doi:10.1006/jmbi.2000.3557 available online at http://www.idealibrary.com on J. Mol. Biol. (2000) 297, 803±808

Infrared Dichroism of Twisted bbb-Sheet Barrels. Thestructure of E. coli outer membrane proteins

Derek Marsh

Max-Planck-Institut fuÈ rbiophysikalische ChemieAbteilung SpektroskopieD-37070 GoÈttingenGermany

E-mail address of the corresponddmarsh@gwdg.de

Abbreviations used: ATR, attenu

0022-2836/00/030803±6 $35.00/0

The infrared dichroic ratios of the amide bands from oriented b-barrelsyield an experimental value for the mean orientation, b, of the b-strands,relative to the barrel axis. For a barrel of n strands, this then gives theshear number, S, that characterizes the stagger of the b-sheet. Combiningvalues of b and n speci®es the barrel geometry by using the optimizedmodel of Murzin, Lesk & Chothia for regular barrels. Application to pub-lished infrared data on the Escherichia coli outer membrane protein,OmpA yields S � 9 ÿ 10 (n � 8), a barrel radius of 0.81(�0.01) nm, andan internal free volume of 0.031 nm3 per residue, where the averagetwist of the b-sheets is y � 28 �, and their coiling angle is e � 1 �. Hydro-phobic matching of the 2.6 nm transmembrane stretch partly determinesthe shear number of the OmpA b-barrel.

# 2000 Academic Press

Keywords: b-barrel, porin (OmpA, OmpF); infrared dichroism;shear number; b-sheet twist/coil

The axial symmetry of regular b-barrels, coupledwith the helical nature of the individual b-strands,means that the average tilt, b, of the strand axesfrom the barrel axis can be determined directlyfrom the dichroic ratios of the infrared amidebands that are measured by using plane polarizedradiation with oriented samples (Tamm &Tatulian, 1997; Marsh, 1997, 1998). Because of theconstraints on closed barrel structures that arisefrom hydrogen bonding of the ®rst strand to thelast, this experimental information is suf®cient tospecify the overall structure of the b-sheet (i.e. theshear number, S), if the number, n, of strands inthe barrel is known (McLachlan, 1979). It is thenpossible to specify the structure of an equivalentregular b-barrel (i.e. one with the same values of nand S), by using the optimized geometrical modelof Murzin et al. (1994a). The latter authors havedemonstrated that these idealized barrel structuresreproduce rather well the major features, in par-ticular the twist of the b-sheet and the coiling ofthe b-strands, for a wide range of b-barrels thethree-dimensional structures of which are alreadyknown (Murzin et al., 1994b).

The principal interest here is for b-barrel proteinsthat potentially form pore structures in mem-

ing author:ated total re¯ection.

branes. Such membranous samples can readily beoriented to determine the dichroic ratios of theamide bands by using polarized infrared spec-troscopy (Nabedryk et al., 1988; Rodionova et al.,1995). The methods described by Murzin et al.(1994b) work well for porin from Rhodobactercapsulatus, the structure of which is known (Weiss& Schulz, 1992). It is shown here that the infrareddichroism data from the analogous matrix porinOmpF of Escherichia coli (Nabedryk et al., 1988) areconsistent with this analysis. Structural data arethen derived from infrared measurements on adifferent outer membrane protein, OmpA of E. coli(Rodionova et al., 1995), the three-dimensionalstructure of which has recently been determined(Pautsch & Schulz, 1998). These results indicatethat linear dichroism measurements from polarizedinfrared spectroscopy therefore may be combinedwith the barrel geometry to obtain the overallstructural parameters, and the sheet and strandcon®guration, for b-barrels the detailed three-dimensional structure of which is not known.

Infrared dichroic ratios

The strands of the b-barrels considered are onlyslightly coiled, and as a consequence, the resultanttransition moments of the major amide I and amideII bands are oriented perpendicular and parallel,respectively, to the axis of the b-strand (Miyazawa,1960; Marsh, 1997). The orientation, �j, of the tran-

# 2000 Academic Press

Figure 1. Orientation of a b-barrel in the membrane.The axis of the barrel is tilted at an angle a to the mem-brane normal, z, which corresponds to the direction ofuniaxial sample alignment, and the b-strands are tiltedat an angle b to the barrel axis. The orientations, �I and�II, of the amide I and amide II transition moments,respectively, are also indicated.

