J. Mol. RioL (1978) 121, 41-54
Helical Channels in Crystals of Gramicidin A and of a Cesium-Gramicidin A Complex : an X-ray Diffraction Study
X-ray cryst,allographic studies of’ gramicitlin A crystalliz:1,d from methanol (l’Y1) and othtmol (1’2 1’1 ‘) 2 1) > cmd of a Cs + gritmicitlin .1 complex (~rystallizrtl front rnt%hanol (2’222,, P2,2,2 or I’2,2,2,) WV reported her(a. ‘l’lrc~ asymmetric unit consists OF two molecules of’ gramicitlin A in th(l native crystals and four molecules in the crsium complex crystal. Pntter;;on analyses sholv that gramicidin A in t’hnsc crystals f’orms a cylindrical hnlical channel. In thr two types of nuti\-6, gra,rnicitlin crystals, the diamett~r of’this channc,l is ithotzt 5 -4 ;tnd its length is about, 32 ;f. Cesiurn ions art’ bound inside this channc~l in caryat,wlsof the cc4urn grarnicitlin A complex. The channel in t>his compkxx is considerably shorkr (26 ?I) a.ntl wider (6.8 .!I) th an in the native forms. The l’attcbrson maps of’ thirsty thrre cryst.a.1 forms are compatiblr wit,h rithcr t,hc singl+stranded /?-helix (Urry, 1971) or tht, clouhlc-strnndect parallel or ilnti-parallrl b-h(%lis (Vwtch et (11.. 1974).
1. Introduction Gramicidin A is a linear polypeptide antibiotic of molecular weight 1879, isolat,ed from Racillu,r hrecis, which renders biological membranes and synthetic lipid bilayers permeable t’o alkali cations and protons by forming t)ransmembrane channels (Chapped & Crofts, 1965; Harris & Pressman. 1967: Mueller & Rudin, 1967; Hladk,v & Haydon. 1970). The amino acid sequence of gramicidin A (Sarges & Witkop2 1965) is: fornlyl-L-~‘al-Gly-L-Ala-D-Leu-1,-Ala-D-Val-L-Val-D-ValL-Trp-D-Leu-:,-Tr6-D-L~u-L-Tr~-D-L~~~-r.-T~p~~IfCH,C~,OH 10 12 13 15 0 I1 14 The active channel-forming species is a dimer of gramicidin A, and most, of the dimers in a membrane are active channels (Tost’eson et al., 1968; Urry et al., 1971; Bamberg & L&uger, 1973; Zingsheim & Neher, 1974; Kolb et al., 1975; Veatch et al., 1975: Veatch & Stryer, 19i7). Three models have beeu proposed for t’he structure of t,his dimcr: a head-t.o-head single-stranded P-helix (originally called a n-(L,D)-helix. Urry, 1971) (Fig. 1 (a)) and two intertwined doublr-helical structures which resemble P-pleated sheets that have been rolled into helices (Veatch et al., 1974). The st.rauds in the double helix can be antiparallel (Fig. 1 (b)) or parallel (Fig. l(c)). These models provide ways of forming a helix from an alternating L,D sequence of amino acids so t)hat. all of thtb side-chains are on the oubside of the helix. away from possible strlric 41
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FIG. 1. Comparison of proposed models of gramiridin A. The oc-calshon positions are plottctl as a Thr lwsitions of ow strand are function of 4, the radial co-ordinate, and z, the axial co-ordinate. denoted by (cm), and of the second strand by ( A). (a) Single-stranded p-helix having 6.3 residues/turn and a p&h of 5.0 .$ (Urry, 1971). (b) Intertwined antiparallel ~-stranded P-helix having 5.8 resitlws/turn and a pitch of 1 1.2 x (Veatch & Blout, 1974). (c) Intertwined parallel %strandetl P-helix having 5.X rcsitlurs/twn and a pitrh of 11.2 x (Veatch & Blout, 1974).
