.J. Mol. Biol. (1992) 226, 835-850

Modeling

of the Structure of Bacteriorhodopsin A Molecular Dynamics Study Fritz Jfhnig

Max-Plan&Institut 07-400

fiir Biologic, Corrensstrasse Tiibingen, Germany

38

and Olle Edholm Department of Theoretical Physics Royal Institute of Technology S-10044 Stockholm. Sweden (Received 12 November 1991; accepted 30 Narch

1992)

Secondary structure predictions for membrane proteins are relatively reliable and permit the construction of model structures that may serve as initial conformations for molecular dynamics simulations. This might provide a scheme to predict’ the three-dimensional structures of membrane proteins. The feasibility of such an approach is tested for bacteriorhodopsin. We were not able to fully predict the kidney-shaped structure of bacteriorhodopsin. However, features compatible with this structure developed in a simulation starting from a circular arrangement of the seven predicted helices. When instead we started from the kidney shape, assigning the seven predicted helices in different ways to those on the structure. we could distinguish between the different assignments on the basis of energy and tilt of the helices. In this way we could select the correct assignment from a few others. For the correct assignment, the helices spontaneously adopted a tilt that agrees remarkably well with the experimental model structure derived by others. The root-mean-square deviation between our best molecular dynamics structure and the experimental model structure is 38 A. caused mainly by deviations in the internal degrees of freedom of the helices. h’eywords:

hydrophobic

effect: lateral

1. Introduction One of the outstanding problems of molecular biology is the calculation of the three-dimensional structure of proteins from their amino acid sequence. This is equivalent to solving the folding problem. For two reasons this problem cannot be solved at present. First,, typical times for protein folding are seconds or even minutes, whereas typical times that can be simulated on supercomputers, say in hours of computer time, are less t’han nanoseconds. Hence. only a very small part of the phase space can be sampled. Second, the interaction potentials used are not good enough to model the structure of proteins at atomic detail and at long times. Therefore, protein folding cannot be calculated at present (for a review, see Karplus & Petsko. 1990).

arrangement’;

helix

tilt

For membrane proteins, however, there may be a chance to overcome the first problem by utilizing secondary structure predictions, thus limiting the phase space t’o be sampled. In the past ten years, considerable progress has been made in the prediction of the secondary structure of the membranespanning segments of such proteins (for a review, see Fasman & Gilbert, 1990). They are folded in rzhelices or P-strands that are either hydrophobic or amphipathic (Jihnig, 1990). What is left’ open, then, is t’hr arrangement of t’hose segments in the membrane. This includes both their positions in the membrane plane and their orientations relative to the membrane normal, since they need not be exactly parallel to it. The problem of arranging helices and B-strands in the membrane seems to be easier than the problem with soluble proteins and

