Helix packing in membrane proteins

J. Mol. Biol. (1997) 272, 780±789

Helix Packing in Membrane Proteins

James U. Bowie

Department of Chemistry andBiochemistry, UCLA-DOELaboratory of StructuralBiology and MolecularMedicine, 405 Hilgard AveLos Angeles, CA 90095-1570USA

Abbreviations used: TM, transmcytochrome c oxidase; PRC, photoscenter; BRD, bacteriorhodopsin.

0022±2836/97/400780±10 $25.00/0/mb

A survey of 45 transmembrane (TM) helices and 88 helix packing inter-actions in three independent transmembrane protein structures revealsthe following features. (1) Helix lengths range from 14 to 36 residueswith an average length of 26.4 residues. There is a preference for lengthsgreater than 20 residues. (2) The helices are tilted with respect to thebilayer normal by an average of 21�, but there is a decided preference forsmaller tilt angles. (3) The distribution of helix packing angles is verydifferent than for soluble proteins. The most common packing angles forTM helices are centered around �20� while for soluble proteins packingangles of around ÿ35� are the most prevalent. (4) The average distanceof closest approach is 9.6 AÊ , which is the same as soluble proteins. (5)There is no preference for the positioning of the point of closest approachalong the length of the helices. (6) It is almost a rule that TM helices packagainst neighbors in the sequence. Of the 37 helices that have a sequenceneighbor, 36 of them are in signi®cant contact with a neighbor. (7) Anantiparallel orientation is more prevalent than a parallel orientation andantiparallel interactions are more intimate on average. The general fea-tures of helix bundle membrane protein architecture described in this sur-vey should prove useful in the modeling of helix bundle transmembraneproteins.

# 1997 Academic Press Limited

Keywords: bacteriorhodopsin; cytochrome c oxidase; photosyntheticreaction center; protein structure

Introduction

Popot & Engelman (1990) have proposed a two-stage model for helix-bundle membrane proteinfolding. In the ®rst stage, transmembrane (TM)helices insert into the bilayer with appropriate top-ology. The second stage involves side by side pack-ing of these preformed helices to produce the ®nalfolded structure. Considerable experimental evi-dence favors this hypothesis in general terms (seeBormann & Engelman, 1992), although membraneprotein folding may be more complex in detail(Riley et al., 1997). The two-stage model can serveas a useful paradigm for membrane protein struc-ture prediction. The ®rst challenge is to predict thelocation of the TM helices in the sequence andtheir topology. The second challenge is to opti-mally pack these helices together into the correcttertiary structure. In one form or another, thisapproach has been used implicitly in membrane

embrane; CytOx,ynthetic reaction

971279

protein modeling attempts (Adams et al., 1995;Baldwin, 1993; Sansom et al., 1995; Suwa et al.,1995; Taylor et al., 1994; Treutlein et al., 1992;Tuffery et al., 1994).

The prediction of the location of TM helices andtheir topology is one of the primary successes inprotein structure prediction (Edelman, 1993;Engelman et al., 1986; Jones et al., 1994; Rost et al.,1995, 1996; Sipos & von Heijne, 1993; von Heijne,1992). Although there is much room for improve-ment, it is often already possible to develop a lim-ited set of possible topological models fromsequence information. Certainly this situation canonly improve with more structural information.Moreover, membrane protein topology is some-thing that can often be addressed through bio-chemical experiments. Thus, it seems likely that thesuccess of membrane protein structure predictionwill depend largely on the second challenge, cor-rectly packing topologically arranged helices.

The packing preferences of helices in solubleproteins has long been a subject of study and anumber of elegant models describing the interdigi-tation of side-chains have been described (Chothiaet al., 1981; Crick, 1953; Richmond & Richards,

# 1997 Academic Press Limited

Membrane Protein Helices 781

1978; Walther et al., 1996). A statistical analysis ofpacking preferences for TM helices has not yetbeen performed, however, largely due to the lackof structural information. Although knowledge ofmembrane protein structures is still limited, thesituation has been dramatically improved by therecent structure of bovine heart cytochrome c oxi-dase (CytOx; Tsukihara et al., 1996). The structureof CytOx has more than doubled the number ofindependent TM helices available for analysis. Atthis point, there are three independent helix bundlemembrane protein structures that have been madeavailable by deposition in the protein databank:the photosynthetic reaction centers (PRC), bacter-iorhodopsin (BRD) and CytOx (Allen et al., 1987;Chang et al., 1991; Deisenhofer, 1981; Deisenhofer& Michel, 1989; Grigorieff et al., 1996; Hendersonet al., 1990; Tsukihara et al., 1996). As a result, thereare now suf®cient data to describe some basicfeatures of helix-helix packing in transmembraneproteins.

