Proc. Nail. Acad. Sci. USAVol. 82, pp. 3665-3669, June 1985Biophysics

Intrinsic curvature hypothesis for biomembrane lipid composition:A role for nonbilayer lipids

(Ha phase/lipid phase transltions/phospholipid)

SOL M. GRUNERDepartment of Physics, Princeton University, Princeton, NJ 08544

Communicated by Philip W. Anderson, February 7, 1985

ABSTRACT A rationale is presented for the mix of"bilayer" and "nonbilayer" lipids, which occurs in bio-membranes. A theory for the Lr-HI phase transition andexperimental tests of the theory are reviewed. It is suggestedthat the phase behavior is largely the result of a competitionbetween the tendency for certain lipid monolayers to curl andthe hydrocarbon packing strains that result. The tendency tocurl is quantitatively given by the intrinsic radius of curvature,R., which minimizes the bending energy of a lipid monolayer.When bilayer (large R.) and nonbilayer (small R.) lipids areproperly mixed, the resulting layer has a value ofRO that is atthe critical edge of bilayer stability. In this case, bilayers maybe destabilized by the protein-mediated introduction of hydro-phobic molecules, such as dolichol. An x-ray diffraction inves-tigation of the effect of dolichol on such a Upid mixture isdescribed. This leads to the hypothesis that biomembraneshomeostatically adjust their intrinsic curvatures to fall into anoptimum range. Experimental strategies for testing the hy-pothesis are outlined.

All biological membranes contain a great diversity of lipids(1). As Raetz (2) has succinctly noted, "The metaboliccontrol and biological significance of lipid heterogeneity arenot well understood. Several fundamental questions remainunresolved in this area (and in all organisms). These includethe following: (1) What mechanisms regulate (or set) the totalmembrane phospholipid content of cells? (2) What regulatesthe ratios ofpolar headgroups and fatty acid species? ... (6)What are the functions of the individual phospholipid spe-cies?" Our lack of understanding is poignantly illustrated byexperiments with bacteria in which the fatty acid synthesispathways have been genetically or chemically disabled (3, 4).Thus, these bacteria are dependent on fatty acids provided inthe nutrient medium. If the available fatty acid mix ischanged, the cells respond by complicated readjustments ofthe fatty acids incorporated into the membranes (4). The cellsappear to bejuggling the membrane lipid composition to seekhomeostatic control of some crucial membrane quantities.We do not know what these quantities are.

It recently has been recognized that a large fraction of thelipids of many biological membranes form the liquid-crystal-line HI, phase (refs. 5 and 6; Fig. 1) when purified andhydrated under physiological conditions (7). These are some-times referred to as "nonbilayer" lipids. The remaining,so-called "bilayer," lipids primarily form bilayers whenpurified and hydrated under the same conditions. This has ledto a lively debate as to whether nonbilayer lipid structures arebiologically important. Membrane lipids are in the bilayerform most of the time in the cell; therefore, it has beenargued, the nonbilayer preference of certain purified lipids isa consequence of isolation of the lipid and is irrelevant to the

mixed-lipid in vivo system. The counterargument has beenthat, although membranes are bilayers most of the time, theyalso must be capable of forming transient, nonbilayer struc-tures because vital processes such as fusion, endocytosis,etc., are topologically impossible with intact bilayers. It hasbeen suggested that the underlying molecular characteristicsthat cause certain lipids to form nonbilayer phases uponpurification and interbilayer contact also enhance the forma-tion of transient nonbilayer features in functioningbiomembranes (7, 8).

In this article I review some recent theoretical and experi-mental results as to why certain lipids undergo the transitionfrom stacked bilayer, or La (5, 6), to the liquid-crystalline HI,phase. It is postulated that a quantity called the monolayerintrinsic radius of curvature most fundamentally distin-guishes the bilayer from the nonbilayer lipids. New experi-mental results are then presented on the phase-modulatingbehavior of naturally occurring dolichols as a further test ofthe theory. It is shown that the phase-modulating ability ofdolichol is dependent on the lipid mix having a sufficientlysmall value of the intrinsic radius of curvature. This leads tothe hypothesis that the intrinsic radius of curvature is aquantity that is homeostatically controlled in living bio-membranes.