-__ might IN, sol\ahh~ I)!, t~~olt~c~ttlar clyt~;tttti(~h (.I] l)i) simulations. ItI favorablr cases. experitnentat data tnit~. 1ttt availablt~ that reduce the tturnbet~ of poSSil)lr arrangpemcnt8s. For example, A lo~~-r~~sol~~tiot~ strtttat IIW may exist. ltrovidirtg thr, positions and orirtttations of t-he helives or p-strands hut not thp patIt of t hr polypeptide chain. Then ottp uould just h;tv~ 10 drtermitic~ ttlP iC3Signmrnt of’ the prtvlic*le(l a-hrlic~vs or B-sf’rands t,o thclsr~ in t,ttr st~ruc*turr~. This might IX> possible hy performing >I I) xirnulatic~tts ott differenl a~ssignments and cvmparinp thcbir vtterpic~s to find 1hat of ton-rhst cv~rgy. In t hrl tnort’ gc~ttcval (‘asp. when a lou-~rrsolution strucat urc is lacking. oti(’ n~outd c+onsider a number of difiercnt arrangetnettth of’ t hv prrdibd cr-helices or /j-strands and st,udJr their tirnr development in Ml) sirnutat,ions. tttvrtal)!. sampling thv ~onforrnationat space in the vicinity of’ t hr differenf arrangements. Tf’ onca of thvrti was already c~lose to t h(l ~rrec:t arrangement 1 this ma,>. ltr fintnd. It is again dist,inguished from t hr ot hrrs hy its towrr energ?-. sucal-I an ambitious approach is fvasihit,. \l’hrthvr is highly quc~stiona~blc. As mertt ion4 Art&y. prvsc~nl MI) simula,tions arc not a~irratt~ vnough to providt, t hv structure of proteins at at ontic* WSO~IIt ion. N’hcn a protein strut-turcb is sirnulat rd st.artinp f’brn it,s know-n S-ray structure. during an 1147) IIIII t ttc struc?urcJ changes to some’ rstetrt and thr final st rn(%ure drviatrs from the S-ra>r strrtca1 IIW. For. vac’uutrt sirnulatjions. the root -meat)-square (r.m.s.) dr\iation of thta final 111) struc*tutv from the S-t’+>. st rttcaturr was found to be about 3 A (1 A-1= 0.1 tint). water this trrtttit~et~ for simulilti0tls inc4uding dtvrrased to ahoul 1 .A (van Cttnstc~ren r4 01.. 1983). Tttc~sr simulations were extended over 25 1tic~tsirv~~t~ds only and their corivfqq3i(~~ was not tvstc4. Jlorrover. thr simulations with water u’erc IF’fi)rrtA on a full unit cell of the prot,rin captat. I+‘ot tltrsv t,wo r~asot~s. the abo\-rb tiumhc~rs should 1~1 vottsidrrcd as Iowcbr limits. Thus, althougtt thf glol)at struc+ure was stilt c%orrcvt in ttiv M 1) strtic, t II~P. alornica drtails wert‘ wrong. .Atiatogor~sl~. if’oti(a strut-turr and w’vr(* 10 start from an arhitrarv suc~wd in reac>hittg the c*orrrc4 glohat sl ructttre~. 1tits stritc~tur~ may still he wrong at atomic, rc~sotutiotr. If. howcvrr. the afomic details arc wrong. it is har(I t.0 hrlievc~ t.hat the cvrr’rct global struct urv (‘aft 1)~ fouttti. I)rspitv these ohjectionh. WC‘ c~onsidrrr4 this approach worth a trial and chosr l)ac~trriorhodoy)sirt (RR) for a test. This has Hun OIIP of tl~r Iwslmtmhrarir protri tis e’vcbr sitivc c*hilrac*t Prized Hrndrrson KT I:nu’in (1975) determined its thrcvdimensional structure at 7 4 rrsolut~ion using elrc*t)rott diffraction. Over the years. thr resolution has htyrt improved continuously (Henderson rf CL/.. 1986: Baldwin it nl.. 1988) and now a model for the is a\-ailahlv structure at, at omit resolutiotl (Henderson rt nl.. 1990). Rrsdts from nrutron t ,2bhrrviatic~rts used: MD. rrtolrc~ular tiynattiic-s: t’.ttt.s.. root~niewn-syuitr~~ I3Tt. l~~~c~trrior.llotlc,l,sitt.

INSlOE

pro 0A& Met

GUY Met

0LYS Ser Thr Phe GUY

0 ASPGin

Asn Val Thl *

30 B

Pro _ 63 lily Thr IIP G!n

ily Tv GIY Tv leu Tv Thr IIe Met Pro Asn Val Gln Pro Phe GlY G\@

..,. LYS Cl Thr

‘_,

-TY~

Val Pro

teu

,Thr AsnJle\’