Results and Discussion

The helices

The three proteins used in this work contain atotal of 45 TM helices, which are listed in Table 1.According to the stringent criteria of the DSSPalgorithm, four of the 28 TM helices in CytOx con-tain breaks or irregularities. Nevertheless, theseTM regions appear qualitatively as continuoushelices and f, c angles in these breaks remain inthe helical range. Consequently, these regions weretreated as continuous helix in this survey. Theaverage rise per residue for the high-resolutionstructures 1OCC and 1PRC was found to be 1.49 AÊ

with a standard deviation of 0.05 AÊ , which is veryclose to the value expected for ideal a-helices. Intheir analysis of soluble protein helix packing,Chothia et al. (1981) found an average rise per resi-due of 1.51 AÊ , similar to our value and the idealvalue. Walther et al. (1996) found the average riseper residue of 1.45 AÊ , which deviates substantiallyfrom the expected value. The reason for this discre-pancy is not clear.

The lengths of TM helices vary widely, rangingfrom 14 all the way up to 39 residues, with anaverage length of 26.4 residues. The distribution ofhelix lengths is shown in Figure 1. Although TMhelices can be quite short, there appears to be anabrupt increase in frequency beyond 20 residues,the number typically considered optimal to spanthe bilayer (Engelman et al., 1986). Thus, most ofthe TM helices extend beyond the membrane andform part of the soluble domain structure. It maytherefore be appropriate to use the vast databaseof soluble protein structures to help de®ne criteriafor predicting TM helix endpoints. In fact, Wallinet al. (1997) have recently shown that the residuecomposition near TM helix endpoints is similar tothe composition of helix endpoints in soluble pro-teins.

Tilt angles

It is clear from from a cursory glance at thestructures of helix bundle transmembrane proteinsthat the helices rarely pass through the bilayer par-allel with the membrane normal. Yeates et al.(1987) reported that the TM helices in PRC aretilted with respect to the membrane normal anaverage of 25�. The tilt angles, t, are given inTable 1 for TM helices in CytOx and BRD, struc-tures for which it is more straightforward tospecify an accurate membrane normal (seeMaterials and Methods). For these proteins, theaverage tilt angle is 21�, quite similar to the valueobtained by Yeates et al. (1987). The values varywidely, however, ranging from 5.2� to 39.3�.Figure 2(a) shows the distribution of t for CytOxand BRD. Within the allowed range of tilt angles,there appears to be little preference for any particu-lar angle.

The histogram shown in Figure 2(a) is highlymisleading, however, since the random probabilityof a particular tilt angle increases signi®cantly athigher tilt angles. As shown in Figure 3, this occursbecause there are simply more ways to generate alarger angle than a smaller angle in three dimen-sions. As the random probability of a tilt angle isproportional to the cosine of the angle, the distri-bution of tilt angles was replotted as a function ofcos(t) (Figure 2(b)). Viewed in this way there is adecided preference for the helices to be normal tothe membrane (cos(t) � 1.0). In other words,although the TM helix tilt angles are distributedroughly evenly from 0 to 40�, more TM helices areoriented closer to the bilayer normal than wouldbe expected at random. Thus, in the absence ofother structural constraints, one might expecthelices to be oriented parallel with the membranenormal. This appears to be the case. In model iso-lated TM helices, the TM helices were found to ori-ent in the direction of the bilayer normal (Huschiltet al., 1989).

Packing angles

The theory of helix-helix packing has been trea-ted in a number of classic papers (Chothia et al.,1981; Crick, 1953; Richmond & Richards, 1978;Walther et al., 1996). Most of these treatments viewthe helices in terms of knobs (the side-chains) andholes (the space between side-chains). The recentwork by Walther et al. (1996) provides a completemathematical treatment of knobs into holes pack-ing. The model described by Chothia et al. (1981) isdistinguished from the others by treating sets ofside-chains as ridges and associated grooves.Although the treatments used by Walther et al.(1996) and Chothia et al. (1981) are quite different,they both predict three predominant classes. Thetheoretical treatment of helix-helix packingdescribed by Chothia et al. (1981) predicts preferredpacking angles, , of ÿ52�, �75� and �23�, whileWalther et al. (1996) predict similar preferred