BACKGROUNDWhat underlying molecular characteristics enhance the for-mation of nonbilayer structures? The concept of molecularshape has been identified most often as the importantcharacteristic: lipids with nonuniform ("cone-shaped") aver-age cross sections pack side-by-side into curved layers (7, 9).A difficulty with a literal formulation of the shape concept isthat, above the chain melting temperature, lipids are highlyflexible and do not have a specific shape. To illustrate,consider the average molecular volume occupied by a lipid inpure system just below and above the temperature at whichthe system undergoes an La-to-HIu phase transition. Belowthe transition temperature, in the bilayer geometry, theaverage molecular area is uniform in cross section; above thetransition temperature, it is tapered. In other words, theaverage molecular volume is, to a great degree, determinedby the phase. The argument that the average molecularshape, in turn, determines the phase is then circular.A more quantitative formulation of the shape concept

would involve a determination of the free energy per mol-ecule when it occupies a given molecular volume of a givenshape. This was the approach used by Kirk et al. (10) informulating a theory of the Ld-HII phase transition. It wasassumed that the shape-dependent free energy per moleculemay be partitioned into components arising from elastic

Abbreviations: Ole2-PtdCho, dioleoyl phosphatidylcholine; Ole2-PtdEtn, dioleoyl phosphatidylethanolamine; PtdCho, phospha-tidylcholine(s); PtdEtn, phosphatidylethanolamine(s); TBH, transi-tion temperature between L. and HI, phases.

3665

The publication costs of this article were defrayed in part by page chargepayment. This article must therefore be hereby marked "advertisement"in accordance with 18 U.S.C. §1734 solely to indicate this fact.

Dow

nloa

ded

by g

uest

on

Mar

ch 1

6, 2

021

Proc. Natl. Acad. Sci. USA 82 (1985)

bending of the lipid monolayers and hydrocarbon-packingenergies. It was additionally necessary to include lattice-specific contributions, as, for instance, from hydration andelectrostatic potentials.

Lipid monolayers (which form bilayers when placed tails-to-tails) are practically flat in the La phase but are rolled intotight cylinders in the HI, phase. The theory assumes that anelastic free energy, ILE, is given to lowest significant order by

LE = k (11R -11R)2. [1]

Here, k is an elastic constant and R is the radius ofcurvature of the lipid/water interface. We define the sign ofR as positive for the HI, phase and negative for the HI phase(6). RO is the "equilibrium," or "intrinsic," radius of curva-ture, which is defined self-consistently as the radius ofcurvature that minimizes ILE A lipid monolayer for which R= Ro is elastically relaxed. RO is postulated to be a propertyof the lipid and does not vary appreciably with the lipidgeometry. Factors that widen the splay of the tails (e.g.,temperature or unsaturation) decrease R.. Factors whichincrease the effective headgroup area (e.g., charge of theheadgroup) increase Ro. If no other energies competed with9E, lipid monolayers would curl so that R = R. to lower theelastic energy. We call the tendency for lipid monolayers tocurl so as to lower ALE the expression of the intrinsiccurvature.Hydrocarbon-packing constraints were suggested as pre-

venting the expression of large radii of curvature. We assumethat, for a given lipid, temperature, and geometry, the lipidtails have a well-defined mean length that is the result of thenumber ofgauche rotameric carbon bonds (11) excited in thehydrocarbon. For example, in the H1, phase (Fig. 1), we takethis length to be approximately equal to dH,,. Chains that arestretched beyond this length (i.e., to fill the stippled area ofFig. lb) are in a high-energy state, much as stretched polymerstrands. Furthermore, it is readily verified from the geometry(Fig. lb) that the distance, dmax, to the point in the stippledarea furthest removed from a water cylinder is

dmax = (2/\/3)(Rc + dH1) - R, [2]

where R, is the radius of the polar (crosshatched) core. Also,the ratio of the stippled area (stressed hydrocarbon) to thearea of the lipid annulus (relaxed hydrocarbon) in the lattice(Fig. 1) is