4

Val Tyr ser

OUTSIDE Figure 1. Modrl for the folding of KR dtBrivc,d from a simJ)lta hydroJ>hobivity analysis (Jiihnig. 1990). Thr rtvtanglrs reJtrt*srnt trretnhranr-sJ)anning a-helices with boldfacr Irtters denoting t)he residues on the most h~vdro~lhilic sidrs of the hrlicvs. Numbc~rrcl residutbs rrJ)rrsrnt markvrs for the middle of t’hr most hydroJlhobic2 sides of the hrlic*cls. (“irvlrs and square denote J)ositi\-rly and negatively c-barged residurs. resJ)tv%ively. as determined at nrutral JtH. I!W?: J{rrs r,t rrl I!#!+). This leads t)o norr-int,eger valut~s Mg’ for thr markrr rvsidurs. ittc-Juded in Tablr I, Thesr valurs agrvtl with thr result of Rrrs of frl. (1989). rxctyt for helix K where these authors obtainrd N’,3’ = 534. Tnit ial c,ottfortliatioris wire c*onstructrd ti)- generating 7 srparatr regular a-hrJic% segments that invltrde the J~redict~vdtttrtnlirattr-sJ)atittili~ helixes A through (:. Sincar thr (‘-tc~rrrtinal region was shown to ht, unnecessary for ljrcjJ)et‘ fitnc*tioning of IiR (Wallac-r Hr Hrnderson. 1982). it ~vas calra\.tvl off aftrr rrsitlur 227 Iraving A polyyptide (*hain u ith a c~hrontollhot~c of 2105 atoms. The hrlical srgmcknt:, wt’rt~ orient~vd Itrtyrndicular to thti membranc~ Jllanr~ w-it,h t,hts J4yJqtidt. c>hain going up and down and were rotatrd in thr J~lanr such that the marker residucbs ‘M, sJttvif:vitrg the most hydroJthobic* sides J)ointrd towat the JiJ)id Jlhastb. I,ikrwisr. the>, wvre I)ositionrd along tht, tttc~tnbranc~ normal such that thr marktv rrsidrrrh \vc’rt’ in thr tnidtllr of thr mrmbratre. For thth JGtiotls of’ thr helicars in tllr tnrmbranr Jilane 3 different arrartgrment,s \4ere ~mJlloy4. (I ) A circular arrangemrnt with thtl 7 hplives A through C Jjlaced at equal dist,ancrs of 1-I ~4on a citvlr of radius 16 Lq. The arrangement of the hrlicvs on tht, (*ir(.lta was either clockwise or vounterclocakwisr. (2) A hrxagonal arrangement with helix A in the c-rntrv of a virc~lr of radius IO A and helicrs f3 through (: at qua1 distancvn and &c:kwise order on thr circlr. (3) A kidntly-shaJ)vd arratqyment nit)h hrlicrs A through (: J)Iac~d at thr t~xJleritnenta1 J)ositions I through 7 of the htllicvas in the tnc,mhranr Jjlanr. The Jlositions I through i

vetv tArther rtsatl from t,hr 2-dimt~nsiottal rl~v~trort drnsit) at low rrsolutiott (Henderson B I‘nwin. 1975) or were drtrrminrd front the 3-ditn~nsional model struct.urr (Hrndthrson ef ~1.. 1990. and personal communic~ation) as thr caettt,tsrsof mass of t,hr helives in t’hr membrane plane. For thr assignment of helix-es AAt,hrough (: to Jlositions I through 7. the 5 most Jtrohahle assignments avc~ording to JCngrlman rt /I/. (1980) were c-hosrn The conformation of the chromophorr retinal. hound cvvalentjJ>- to I,vsPl(i W?I a Schiff base. was vhostin to be all-lrnlts along the Jtolyenr chain and thv c.ortnfvtion t,o thr iononr ring was lis-lrcx7t.s as found sJ’t‘(‘tros~opic,aJl~ (Harhisotr rt al., 1986). Thr chromophore was orient’ed with the J)olyene chain JIarallrl to ttlfl mrmhrane plane and pointing in directions that Jlrovide oJltima1 packing inside the protein for the dif&rPnt assignmmtn. The Jjlane of the J)olyene chain was fterpendicytlar to the membrane ~Aanr. with thr ring point!ing pither uyard or downward.

The surrounding lipid and wat’rr molt~vulrs werr not treated explicitly, but modeled by a hydroJ)hobic Jlotential (Edholm & ,Jiihnig. 1988). To rash atom a hgdroJlhobicity parameter hi was attributrd Mined as the difference of its free energies in lipid and Matrr (Eisenherp & McJ~ac~hJan, 1986). The hydrophobic, J)otrntial was assumed to vary exponrntiallv across tht, tnrtnbrant~

surfaces to provide it strong at,trac*t i\.tt 01’ rrpulsi\~t~ ti,rc~, in a small region around the surfa~s.

for /ql 2 co

bhphobic = ‘

; 2 hi{“-exp[(IZil t

--z,)/i]}RJ471

I

for ]ql I zO.