804 �-Barrel Infrared Dichroism

sition moment, relative to the barrel axis, is there-fore related to the strand tilt, b, by �I � p/2-b forthe amide I band, and by �II � b for the amide IIband. Figure 1 depicts the various angular relation-ships in an oriented membrane. For a regularb-barrel, the transition moments are distributedwith axial symmetry about the barrel axis becauseof rotational disorder within the plane of the mem-brane (see Marsh, 1998). In a polarized attenuatedtotal re¯ection (ATR) experiment, the orientation ofthe transition moment is then related to the infrareddichroic ratio, Rz

ATR, by the following expression(Tamm & Tatulian, 1997; Marsh, 1997, 1998):

hP2�cos �j�i �E2

x ÿ E2yRATR

z � E2z

hP2�cos a�i�E2x ÿ E2

yRATRz ÿ 2E2

z ��1�

where j � I, II for the amide I band and theamide II band, respectively. Here (Ex, Ey, Ez) arethe components of the radiation electric ®eldvector in the sample, relative to those at incidence(see, for example, Marsh, 1999), and a is theorientation of the barrel axis relative to thenormal to the orienting sample substrate. Angularbrackets designate averages of summations overthe angular distributions and different strands,and P2(x) � (1/2)(3x2 ÿ 1) is a second orderLegendre polynomial.

In a polarized transmission experiment, withdichroic ratio Rz

T, the corresponding relation is(Marsh, 1997):

hP2�cos �j�i � RTz ÿ 1

hP2�cos ai�3 sin2 i=n2M � RT

z ÿ 1� �2�

where i is the angle of incidence of the infraredradiation, and nM is the refractive index of thesample. The same convention for the amide I andamide II bands holds with respect to �j, as forequation (1).

bbb-barrel and sheet structure

A right-handed twist of the b-strands about thebarrel axis is assumed, as is the case for all knownb-barrels (Liu, 1998). The stagger in the hydrogenbonding between adjacent strands of the b-sheetsis speci®ed by S, which is de®ned as the displace-ment in number of residues by following the lineof hydrogen bonding, perpendicular to the strand,from a given residue on traversing around the bar-rel to arrive back at the same strand (see Figure 2).For an n-stranded barrel, the shear number isrelated to the tilt, b, of the strands by (see,McLachlan, 1979; Chou et al., 1990):

S � �d=h��p= sin�p=n�� tan b �3�where h is the rise per residue along the strand,and d is the separation between adjacent strands.Correspondingly, the radius of the barrel, R,(de®ned by the strand backbone) is related to thestrand tilt by (McLachlan, 1979):

R � d=�2 sin�p=n� cos b� �4�These latter two equations relate structural par-ameters of the sheet to the infrared observable, b.

Twist and coiling of bbb-sheets

To form a barrel structure, the component b-strands must both twist about their axis and mustcoil around the barrel axis. In the study by Murzinet al. (1994a), the twist and coiling of the strands isexpressed in a local coordinate system. The meantwist about an axis perpendicular to the stranddirection is y, that about an axis parallel with thestrand direction is t, and the mean coiling alongthe strands is e, with that perpendicular to thestrands being Z (see Figure 2).

The two angles of orthogonal twist are relatedby:

sin�t=2� � �h=d� sin�y=2� �5�

Figure 2. Inter-residue hydrogen bonding pattern (broken lines) of the antiparallel b-strands (continuous lines) inan n-stranded b-barrel structure. The last strand (n) is hydrogen-bonded to the ®rst strand (1), and the dotted linetraces the residue offset that de®nes the shear number, S. The local coordinate system used by Murzin et al. (1994a)to de®ne the twist and coiling angles of the sheet is indicated by the exaggerated displacements of the residues (greyballs) relative to the ideal positions for a planar sheet (®lled dots). The twist of the b-sheet is y about an axis perpen-dicular to the strand direction and t about an axis parallel to the strand direction. The coiling of the b-sheet along thestrands is e, and that along the line perpendicular to the strands is Z.

�-Barrel Infrared Dichroism 805

where for small half-angles the approximationsin(x/2) � x/2 holds. The relationships betweenthe twist and coiling parameters are established bytraversing the barrel surface to arrive back at theoriginal residue. This is achieved with n steps in adirection perpendicular to the strand direction andS steps along the strand direction, and conse-quently (Murzin et al., 1994a):

nyt � Set � 2p �6�where the projections yt and et of the angles y ande, for tangential vectors along the circumference ofthe barrel, are given by:

sin�xt=2� � sin�x=2�= sin b �7�with x � y or e. Correspondingly for the comp-lementary angles of twist and coiling (Murzin et al.,1994a):

Stt � nZt � 2p �8�where the projections tt and Zt of the angles t andZ, for tangential vectors along the circumference ofthe barrel, are given by:

sin�yt=2� � sin�y=2�= cos b �9�with y � t or Z.