Table 1. Description of the transmembrane helices

Residue numbersTilt Length

Protein Helix Chain Start End angle (AÊ )

Cytochrome c oxidase1 A 12 41 27.6 42.8

2A A 51 672B A 70 75 21.7 49.62C A 77 873 A 95 115 30.4 31.44 A 141 170 35.1 43.35 A 183 212 39.3 43.36 A 228 261 37.8 50.17 A 270 283 35.8 19.6

8A A 299 3108B A 313 327 33.6 43.89 A 336 357 31.5 31.9

10A A 371 38210B A 385 401 15.1 40.311 A 407 425 17.2 27.012 A 448 478 19.0 45.513 B 15 45 18.4 45.414 B 60 87 15.6 42.315 C 16 37 14.3 29.216 C 41 66 30.0 37.117 C 73 106 5.3 48.718 C 130 152 5.3 33.819 C 156 183 16.5 40.620 C 191 223 19.0 47.621 C 233 256 16.9 33.622 D 77 102 37.4 38.0

23A G 13 2223B G 24 37 21.0 34.124 I 12 50 8.3 56.425 J 26 54 30.7 42.026 K 9 35 13.2 35.427 L 18 44 16.9 38.528 M 12 35 26.9 32.1

Photosyntheticreaction center

1 L 33 53 ± 29.82 L 84 111 ± 40.93 L 116 139 ± 33.24 L 171 198 ± 40.65 L 226 249 ± 35.36 M 52 76 ± 36.17 M 111 137 ± 39.28 M 143 159 ± 24.49 M 198 223 ± 36.410 M 260 284 ± 36.4

Bacteriorhodopsin1 10 32 21.7 32.02 38 62 5.2 36.43 77 100 7.9 34.54 105 127 8.6 32.45 134 157 15.2 34.16 166 191 16.3 37.57 202 225 15.5 32.9

Helices with the same number and an associated letter designation were treated as part ofthe same helix.

782 Membrane Protein Helices

angles of ÿ37�, �83� and �22�. Following Waltheret al. (1996), the three classes will be referred to asa, b and c, repectively. In the survey by Chothiaet al. (1981) and the much larger survey by Waltheret al. (1996), the a class is by far the most prevalentpacking angle. Walther et al. (1996) found onlyminor peaks in the angle distributions corre-

sponding to the b and c classes. I have recentlyshown that when the distribution of helix packingangles is corrected for statistical bias, the true pre-ference for particular packing angles in solubleproteins is not as strong as previously thought. Infact, a wide range of angles ranging from aboutÿ40� to �30� is about equally favorable (Bowie,

Figure 1. The distribution of helix lengths. CytOx helicesare shown as black bars, PRC helices are indicated bythe dark gray bars and BRD helices by the stippledbars.

Figure 3. Tilt angle probabilities. There are many waysto select a given tilt angle in three dimensions. The ran-dom probability of selecting a particular angle is pro-


1997). Thus, steric compatibility is not a particu-larly strong constraint for helix interactions in sol-uble proteins.

Figure 2. The distribution of helix tilt angles. (a) Thedistribution of helix tilt angles without any probabilitycorrection. (b) The distribution of helix tilt angles as afunction of the cosine of the tilt angle, which corrects forthe probability of a particular angle. Only helices inCytOx and BRD are included, since it was possible tode®ne an accurate membrane normal for thesestructures.

portional to the circumference of the annulus drawn byrotating the helix axis vector 360� about the helix 1 axis.The smaller the angle, the smaller the annulus. The cir-cumference is proportional to sin(t). The probability of arange of angles is proportional to the area on the sphereswept out by the range of angles. This area is pro-portional to cos(t1) ÿcos(t2).

Do TM helices show a different distribution ofpacking angles? The 45 helices analyzed here wereinvolved in 88 packing interactions. The list ofinteractions is given in Table 2. Figure 4(a) showsthe distribution of angles for the 88 helix pack-ing interactions in the dataset. In contrast to sol-uble proteins, there is a strong peak centeredaround the angles corresponding to the c class ofhelix packings. Moreover, the range of the distri-bution is decidedly smaller than that seen for sol-uble proteins. No observed angle in TM helixpackings greater than 67� or less than ÿ56� wasobserved. In contrast, a signi®cant fraction of helix-helix packing angles are outside this range in sol-uble proteins. In a database of 2145 helix packingsin soluble proteins, 645 or 30% were outside thisrange (Bowie, 1997). Thus, the helix packing angledistribution for TM helices is very different fromthe distribution seen for soluble proteins.