interference with the polypeptide backbone. Such an arrangementj of the side-chains seems mandatory because of the large number of bulky groups in the amino acid sequence of gramicidin A. In each of these models, t,hc true helical repeat is an L,Udipeptide unit. Urry et al. (1975) have presentjcd spectroscopic evidence suggest,& that double-stranded helices may predominate at, t)he high conccnbra,tions required for the cryst,allization of gramicidin, whereas the single-stranded P-helix may be tlw preferred conformation at lower concentrations and temperat,ures. Y-ray diffraction patterns of fibers of poly(y-benzyl-n,L-glutamate) indicate that t,his synt,hct,ic polypepbide exists in bot,h single-st’randed and double-stranded P-helical conformations (Heit,z et al., 1975; Lotz et al., 1976). Crystals of gramicidin A suitable for X-ray diffraction were tirst reported by Syngo (1949). Hodgkin (1949) and Cowan & Hodgkin (1953) reported preliminary crystallographic data for gramicidins A and R, and suggcst,ed that gramicidin might, have a helical structure. Ceatch (1973) reported cell dimensions for gramicidin A crystallized from et)hanol and from methanol, and also observed that, a crystalline complex results from 1: 1 mixtures of gramicidin and CsCl. C&CO, or CsSCS. WC haw rollected data to 1.3 A resolution on 1 hew two native gramicidin A crystal forms, and haw A uith CsSCN and mrasured its tliffractctl crystallizetl a complex of gramicidin
GRAJZICIDIX
A CHANNELS
Ih’
C’KJ~TS’I’XLS
13
int enskies to 4.9 ;i resolution. The polypeptide chain in each of these cr)-stal forms has a helical conformation surrounding a central channel. Cosium ions arc bountl inside this channel, which is considerabl>- shorter and wider in t’hc ccsium complcs t’han in the cryst,als of native gramicidin.
3. Results The space group and cell dimension information for each of the thrw crytital forms is summarized in Table 1. The p2,2,2, crystal form of nat’ive gramicidin .I, which is known to contain a dimer of gramicidin in its asymmetric unit (Vratjclr, 19+X3), has a volume per unit protein molecwlar weight) (l’/M) of 1.72. This vale corresponds to those for the most t.ightly packed protein cryst.als having a low content
44
Gramicidin Gramicidin Gramicidin CsSCN t Volume $ P222,,
A A A-
P2,2,21 1’2, $
24.61(l) l&20( I) 32.07(l)
32.28(2) 26.63(s) 52.29(3)
per unit protein molecular P212,2 or P2,2,21.
weight
32.53(2) 3%.18(l) 31.20(2)
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of solvent (Matthews, 1968,1976). The other crystal forms have V/M values of 1.73 and 1.74, when one presumes that the asymmetric unit is a dimer in the P2, native gramicidin crystals and two dimers in the crystals of the cesium-gramicidin complex. (a) P2,Z12,
crystals
of native
gramicidin
The 8 A Patterson map (Fig. 2(a)) of the crystals grown from ethanol consists of three cylinders oriented parallel to the z axis, and centered at the (z,y) positions (0, 0), (0, 4) and (4, a). The peak which is centered at (0, 0) in this Patterson map is due to intramolecular vectors bet’ween atoms in the same gramicidin dimer, whereas the other two peaks are Harker peaks representing int)ercylinder vectors between 0.0
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FIQ. 2. (a) The z = 0.5 section of the Patterson map of the P2,2,2, crystal form at 8 L% resolution. The map is nearly the same on any section perpendicular to the z axis at this resolution, indicating that the overall shape of the molecule is a cylinder which is oriented along tho crystallographic z axis. The peak at the origin arises from self vectors within a cylinder, whereas the other 2 peaks are Harker vectors between cylinders. (b) Packing diagram illustrating the arrangement of the cylinders of gramicidin A projected on the zy plane. The cylinders nearly fill the entire P2,2,2, unit call in the z direction.