The surfaces are at fz, and specify the hydrophobic core of the membrane. Its thickness was usually assumed t,o be 30 A corresponding to zO = 15 8. The decay length 2. d&ermines the thickness of t.he region over which the protein atoms are attracted or repelled and was chosen to be 2 A. The hydrophobic potential should act, only on protein at,oms that, are exposed at. the prot.ein surface and not, on those that are buried in the interior of the protein. Therefore. the exposed surface area, or rather the (‘orresponding solid angle Ri. was calculated for each atom and the hydrophobic potential Vt,:hphobic contains a factor 52,/4z. This fartor may be calculated in good approxitnation in the following way. Consider the sum of all unit erectors tij pointing from an atom i towards the S- I rteighbortng atoms ,j: &

pij. I1 I

Xctually, we used a cutoff of 9 .A in the sum. If the neighboring at,oms are assumed to be distributed hotnogeneously, the above expression becomes equal to:

where R: is the complement of the surface solid angle Q,. If, furthermore. the opening angle is assumed to be cornshaped. t,he integral ran easily be calculated and one obtains:

llsuall\tl-IV tttittitl ~~ottfortttat~ttrrt~ wf’t’t’ rlt.,Lt c~tirbrg\ nt~nttniz;tl for 2000 steps. l;or l.his antI thf~ f’ttsttittg R?f) sirnulatiotts. thr (PROMOS lta,vkagt* Mas usc~i (I\’ 1:. v;ttt (:unstc~rrtl & H. .I. (‘. tirrrndscxtt. tlottrd.

cknsity map of’ Henderson & I ‘nwin ( I%.;/. which involves some inaccuracv. Thtx c:hromo~)hctt.~~ was added to the side-chain bf I,ysl”l(i. Its ('OIIformat,ion was all-trans alone t,he polyertr chain \vii It a 6s-trans connect.ion to the ionone ring. as ohs~~rvc~l experimentally (Harbison PI nl.. 1985). The poIjrenc% vhaitt was oriented parallel to t.tte tnemhranr plane in a direction to provide optimal pa(:king ltrtwevtt t hta helices, and the ring was pointing upw~~r(f tbwards the inner side of the mctnhrane. The initial conformations were energy-minimizrcl and subjected to MD simulations of 2.5 picoseconds. For assignment 1. t,he corresponding st,ruct’ures art’ shown in Figure 3(a) to (c) as pro,ject,iorts int.o the membrane plane. During energy minirnizatiort. again on1y the loops between &he helices rst,altlishctl. while the rnembra,lle-spartnin# ttetic.cs remained ortalt.ered. During the Ml) run. the helices alsO underwent~ changes and hrlicrs rZ. F:. (: l)e(~;tme tilted. The two-dimensional density of’ tht, M I) struct.ure is in qualit,ative agreement. wit tr t hc) experiment,al density included in Figure 3(d). The projections of t,he MI) st,ruc%ures for t hr fivcl assignments investigated are compared in Figurfb J(a) to (e), Evidently. the good agreement with the experimental density oht,ainrtl for assi~nmrrit I is not rc>ached for any other assignment. .\ssigttmt~nt 17, which differs from assignmclnt I (ml>, hy I hrl intercshange of helicvs I\ ancl H. >icltis a stmilat strucat,tlre. hut the helix at position I is no longer tilted. The densities for the other assignrrrvnts the f~xprrirtir~rltal from t1rviat.r more strongly ctetisity. For a qaant,itativr c*ompa.risoti with cixi) taking the average over fivr picoseconds and t hc remaining fluctuations of the averaged rnergy hil\rr an amplitude of about 50 kJ/mol. This uncertaint’? must he taken into accaount when comparing the avrragrd energies after 25 picoseconds of different struct,ures. Onl~~ energy differrncacs larger thatt 3) kJ/mol c’an he csonsidered as mraninyful.

