Homonuclear Three-dimensional NOE-NOE Nuclear Magnetic Resonance/Spectra for Structure Determination of Proteins in Solution J. Habazettl, M. Schleicher, J. Otlewski and T. A. Holak Maz-Planck-Institut fiir Biochemir D-8033 Ai’artinsried bei Miinchen. Germarq (Received 2 March! 1992; accepted 29 ?June 1992) The solution structures of two proteins ((YMTI-I, a trypsin inhibitor from (,‘ucurbita ma.ri77~rr, and hisactophilin. an actin binding protein of 118 amino acids) have been determined based on t’he NOE data derived solely from the homonuclear 3D NOE-NOE magnetic resonance spectroscopy. Two different approaches for extract’ion of the structural information from the 31) NOE-NOE experiment, were tested. One approach was based on the transformation of the 31) intensities into distance constraints. Tn the second, and more robust approach. the 31) NOE intensities were used directly in structure calculations, without the need to transform them into distance constraints. A new 2D potential function representing t,he 311 NO&NOE intensity was developed and used in the simulated annealing protocol. For CMTT-I, a comparison between structures det’ermined with the 3D NOE-NOE method and of’ various 21) NOE approaches was carried out. The 3D data set allowed better definition t,he structures than was previously possible with the 2D XOE procedures that used thf isolated two-spin approximation to derive distance information.

Keywords: 31) n.m.r.:

1. Introduction Multidimensional r1.m.r.t spectroscopy has heen shown to be of great) value in extending the methodology of protein structure determination by t1.rn.r. The main advantage of multidimensional over 21) n.m.r. experiments lies in their potential t,o alleviate resonance overlap. A number of homonuclear (Griesinger rt ccl.. 1989; Vuister fd nl., 1989: Oschkinat et al.. 1990) and het,eronuc4ear (Fesik B Zuiderweg, 1988; Marion et al., 1989: Zuiderwrg 8 Fesik. 1989; Kay et ~2.. 1990) 3D and 11) n.m.r. experiments have been described recently. For the purposes of a,ssignment of proteins larger t,han approximately 130 amino aclids. t hr heteronurlrar i- Akthrrviationa used n.m.r., nu~lrar tnagnf~tic~ rrsonanw spwtrosc~opy: %I). trio-dimensional: 41). thrfvtlitnf~nsional; 1T). fi)ur-dimensional: (‘JITT-T. (‘cnc~rhitn

mrr.ri,mrr t,rypsin inhibit,or I; X\‘OE. Xurlrar Overhausrt effect: IL’OESY. two-dimensional NOE: spfx~troscwpy: FYI). f’rrr induc%ion decay: tJR. jurnprpt,urn: TO(‘8\7. total cwrrelation spectroscopy; HMQC. heteronuclrat multiplr quantum wrrrlation; 31) NOE- NOE, thrrr dimrnsional h’OF:- SOE: L)IS(:E:O, tlistjancr gromet,rj prcjgratn; E.c’OSY. exclusivf~ cwrrrlation spectroscopy: SA. simulatfd annealing: r.m.s.. root mran square: r.tn.s.tl.. r.m.s. difference.

protein

st’ructures

3D experiment seems t’o be more useful than thr homonuclear experiment. The heteronuclear experimerit’ has higher sensitivity as it involves large heteronuclear coupling constants compared to the proton linewidth. It also has higher spectral resolut)ion due t,o t,he larger chemical shift dispersions of’ “N and 13(” nuclei compared to t)hc ‘H shifts. The number of cross-peaks in a heteronuclear 31) spe’c’~ trum is equal to t)hat of the corresponding homonuclear PI) spectrum, whilst additional csross-peaks complicate a homonuclear 31) sprc%rum. However. on(ae the assignments have heen made, the homonuclear 31) NOE spect’ra contain more information relating to distance criteria than the corresponding 31) hetrronuclear spectra (Fairbrother et trl.. 1!)92). This informat,ion is crit’ical for an accurate st ruc+urr determination. Rrc~~ntly t hr pot’ential of homonuclear 31) SOLNOE experiment has I)een dt~tnonstrated for the differentiat~iori of spin diffusion pat’hways (Boelens rt crl.. 1989: Krrg rf r/l.. 1990: Kessler rt (~1.. 1991). Also. 31) NOE--NOE spectra (San be used to assess t’he amount of’spin diffusion in 2D POESY spectra (Habnzettl et nl., I!Nl). Tn this paper, we describe two different approachcas for the structure dctermination of proteins based on t,he information derived from the homonuclear 3D SOE-NOE experiment. One

31) NOE-NOE

n.m.r.