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atottis in s?.Jtrtttc,tr~-rc,latc~cl ~not~~t~~s itt t Iw f’2,2,2, unit ~11. ‘t’h(~ (*o-orclitti~t(v 01’1 I)(. Harkcr pea,lis stlo\\- that thcl (J. y) co-ortlillatcs of t,lltk wlltcrs of the f;)ur c~>,tilltt~~rsitI the asymmc+ric unit of thca car?-stal aw (I). 4). (0. i), (a, #) antl ( f.3). ‘L’tit~ rtwtt is it packing arrangement) (Fig. 2(b)) in \\-hich the d&anrcs bc~twwn the wtltcw of’ tllc. cJ4iriders arc Il.7 A and 16.1 A in the two ilniqiw diwctions. Thtb c~~lintlt~rs tilt t II(L cnt8iro length of the unit, cell in the z direction. Tl~c maximum pwmissibl(~ I(~ugt II for t’he dimcr of gramicidin packed in this T\‘ay corresponcls to t tic%c-axis tlimr~nsiot~ of the cq&al. which is 32.6 A. d higher resolution l’at,tcrson map (Fig. 3 (a)) revra,ls that’ t hc (a>-linder has a hole. A portion near the origin of the z = 0 wction of the obscrvcd Patterson map WIculatrd at’ 3 ;\ resolution demonstrates that, the helix tliametcr vectors arr separat,ccI from bhe origin of the map by a t,rough of negat,ive densit?;. This trougll is not swn in maps of 5 A and lower resolut,ion. but) appears when data of 4.5 4 or higtwr rwolutiou are included. The radius of the ring around the t,rongh in t,hr obsw\-cd Pattjrrson map (Fig. 3(a)) is 1.5 A. The density of the Patt.rrson fun&ion of a circle of radius Y is proportional to [Z(4r2 ~ Z2)I- l% where 1 is t~ht~ length of the l’at~tJt~rson vector. ‘I’hc~ correspoiiding z = 0 sect-ions of the Patterson maps oft he rnotlcl structures art‘ shown in Figure 3(b) and (c). The maps of the models also contain rings around the origin, and t)he radius of each ring is slightly less than or equal to the tliamctcr of thra particular helix. Thus, the diamet)er of the hole in the gramicidin A helix crystallizctl from &ha& is about’ 5 A. All references to diameters of hclices refer to approxirnatck average distances betjwwn the cnnt’ers of atoms in the polvpeptidt, backbow. NIlcw van der Waals’ contact tlist’ances are considered, t,he corrcspontling tliamc~tc~rx nw about, 1.5 A less. At 1.3 a rrsolutjion the strongest, peaks of t)hc three-dimensional Patt’rrson map occur along the z axis art 1.94, 5.58, 11.98 and 16.3 A (Fig. 4(a)). Also. tjhcrtb are man? rings around t,he z axis at various levels of const’ant’ z \vhich are also present in tjho high-resolut’ion Pat’terson maps of idealizrd helical structures. One is tcmpt,cd to account for t’hc Patterson peaks that occur along the z axis by considering t,he WJ~tribut,ion from an idealized helix. For example, the 5% ,A peak could I-eprwwt either the pit,ch of a single-stranded helix or t,hc axial separation of the tl\o strands of a double-Aranded helix. Then t’he 12 LA peak I\-ould 1,~ ritjhrr the rise in x per t \z o turns of a single-st,randed helix or the pitch of one strand of a double-stjrandetl helix. The 2 Lk peak (which would be a ring around the z axis a,t rrr>- high resolut~iori) would correspond to t,he helical rise per residue (or repeating unit). ‘Chew t hrw fcat’ures are present at’ the predicted locat’ions in Pat’terson maps calculated for simple model helices consisting of point atoms on an imaginary wiw. Howcwr. t)hc: situat’ion is more complex for lielices consisting of peptide u&s containing a~torris at, various distances above and belo\v the imaginary wire. Then. t)ht> positions of the maxima of t,he Pat)terson peaks do not newssarily correspond to t hc charact,cristic helical paramet’ers of the model. The situat’ion is part)icularly far rcmovr~tl from t lw ideal one for the case of an alt,ernat’ing (L, u)-helix (M~h&her singlc- or tlortbl~stranded) in which the clcctron-dense carbon,vl oxygen atoms arr altcrnatjely far above and below the helical wire containing the nit,rogen. m-carbon and carbony carbon atoms. Pattjerson maps calculatrcl at 1.3 A using various helical modt~ls for t>he polypeptide backbone show mow peaks along the helix axis t tl:tn arc present it1 the observecl map. In fact, the observed Patterson map dots not’ favor otw of’ the two proposed models (Fig. 4 (b)). Indeed, the calculated Patterson maps for the t’wo
I
Fro. 4. (a) The y = 0.0 section of the origin-removed Patterson map of the P2,2,2, crystal form at 1.27 A wsolution. The peaks along the I axis at 1.9, 5.6, 12.0 and 16.3 A are the highcnt pewks on the 3.dimensional map. (b) Comparison of the observed map with axial Patterson maps of model helices. Each model was put into the unit cell of the P2,212, gramiridin A crystals. The models contain 158 atoms: all of the non-hydrogen polypeptide backbone atoms, the N-terminal formyl, the C-terminal N-C’., ant1 the @arbons. I, Observed Patterson map. II, Map of a formyl-to-formyl single-stranded ,%hclix (Urry, 1971) having 6.3 residues/turn ant1 a pitch of 6.0 A. III, Map of an antiparallel P-tlouble helix (1.‘catch et aE., 1974) having a pitch of 11.2 L[ and 5.8 residues/turn.