final

l,ikcwisr. w ttisted the tlq)rntietrc~c~ of’ t ht. 31 1) struc+,ure on the initial conditions by varying thtl length of the energy minimization. This had no sc’vere rffect on thtl SI I) st ructuro. Howe\-VI,. wttcsn t hc- conformations of t hr sidechains in t hr init ial structure wcbry c~ompletely ra.ndomizc4. thr st ru(*t.ure did not improve during art Ml> simulation. Tht t*nrrgy of t,hr ,\/I I) structure was significantly highc,r t hart for the case without randomization. This ma> indicate that it is important not to have side-chains that are too disordered in the initial structure. I~nsfd The most obvious error of the Xl I) st,ruc?ure or1 t.he rnarker residues :V/(H1), t,hr ahsenc*r of tilt of helix F, might he a consequenct~ of the weak st,ru(*ture prediction for this helix. t)hr marker rrsiduc> .II, not having been sprcified uniquely (see Method). To t,est, this possihilitg. t*he value M(F1) = 188, whit-h wits the maximally possible value, was replac4 0~. thtl minimally possihlr value MB’ = 181 This rtaplacement caorresponds to a downward shift of’ helix F by IO.6 ‘4: so that the chrornophorr ~KYXJ~W sandwiched between the t,wo Trp residues 182 a,nd 189 of this helix (Fig. I). When this new initial Wild strucbre based on t,hr marker residues ME’ subjected to an MI) simulation. helix F st,iII did trot tiltj properl?;, yielding 0, = 5”. and thr energy of the MI) structure was about 100 k,l/mol higher t.hxn before. When, however. in addition to t,hr downward shift of helix F, the ring of the chrotnophore~ was rotated t)g 180” to point downwa,rd in the init ia,l

LrrrticaI position of the helices and of 100 in their orirntation about t,he long axes. ‘l’ht~ actual positiotts and orientations may well correspond t,0 noninteger values for t,he marker residues. Therefore. a analysis was prrformed rrfinrd hydrophobicity based on t,hr hydrophobic moment (Eisenbrrg et ctl., IS%?: liees ef al., 1990). The marker residues NE’ obtaitwd in this way are no longer int,egw numbrrs (Table I ). Their values agree with tjhow dt4ermined by ritvs ef al. (1990). except for helix K. A possible error source for the lateral positions of t hr heliws on the kidney shape lies in t,htb way t,hey were t~xtracttvl from thr experimental data by wading thetn from the two-dirnerrsional electron dt’ttsity map (Her&won bi I’nnirt. 3975). Irrtpro~~d values for the h&x positions could bts obt.ained from t hr nurrwric~al data for the t\vo-tlirnension;rl elec*tron dewsit? or frotn a t.hree-dimetlsiortal strwt ure. st.ill at low twoluticm. as t,he wntws of mass of the hrlicw in t,he mrmbranr planr. Sin,+t, such Ion-rtwlut.iott data w~t’r~ not available 1.0 its. wt’ drduc~etl t hts helix positions from the expwimrntal structure at higher resolution (Henderson rt trl.. 1990. and pers0na.l c~ornmuni~ation). IZascstl on the improved valurs .W(,J’ for t hta tnarker rrsidut~s and thr improwd lateral posit.ions of the he1it.w. a IWW initial conformation was c*ottst rutted. The r.tu.h. deviation of this initial sttyccsturtl \vas 1.5 -4. ~IIW. c~onsiderably smaller than thv r.rl1.s. tlrviaticm of ti to i X of the previous initial strucatrtws. This decwasr is caused to ahout tylnal wright 1)y t ht* itnprov~tl marker rcsidws ant1 thr> improved latttrai positions. as sholvtr by vonstruc.t ing initial strttcat ttrtls ha.wl on either improve-(1 rnarkw ty:sitlttt?s or itnlwovt~d lateral positions. l)uring an SIT) run. t hrl r.rt1.s. drviation dwreaswl front 4.5 X t.0 3.X X. \\‘hen t hr simnlation was rxtertdetl to 7~ pi(y)swwnds and an average st~rwturr dt:t,wmined I)etwertl 25 pi(v~seconds and 75 piwsec*onds and an average st.ru(atnrr df%rrminrd Iwt~wwn 2.5 pi(+n-