Spectra for Proteins

approach is based on the transformation of the 3D intensities into distance constraints using the approximation lijk cc rij6r,i6, where Zijk is the intensity of the 3D NOE-NOE peak, and the rs are distance constraints extracted from the 3D peak. In a preliminary report on this approach, we already showed that a large number of distance constraints can be extract,ed from the homonuclear 3D spectrum to provide sufficient input data for “the highresolut’ion structures” (Holak et al., 1991). A detailed description of t’his approach is given in the present paper, Tn the second approach, the 3D NOE intensities are used directly in structure calculations. without being transformed into distance constraints. A new 2D potential function representing t’hr 31) NO%NOE intensity is developed and used in the simulated annealing protocol. The two methods are test’ed on two proteins: CMTI-I, a trypsin inhibitor from Cucurbita maxima. and hisactophilin, an a&in binding prot’ein of 118 amino acids from Dictpsfeliwn discoideurn.

2. Materials (a) Samples.

acquisition

and Methods of spectra and inteption

The humonuclear 31) NOE-NOE spectra were acquired from a 15 mM sample of CMTI-I at pH 4.3 in 2 mM-sodium acetate. 9O’jb H,O/lOqb ‘H,O. CMTI-I was isolated from the se& of’ C’ucurbita maxima and purified as described previously (Holak it al.. 1989a). The spectra were recorded at 25”(: on a Bruker AMX-600 spectrometer. The 31) experiments were carried out using a pulse sequence described by Boelens ef al. (1989). Two 3D NOE-XOE spert ra were acquired for CMTI-I. In the first 31) NOEL-NOE (Axperiment. 2 identical mixing times of 140 ms each were used. In the second. both mixing times were 50 ms. Each FIU consisted of 8 scans. The data set, consisted of t, x t, x t, = 256 x 256 x 512 points over a spectral width of 7400 Hz in all 3 dimensions, resulting in a t,ot,al measurement t,ime of 6 days. Only subvolumes containing t)he ?jH resonances in F3 were processed. Appropriate Lorent,z-to-Gaussian transformations and a I -time zero-filling in all 3 dimensions were applied. together with a baseline correction by a 3rd order polynomial in the F3 dimension. Hisactophilin was rxpressed in E. coli and purified essentially as described by Scheel et al. (1989). Compared to hisactophilin of I)irtyosfrlium discoideum, the E. coli pol,vpeptide cont,ains an insertion of 4 additional amino acids Glp-Glu-Pha-(:ly after the initial methionine, i.e. the total numbclr of residues is 122 (Scheel et al.. 1989). As there were no trivial NOE connectivities assignable to the insertion amino acids. we numbered the residues acrordiny to t)hr amino sequence of hisartophilin from nictyoatrii,,~m discoidcxm. The 3D NOE--NOE spectra for hisactophilin were acquired by a JR pulse sequence as descbribrd b,v FLOSSuf (II.. 1991). The mixing t,imes were 100 ms anti the dataset consisted of I, x t, x t, = 240 x 256 x I K (K, kilobyte; 1027 points) over a spectral width of 7400 Hz. Eac*h FTD consisted of 8 scans resulting in a total measurement time of 4 days. Other spectral and processing parameters were similar t,o t,hosr used for t,hr (‘MTI-I spect,runl. The spectra were acquired from a I.7 mM sample of hisactophilin at pH A5 in 50 rn3r-KH,PO,. Tt, c.an be appreciated that,, with 31 histidines and 15

in Solution.

157

addit,ional glycines. the assignment of the spectra was not. an easy task. The n.m.r. spectra of hisactophilin were assigned with the 2D and 3D n.m.r. methods based on the following spectra: 2D NOESY, 2D TOCSY. 3D NOESYHMQC, 3D TOCSY-HMQC. 3D NOE-NOE JR. Prot)on and nitrogen resonances of most backbone and side-chain atoms were assigned. except those at the amino terminus of the protein (3 first-insertion amino acids and Metl) and in the loop between residues 26 to 30, whose assignments could not be confirmed because of the paucity of NOE connectivities to these residues. The heteronuclear 3D techniques proved to be very useful for the assignment of glycines because of their unique 15N chemical shifts. Also, the overlap of the proton NHs in the most crowded region. between 8.3 and 8.9 p.p.m., was most,ly removed by spreading resonances into the “N dimension. The 2D pot)ential function for the 3D NOE~NOE intensit,ies has been incorporated into the X-PLOR program (Briinger, 1988). Data processing, peak-picking and simulation of the spectra was performed with our own software. which is available upon request. The 31) cross-peak int,ensities in the sprcatra were semi-quantified by measuring the int,ensit). of the highest point in a volume around the 3D crosspeak. This intensity is directly proportional to the volume of the 31) cross-peak provided that t,he linewidt,h of every peak in all 3 dimensions is similar and larger than the multiplicit,ies of the signals. This is the, (‘asp in the RD SOE~~OE spe&um.