48
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Ioms. A section of the Pat’terson map perpendicular t’o the ,r/ axis at !/ = 0.1 is showu in Figure 7 (b). Surrounding the C&a peak (due to vectors between Cs ions 5 a apart) is a ring due to vectors from t,he helical polypeptide backbone to t,he Cs ion. This ring of radius 3.4 ~1 is cont’inuous along the 9 axis in the Patterson map, as shown by thf> line of density along z = 3.4 A in Figure 7 (a). The density in the ring is about. 1 of the density in the cent.er of one of the C.+Cs peaks, as would bth expect.erl for a (‘(sprptide peak. Since 3.4 A represents t,he distance from the CY t,o the peptidr, t,hc diamet,er of the channel is about twice this value, namely 6.8 a. In t,his case, the radius of t,hn Pat’terson ring gives the radius of t hc channel, \vhereas for the nat ivc gramicidin crystals the radius of the ring i II the Patterson map represcms thediameter of the channel. The difference is that iu native gramicidin the channel is rmpt y, whereas in t,he Cs complex it is tilled. q
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GRAMICIDIN
A CHANNELS
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Fu:. 6. Zero-layer precession photographs ((a and (b)) and packing diagram ((c)) of crystals of a complex of gramicidin A with CsSCN. (a) (I), k, 1). (b) (h. 0, I). (r) Packing diagram illustrating the arrangement of cylinders of gramicid in A in thr> (‘s-cwmplrsrd crystals. The packing is nearly trtragonal.
Additional evidence that the helices are oriented along b is t,he characteristic helical cross pattern on the (0, k, 1) projection precession photograph (Fig. 6 (a.)), in which the first maximum occurs on the row k = 10. The calculabed helical strand separation is about 52*3/10 = 5.23 a. A projection Fourier map (Fig. 8(a)) confirms our interpretation that cesium binds in the center of t’he gramicidin A channel. The map was calculated using the observed amplitudes and phases computed for cesium at)oms at the positions indicated by thr packing diagram in Figure 6(c). The map shows t)he cent,ral cesium atoms, which were put into the phase calculation, and a ring around the central density, which arises from the observed structure factors. The diamet’er of t,he ring agrees with the diameter of 6.8 A for the helical polypept)ide backbone, based on the Patterson map (Fig. 7). The difference Fourier synthesis (Fig. 8(b)) sh ows the same ring without the cent,ral Cs atom. These projection Fouriers are unaffected bythe uncertainbyregarding the space group. There remains an ambiguity as bo the true space group of the Cs-gramicidin cr,vstals. The space group is not strictly (‘222,, because about 10% of the h + li = 2r, -+ 1 reflections to a resolution of 2.9 A are in fact observed. The true space group is therefore of the I’ class and could be either P222,, p2,2,2 or P2,2,2, depending on whether t’he a and 0 axes are parallel to S-fold or 2-fold screw axes. The nearI? t,etragonal packing (Fig. 6(c)) could account for the observed pseudo C-centering for t,wo reasons. First, the Cs ions located along the axes of the cylinders cont.ribute on average more than 40% of the diffract,ed amplitude. Second, the approximat,ely
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FIG. 7. (a) The z : 0.0 section of the origin-rcmovcd Patterjon map of the Cs-gramicidin crystals. The high density along the y axis represents Cs-Cs vectors plus an additional contribution due to helix repeat vectors. The map shows that Cs ions are stacked in the y direction. (b) The y -= 0.1 section of the origin-removed Patterson map of the Cs--gramicidin crystals. The central peak due to a Cs-Cs vector is surrountled by a ring of Cs-peptide vectors. The radius of the ring represents the average distance from the Cs atoms to the polypeptide backbone of the helix, 3.4 A. Therefore, the diameter of thp channel in this crystal form is about 6.8 A, as comparr~l to about 5 a for the native crystals.
cylindrical shape of the gramicidin dimer may lead to t’he appearance of a translational symmetry element when in fact none exists. It remains to be determined whether the two chains of gramicidin A are oriented parallel or anti-parallel with respect to each other in the Cs-gramicidin A dimer. If the axes of the cylinders coincide with crystallographic 2-fold axes-as would be the case if the center of a cylinder were located at (0, y, )) in t,he space group C222, or P222,, then the cylinder would be composed of a double helix of intertwined parallel strands of gramicidin A. On t,he other hand, if the axis of the cylinder were to lie between parallel 2-fold axes or to coincide with a 2, axis, then the two strands of a cylinder need not be parallel.