A = (Rc + dH11)2(2 sin 600 - iT/2) [3](w/2)(2 RCdHl + d 11)

Ifd is kept constant, both dmax andA are seen to increase withR,. Thus, increasing the water-to-lipid ratio of the HI, phaseincreases the hydrocarbon-packing free energy. In sum, thispacking energy competes more effectively with the decreasein ALE as R increases toward large values ofR,-i.e., the largerthe radius of the water cylinder, the harder it is to pack therelaxed chains.

It is important to realize that an increase in the hydro-carbon-packing free energy will occur whenever the lipid tailsare not all at the same mean relaxed length. This occurswhenever tails-to-tails lipid monolayers do not have parallellipid/water interfaces. Thus, the competition between pack-ing energy and ALE occurs for many curved structures, notjustthe HI, phase. It is a general phenomenon associated withlocal expression of the intrinsic curvature.

If the amount of available water is limited, the lipidcylinders may be unable to expand to express large values ofRo. However, in the presence of excess water, hydrationrepulsion (12) promotes separation of the headgroup surfaces(10). Likewise, electrostatic repulsion of charged lipid sur-

a

.9,~~~~~~~~~~~~~~

dMAX

b

FIG. 1. Schematic cross sections through seven unit cells of anHI, lattice. (a) Lipid headgroups are represented by black dotsattached to hydrophobic tails (wavy lines). The crosshatched areasrepresent water. The water-cored, lipid-coated cylinders extend outof the plane of the page. (b) HI, phase is shown in a simplerschematic. Each annulus represents hydrocarbon at a nearly relaxedlength, while the stippled areas are stressed hydrocarbon. The polarcore has a radius, R,, while dmax is the maximally extended meanhydrocarbon length.

faces can contribute to a decrease in the overall free energyas the surfaces separate. For zwitterionic (dipolar) lipids, theelectrostatic contribution is assumed to be small.Given the background discussed, above, we are in a

position to understand why the La phase extends to hightemperatures for some lipids, such as phosphatidylcholines(PtdCho), but yields to the HI, phase for other lipids, such asunsaturated phosphatidylethanolamines (PtdEtn). First ofall, let us consider a zwitterionic lipid in excess water, so asto reduce charge and hydration repulsion effects on the phasebehavior. Consider a lipid that has a large equilibrium radiusof curvature, say RO 20 A. In the La phase, R = oXand, inEq. 1, ALE = kRJ-2. The lipid monolayers would like to curl sothat R = RO to lower AE, but in order to do so a large numberofhydrocarbon groups would have to extend into the stippledareas of Fig. lb, thereby raising a competing packing energy.Raising the temperature reduces RO because ofentropic splayof the hydrocarbon. But, by Eqs. 2 and 3, the hydrocarbon-packing energy falls as the cylinder radius falls. At sometemperature the decrease in elastic energy that results fromcurling the layers competes favorably with the increase dueto packing the hydrocarbon, and the system then undergoesthe L,-to-HIi transition to lower the total free energy.Now consider two lipids that have the same type oftails but

different values for RO at a given temperature. If they were tocurl to express the intrinsic curvatures, then ALE would