Optimized regular bbb-barrel

Equations (5)-(9) can be used to express all twistand coiling parameters in terms of a single angularvariable, say y. Murzin et al. (1994a) establishedoptimized values by minimizing a function repre-senting parabolic deviations of the free energyfrom the individual unconstrained minimumvalues, using equal weightings, i.e.:

d=dy��yÿ yo�2 � e2 � Z2� � 0 �10�where yo is the most favourable value of y in anunstrained sheet. If the approximations for thesines of the half-angles are used in equations (7)and (9), this results in:

y �fyo � �2p=n��h2 cos b=�d2 tan b�

� sin b�g=�h2=�d tan b�2 � 1= cos2 b� �11�where the orthogonal twist angle t is given by thecorresponding approximation obtained fromequation (5):

t � �h=d�y �12�The coiling angles are then given in terms of thetilt angle and y by the approximation:

e � �h=d��2p=nÿ y= sin b� cos b �13�from equations (3), (6) and (7) and by the corre-sponding expression:

Z � �2p=n� cos bÿ y tan b �14�from equations (3), (8) and (9). Although equations(11)-(14) are small-angle approximations, theyemphasize the way in which the various twist andcoiling parameters are directly related to the infra-red observable tilt angle b. These analyticalexpressions reproduce the results of the numericalcalculations presented by Murzin et al. (1994a).

Application to OmpF

The matrix porin OmpF forms a 16-stranded b-barrel that traverses the outer membrane of E. coli.Polarized transmission infrared measurements

806 �-Barrel Infrared Dichroism

have been performed on puri®ed OmpF inoriented membranes of dimyristoyl phosphatidyl-choline (Nabedryk et al., 1988). The dichroic ratiosof the amide I and amide II bands were Rz

T � 1.10and 1.13, respectively, with an angle of incidencei � 40 �. Combining these two measurements withthe appropriate versions of equation (2) (andnM � 1.5), leads to a value of hcos2bi � 0.52. Thiscorresponds to an effective mean value for the tiltof the strands relative to the barrel axis of b � 44 �.The conjugate parameter that characterizes theorientation of the barrel in the membrane ishP2(cosa)i � 0.69 (cf. equation (2)). An error of 5 %in the dichroic ratios corresponds to a maximaluncertainty of 4 � in orientation of the b-strands,and an uncertainty of 15 % in the refractive indexhas negligible effect. It is also of interest to com-pare with values obtained from the correspondingexpressions for a planar sheet (Marsh, 1997), to getsome indication of the effects of non-axiality aris-ing from ¯attening of the barrel (Cowan et al.,1992). These latter expressions yield comparablevalues for the strand tilt: hcos2bi � 0.51 corre-sponding to an effective tilt of b � 44 �, indicatingthat strand tilts obtained from infrared dichroicratios are relatively robust.

Application of equation (3) leads to a shear num-ber for the b-barrel of S � 21.3, with d � 0.473 nmand h � 0.345 nm for an antiparallel sheet (Arnottet al., 1967). For porin from R. capsulatus (and fromRhodopseudomonas blastica), the shear number is:S � 20, �S � � 1, where �S is the deviation in Sarising from uneven b-bulges in a non-regular bar-rel (Liu, 1998). For a regular b-barrel, S must be aneven integer. The corresponding value for theradius of the OmpF barrel is: R � 1.68 nm, calcu-lated from equation (4). For comparison, Murzinet al. (1994b) have determined the following aver-age values: b � 42 � and R � 1.58 nm from the pub-lished three-dimensional structure of the 16-stranded porin from R. capsulatus (Weiss & Schulz,1992). The three-dimensional structure of OmpFagain reveals a 16-stranded antiparallel b-barrelwith shear number S � 20 and strand tilts in therange b � 35-50 � (Cowan et al., 1992). The meanstrand tilt is 45 �, as calculated from the meansquare cosine of the orientation of the individualpeptide units using the PDB ®le 2OMF. The lattercorresponds to the observable infrared quantityand is in good agreement with the experimentalvalue quoted above. The parameters characterizingthe twist and coiling of the b-strands in OmpF are:y � 17(�0.9)�, t � 12(�0.7)�, e � ÿ 1(�1.7)� andZ � 0 �(�2.5)�, deduced from the infrared data byusing equations (11), (14), with yo � 18 � (see Janin& Chothia, 1980; Chothia & Janin, 1981). Thevalues in parentheses represent uncertainties aris-ing from a 5 % error in dichroic ratios. The corre-sponding average values deduced from the three-dimensional structure of R. capsulatus porin are:y � 13 �, t � 10 �, e � 2 � and Z � 0 � (Murzin et al.,1994b). Thus the structural parameters derivedfrom infrared spectroscopy and geometrical con-