4. Discussion Several
can be drawn from these X-ray of native gramicidin and complex: (1) the asymmetric unit consists crystal forms, and four polypeptide chains
conclusions
P2, and P212,2, crystals gramicidin the native
crystallographic studies of the of the crystals of the cesium of two polypeptide chains for for the crystal of the cesium
GRAMICIDIN
A CHANNELS
IN
53
CKYSTALS
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Helical Channels in Crystals of Gramicidin A and of a Cesium-Gramicidin A Complex : an X-ray Diffraction Study
X-ray cryst,allographic studies of’ gramicitlin A crystalliz:1,d from methanol (l’Y1) and othtmol (1’2 1’1 ‘) 2 1) > cmd of a Cs + gritmicitlin .1 complex (~rystallizrtl front rnt%hanol (2’222,, P2,2,2 or I’2,2,2,) WV reported her(a. ‘l’lrc~ asymmetric unit consists OF two molecules of’ gramicitlin A in th(l native crystals and four molecules in the crsium complex crystal. Pntter;;on analyses sholv that gramicidin A in t’hnsc crystals f’orms a cylindrical hnlical channel. In thr two types of nuti\-6, gra,rnicitlin crystals, the diamett~r of’this channc,l is ithotzt 5 -4 ;tnd its length is about, 32 ;f. Cesiurn ions art’ bound inside this channc~l in caryat,wlsof the cc4urn grarnicitlin A complex. The channel in t>his compkxx is considerably shorkr (26 ?I) a.ntl wider (6.8 .!I) th an in the native forms. The l’attcbrson maps of’ thirsty thrre cryst.a.1 forms are compatiblr wit,h rithcr t,hc singl+stranded /?-helix (Urry, 1971) or tht, clouhlc-strnndect parallel or ilnti-parallrl b-h(%lis (Vwtch et (11.. 1974).
1. Introduction Gramicidin A is a linear polypeptide antibiotic of molecular weight 1879, isolat,ed from Racillu,r hrecis, which renders biological membranes and synthetic lipid bilayers permeable t’o alkali cations and protons by forming t)ransmembrane channels (Chapped & Crofts, 1965; Harris & Pressman. 1967: Mueller & Rudin, 1967; Hladk,v & Haydon. 1970). The amino acid sequence of gramicidin A (Sarges & Witkop2 1965) is: fornlyl-L-~‘al-Gly-L-Ala-D-Leu-1,-Ala-D-Val-L-Val-D-ValL-Trp-D-Leu-:,-Tr6-D-L~u-L-Tr~-D-L~~~-r.-T~p~~IfCH,C~,OH 10 12 13 15 0 I1 14 The active channel-forming species is a dimer of gramicidin A, and most, of the dimers in a membrane are active channels (Tost’eson et al., 1968; Urry et al., 1971; Bamberg & L&uger, 1973; Zingsheim & Neher, 1974; Kolb et al., 1975; Veatch et al., 1975: Veatch & Stryer, 19i7). Three models have beeu proposed for t’he structure of t,his dimcr: a head-t.o-head single-stranded P-helix (originally called a n-(L,D)-helix. Urry, 1971) (Fig. 1 (a)) and two intertwined doublr-helical structures which resemble P-pleated sheets that have been rolled into helices (Veatch et al., 1974). The st.rauds in the double helix can be antiparallel (Fig. 1 (b)) or parallel (Fig. l(c)). These models provide ways of forming a helix from an alternating L,D sequence of amino acids so t)hat. all of thtb side-chains are on the oubside of the helix. away from possible strlric 41
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FIG. 1. Comparison of proposed models of gramiridin A. The oc-calshon positions are plottctl as a Thr lwsitions of ow strand are function of 4, the radial co-ordinate, and z, the axial co-ordinate. denoted by (cm), and of the second strand by ( A). (a) Single-stranded p-helix having 6.3 residues/turn and a p&h of 5.0 .$ (Urry, 1971). (b) Intertwined antiparallel ~-stranded P-helix having 5.8 resitlws/turn and a pitch of 1 1.2 x (Veatch & Blout, 1974). (c) Intertwined parallel %strandetl P-helix having 5.X rcsitlurs/twn and a pitrh of 11.2 x (Veatch & Blout, 1974).