(b) Th tory The intensity of a 31) NO&SOE (aross-peak, ), bet,ween spins i. j and k. is proportional to fijk(Trnl. Tm2 thr product of the individual NOE transfer eficirncies of each mixing time (Boelens rt 01.. 1989: Grirsingtr et nl., 1989): Iijt(Tmt’ Tm2) = clrxP(-Rz,z)lijlexP(-RT,, )Ijk-Akk((l). (1) where T,, is the first and T,,,~ the second mixing time. R represents the cross-relaxation matrix. d,,(O) the equilibrium magnetization of spin k. and c is a constant. Tf %I = 7m2. and as R is symmetric. the intensity of a bac.k-transfer peak is given by: I,,,(L) = c[‘=p( -&,,)]~&.(W (2) which is proportional to t,he squarcl of the intensity of the corrrsponding XD peak Ii, with mixing titnr T,. Expanding the exponentials in eqn (1) and neglecting all trrms higher than 2nd order in T,,,~ or T’,~. a cnross-p(Lak (i #,j # k) is thrn given by: ‘tj/c(Tml, Tm2)=

CT~IT,~IZ)~R~~-~~~(O).

(1%)

As the cross-relaxation rate. Rij. is proportional to the inverse of the 6th power of the distance separation, rij, of the 2 prot,ons i and j, the distance constraints can be derived from 31) NOE-NOE intensities by appropriate scaling with knnu-n distances using the al)l)rosimatioll: lijk = Kr,g%,;“, (4) where rij and rjk are the distances between protons i. j and j, k respectively. and h’ is the scaling c>onst,ant For (i #,j = k). the expansion results in:

Jr,j(Trnl.Tm2)= ‘.(-Tnz~Gj

+O.~T,~,,X:,R~,Rqj+~ml zm2R,jR,j)Ajj(0).

whic.h, after neglect,ing 2nd o&r proportional to Rij.

terms in T,,,,.

(5) T,,,~,

is

In the first method of the structure determination from 31) ~\‘oE~~~?U‘OE data. only distant constraints tlrrivcvl from rqns (2). (4) arid (5) \verp used in the c~al(~ulations. ~-\llout 10 t,o 50”,, of the distance wnst,raints \vew c~xtractrd from the 31) XOE~ NOE spwtrum ivith both mixing times of ;iO 111s.thr rest of the distance constraints from a spectrum wit,h both mixing times of 110 ms. Thv litttw slw’trum rxhihitrd a bflttclr signal-to-noiw ratio. Three srpratr c4ibration cwnstants (KS) wcxre tlrtrrv minrd using the cvnnwtivitiw that involved known inter f)roton distance: I caonstant for the cross-peaks with 2 of the 3 F,. F2 and b; frequencies equal (the 2Y, ant1 AT1 cw~ss-p&s). I for the back transf’rr peaks ant1 I for th(b “rtlal” 31) 9OE SOE cwss-peaks with 3 different frrqurncirs. The S, atld ‘\T2 vross-peaks are tlw to t hr ditwt XL’obZs during the tirst ant1 srconcl fnisitlg titrlw. wsprctivcJly (I~orlrns P( nl.. 1989: I{rrg it ~1.. 1990). ‘I’ht, .V, and ‘V2 peaks art’. in thr lincsar af)l,l,oxirnation in t,, and z,z. proportional to the tlistanvv. rL;“. of rq~l (-5). Thc,rttforr thr valihration constant for the S, and .V2 praks (‘an he usfvi dirrc+ly to cA(~ulatf~ tlistanc~v (v)tistraints from the f~uprrimetital intrnsitirs on thr .VI anti s, lines. Fol, c~sarnplf~. thts .Y2 c.onnwtivit>, 22/jz “-” l-4 222; in Fig. I gives the distanctn cx)nstraint twt\vwn (‘\K~.)(‘~*H and (‘vs22HS (the Ilotat,ion L’g, z/!l, ““N c.;,r~t~c~s,““l~ls to thv mss-peak (14’, = ( ‘vs;P2(‘P2H) -( Fz = (‘vs~?l(‘~‘H) - (I;; = C’ysL’dHN) on thtk A?1 linrs at the NH ;lm’idr plane of rrsitlur C1ys22). As thr hsc~ktransfiit~ peaks arv proportional to r I2 In the 2nd ordrr approximat ion in T, (ec4n (2)). the ttistanc,r wnstrxint c’ibn ;tlso tw c~al(~ulatrtl directly from the 31) intensity. For the 91) wowpeaks with 3 different frequencies. the tlistanw cxjnstraint vorrrspontling to I of the 2 NOlC transfers h;ts to Iw known in order to c*alculatr the tlistancar cwnstl,aint irl\-olvrd in thr ot1lc.r transfer (rqns (3) anti (4)). Thew rr+rrncv tlist,atic.r c.onstraints \vere acyuiwtl t’rottl tlrt* tiistanw c.onstraints ohtainetl from thtl AV, and S, (‘row lwaks and from thtl hac*ktransfer ptsaks M ith I c,alihration c*onstarlt. The interproton distancrs tirrived from known amino avid gromrtries wvre also used. For example. the tlistanw (‘“H(i) NH(i), \vhic*h is usually equal to ?,!I24 (I .% = I()-’ nnr) for the amino witis not in the r-hrlic4 c~otrfi)lni~~t~ioti (thr I)rotvins studirti hew) (1j’iithric.h use of such caalihrations is discussed in morr dthtail in tht I)iscussion (Holak rf ~1.. 1989~). Altogether. 541 tlistanw rvmstraints wrre obt,ained from the 37) XOE SOE HJMYtrum. A c~atalogur of‘ the number anti tvI)t’s of the c*onstraints is given in Table 2. Of the tot,al h4l clist;lnw cwnstraints. 312 \vt’rti derivtvi from 3-f’requtwy peaks