As with tilt angles, the probability of large angles is higher than for small angles (seeFigure 3 and Bowie, 1997). Thus, to extract truepacking angle preferences from the distributionshown in Figure 4(a), it is necessary to normalizeby the expected random distribution. In the case ofmembrane proteins, the random distribution willbe affected by constraints on tilt angles, so it is notpossible to calculate the theoretical distributionfrom ®rst principles. Consequently, I found the

Table 2. Helix packing interactions

Minimum Number ofProtein Helix1 Helix2 distance (AÊ ) (deg.) contacts Orientation

Cytochrome c oxidase1 2 7.1 24.6 38 A1 3 10.1 20.2* 14 P1 10 12.8 34.3 5 A1 12 9.7 29 11 A1 27 10.2 ÿ44.5 17 P2 3 10.8 11.7* 10 A2 4 11.3 15.5 17 P2 5 11 35.6 11 A2 6 11.2 45.3 16 P2 10 10.8 36.4 18 P2 27 8.3 ÿ32.8* 5 A3 4 8 19.2 24 A3 15 7.1 ÿ30.1* 15 P3 16 13.4 ÿ12.9* 7 A3 25 10.7 21.1* 4 P4 5 7.6 29.6 26 A4 15 9.4 ÿ26* 10 A4 17 8.9 ÿ40 12 A5 6 8.3 19.4 28 A5 7 9.4 6* 11 P5 17 9.8 ÿ40.9 15 P6 7 8.9 ÿ14* 7 A6 8 9.8 10.6* 11 P6 9 9.7 32.6 12 A6 10 9.2 42.2 19 P6 17 8.5 ÿ36.6* 7 A7 8 9.5 22.5 15 A7 23# 12.3 ÿ55.6 7 P8 9 10.1 22 14 A8 13 9.7 15.3* 6 P8 14 9.1 ÿ24.8 18 A9 10 8.2 21.9 25 A9 11 9.7 14.5* 11 P9 13 8.8 ÿ19.5* 12 A

10 11 10.2 ÿ9.2* 12 A10 12 13.4 9.1* 8 P11 12 6.8 18.3 22 A11 22 8.8 ÿ47.4 14 P11 28 14.9 ÿ26.8* 3 P12 22 9.3 ÿ56.4 13 A12 26 14.5 ÿ31.7* 4 A12 27 6.8 ÿ28.7* 13 A12 28 9.6 ÿ42.1 15 A13 14 8.7 14.5* 17 A13 24 8.8 ÿ18.9 29 A15 16 7.2 23.4 22 A15 25 9.3 39.3 17 P16 20 13.1 ÿ39.5 3 P16 25 9.6 32.8 16 A17 20 8.1 19.8* 13 A17 21 10.7 ÿ11.8 23 P18 19 7.8 17.5 23 A18 20 13.6 24.3 4 P18 21 10.1 19.5 20 A18 23 8.7 16.2 21 A19 20 9.7 22.8 24 A19 21 13.5 32.5 9 P19 23 12.5 21.3 10 P20 21 9.3 21.6 25 A22 26 6.6 25.1 30 P22 28 12.2 ÿ25.3* 11 P27 28 8.2 ÿ13.9* 21 P

Photosynthetic reaction center1 2 7.6 23.2 23 A2 3 9.3 20.4* 18 A3 5 9.1 ÿ6.8* 16 P3 9 7 ÿ50.4* 7 A4 5 7.6 19.6 20 A4 8 6.1 ÿ38.4* 9 A4 9 9.2 67 13 P

continued


Table 2ÐContinued

Minimum Number ofProtein Helix1 Helix2 distance (AÊ ) (deg.) contacts Orientation

4 10 7.8 54.2 14 A5 9 7.6 52.5 16 A6 7 7.7 23.5 22 A7 8 9.1 8.9* 16 A8 10 8.4 16* 18 P9 10 8.1 19.1 23 A

Bacterio-rhodopsin1 2 8.1 21.8 22 A1 7 9.6 8.9* 19 P2 3 8.6 8.3* 24 A2 7 9.8 17.5* 11 A2 4 # 7.8 10.1* 13 P2 5 # 11.2 13.1* 10 A3 4 9.8 ÿ13.1 13 A3 5 11.2 19.2* 4 P3 6 11.9 23.1 10 A3 7 11.9 23.4 15 P4 5 8.1 22.9 20 A5 6 11.2 9.5 17 A6 7 9.9 10.1 20 A