interference with the polypeptide backbone. Such an arrangementj of the side-chains seems mandatory because of the large number of bulky groups in the amino acid sequence of gramicidin A. In each of these models, t,hc true helical repeat is an L,Udipeptide unit. Urry et al. (1975) have presentjcd spectroscopic evidence suggest,& that double-stranded helices may predominate at, t)he high conccnbra,tions required for the cryst,allization of gramicidin, whereas the single-stranded P-helix may be tlw preferred conformation at lower concentrations and temperat,ures. Y-ray diffraction patterns of fibers of poly(y-benzyl-n,L-glutamate) indicate that t,his synt,hct,ic polypepbide exists in bot,h single-st’randed and double-stranded P-helical conformations (Heit,z et al., 1975; Lotz et al., 1976). Crystals of gramicidin A suitable for X-ray diffraction were tirst reported by Syngo (1949). Hodgkin (1949) and Cowan & Hodgkin (1953) reported preliminary crystallographic data for gramicidins A and R, and suggcst,ed that gramicidin might, have a helical structure. Ceatch (1973) reported cell dimensions for gramicidin A crystallized from et)hanol and from methanol, and also observed that, a crystalline complex results from 1: 1 mixtures of gramicidin and CsCl. C&CO, or CsSCS. WC haw rollected data to 1.3 A resolution on 1 hew two native gramicidin A crystal forms, and haw A uith CsSCN and mrasured its tliffractctl crystallizetl a complex of gramicidin
GRAJZICIDIX
A CHANNELS
Ih’
C’KJ~TS’I’XLS
13
int enskies to 4.9 ;i resolution. The polypeptide chain in each of these cr)-stal forms has a helical conformation surrounding a central channel. Cosium ions arc bountl inside this channel, which is considerabl>- shorter and wider in t’hc ccsium complcs t’han in the cryst,als of native gramicidin.
3. Results The space group and cell dimension information for each of the thrw crytital forms is summarized in Table 1. The p2,2,2, crystal form of nat’ive gramicidin .I, which is known to contain a dimer of gramicidin in its asymmetric unit (Vratjclr, 19+X3), has a volume per unit protein molecwlar weight) (l’/M) of 1.72. This vale corresponds to those for the most t.ightly packed protein cryst.als having a low content
44
Gramicidin Gramicidin Gramicidin CsSCN t Volume $ P222,,
A A A-
P2,2,21 1’2, $
24.61(l) l&20( I) 32.07(l)
32.28(2) 26.63(s) 52.29(3)
per unit protein molecular P212,2 or P2,2,21.
weight
32.53(2) 3%.18(l) 31.20(2)
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of solvent (Matthews, 1968,1976). The other crystal forms have V/M values of 1.73 and 1.74, when one presumes that the asymmetric unit is a dimer in the P2, native gramicidin crystals and two dimers in the crystals of the cesium-gramicidin complex. (a) P2,Z12,
crystals
of native
gramicidin
The 8 A Patterson map (Fig. 2(a)) of the crystals grown from ethanol consists of three cylinders oriented parallel to the z axis, and centered at the (z,y) positions (0, 0), (0, 4) and (4, a). The peak which is centered at (0, 0) in this Patterson map is due to intramolecular vectors bet’ween atoms in the same gramicidin dimer, whereas the other two peaks are Harker peaks representing int)ercylinder vectors between 0.0
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FIQ. 2. (a) The z = 0.5 section of the Patterson map of the P2,2,2, crystal form at 8 L% resolution. The map is nearly the same on any section perpendicular to the z axis at this resolution, indicating that the overall shape of the molecule is a cylinder which is oriented along tho crystallographic z axis. The peak at the origin arises from self vectors within a cylinder, whereas the other 2 peaks are Harker vectors between cylinders. (b) Packing diagram illustrating the arrangement of the cylinders of gramicidin A projected on the zy plane. The cylinders nearly fill the entire P2,2,2, unit call in the z direction.