(i #,j # k).

(‘onnec:t.ivit~ Irrtrarrsidur Long (Ii-,jl L 5) Medium (Ii-,jl < 5) SequenW Total All distance constraints§

Total 161 iti4 5I I 65 541 6.50

i#j#k I I3 III %7 ti I 31% 109

A-, .v,: 1x 59 “4 101 229 %4I

t A complete list of distance constraints has heen deposited as a supplement,ary material in Holak rl al. (1991). $ A’,, ;V, or back transfer peaks. § Number of distance constraints that could be calculated from different ronnectivities that, provided redundant distance information.

(4

h PPM1 3

6

1Cx21y,22N

0 0

22,&2@22N /

13al3CY13N.

2(r&22a22N

/

01

-

P

Fig.

(d) Intensity

constraints NOE-NOE

derived from spectra

the 30

The total energy potential of a macromolecule in t,he molecular dynamirs and in the energy minimization steps is a (‘on1 bination of experimental and empirical structure information: Ettotal =

Eempirical

+

Ee:experimental

(6)

energy function, Eempirica,, is used to The “geometric” maintain geometric ideality of the system. that is bond lengths. bond angles, planarity, chirality and repulsion. The energy constants depend on the calculational procedure. Two different experimental energy functions were used in the structure calculations: Ee:experimen*al

=

C (ij)

Eiislance

+

C (ilk)

GLsity~

(7)

1.

where E’id,s,ance is a square-well potent’ial that involves a distance constraint, rij, between protons i and j. This distance constraint may be determined from a 2D POESY or from a 311 IVOE-,?V’OE as described above. Tn the energy function t(:~~e.sity. the structural information of a 3D NOE-KOE cross-peak Zip is used as a single pseudoenergy constraint. We use here the same approximations as in the first method. The cross-peak Iijk is directly proportional to the product of the 2 cross-rates, Rij and Rjk (see eqn (3)). and the corresponding theoretical 31) XOE-l\iOE intensity can be calculated from a strutst,ural model of the pro&in by: IF.n’C Ilk = TT-67Y6. 11 Ik

(8)

where rij and rjk are the distances between protons i. j and ,j. k. respectively. and the proportionality constant is set equal to 1. The gradient of the energy function Eijn:ensity

/

6 Figure spectrum the F; is intensity

5

4

3

---rT-T7------r~-;

""""

2

1

0

1. (a) Cross-section for F3 at the position of the ($322 and Met8 amide proton taken from a 31) IVOE NOE of CMTT-I. There were 2 mixing times. of 140 ms each. Some NOES at the F, and F2 frequencies are labelled: always 22N and 8N. (b) Th P calculated spectrum for I of the st,rurtures of CMTT-T determined from the constraints.

acts on the coordinates of the starting structural model unt,il the oalculated intensities Z$ of the model fulfill the measured intensities Z$. The energy function is given by: [(l;$c)-l/l2

-(~;!$-AJ~/‘~]~ if IF?” ilk < /?‘-A vk

[(Z~~)~“12-(Z~~+A”)~“12]2 if

I0

ZFfiC 1l.Q > I$-

I AU

(9)

else

where k, is the force constant, and A, and A, are the lower and upper error bounds. respectively. The intensity Z$ is

the measured 31) X0& NOE intensity divided by thr calibration constant K determined after eqn (4) and as described in section (b), above. The difference between t.h(s calculated and observed 3D h’OE-NOE intensitv is now a driving force on the coordinates of t)he protein in the dynamical or energy-minimizing step of the structure calculation. Tf the observed intensity Z$ and the 31) NOI? intensity I$ calculated from the structure model are the same within the error bounds (A.. A,), the energ term ,q!ijk’ ,n,enSi,yis then zero and the force of this ronatraint on the co-ordinates of the model structure is also zero. Tf the difference between the observed and c*al(*ulated

30 NOE-NOE

n.m.r.