3666 Biophysics: Gruner

Dow

nloa

ded

by g

uest

on

Mar

ch 1

6, 2

021

Proc. Natl. Acad. Sci. USA 82 (1985) 3667

approach zero for both lipids. But the lipid with a larger valueof R0 would have a larger rise in hydrocarbon-packingenergy. Thus, the lipid with a larger value ofRo would remainin the La phase to higher temperatures.The picture of the phase transition, described above, can

be tested by devising an experimental situation where thehydrocarbon-packing energy, which opposes the formationof nonbilayer structures, is removed. This can be done byadding a small quantity of a hydrophobic substance, such asa light oil, to the lipid. The oil can migrate in the hydrocarbonregion and relax packing stress by preferentially partitioninginto volumes where the chains are stressed, such as thestippled areas of Fig. lb. In this case, expression of curvatureis not accompanied by a large increase in packing free energy,and one expects that curved structures would be expressedat relatively low temperatures.Experimental support of these ideas was obtained by Kirk

and Gruner (13). The lipids dioleoyl phosphatidylethanola-mine (Ole2-PtdEtn) and dioleoyl phosphatidylcholine (Ole2-PtdCho) were used. In excess water, both lipids were in theLa phase at -50C. However, whereas Ole2-PtdEtn had aLa-to-HII transition temperature (TBH) between 5 and 10'C,Ole2-PtdCho was still in the La phase even at 80'C. It was firstshown that the addition of a few percent oil to Ole2-PtdEtndramatically lowered TBH. The lipid went into the HI, phasealmost as soon as the temperature exceeded the chain melting(Lo to La) temperature. It was then shown that 3:1 Ole2-PtdEtn/Ole2-PtdCho mixtures have a TBH 50-550C withoutoil, but TBH was reduced to -5 to 0OC when a few percent oilwas added. Moreover, the lipid cylinders that resulted hadwater cores with a radius that was considerably larger thanthat for pure Ole2-PtdEtn HI, cylinders. The HI, dimensionsincreased further when the fraction of Ole2-PtdCho in themixed system was increased.These results may be interpreted by assuming that Ole2-

PtdEtn had a small value of R0, whereas Ole2-PtdCho had alarge value. The addition of oil removed most of the hydro-carbon packing stress and allowed the expression of curva-ture at dramatically low temperatures. HI, phases of Ole2-PtdEtn with oil had small cylinders because R. was small forthis lipid. When Ole2-PtdEtn and Ole2-PtdCho were mixed,the value of Ro for the mixture fell between the extremes ofthe pure components. Thus, the Ole2-PtdEtn/Ole2-PtdChoHI, phases had large cylinders, the radii of which increasedwith the fraction of Ole2-PtdCho. Most fundamentally, itappeared thatOle2-PtdEtn formed HI, phases at temperatureswhere Ole2-PtdCho was still in the La phase because Ro wassmaller for Ole2-PtdEtn than for Ole2-PtdCho.These experiments are highly suggestive of bilayer control

mechanisms that may be active in living biomembranes. Thedilemma faced by biomembranes is that they must be stableas bilayers most of the time but subject to disruption duringlocalized events such as membrane fusion, endocytosis, cellfission, etc. What value of Ro is optimal for such behavior?If Ro were very small, then bilayers would be readilydisrupted by the formation of curved structures because thehydrocarbon-packing energy, which opposes the formationofcurved structures, is small for small radii of curvature. Thisis the case, for instance, forOle2-PtdEtn. On the other hand,if Ro were large, then expression of curvature of the order R

Ro would engender a large hydrocarbon-packing energy.This makes bilayers very hard to disrupt, as is the case forOle2-PtdCho. However, if R. were maintained at intermedi-ate values, then the competition between curvature andhydrocarbon packing would be such that bilayers are stableuntil hydrophobic molecules that affect the packing areintroduced. This is the case with Ole2-PtdEtn/Ole2-PtdChomixtures in the presence of oil. Protein-mediated introduc-tion of hydrophobic molecules may be a mechanism for localdisruption of bilayers. It was noted at the beginning of this

paper that biomembranes appear to be a mix of bilayer (i.e.,large R.) and nonbilayer (i.e., small R.) lipids. The mix mayresult in intermediate values of R., which put the bilayer onthe edge of stability.As suggested by Kirk et al. (10), electrostatic and hydra-

tion contributions also affect the phase behavior. Bilayerstability is sensitive to these factors, especially when Ro is ofintermediate values. Local modulation of the surface chargeor surface hydration also may be mechanisms for the localdestabilization of bilayers.Do biomembranes contain hydrophobic molecules that