The minimum interaxial distance was calculated within the extent of the helices themselves. Asterisks (*) indicate that the observedinteraxial distance is not the global minimum for in®nite axes. A refers to an antiparallel orientation, P to a parallel orientation.


expected random distribution from TM helices thatare not in contact, as non-contacting helices shouldhave no orientational constraint that is due topacking. This distribution is shown in Figure 4(b).Within the limits of the small data set, the distri-bution is roughly symmetric about zero degreeswith peaks at about ÿ30� and �30�. Thus, part ofthe preference for the c class of packing angles isdue to statistical bias. Nevertheless, the normalizeddistribution shown in Figure 4(c) still shows a sig-ni®cant preference for c class packings, as indi-cated by the obvious preference for angles in therange of 0 to 30�. These angle preferences are insharp contrast to soluble proteins, which show amuch broader range of preferred angles with adecided bias toward negative angles (Bowie,1997).

Why are the packing angles more restricted forTM helices than for soluble protein helices? Nodoubt much of the restriction comes from the limi-tations on tilt angles described above. Anadditional possibility is that the steric constraintsmay be more stringent for TM helix interactions.Part of the reason soluble protein helix packinginterfaces are so accommodating is that the helicestend to be relatively short, with an average lengthof 12 residues (Bowie, 1997). As a result, the pack-ing interfaces tend to be relatively small, requiringsteric compatibility of only a small number of side-chains. TM helices tend to be quite long (26.4 resi-dues), however, and the packing interfaces can belarge. Consequently, there may be a strongerrequirement for regularity of the packing becausesuch extensive, regular interdigitation of side-chains can occur only at certain interaxial angles(Chothia et al., 1981; Crick, 1953; Richmond &Richards, 1978; Walther et al., 1996). Moreover, inthe absence of the hydrophobic driving force, ef®-

cient packing may play a relatively more importantrole in stabilizing TM helix interactions than itdoes for soluble proteins.

Distance of closest approach

From the analysis by Richmond & Richards(1978), Walther et al. (1996) and Reddy & Blundell(1993), the c class packing interactions, whichapparently predominate in membrane proteins,maintain greater interhelix distances than the aclass packings that predominate in soluble pro-teins. Thus, one might expect that the averageinterhelical distance in membrane proteins wouldbe larger than for soluble proteins. This is not thecase, however. The distances of closest approachfor the TM helix interactions are quite similar tosoluble proteins. The average distance of closestapproach for TM helices in contact is 9.6 AÊ (stan-dard deviation 1.9 AÊ ). The average value for the2145 helix packings in soluble proteins is also9.6 AÊ .

Positioning of the axes of closest approach

The segment connecting the points of closestapproach of the interacting helices is akin to anaxis about which the two helices are rotated. Mod-eling of TM helix interactions would be greatlysimpli®ed if positioning of the rotation axes wasrestricted in some manner. For example, if allrotation axes were in the center of the bilayer, thenumber of ways to position two interacting heliceswould be more limited than if there were no pre-ference. In fact, rotation axes have generally beenplaced in the center of helix-helix interactions inmodeling efforts (Sansom et al., 1995; Taylor et al.,1994; Treutlein et al., 1992).

Figure 4. The distribution of helix packing angles. (a)The number of helix packings found for a given rangeof angles. CytOx helices are shown as black bars,PRC helices are indicated by the dark gray bars andBRD helices by the stipled bars. A total of 88 helix pack-ing interactions contribute to the distribution. (b) Thefraction of non-contacting helix pairs in a given range of angles. The distribution is from 777 helix pairs. Thisrepresents, as well as can be estimated at this point, thedistribution expected in the absence of any packingin¯uences. The error bars represent one standard devi-ation according to the Poisson distribution. (c) The angle preferences for a given range of angles. To deter-mine packing angle preferences, the fraction of helicesfound in a given range of angles (from (a) converted tofractions) was divided by the expected or random distri-bution of (b). In this distribution, a value of 1 indicatesthat the fraction observed is not different from thatexpected by chance. The error bars represent one stan-dard deviation according to the Poisson distribution. Allthe error was assumed to reside in the contacting helixdistribution, since the number of these interactions wasso much smaller.