ISpectra for Proteins

in Solution

161

lntenstiy 2L

”

4

6

‘,] 1x1

Figure 2. Logarithmic plot of the 3D NOE-NOE intensity potential for a peak li+,+k. rij and rjr are the distances between protons i. j and j, k. respectively. The energy in the “white” area is zero and increases with increasing distance from this area. The lines in the plot. give the lower distance boundaries of the repel function (1.6 w).

intensities is not zero wit)hin the given error bounds. a force act.s on the co-ordinates in the direction to make the structurcb model fulfill the constraint. The negative 12th root of the intensities was taken to set this energy in comparable size to the other NOE distance constraints. The full potential for 1 intensity constraint is shown in Fig. 2. It is a 2D function with the 2 variables. rij and rjk, at the .c-axis and y-axis. respectively. The contours shown in Fig. 2 correspond to the energy heights. In the central ‘.empty” area in the contour plot. the energy is zero and increases as a square function with increasing distance from this area. The energy function in Fig. 2 corresponds t,o an observed intensit)- 1;: of 8.72 x IV6 units. i\ssuming that the 2 distances rij and rjk are equal, this would correspond to a distance of 2.64 a for both proton pairs (2.64- ” = X.72 x 1W6). The upper and lower errors in intensity, AU and A,. respectively. are chosen such that an upper and lower error in the distance of 0.3 A for both proton pairs at the same time is allowed. In the example above. it corresponds to AU = 2.84 x 11)-’ and A, = 6.32 x lW6 units. The error bounds to the distances were restrained t,o W3 A. as only more intense 31) cross-peaks were used in the calculations. The intensities used for the calculations corresponded to the maximum distancae constraint of 3.3 4. assuming that the distances involved in the 31) peak arc equal. In Fig. 3, the upper and lower errors in the experimental intensities are plotted against the obst>rred int,ensity. The plot shows that an upper bound of 0.3 .q of the distance corresponds to the lower bound error in the intensity up to 75%. The (k3 .& differencar in the lower bound of t,he distance corresponds to the error in t,hr upper bound of the intensity of 450°h. These relationships reflect t,hr dependence of the 31) XOE-KOE intensity on the distances through the equation Zijt cc rz;“r,i6. In the c-asr of pseudoatoms, which represent methyl groups or st,rreospec~ifically unassigned mrthylenr

I P,t

Figure 3. Upper (horizontal lines) error bounds A, and lower (vertical lines) error bounds A, in the rxperiment,al intensity plotted against the intensity I$.

protons, the lower error bound of t,hr intensity Ar is increased so that the intensity error hounds rorrrspond t,o an upper distance error of 1.3 h. The example in Fig. 2 shows that. if the distance dij were 1 .%. the distance dj, could be verv large (for example 10 A) without violating the allowed intensity range. But with the repel funct,ion present. the lower distance is limited to 1.6 A. This allows only distances above and on the right side of the lines in Fig. 2.

(tl) Sinrulatrd

annealing protoml mnstrain,ts fmly

using

distnnw

The structure of CMTT-I. based on the distance constraints derived from the 31) NO%SOE spectra. was determined using the hybrid met,hod of DTSGEO and dynamic simulated annealing (Holak et al.. 1989a). The basic protocol used for the calculations has heen presented previously (Holak et al., 1989a.c). The prot,ocol cottsists of 4 st,ages. In stage 1. the c-o-ordinat,es of the subst,ruvtures are obtained from the distance geometry program DISGEO (Havel. 1986: Have1 6 li’iithrirh. 19X.5). In the 2nd st,agr. all the atoms missing in the substructures are added. Step 3 consists of dvnamical simulated annealing (Bilges et al.. 198X). i.e. riising the temperature of the system, followed by slowly cooling the system t,o overcome local minima and locate the region of the global minimum of the target function. The 4th stage involves 200 c~ycles of constrained Powell nlitrimization. These last 3 stages were carried out with the program X;-I’LOR (Briinger. 1988). ,411 protons were rxplicit,l> defined in the dynamic simulated annealing calculations. The mrthylene protons and methyl groups were assigned arbitrarily to H, and H,. or Me, and $lr,. for protons resonating at lower and higher t1.m.r. fields. respectively. In the protocol that uses substruc+urrs. the force constants for the bond lengths. bond angles and planarity art> the same as t)hose used in the refinement of the structures using NOE-derived distance c-onstraints (Holak et al.. 1989a). The pseudoenergy target fun&on used in the calculations was a square-well potential. The 21) NOESY distance constraints have not been used in the

l)r simulatrtl annt~alirig strl). tht. fort~t~ c~onstants bt’I’v ;iO IiC’ill lllol~1 .p\-* for ihe tlistant.ts t,(mstraints and 30 kt,al mol ’ .r\ * for thr inttJnsit>t~onstraints. The strrct~t~lrc~ (.al~.ul;tlion of hisat~tol)hilin with all tht, availahlt~ NOE tIa(;t iook J~l~t~~~f~ssoi~ ilrlit lirtlc, ori :I a~~~~roxirilatt~ly Zi.5 Ii t.rntl~nl