Figure 7. Sterro pi&n-r of the average AIlI structure based cm the marker residues M3) H and improvrd lateral positions of the hrlicrs on the kiclney-shapr for irssignment I. The Ijwkbnnr of the polyprptidp chain t,yethtar with the vhromophow is plottrtl. Thr straight. lines mark t,hr boundaries of the hydrophohitx core of the rnrmhranr (assum& t,o be 30 .\ thivkl.

seconds and 75 picoseconds, the r.m.s. deviation of st.rueture the average was.T slightly lower. Ar = 3.75 A. A stereo-picture of this improved st.ructure is presented in Figure 7. The tilt, angles and the extensions of the helices in the improved struct,ure are included in Tables 3 and 1. and essentially agree with those for the previous structure based on the marker residues Mg). The internal structure of the helices, however. has slightly changed. Pronounced kinks now occur in helix A at residues 19-20, in helix J3 at residues X-56, in helix C’ at residues 87-88 and in helix F at residues 180-I 81, The energy of the improved structure after 25 picoseconds was essentially the same as for the previous struct,ure. but had not yet reached a constant level. t\fter 50 picoseconds, it leveled off and became lower than t’he energy of the previous structure by about 100 kJ/mol. Therefore, the improved structure is predict,ed to be more stabk t.han the previous structures based on the marker residues MJf’ and M ‘,‘I but t,his predictSion is again weak due to the small ‘energy difference involved. The decompositions of the r.m.s. deviat,ion of the improved structure are included in Table 5. The r.m.s. deviations in the plane of the rnembranr and perpendicular to it are Axy = 3% A and AZ = 2.0 r\. The cont,ributions of t,he individual helices indicate that helix I> still has t,he largest error. The analysis in terms of position, tilt, long axis orientation and internal degrees of freedom shows that) the internal degrees of freedom are now dominating, They contribut,e 5S’$/, of the r.m.s. deviation. while the other factors ront.ribute 200/,, I~?o and lOoi,. respectively. The phase errors of the improved MU structure based on the marker residues Mf) were also determined. They are only marginally better than those of the previous st’ructure based on the marker residues I4jf’ (Table 2), indicat.ing that the improved structure is good down to about 7 ;i resolution. This result refers to the ent,ire protein comprising the membrane part and the peripheral part There are good reasons to believe that in our approach the membrane part is modeled bett’er than the peripheral part, hence, the struct,ure of t,he membrane part may actually be better, than specified by a resolut,ion of 7 A. An indication for that is provided by the r.m.s. deviation of the Ml) strut&tures from the experimental structure. This yuan tity refers to the membrane part only and decreases from 7 A to 38 A on going from the previous MI) structure to the improved structure.

4. Conclusions The results from the MD simulations allow US to give the following answers to the questions raised in the Introduction. (1) The kidney shape for the arrangement of the helices in the membrane plane could not be fully predicted, but when starting from a circular arrangement, the symmetry of the circle was broken in the correct way to permit the later

