 10.1126/science.1219218. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 56.Lee AG. Lipid-protein interactions. Biochem Soc Trans. 2011;39:761–766. doi: 10.1042/BST0390761. [DOI] [PubMed] [Google Scholar]
- 57.Lindblom G, et al. Membrane lipid regulation in Acholeplasma laidlawii grown with saturated fatty acids. Biosynthesis of a triacylglucolipid forming reversed micelles. J Biol Chem. 1993;268:16198–16207. [PubMed] [Google Scholar]
- 58.Morein S, Andersson A, Rilfors L, Lindblom G. Wild-type Escherichia coli cells regulate the membrane lipid composition in a “window” between gel and non-lamellar structures. J Biol Chem. 1996;271:6801–6809. doi: 10.1074/jbc.271.12.6801. [DOI] [PubMed] [Google Scholar]
- 59.Lees JG, Smith BR, Wien F, Miles AJ, Wallace BA. CDtool - an integrated software package for circular dichroism spectroscopic data processing, analysis, and archiving. Anal Biochem. 2004;332:285–289. doi: 10.1016/j.ab.2004.06.002. [DOI] [PubMed] [Google Scholar]
- 60.Whitmore L, Wallace BA. DICHROWEB, an online server for protein secondary structure analyses from circular dichroism spectroscopic data. Nucleic Acids Res. 2004;32:W668–W673. doi: 10.1093/nar/gkh371. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 61.Whitmore L, Wallace BA. Protein secondary structure analyses from circular dichroism spectroscopy: Methods and reference databases. Biopolymers. 2008;89:392–400. doi: 10.1002/bip.20853. [DOI] [PubMed] [Google Scholar]
- 62.Nakamura M, Tsumoto K, Ishimura K, Kumagai I. Detection of biotinylated proteins in polyacrylamide gels using an avidin-fluorescein conjugate. Anal Biochem. 2002;304:231–235. doi: 10.1006/abio.2002.5595. [DOI] [PubMed] [Google Scholar]
- 63.Schneider CA, Rasband WS, Eliceiri KW. NIH Image to ImageJ: 25 years of image analysis. Nat Methods. 2012;9:671–675. doi: 10.1038/nmeth.2089. [DOI] [PMC free article] [PubMed] [Google Scholar]
Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.