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atottis in s?.Jtrtttc,tr~-rc,latc~cl ~not~~t~~s itt t Iw f’2,2,2, unit ~11. ‘t’h(~ (*o-orclitti~t(v 01’1 I)(. Harkcr pea,lis stlo\\- that thcl (J. y) co-ortlillatcs of t,lltk wlltcrs of the f;)ur c~>,tilltt~~rsitI the asymmc+ric unit of thca car?-stal aw (I). 4). (0. i), (a, #) antl ( f.3). ‘L’tit~ rtwtt is it packing arrangement) (Fig. 2(b)) in \\-hich the d&anrcs bc~twwn the wtltcw of’ tllc. cJ4iriders arc Il.7 A and 16.1 A in the two ilniqiw diwctions. Thtb c~~lintlt~rs tilt t II(L cnt8iro length of the unit, cell in the z direction. Tl~c maximum pwmissibl(~ I(~ugt II for t’he dimcr of gramicidin packed in this T\‘ay corresponcls to t tic%c-axis tlimr~nsiot~ of the cq&al. which is 32.6 A. d higher resolution l’at,tcrson map (Fig. 3 (a)) revra,ls that’ t hc (a>-linder has a hole. A portion near the origin of the z = 0 wction of the obscrvcd Patterson map WIculatrd at’ 3 ;\ resolution demonstrates that, the helix tliametcr vectors arr separat,ccI from bhe origin of the map by a t,rough of negat,ive densit?;. This trougll is not swn in maps of 5 A and lower resolut,ion. but) appears when data of 4.5 4 or higtwr rwolutiou are included. The radius of the ring around the t,rongh in t,hr obsw\-cd Pattjrrson map (Fig. 3(a)) is 1.5 A. The density of the Patt.rrson fun&ion of a circle of radius Y is proportional to [Z(4r2 ~ Z2)I- l% where 1 is t~ht~ length of the l’at~tJt~rson vector. ‘I’hc~ correspoiiding z = 0 sect-ions of the Patterson maps oft he rnotlcl structures art‘ shown in Figure 3(b) and (c). The maps of the models also contain rings around the origin, and t)he radius of each ring is slightly less than or equal to the tliamctcr of thra particular helix. Thus, the diamet)er of the hole in the gramicidin A helix crystallizctl from &ha& is about’ 5 A. All references to diameters of hclices refer to approxirnatck average distances betjwwn the cnnt’ers of atoms in the polvpeptidt, backbow. NIlcw van der Waals’ contact tlist’ances are considered, t,he corrcspontling tliamc~tc~rx nw about, 1.5 A less. At 1.3 a rrsolutjion the strongest, peaks of t)hc three-dimensional Patt’rrson map occur along the z axis art 1.94, 5.58, 11.98 and 16.3 A (Fig. 4(a)). Also. tjhcrtb are man? rings around t,he z axis at various levels of const’ant’ z \vhich are also present in tjho high-resolut’ion Pat’terson maps of idealizrd helical structures. One is tcmpt,cd to account for t’hc Patterson peaks that occur along the z axis by considering t,he WJ~tribut,ion from an idealized helix. For example, the 5% ,A peak could I-eprwwt either the pit,ch of a single-stranded helix or t,hc axial separation of the tl\o strands of a double-Aranded helix. Then t’he 12 LA peak I\-ould 1,~ ritjhrr the rise in x per t \z o turns of a single-st,randed helix or the pitch of one strand of a double-stjrandetl helix. The 2 Lk peak (which would be a ring around the z axis a,t rrr>- high resolut~iori) would correspond to t,he helical rise per residue (or repeating unit). ‘Chew t hrw fcat’ures are present at’ the predicted locat’ions in Pat’terson maps calculated for simple model helices consisting of point atoms on an imaginary wiw. Howcwr. t)hc: situat’ion is more complex for lielices consisting of peptide u&s containing a~torris at, various distances above and belo\v the imaginary wire. Then. t)ht> positions of the maxima of t,he Pat)terson peaks do not newssarily correspond to t hc charact,cristic helical paramet’ers of the model. The situat’ion is part)icularly far rcmovr~tl from t lw ideal one for the case of an alt,ernat’ing (L, u)-helix (M~h&her singlc- or tlortbl~stranded) in which the clcctron-dense carbon,vl oxygen atoms arr altcrnatjely far above and below the helical wire containing the nit,rogen. m-carbon and carbony carbon atoms. Pattjerson maps calculatrcl at 1.3 A using various helical modt~ls for t>he polypeptide backbone show mow peaks along the helix axis t tl:tn arc present it1 the observecl map. In fact, the observed Patterson map dots not’ favor otw of’ the two proposed models (Fig. 4 (b)). Indeed, the calculated Patterson maps for the t’wo
I
Fro. 4. (a) The y = 0.0 section of the origin-removed Patterson map of the P2,2,2, crystal form at 1.27 A wsolution. The peaks along the I axis at 1.9, 5.6, 12.0 and 16.3 A are the highcnt pewks on the 3.dimensional map. (b) Comparison of the observed map with axial Patterson maps of model helices. Each model was put into the unit cell of the P2,212, gramiridin A crystals. The models contain 158 atoms: all of the non-hydrogen polypeptide backbone atoms, the N-terminal formyl, the C-terminal N-C’., ant1 the @arbons. I, Observed Patterson map. II, Map of a formyl-to-formyl single-stranded ,%hclix (Urry, 1971) having 6.3 residues/turn ant1 a pitch of 6.0 A. III, Map of an antiparallel P-tlouble helix (1.‘catch et aE., 1974) having a pitch of 11.2 L[ and 5.8 residues/turn.