rIl

Thr

tdcnlations

were also t*arrird out with the ,Y-I’LOR~ In-ograrn and were based on a protocol similar to that used for the distance const’raints only. The psrutlor~nergy target funcation was the 31) int,eniity funcAtion in rqn (9). As t’hrre are no distance ctmstraint,s. it was not J)ossihlr to use I)TS(:EO to create starting structures. Thr starting strut*tures were therefort, built, with X-I’T,C)R I)? randomly grilrratinp 4 and li/ angles. 1n the c~alt~ulat,itms startirlg from random structures. NY used higher forty vonstant,s for thr bond lengths. bond angles. improl)ers atrtl [Aanarity. t)ecause high forces originating from at+ t~eni~)orarily on thta I)rotriri. esprvially at ‘experimental thtl beginning of the folding. The t~alt~ulations start)4 with an initial minimization of 60 stq)s and with a loa- van tier \2'dS ft,rtY? tY)nstant of lllt~l-l 4-* 0.1 kcal (I t.aI = 4.2 *I). ill1 Ei”,e”si,y k, forcat, constant of 1 kt,al lllOl ' .A-~* and a dihedral angles (kdihedral) forvr tvnstant of 5 kt.al molrad ‘. The fortBe constants to maintain ~~or~tl Irngths (kbonda). bond angles (kanglea) and improl)ers (kimpr) were set to 1000 kcal mol ml &*. 500 ktaal mol I ratI- 2 ant1 500 kt-al mu-’ ratI-* rrsyW.ively. Tn tht, followinp 337.50 t,imrstel)s (2 fs) of high t,emperaturr dvnallliw. the forve c*onstants kbonds. lZangles and iimpr werf’ set to 500 kt,al rtrol~’ 4~ l. 400 and ZOO kval mol-’ rad-*. rvsl)ct~tively. In the simulat,rd-alinraline stag” of high tr~nryraturr dynamic3 (X)00 timestrl)s of 2 fS). thr forcv cY,~lst;rllt k,,, was int~rcasrd to -C kcal molt’ -4-l. k, to 100 kt.aI mol-’ A-*. and kdihedra, to 200 kcal moi-’ rad ‘. .\titbr caooling thr system. the final stage involved 200 t~yt~lt~s of c*onstrainrd Powell minimization with kbonds = IWO kval mom’ .A ~2. kangles = ,500 kval mol ’ rad - 2. and The t*alculatitm of a strutakimpr = 500 kcal rnol- ’ ratI-‘. turta of (‘MTT-1 with Xti intensity t*onstraints took alyroximately I h caentral In-ocessor unit time on it (‘ONVEX (‘220 t*oml)utjer. The intensity constraints were oi)tainetl either from the 31) N;OE~NOE q)ectrum with both mixing t,imes of .5Oms (40 to .50°, in number) 01’ front a sy)rt*trum \vith both mixing times of 110 ms. The numl)c~r of intensity tvnstraints used in this arction was smallrr than that rxtract,ed from t,hti 110 ms syvtrum only (SW srtation (P)) because weaker intensities were not ~~srtl in the t~alt~ulatit~ns.

Structures of (‘MTT-I and hisact,ophilin were also determint~tl from both dist,ancr and intensit,y constraints ]-)resrnt in the calculations. For (“MTT-1. the 3D NOES on t,hr LV, and 3, l’lanrs were introduced as distance taonstraints. The same protocol as in the calculations with 31) intensity tsonstraints was used. with the exception that the fort,r constant of the distance constraints was IO0 kval mol-’ &*. For hisactophilin. there were 1287 distance constraints derived from the 31) SO&I%OE eqeriment. during our earlier n.m.r. study on hisactophilin. Out, of this number. 1150 connr&ivit,irs vould also be identified in the 21)

~‘ONVF:S

(‘2L’O

c~lrnlJ,rltf~r.

:\s

mer~tion~~tl iti set,titm (a). t~~rnparrtl to tiisat~tol~hili~~ of l~ictyostrlicrru discoid~um. thfa E. voli pc)lyf)v~)titlt~ taontains an ilrsrrtioli of’4 addititmal arniiio xt,itls afttsr t Iit> irlitial nit&i hionilrc~. Thrs str1rc.t IIW (.al~~ulatiorr> NC’V’ ~~arric~l out fiH thv amino ataitl st’tji~t~~i(‘(’ of his;it~tol~lrilir~ fr~om /Jicfyo.st~,/ium di.scGdetrm as thrrta \vt-rt’ no trivi;tl SOE twnnrctivitif3 ;rssignal)lr to theatldition;LI amil10 irc,itl fragment