straints are in reasonably good agreement with thethree-dimensional structures for this class of porinmolecule.

Application to OmpA

OmpA is one of the most abundant integral pro-teins of the outer membrane of E. coli. The three-dimensional structure of the N-terminal membranedomain (residues 1-171, OmpA171) has been deter-mined recently (Pautsch & Schulz, 1998). Thisdomain is monomeric with a structure that consistsentirely of a rather regular 8-stranded antiparallelb-barrel with a shear number of S � 10. The overalltransmembrane topology is closely similar to thatpredicted originally on the basis of vibrationalspectroscopy and hydropathy analysis that tookinto account the two-residue periodicity of theb-sheet (Vogel & JaÈhnig, 1986). The b-sheet contentof the whole OmpA protein has been determinedby vibrational spectroscopy as 45-55 % (Rodionovaet al., 1995; Vogel & JaÈhnig, 1986). Of the total 325-residue protein, the b-sheet structure is thereforefound mostly in the 171 residues of the N-terminaltransmembrane b-barrel.

Polarized ATR infrared measurements have beenmade on OmpA inserted in oriented bilayer mem-branes of different phosphatidylcholine species(Rodionova et al., 1995). The dichroic ratios ofthe amide I0 band were measured to beRz

ATR � 2.07(�0.71), 1.81(�0.05) and 1.94(�0.04)in membranes of dipalmitoyl, dimyristoyl andpalmitoyl-oleoyl phosphatidylcholines, respect-ively. Dichroic ratios are not available for theamide II band because measurements were per-formed in 2H2O. The dichroic ratios of the amide I0band indicate that the degree of orientation of theb-barrels differs between the different lipid hosts.The orientation is highest in dipalmitoyl phospha-tidylcholine, because bilayers of this lipid are inthe ordered gel phase. The dylcho orientation islowest in dimyristoyl phosphatidylcholine,probably because of problems with hydrophobicmatching in the ¯uid phase of this short-chainlipid host. It therefore seems reasonable to assumethat the value of hP2(cosa)i in the disordered ¯uidphase of palmitoyl-oleoyl phosphatidylcholine isclosest to that determined above for OmpF, andsecondly that hP2(cosa)i � 1 in the ordered phaseof dipalmitoyl phosphatidylcholine. These twoindependent alternatives are shown below to giveconsistent results.

Applying the version of equation (1) appropriateto the amide I band, with hP2(cosa)i � 0.69 (1.0),yields a strand tilt of b � 40(�1)� (40(�2)�), for thepalmitoyl-oleoyl phosphatidylcholine (dipalmitoylphosphatidylcholine) host. This is in reasonableagreement with the mean tilt of b � 45 � found forthe X-ray structure (Pautsch & Schulz, 1998). Cor-respondingly, a shear number of S � 9.4(�0.3)(9.5(�0.7)), with a barrel radius R � 0.81(�0.01)(0.81(�0.3)) nm, is obtained from equations (3) and(4), respectively, by taking d � 0.473 nm and

�-Barrel Infrared Dichroism 807

h � 0.345 nm. Parameters governing the twist andcoiling of the b-strands in OmpA: y � 28(�0.3)�,t � 20(�0.2)�, e � 1(�1)� and Z � 11(�2)�, arededuced from the infrared data for both palmitoyl-oleoyl and dipalmitoyl phosphatidylcholine mem-branes, by using equations (11)-(14) with yo � 18 �.The uncertainties correspond to the larger of thetwo experimental errors.