release packing stress in a manner similar to the way oilaffects 0le2-PtdEtn/0le2-PtdCho mixtures? Consider, forexample, the polyisopreniod lipids known as dolichols. Theselong (-90 carbons) hydrocarbon lipids are necessary cofac-tors for the attachment of sugars to membrane proteins in therough endoplasmic reticulum (14, 15). The sugars are syn-thesized outside the endoplasmic reticulum lumen, but theprotein attachment site is inside the lumen. Dolichol isthought to be involved in the transfer of sugars across theendoplasmic reticulum membrane and the eventual attach-ment to the proteins (16, 17). Neither the details of how thesugars are shuttled across the membrane nor the exactfunctional roles of dolichol are known.Jensen and Schutzbach (18) used 31P NMR to investigate

the effect of dolichol on PtdEtn/PtdCho mixtures. In theabsence of dolichol, a 2:1 PtdEtn/PtdCho (390C) mixtureyielded the 31P-NMR spectrum expected from a predomi-nantly bilayer organization. Upon the addition of dolichol,the spectrum was altered so that it was similar to that seenwith lipids in the HI, phase. These authors also investigatedthe activity of mannosyltransferase II when reconstitutedwith various lipids. This membrane-bound enzyme catalyzesthe transfer of GDP-mannose to a dolichol-linked oligosac-charide. The enzyme was optimally active above the lipidchain melting temperature when reconstituted in unsaturatedPtdEtn and was relatively inactive when reconstituted insaturated PtdChos (19). When reconstituted in PtdEtn/PtdCho mixtures, the activity grew as the amount of PtdEtnincreased (18). Jensen and Schutzbach (18) argued that theincreased activity was associated with the tendency for thelipid to be in a nonbilayer form and not with the presence ofPtdEtn because the enzyme was relatively inactive whenreconstituted with the bilayer lipid dielaidoyl phosphati-dylcholine (TBH 60°C). These studies are of interest bothbecause of the effect of dolichol on PtdEtn/PtdCho mixturesand because of the possibility of an enzyme that is active inlipids that readily promote curved, or nonbilayer, structures.

I now report on the use of x-ray diffraction to furtherinvestigate the effect of dolichol on PtdEtn/PtdCho mixtures.

METHODS

Porcine liver dolichol in carbon tetrachloride (98% C80-C105;Sigma) was vacuum dried and resuspended in chloroform;otherwise, procedures and material sources were as de-scribed (13). Briefly, Ole2-PtdEtn, Ole2-PtdCho, anddolichol, each dissolved in chloroform, were mixed in x-raycapillaries and dried under reduced pressures. Bufferedsaline solution was then added to excess to the lipid, and thecapillaries were sealed and allowed to equilibrate at 5°C forat least 12 hr. X-ray diffraction was performed by using thePrinceton SIV x-ray detector beam line (20, 21). The x-raydata were used to determine the phase behavior of the lipidat roughly 5°C intervals in an ascending temperature seriesfrom 0°C. The data to be shown indicate the lipid phasepresentand the basis vector lengths for each phase ateachtemperature. Also note that the 3:1 mix of lipid is nominal.The effect of mixing errors of several percent in the PtdEtn-to-PtdCho ratio is to shift vertically the HI, curve of Fig. 3.

Biophysics: Gruner

Dow

nloa

ded

by g

uest

on

Mar

ch 1

6, 2

021

Proc. Natl. Acad. Sci. USA 82 (198S)

For this reason, the absolute values of HI, basis vectorlengths should be considered to be accurate to only 2 A.