3. Results

Three sets of structures were ~alt*ulatc:cl for (MTI-I. In the first, set, the stereospecific* assignments of the prochiral tsentres obtain4 in the previous study (Holak rt al.. 1989~) and from the E.COSY spectrum were retained in the c~alculations. Fourteen x1 angle constraint,s with t,hr bounds + 30” were used in these calrulations. The second stlt was obtained using the floating chirality method in the simulated annealing stag distance (*onstrain&, was 0+49 for t)hese 229 distance caonst raint,s. Again. out of 336

Table 3 il~raye

deviations

from idea&y

Structure (‘ombinedt :%I)-Intensitv$ Hisactophilin t (‘alculatrd with a wmbination of intensity rwnstraints and distanw constraints. 2.L9 distance constraints were derived from crosspeaks with the 2 E’ frrquencies rqual. $ (‘alculated with intensity constraints derived from 31) NOI%NOI? SJWtrUtn only.

30 NOE-NOE

n.m.r.

A’pectra

for

Proteins

165

in Solution

Table 4 =ftowLic r.m.s. differences

(8)

between structures of CMTI-I and 3D n.m.r. data Hravy

backbone atoms

determined

with

2D

All heavy atoms

3 I) distancet NY-sus 3D distance 31) intensityf ~crsus 31) intensity (‘ombined§ versus combined 3D distance WGSUS2Dll (‘ombined UCTSUS 2D 21) twst~s rrfinedf 3D distance WTSUSrefined 31) intensity ZWSU,Srefined (‘om bined ~rsus refined 21) I’cIs1L8X-ray 31) distance I’prs?LsS-ray 31) intensity IW~~.E X-rag (‘ombined versus Y-ray Refined WTSUSX-ray 31) int,ensit,y W~SUScombined 3 1) distance PPISW c*ombined Ail r.m.s.d.s determined for residues 3 to 29. t Strncturrs calculated with distance constraints derived from 31) NOE-NOE sprcstrum. : (‘alc*ulated with intensity constraints derived from 31) NOE-~NOE spectrum only. $ (‘alrulated with intensity constraints and distance constraints of peaks wit,h 2 freyurn~+s ~lrriv~~d from 31) NOE-SOE spectrum. Ij (‘alculat.ed with distance constraints of a 2D NOISY spectrum (H&k rt nl.. IWOn) c Rrtined with t,he frill relaxation matrix approach (Silgps of ctl.. lO!#l).

intensity constraints. the ten st’ructures had no intensity violations that corresponded to a distance violation larger than 0.5 A for the t,wo distances defined by the 31) NOE-NOE intensity. The reproduction of the disulphide bridges was similar to the calculations with intensity constraint,s only. The deviations from idealized covalent bond geometry was also almost the sa,me. The average r.m.s. difference among the structures itself was 0.52 A f @I 4 a for the backbone atoms and 1.22 A&-019 A for all heavy at)oms. (d) Strwturr

CJ~

distance

hisactophilin from a combination and i,ntensity constraints

of

Ten structures were calculated for hisactophilin. as described in se&ion (g) above. The floating chira-

rqual

lity method was used to obtain stereospecific assignments at prochiral centres in an identical manner as for CMTI-I. X11 ten structures satisfied the experiwere no distance constraints. There mental constraint violations greater than 05 A. The r.m.s. differences from the experimental constraints, which were calculated with respect to the upper and lower limits of the distance constraints, was 0.12 8. The structures, shown in Figures 7 and 8, also exhibited very small deviations from idealized covalent geometry (bonds, angles and impropers, standard deviations), and had very good non-bonded caontacts having negative Lennard-Jones-van der Waals’ energies. The average of the r.m.s. differences among the 3D NOE-XOE structures was 2.48 A iO36 A for t,he backbone atoms and 3.57 A+@63 A for all heavy atoms. The corre-

Figure 7. Stereoview of the backbone atoms (N. CCL C) of the 10 hisactophilin structures best-fitted to all amino acids with the rxcrption of residues 25 to 33, 47 to 49, 55 to 60, 65 to 74 and I1 7 to 118. The amino acid polypept,ide of hisartophilin of Dictyostelium diacoideum was used in the calculations (see Material and Methods. srction (a)).

Figure 8. Stereoview of thr ~(*Il-d&iwd parts of thr structure. t,he nholr hackbonr is shown. and for t,lre othrr t~xw~)tion of residues 25 to 33. 17 to 441.55 to 60. 65 to 74 least-squares fit of the parts of thra I)wkbonr atoms shown r.m.s.d.s werr sponding 2.52 -4 f 0.35 A, respectively, segments of a high variability iMtd 8: see also discussion).