formatiotl of tht, c~orr. i;‘) ‘1’11(~ assignment of the predicted helices to t hos:rl on t trc, kidney shape could be determined. although IIO~ very reliably due to the small differrrrc~rs ~II t I-It, phase errors and the energies of t,hth most fa\~orahlt~ assignments. (3) The t,ilt of the helicses whc~~rstart,ing from t,hr kidney shape established in rssent.iaIly I hrl correct way. (4) The M 1, structurr ctbtained b,v starting from ii refined structure prcdi(tic)tl and accurate values for the lat’rral positions of’ t trc, helices has an r.rn.s. deviation of 3,s 4 from t,hrJ experimental structure. A first remarkable result, is tbe correct symrrlrtry~ breaking of a.n initial circle for t,hr arrangement ot the helicrs in the metnbranr plane. Thr hrliccs started to move in directions consistent lvith t,hc later formation of the kidney shape with the caorrec.t assignment, of helicaes. (Ibv~ously. t’he interactions between neighboring helices on the cnirclt>difh~r sufficiently t,o induce t,tie correct. flattening of’ the cGrc:lr. Such a flattening did not, oww with a polyisolcucir~~ chain. These results should be considered as a first step towards the determination of the correct lat,rral arrangement of the hrlices, and further st.udicbs art required to find out what is possible and what is not.. A second remarkable result is the spontaneous establishment of the c*orrect tilt of the helixes. This implies that. tilting of the helices is a fast ~JIY~WSS that oc(*urs within t,he time range acacessiblr lo h!lJ simulat,ions. This fast t~stablishment of thri tilt allowed us to distinguish between diflerent itssigrlm ments of the helices. Only for the correct assignment did t,he helices tilt correc%ly wit,h the energy of the struct,urr becoming minimal. The reason for the tilt of the helices is not (om plet,ely clear. Tt is known that helices tend to adopt a supercoil, i.e. to twist about ea,ch other wit,h the ridges filling the grooves ((“ohen & Parry. 19X6). This leads t.o a tilt of about, 18” of thts helices relative IO ea,ch other. However. the supercoil does not seem to occur in any case. for KR its format ion depended on the assignment, of the helictes, i.fA. on the amino acid residues of the neighboring helicaes. Bulky side-chains at the interfacbr may rare\ mt a supercoil. small side-chains promote it. ,411 open question is t,he role of the Pro residues: t tI(xy tn:hy prevent or promote a supercoil depending on I hr direction of the kink they induce. In the MI) strut.ture, helixes 13. (‘. F. which all contain a Pro rrsitiur. were found to be kinked in approximate agreemt*nt m-ith the experimental structure. To stud\. this problem further, one might perform MI) simulations starting from a polyisoleuc~ine cahain arld pradua~ll~ replace Tlr residues by residues of’ the KK chain using. first. t>he Pro residues. In this way one may find out which residues are clssential for the c~c~rrrcd tilt of the helicrs. The M 1) structures for different arrangemerits of’ the helices in t)he membrane plane and for diff‘ercnt assignments of the predicted helices t,o those on t,tw kidney shape differed in their energies. The energy differences involved. however. were sometimes small so that a prediction of the most stable structure on

Modeling

of Bacteriorhodopsin

the basis of the energy alone becomes weak. Tn such extended simulations and cases. prolonged averaging of t,he energy may be tried t)o overcome the problem. The r.m.s. deviation of the best MD structure from the experimental structure was 3.75 A. st,arting from an initial structure with 4.5 A. Obviously, the better the initial structure. the more effective the Ml) simulation. The initial structure in t,his case was based on a refined secondary structure prediction and accurate lateral positions of the helixes on t,he kidney shape. The r.m.s. deviation of t,he MD structure is dominated by errors in the internal degrees of freedom of the helices, i.e. in the positions and orient’ations of the amino acid sidechains. Tn the plane of the membrane, the r.m.s. deviation of t,he best MD structure is 3.2 A, and perpendicular to it CO A. These values have to be compared with the resolution of the experimental structure, which is 3.5 ,A in the plane of t,he membrane and about 10 L% perpendicular to it. corresponding to uncertainties in the positions of the atoms of about, 1.2 A and 3 A, respectivel) (R’. Henderson. personal communicat8ion). Hence. the positions of t.hr atoms in the best MD structure lie outside the range of the experimental data, at least, the positions in t’hr plane of the membrane. The main source of error in the MD simulations is supposed to lit, in t,he t,reatment of the environment of the protein. Although a hydrophobic potential was introduced. the sirnulations essent,ially repro’sent vacuum simulations. For soluble protems, it is known. as rnrntioned in the Introduction. that va~um simulat8ions do not describe protein strutturps bet’ter than up to an r.m.s. deviation of about 3 .A from the *Y-ray struc%ure (van Gunsteren et ~1.. 1983). Tf water molecules are added. this value decreases t,o about 1 .q. With the best MD struct’ure obt’ained in our studies. we are close to the upper limit reachable wit,h vacuum simulations. one should expect to get an improvement

Hence. of the

struc*tjure by including water and lipid molecules in the simulations. For this purpose. explic*itly however. the interaction potentials for water and lipids

should

be

improved,

as

seen

in modeling problems encaountered (.Jiinsson et al., 1986) or a lipid bilayer Kerrndsen.

from the a micelle

(Egberts 8:

198X).