RESULTS

As noted earlier, the phase behavior of 3:1 Ole2-PtdEtn/Ole2-PtdCho mixtures in excess water has been examined by Kirkand Gruner (13). Above 0C, the mixture was in the La phasewith TBH = 50-550C. Upon the addition of 5% (wt/wt)dodecane, TBH was depressed below 0C, and the lipid wasin the HI, phase to at least 850C. Results of x-ray diffractionupon the addition of2% (wt/wt) dolichol are shown in Fig. 2.At 0C, the diffraction was dominated by a lamellar signatureconsisting of equally spaced Bragg orders (Fig. 2). Thepresence of a second phase was indicated by weak peaksassociated with another lattice. As seen in Fig. 2, the rise intemperature was accompanied by a monotonic decrease inthe intensity of the lamellar diffraction. Concomitantly, theintensity from the second lattice was seen to grow into awell-defined pattern with peak spacings in the ratio1:V3:2:V\7, indicative of hexagonal packing. This is inter-preted as an La phase, which predominated at low tempera-tures. As the temperature increased, more and more of thelipid was converted to an HI, phase (Fig. 3).The phase behavior of Ole2-PtdCho with 2% dolichol was

I 29

I II

FIG. 2. The low-angle x-ray diffraction from a suspension of 3:1Ole2-PtdEtn/Ole2-PtdCho with 2% dolichol in excess buffer. Thenumbers show the specimen temperature. The ordinate is the x-rayintensity and the abscissa is the scattering angle, with 0° at the left.The tic marks immediately below each graph are the expectedpositions of peaks from a hexagonal lattice fit to the pattern. Thelower set of tic marks represents the peak positions of a coexistinglamellar lattice. The beam stop shadow and camera scatter are the dipand bump, respectively, on the left of each graph. Note that thelamellar lattice intensity decreases and the hexagonal lattice intensityincreases as the temperature rises. At 390C, the only trace left of thelamellar lattice is a high-angle shoulder on the most intense hexago-nal peak.

90k

80k

701-

60H

I ~ ~~~~~~~~~I

0.

0

U UUrn0

-40 0 40 80T, 'C

FIG. 3. The basis vector lengths vs. temperature for the phasesobserved in the mixture of 3:1 Ole2-PtdEtn/Ole2-PtdCho with 2%dolichol (73.5% Ole2-PtdEtn/24.5% Ole2-PtdCho/2% dolichol). *,Lamellar lattice; *, hexagonal lattice. The large error bars on thehexagonal phase at low temperatures stem from the difficulty ofdetermining the peak positions of this weakly phase-separatedlattice.

also examined. The mix was in a La phase over the investi-gated range of 0-800C.

DISCUSSION

The x-ray data show dolichol to be a potent mediator forexpression of lipid curvature. The fact that dolichol affectsthe phase behavior ofthe 01e2-PtdEtn/0le2-PtdCho mixturesbut not of Ole2-PtdCho alone supports the picture of acompetition between expression of intrinsic curvature andhydrocarbon packing. For large values of R., as with Ole2-PtdCho, the Lat phase is preserved upon the addition of smallamounts of dolichol. However, when R. is reduced by mixingin a large amount of 01e2-PtdEtn, the free energy balanceshifts toward the expression of curved structures.At 2% (wt/wt), which is about 1.5 mol %, dolichol

promoted the formation of HI, phases in the 3:1 Ole2-PtdEtn/Ole2-PtdCho mixture even at 00C. This is roughly50'C below the first onset of HI, formation in the absence ofdolichol. Moreover, dolichol promoted a stable balance ofcoexisting La, and HI, phases over a 350C temperature span,a behavior not observed with dodecane (13). Considering thesize of the dolichol molecules, one sees that even onemolecule represents a high local concentration of additionalhydrocarbon volume. Perhaps even a few dolichol molecules,when locally clustered, can promote the expression of localcurvature, provided that the intrinsic curvature, R., is smallenough. The protein-mediated clustering of dolichol, inbilayers of sufficiently small values of R,, may be a potentmechanism for the biological control of bilayer stability.