To look for any such restriction, the center point,de®ned as the midpoint of the segment of closestapproach, was determined for all TM helix inter-actions. The distance of the centerpoints to the cen-tral plane was then calculated. The distribution ofthe distance of the centerpoints to the central planeis shown in Figure 5. As the position of the centerpoint cannot extend beyond the ends of the helices,the extent of the helices places limits on the poss-ible center point positions. For comparison then,Figure 5 also shows the expected distribution ofarbitrarily chosen center point positions. Clearlythe distributions are very similar, indicating thatthere is no apparent restriction or preference forthe positioning of the center points. Thus, TMhelices can form intimate interactions throughouttheir length, either within the membrane or outsidethe membrane.

Interactions between helices that aresequence neighbors

The constraint that neighboring helices mustcontact one another has been used in membraneprotein modeling (Baldwin, 1993). How reliable isthis constraint for the current database? Of the 38TM helices in the database that are in subunits con-taining more than one TM helix, 37 are in contactwith at least one helix adjacent in the sequence. Infact, of the 32 neighbor interactions possible, 28 aremade. This is indeed a strong constraint that canbe applied in the modeling of membrane proteins.

Figure 5. Position of helix interaction centerpoints rela-tive to the central plane. The black bars correspond tothe observed distribution. The gray bars represent a ran-dom distribution given the observed position of helixendpoints relative to the central plane. The random frac-tion is essentially the fraction of all helix density, D,remaining at a given distance from the central plane.The density D(i) in distance bin i is given by:

D�i� � N�de > di�Pj N�de > dj�

where N(de>di) is the number of helix endpoint distancesfrom the central plane, de, that are greater than the dis-tance di. The summation in the denominator is takenover all distance bins.


Does the length of the intervening sequenceaffect the probability that neighboring helices willpack together? The loop lengths in the three mem-brane proteins range from 3 to 38 residues, with anaverage length of 15. Of the four potential neigh-bor packings that do not occur, the loop lengthsare 6, 23, 31 and 38 residues. All but one are longerthan average, suggesting that loop length mayhave some predictive value in determiningwhether neighbors interact or not. The database isstill too small to assess the strength of this corre-lation, however. Clearly, a short intervening loopis no guarantee that two neighbors will packagainst each other.

Parallel and antiparallel packing arrangements

Antiparallel orientations of packed helicesappear to be favored over parallel orientations.First, of the 88 helix packings observed in thisstudy, 55 (63%) are in an antiparallel orientation.Second, the mean distance of closest approach forthe antiparallel helix pairs is 9.1 AÊ while for paral-lel pairs it is somewhat larger at 10.5 AÊ . Appar-ently, parallel helices have a greater tendency tokeep their distance from one another. Third, thesize of the contacting surfaces tends to be some-what larger for antiparallel packings than for paral-lel packings. The average number of atoms incontact for antiparallel packings is 16, while for theparallel orientations the average is 13.

While the antiparallel orientations are more inti-mate on average, it is certainly not an overwhelm-ing difference. Intimate interactions are seen inboth orientations. For example, both types of inter-actions can be very close: the mininum distance ofclosest approach for the parallel class is 6.6 AÊ andfor the antiparallel class it is 6.1 AÊ . Both interactionsurfaces can also be very large: the maximumnumber of contacts seen for parallel packings is 30,while for antiparallel packings the maximum was38. Indeed, parallel helix packing interactions inmembrane proteins can be very stable (Bormannet al., 1989).

There are a number of possible reasons for theantiparallel bias. It has been suggested that thehelix dipole should favor an antiparallel arrange-ment of helices, particularly in the low dielectricenvironment of the membrane (Deber & Li, 1995;Yeates et al., 1987). Moreover, as described above,there is a strong preference for relatively smallhelix-helix packing angles, thereby aligning thehelix dipoles. Theoretical calculations by Ben-Tal &Honig (1996) suggest that backbone electrostaticinteractions are relatively modest for helices thatextend even a few aÊngstroÈm units beyond thebilayer, however, as is the case for most TM helices(see above). Another possibility is that interdigita-tion of side-chains is more ef®cient in the antiparal-lel orientation for c-class helix packings that arecommonly observed in membrane proteins.Indeed, the data reported by Walter et al. (1996)show that antiparallel c-class packings are more