*Anot’hrr source of error lies in the neglect of net electric charges on the amino acid side-chains. This error may not be as severe as it may seem at first glance. The charges outside the membrane may be shielded by count’erions and those inside the membrane may be arranged in pairs of positive and negative

charges.

In the ground

state of HR, of the

four Asp residues located inside the membrane only two are charged, Asp85 and Asp212. and their negative caharges arc probably compensat’ed by the positive caharges on Arg82 and on the Schiff base nitrogen. respectively (Butt et al.. 1989; Gerwert ef al.. 1989: Holz et al., 1989). Hence. the assumption of uncharged amino acid side-chains may be acceptable as a first approximation. However, this approx-

imation

x49

has certainly

to

be improved

in future

studies. \Ve thank .J. PI&s for numerous discussions. and R. Henderson. M. Heyn, D. Oesterhelt and F. Siebert for communication of results prior to publication. We also thank It. Henderson and his colleagues for sending us the at,omic co-ordinates of their structure. Furthermore, the continuous support of P. Ovrrath is gratefully acknowledged. The co-operation of the staff of t,he Rechenzentrum (iarching is gratefully acknowledged. This work was supported by the Swedish National Researrh (louncil in the form of a grant’ to O.E. (K-KU RSY-107) and by allotment of computer t’ime.

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central r& in the function of barteriorhodopsin as a proton pump. EMHO J. 8, 16.57-1663. (‘ohen (‘. Rs Parry, 1). A. 1). (1986). a-Helical (*oiled coils: Hiochcm. Sri. a widespread motif in proteins. Trr&s

11. 245-248. Edholm. 0. Br .J&hnig. F. (1988). The structure of a membrane-spanning studied by polyprptide molecular dynamics. Hiophys. (“him. 30. 2’i9- 292. Egbrrts. B. R- Brrendsen, H. ,I. C”. (1988). Molecular dynamics simulation of a smecticb liquid carystal with atomic detail. J. Chem. Phys. 89. XIX R’i32. Eiarnherp. 1). Cy- YIcLachlan. A. I). (19X6). Solvation elIerg> in protein folding and binding. A\‘~~t~~~e (l~on~dorc). 319. 199%%03. Eisenhrrg, I>.. l\reiss. R,. >I. & Terwilligrr. ‘I’. (‘. (1982). The helical hydrophobic moment: a measure of the amphiphilicity of a helix. Safrrrr (Lop/don,). 299. 371474. Elber. R. h Karplus. M. (1987). Multiple conformational stat,es of proteins: a molecular dynamics analysis of myoglobin. Science, 235. 318-321. En&man. n. hl.. Henderson. R., McLachlan, A. 0. & Wallace. B. A. (1980). Path of the polypeptide in barteriorhodopsin. Proc. ,Vnt. .-l~d. Sri.. I-.S.A. 77, 2023~2027. Fasman. (I:. I). &, Gilbert, W. 4. (1990). The prediction of transmembranr protein sryuencrs and their coniS’ci.15. formation: an evaluation. Trrnds Rioch~m.

89-92.

Frauenfelder. H., Petsko. G. A. & Tsrrnoglou. I). (1979). Temperature-dependent X-rav diffraction as a probe of’ protein structural dynamics. .Vnt~e (London), 280, 558-563. Furois-Clorbin. S. & Pullman. A. (1986).Theoretical study of the packing of a-helices of poly(r,-alanine) into transmembrane bundles. Possible significance for iontransfer. RiochCm. Riophys. Actn. 860, If?- 177.

_-~-______-(:cwwt.

K.. Hess. B.. Soppa. .J. & Owterhdt. I). (I!!H’+. Itok of aspartatc~.96 in protc)tl trattsloc~;itiott I)>, Itac,te~ior)lodo~tsitt. /‘WC. AYrrt. .1cod. ,S’r~i.. I .,,I. I,.. I,utgenbrrp, .I.. Hrrzfelrf. ,I.. Xathies. I