In a larger context, one is led to ask if an organism canafford to let the value of the intrinsic curvature of itsmembranes vary, given that such variation drastically altersthe bilayer stability in the presence of various hydrophobic

3668 Biophysics: Gruner

Dow

nloa

ded

by g

uest

on

Mar

ch 1

6, 2

021

Proc. Natl. Acad. Sci. USA 82 (1985) 3669

molecules. One suspects not. This leads me to propose thatliving organisms seek to stabilize the intrinsic curvatures oftheir bilayers at values peculiar to the membrane concerned.It should be emphasized that this curvature hypothesis is notbased on data-to my knowledge, no real biomembraneintrinsic curvature values have been measured yet. My hopein stating the hypothesis is to provide a rationale for futureexperimentation on the elastic properties of biomembranes.The curvature hypothesis has two parts.

(0) Living cells seek to homeostatically control the netintrinsic curvatures of the bilayer leaflets of their membranes.

(ii) Functionally important geometry-dependent local in-stability of the lipid surface is modulated by local variation ofthe hydrophobic packing, hydration, and/or electrostaticcomponents of the free energy.Biomembranes differ from model lipid bilayers in that they

contain protein and have an asymmetric bilayer leafletcomposition (22). Hence, we suppose that the intrinsiccurvatures include the influence of protein and are definedseparately for the two monolayers in the bilayer. The secondpart of the hypothesis is meant to emphasize that if themonolayer intrinsic curvatures are kept constant, then localmembrane destabilization must proceed by other mecha-nisms. An example might be a protein that introduces a longhydrophobic chain into the region to be destabilized. It is ofinterest to speculate that this might represent a new class ofmembrane proteins: proteins that have a site-specific partthat chooses the location for destabilization and a hydro-phobic tail that is dragged along to assist in the destabiliza-tion. It is suspected that biomembranes mix bilayer andnonbilayer lipids to adjust Ro. If so, then the homeostaticcontrol of the intrinsic curvature provides a rationale for thelipid mix present in biomembranes.

In principle, the hypothesis can be tested. As noted earlier,there exist bacteria whose fatty acid synthesis is disabledand, thus, whose membrane lipid composition can be alteredby appropriate manipulations of the nutrient medium (3, 4).Imagine a number of such nutrient modifications so as toproduce a number of membrane populations. Divide theseinto healthy and unhealthy classes of bacteria. If stabilizationofthe intrinsic curvature is important, then we expect that thebacteria in the healthy class will all have similar values of themembrane intrinsic curvature, while the unhealthy class willhave divergent values. Although it is not yet clear how theintrinsic curvatures can be measured, a strategy similar toKirk and Gruner (13) may be possible: lyse the cells to isolatethe membranes, pellet the membranes in buffer saturatedwith butane or pentane, and see if Hi, phases can be induced.If so, the cylinder radii might be taken as an approximatemeasure of Ro. The difficulties of this procedure because of,say, membrane asymmetry, charge, or heterogeneity remainto be determined.

If the intrinsic membrane curvature is homeostaticallyadjusted by cells, then there must exist proteins that aresensitive to the intrinsic curvature. This is not unreasonable,since typical values are <50 A (10). In addition to man-nosyltransferase II (18), the Ca2+-ATPase of sarcoplasmicreticulum has been shown to be optimally active whenreconstituted into bilayers containing a large fraction ofnonbilayer lipids (23). In the latter case, many different lipidheadgroups were tried, thereby ruling out headgroup speci-ficity.

This suggests that some membrane proteins may require aspecific range of intrinsic membrane curvatures in order tofunction properly. Consequently, the R. specificity of mem-

brane proteins may provide another means of testing thecurvature hypothesis. The experimental strategy would, forinstance, be to assay protein functional activity when theproteins are reconstituted with various lipids (e.g., see ref.23). In so far as the protein is dilute in the bilayer, the Ro valueis nearly that of the pure lipid. The method of Kirk andGruner (13) may then be used on the pure lipid mix to obtainHI, phases. The radii of the water cores may be used as ameasure related to RO. This kind oftest may be relatively easyto perform but may be difficult to interpret, since not allproteins are expected to be sensitive to RO. Moreover, otherlipid factors (e.g., chain length, headgroup type) are probablyimportant to many proteins. Even so, the exploration of theintrinsic lipid-curvature dependence of proteins is a worthygoal since so little is known about membrane proteins.