The shear number for the b-barrel of OmpA istherefore derived to be S � 10, corresponding tothe nearest even integer, in agreement with thatdetermined by crystallography (Pautsch & Schulz,1998). This value (i.e. (S � n � 2), unlike that forOmpF, does not correspond to an unstrained bar-rel, which is characterized by a shear number of:S � n � 4.2 (Murzin et al., 1994a). The packing ofthe amino acid side-chains within the interior ofthe OmpA barrel, and/or hydrophobic matchingwith the surrounding lipids (see, for example, DePlanque et al., 1998) therefore must constrain thetilt of the b-strands to a sub-optimal value. Thesetwo aspects are considered next.

Constraints on the OmpA barrel

In the crystal structure of OmpA17l (Pautsch &Schulz, 1998), the non-polar belt and aromaticgirdles comprise on average ®ve outward-facingresidues in each of the eight b-strands of the barrel(total composition: A4F3G3I2L8M1T3V4W4Y7). Thetransmembrane thickness of this hydrophobicstretch is therefore 10 � hcosb � 2.6 nm. Thisagrees quite well with the width of the hydro-phobic band encircling the trimers of E. coli OmpFand PhoE (2.5 nm, Cowan et al., 1992), and also isreasonably close to that of R. capsulatus porin(2.4 nm, Weiss & Schulz, 1992). This value cantherefore be identi®ed with the hydrophobic thick-ness of the E. coli outer membrane. The implicationthen is that hydrophobic matching at the outerperimeter limits the shear number of the OmpAb-barrel to a sub-optimal value.

The 40 internally facing residues of the trans-membrane section of the barrel have a compo-sition: A3D2E3F1G12K2L1M2Q3R3S3T2V1Y2 (Pautsch& Schulz, 1998), similar to that proposed by VogelJaÈhnig (1986) simply on the basis of hydropathyanalysis. The mean volume per residue of theinternally facing amino acid side-chains is0.061 nm3, using the residue volumes given byChothia (1984). The contribution of the proteinbackbone to the internal volume of a b-barrel isestimated by Murzin et al. (1994b) as 0.040 nm3 perinward-facing residue. The net internal volume ofthe protein per inward-facing residue is given by(cf. Murzin et al., 1994a):

V � hdRÿ Vi �15�where Vi is the mean internal free volume perinward-facing residue. From this, and the value ofR obtained above, it can be calculated that theb-barrel of OmpA occludes an internal free volume

characterized by Vi � 0.031 nm3. This correspondson average to the volume of approximately onewater molecule (0.030 nm3) per inward-facing resi-due. The total free volume occluded within thebarrel lumen therefore corresponds to approxi-mately 40 water molecules. This value compareswell with the number of structured water mol-ecules (i.e. 39 molecules) contained within the crys-tal structure of OmpA171 (Pautsch & Schulz,1998). The value of Vi translates to an effectiveinternal radius of the barrel of Ri � 0.39 nm. How-ever, there is no evidence in the crystal structure ofOmpA 171 for a continuous aqueous pore,although small-molecule permeability and single-channel ion activity have been reported for OmpA(Sugawara & Nikaido, 1994; Saint et al., 1993). Theexistence of free volume within the barrel lumensuggests that the strand tilt in OmpA is not limitedentirely by considerations of side-chain packingwithin the barrel lumen, although the lack of acontinuous pore could imply that hydrophobicmatching is not the only factor that controls theshear number.

Performing a similar calculation for the out-ward-facing residues, yields a total averagevolume per residue of Vo � 0.14 nm3, where thevolume of a glycine residue is used to obtain thebackbone contribution. The corresponding ana-logue of equation (15) is:

Vo � hd�R2o=Rÿ R� �16�

where Ro is the outer radius of the barrel. Thisyields an outer diameter of 2Ro � 2.4 nm, in agree-ment with that obtained from the crystal structure(Pautsch & Schulz, 1998).

Conclusion

Application to the E. coli outer membrane pro-teins OmpA and OmpF that is given here demon-strates that a combination of infrared lineardichroism measurements with the geometricalmodels for regular barrels could yield very usefulstructural information for b-barrel membrane pro-teins, the high-resolution structure of which is notknown. Implementation is straightforward andoffers the possibility to explore the effects of arange of membrane environments relativelyrapidly. The example of OmpA also illustrates thatthe combination with sequence informationadditionally allows certain conclusions to bedrawn about structural constraints imposed by thelipid membrane.

Acknowledgements

I am extremely grateful to Dr Tibor PaÂli for calcu-lations on the X-ray crystal structure of OmpF.

808 �-Barrel Infrared Dichroism

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Edited by G. von Heijne

(Received 1 November 1999; received in revised form 21 January 2000; accepted 24 January 2000)