48
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Ioms. A section of the Pat’terson map perpendicular t’o the ,r/ axis at !/ = 0.1 is showu in Figure 7 (b). Surrounding the C&a peak (due to vectors between Cs ions 5 a apart) is a ring due to vectors from t,he helical polypeptide backbone to t,he Cs ion. This ring of radius 3.4 ~1 is cont’inuous along the 9 axis in the Patterson map, as shown by thf> line of density along z = 3.4 A in Figure 7 (a). The density in the ring is about. 1 of the density in the cent.er of one of the C.+Cs peaks, as would bth expect.erl for a (‘(sprptide peak. Since 3.4 A represents t,he distance from the CY t,o the peptidr, t,hc diamet,er of the channel is about twice this value, namely 6.8 a. In t,his case, the radius of t,hn Pat’terson ring gives the radius of t hc channel, \vhereas for the nat ivc gramicidin crystals the radius of the ring i II the Patterson map represcms thediameter of the channel. The difference is that iu native gramicidin the channel is rmpt y, whereas in t,he Cs complex it is tilled. q
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GRAMICIDIN
A CHANNELS
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Fu:. 6. Zero-layer precession photographs ((a and (b)) and packing diagram ((c)) of crystals of a complex of gramicidin A with CsSCN. (a) (I), k, 1). (b) (h. 0, I). (r) Packing diagram illustrating the arrangement of cylinders of gramicid in A in thr> (‘s-cwmplrsrd crystals. The packing is nearly trtragonal.
Additional evidence that the helices are oriented along b is t,he characteristic helical cross pattern on the (0, k, 1) projection precession photograph (Fig. 6 (a.)), in which the first maximum occurs on the row k = 10. The calculabed helical strand separation is about 52*3/10 = 5.23 a. A projection Fourier map (Fig. 8(a)) confirms our interpretation that cesium binds in the center of t’he gramicidin A channel. The map was calculated using the observed amplitudes and phases computed for cesium at)oms at the positions indicated by thr packing diagram in Figure 6(c). The map shows t)he cent,ral cesium atoms, which were put into the phase calculation, and a ring around the central density, which arises from the observed structure factors. The diamet’er of t,he ring agrees with the diameter of 6.8 A for the helical polypept)ide backbone, based on the Patterson map (Fig. 7). The difference Fourier synthesis (Fig. 8(b)) sh ows the same ring without the cent,ral Cs atom. These projection Fouriers are unaffected bythe uncertainbyregarding the space group. There remains an ambiguity as bo the true space group of the Cs-gramicidin cr,vstals. The space group is not strictly (‘222,, because about 10% of the h + li = 2r, -+ 1 reflections to a resolution of 2.9 A are in fact observed. The true space group is therefore of the I’ class and could be either P222,, p2,2,2 or P2,2,2, depending on whether t’he a and 0 axes are parallel to S-fold or 2-fold screw axes. The nearI? t,etragonal packing (Fig. 6(c)) could account for the observed pseudo C-centering for t,wo reasons. First, the Cs ions located along the axes of the cylinders cont.ribute on average more than 40% of the diffract,ed amplitude. Second, the approximat,ely
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FIG. 7. (a) The z : 0.0 section of the origin-rcmovcd Patterjon map of the Cs-gramicidin crystals. The high density along the y axis represents Cs-Cs vectors plus an additional contribution due to helix repeat vectors. The map shows that Cs ions are stacked in the y direction. (b) The y -= 0.1 section of the origin-removed Patterson map of the Cs--gramicidin crystals. The central peak due to a Cs-Cs vector is surrountled by a ring of Cs-peptide vectors. The radius of the ring represents the average distance from the Cs atoms to the polypeptide backbone of the helix, 3.4 A. Therefore, the diameter of thp channel in this crystal form is about 6.8 A, as comparr~l to about 5 a for the native crystals.
cylindrical shape of the gramicidin dimer may lead to t’he appearance of a translational symmetry element when in fact none exists. It remains to be determined whether the two chains of gramicidin A are oriented parallel or anti-parallel with respect to each other in the Cs-gramicidin A dimer. If the axes of the cylinders coincide with crystallographic 2-fold axes-as would be the case if the center of a cylinder were located at (0, y, )) in t,he space group C222, or P222,, then the cylinder would be composed of a double helix of intertwined parallel strands of gramicidin A. On t,he other hand, if the axis of the cylinder were to lie between parallel 2-fold axes or to coincide with a 2, axis, then the two strands of a cylinder need not be parallel.
4. Discussion Several
can be drawn from these X-ray of native gramicidin and complex: (1) the asymmetric unit consists crystal forms, and four polypeptide chains
conclusions
P2, and P212,2, crystals gramicidin the native
crystallographic studies of the of the crystals of the cesium of two polypeptide chains for for the crystal of the cesium
GRAMICIDIN
A CHANNELS
IN
53
CKYSTALS
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