Note Added in Proof. A recent study of the phase-modulating effectof dolichol (24) has confirmed the behavior of dilichol reported here.

I thank Greg Kirk, George Reynolds, Phil Anderson, AdrianParsegian, Pieter Cullis, Colin Tilcock, and Efriam Racker for helpfuldiscussions. This work is supported by Department of EnergyContract DE-AC02-76EV03120 and National Institutes of HealthGrant GM32614.

1. Quinn, P. J. & Chapman, D. (1980) Crit. Rev. Biochem. 8,1-117.

2. Raetz, C. R. H. (1982) in Phospholipids, eds. Hawthorne,J. N. & Ansell, G. B. (Elsevier, Amsterdam), pp. 435-477.

3. Silbert, D. F. (1975) Annu. Rev. Biochem. 44, 315-339.4. Silvius, J. R., Mak, N. & McElhaney, R. N. (1980) Biochim.

Biophys. Acta 597, 199-215.5. Luzzati, V. (1968) in Biological Membranes, ed. Chapman, D.

(Academic, New York), Vol. 1, pp. 71-123.6. Gruner, S. M., Cullis, P. R., Hope, M. J. & Tilcock, C. P. S.

(1985) Annu. Rev. Biophys. Biophys. Chem. 14, 211-238.7. Cullis, P. R., Hope, M. J., de Kruijff, B., Verkleij, A. J. &

Tilcock, C. P. S. (1985) in Phospholipids and Cellular Regula-tions, ed. Kuo, J. F. (CRC, Boca Raton, FL), Vol. 1, in press.

8. Verkleij, A. J. (1982) Biochim. Biophys. Acta 779, 43-63.9. Israelachvili, J. N., Marcelja, S. & Horn, R. G. (1980) Quart.

Rev. Biophys. 13, 121-200.10. Kirk, G. L., Gruner, S. M. & Stein, D. L. (1984) Biochemistry

23, 1093-1102.11. Nagle, J. F. (1980) Annu. Rev. Phys. Chem. 31, 157-195.12. Rand, R. P. (1981) Annu. Rev. Biophys. Bioeng. 10, 277-314.13. Kirk, G. L. & Gruner, S. M. (1985) J. Phys. (Orsay, Fr), in

press.14. Struck, D. K. & Lennarz, W. J. (1980) in The Biochemistry of

Glycoproteins and Proteoglycans, ed. Lennarz, W. J. (Ple-num, New York), pp. 35-83.

15. Hubbard, S. C. & Ivatt, R. J. (1981) Annu. Rev. Biochem. 50,555-583.

16. Hanover, J. A. & Lennarz, W. J. (1982) J. Biol. Chem. 257,2787-2794.

17. Haselbeck, A. & Tanner, W. (1982) Proc. Natl. Acad. Sci.USA 79, 1520-1524.

18. Jensen, J. W. & Schutzbach, J. S. (1984) Biochemistry 23,1115-1119.

19. Jensen, J. W. & Schutzbach, J. S. (1982) J. Biol. Chem. 257,9025-9029.

20. Gruner, S. M. (1977) Dissertation (Princeton University,Princeton, NJ).

21. Reynolds, G. T., Milch, J. R. & Gruner, S. M. (1978) Rev. Sci.Instrum. 49, 1241-1249.

22. Rothman, J. E. & Lenard, J. (1977) Science 195, 743-753.23. Navarro, J., Toivio-Kinnucan, M. & Racker, E. (1984) Bio-

chemistry 23, 130-135.24. Valtersson, C., van Duyn, G., Verkleij, A. J., Chojnack, T., de

Kruijff, B. & Dallner, G. (1985) J. Biol. Chem. 260, 2742-2751.

Biophysics: Gruner

Dow

nloa

ded

by g

uest

on

Mar

ch 1

6, 2

021