prevalent than parallel c-class packings in solubleproteins. Finally, it is possible that the preferencefor antiparallel packings is the result of the nearcertainty that sequence neighbors will be in contact(see above). Due to topological constraints, theseinteractions must be antiparallel. To test this possi-bility, the orientation of helix packing interactionsbetween subunits were counted. In these cases,topological constraints are minimized. Of the 34intersubunit interactions in the current data set, 19or about 56% are antiparallel. Thus, the preferencefor antiparallel packings is still observed but issomewhat diminished. It seems entirely possiblethat the bias toward antiparallel packings, that arenot due to connectivity constraints, will disappearas more structural data become available.

Conclusion

One of the primary dif®culties in the predictionof soluble protein structure is the enormous num-ber of possible conformations, making exhaustivesearches of conformation space impossible and pla-cing great demands on any energy functions usedfor evaluating potential structures (Levinthal,1969). In contrast to soluble proteins, however,membrane proteins must remain embedded in thebilayer, which forces signi®cant limitations on theirstructure. These limitations will ultimately be ofenormous bene®t for folding membrane proteins.The analysis described here provides some prelimi-nary estimates of the magnitude of the constraintson TM helix interactions and describes some of theways in which TM helices achieve ef®cient packingwhile at the same time satisfying the restrictionsimposed by their complex environment. The fea-tures of TM helix architecture described hereshould prove useful in designing conformationalsearch strategies and evaluation functions for themodeling of membrane protein structure.

Materials and Methods

Structures

The coordinate ®les were obtained from the ProteinData Bank (Bernstein et al., 1977). A number of photo-synthetic reaction center structures are known, so thehighest resolution structure was chosen for analysis. Ofthe two cytochrome c oxidase structures (Iwata et al.,1995; Tsukihara et al., 1996), the larger bovine heartstructure was chosen. The following structures andassociated coordinate ®le codes were used in this work:(1) Rhodopseudomonas viridus photosythetic reaction cen-ter (1PRC, 2.3 AÊ resolution); (2) Halobacterium holobiumbacteriorhodopsin (2BRD, 3.5 AÊ resolution); and (3)bovine heart cytochrome c oxidase (1OCC, 2.8 AÊ resol-ution). For the analysis of soluble proteins, the 25%pdb_select list of structures from March 23, 1997 wasused with the additional limitation to 3.0 AÊ resolution orbetter. This list contains no protein that shares greaterthan 25% sequence identity. The 2145 packing inter-actions from this database are described by Bowie(1997).


Helix parameters

Helical regions were de®ned by the DSSP program(Kabsch & Sander, 1983). Interactions between heliceswere described by the distance of closest approach of thehelix axes, d, and the interaxial angle as described byChothia et al. (1981) except was con®ned to �90�.

Identification of interacting helices

The de®nition of helices in contact was from Chothiaet al. (1981). Helices were considered to be packedtogether if three or more residues were in contact. A resi-due on a helix was considered to be in contact withanother helix if the distance between any atom in theresidue and any atom on the other helix was within0.6 AÊ of the sum of their van der Waals radii.

Definition of membrane normal and central plane

The direction of the membrane normal could be accu-rately de®ned for both CytOx and BRD, since the pro-teins are oligomers. The membrane normal was simplytaken as the axis of rotation for superimposing one sub-unit on the others. PRC proved to be more problematic.Yeates et al. (1987) were able to de®ne an approximatemembrane normal by energy calculations, but the mini-mum energy was not well de®ned. Wallin et al. (1997)used the vector sum of the TM helix axis vectors. I testedthis approach on CytOx and found the calculated normalvector to be off by 9� relative to the normal determinedby superposition of related subunits. As a result, PRCwas not included in calculations that required knowl-edge of the membrane normal.

A central plane was de®ned by a plane perpendicularto the membrane normal, passing through the center ofmass of the TM helix atoms.

Acknowledgments

I thank Todd Yeates, Frank Pettit and Tau-Mu Yi foradvice and careful reading of the manuscript. I am grate-ful to the crystallographers who deposited their coordi-nates in the Protein Data Bank. This work wassupported by a NSF national young investigator awardand a Pew scholar award.

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Edited by G. von Heijne

(Received 21 April 1997; received in revised form 8 July 1997; accepted 14 July 1997)

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Helix packing in membrane proteins