143 A * 024 A and when residues in the were excaluded (Figs 7

4. Discussion (a) Structures

from

SD LVOE-NOE constmints only

usiny

distant

The information in the 31) NO%NC)E experiment is overdetermined: many connectivities are observed at different NH planes, as illustrated for the connectivity 22CaHP28C”H. The assignments are therefore more reliable, in particular for the long-range connectivities between the side-chains of different residues. Around 200 such long-range NOI& could be obt,ained from the 3D SOE-NON spectrum. Such connectivities can also be obtained from 2D spectra of a sample of protein dissolved in *H,O; they are. however, more dificult t’o assign unambigously for cases in which only a single COW nrctivity between protons distant in the primar) sequence is observed. Such was the case for the caonta& between Tyr27 and Leu23. The conneetivit? was observed in t,he Xl) NOES\’ specs27&236,,, trum. but not used previously because of assignments ambiguity arising from partial overlap with the methyls of Leu7. This connectivity was resolved in t,he 31) spectrum; further 27-23 contacts were observed; i.e. 23y-27~ gave three cross-peaks through different connectivities in the plane of 27~. The new distance constraints between 27 and 23 rrsult,ed in their side-chains coming closer together in the 31) NOti-NOT? structure than those based on the 21) NOE8Y spectra (Fig. 4). Apart from this difference. the structures are very similar (Fig. 4). More important new cross-peaks, not observed in the 2J> NOESY due to overlap, involved weak &-6X and 4/?,,,- BN. The contacts are critical in resolving ambiguity in the conformation of the protease binding loop seen previously (Holak et al.. 19891’,). In conclusion. the 3D data set allowed

Lwkbonr atoms of the IO hiwc+ophilin structrtrcss. Icor I structures. the I)ac*kl)onr atonrs of all atnino ac,itls with thr and I I5 to I IX arcs shot5 n. l’ht~ suprr~)osition \VNSdone hy 8 for ail strucat urw. better detinition of’ the st ructurw than ~vas previously possible in the 21) spectra. The 21) n.rt1.r. struct,ures were based already on a vt’rv Iargc number of distance const*raints. totalling 3:L4. The 31) NOEm-XOE experiment provided ,541 tiistancsr csonstraints. In the third set of strnc~tnrw. thrl disulphidc bridges were not defined either as bonds or as distance (aonstraints. These structures wcw almost identical to those calculated with the disulphide bonds specified. Qualit~ativr analysis of the NOESY spectra can usually provide the information needed to establish the presence of disulphide bridges (LVilliamson et al.. 1985; Kline Pt (cl.. 198X). The C?H-(‘OH NO& bet.wren two eysteines usually indicates that, the eysteines pa’ticipate in the disulphide bridge. In (MTT-1. the three disulphidr bridges, whose positions are known from the X-ra) st,ructure. are very close to one another. and it is possible to intjerc~hanpr them without any drastic changes in the secondary and tertiary structure. There are also several (‘“ll--(!aH NO& prwc’nt in the NOR spectra between cysteines, which arc trot involved in the disulphide bridge. For exampIt>, tht connec+vity between 1S/I and 20/I would suggest an incorrect pairing of the c~~steines. Howww. t hr S-~-S pairing csould be determined unambiguously from structures. The S-S distanc*t~ is the n.rr1.r. 2.0 &2.2 ‘4 in t,he disulphide bridge, which \vils the distance observed for the correct S -8 pairing of cystpines. In all other arrangement,s. the tlistance bet’ween sulphur atoms was greater than 5.5 :I. wit)h the exception of the pairing 10-28. for \vhic*h the distance is 3% A. In the 211 NOESI stru(+urt’s. tht, conformat,ion of the disulphide bridge IO-~%2 \vas uniquely defined; the two other disulphide bridges showed the presence of mirror images at the ;q-sulphur atoms (Holak et al.. 1989n). The present stru(.tures exhibit unique c,onformat,iotis for all t hrb disulphide bridges. The ability to obtain structures with the uniquely determined c,onformat,ions of the disulphide bridges could be traced to the presence of new NOES in the 3D spectrum involving cyst,eines.

3D NOE-NOE

n.m.r.

Spectra for Proteins

The quality of the present structures is such that a detailed comparison with the X-ray structure of the inhibitor in the trypsin complex is possible (Bode et al., 1989; Holak et aE.. 1989b). The n.m.r. and X-ray st,ructures are almost identical in terms of the global fold and secondary structure (Fig. 4). There are. however, a few small but distinct differences between the n.m.r. structures and the X-ray st,ructure at residues 17 and 24 to 27. The n.m.r. structures at these regions are more expanded than the X-ray structure; this expansion is not an artifact of the n.m.r. data. For example, the interproton distances 17fl,-46, and 4fl,-17p,,2 are 2.2 a and 3.0 .A in the X-ray structure. respectively. No corresponding NO Es were seen in the 3D SOE-NOE spectrum. As (‘MTT-I has three disulphide bridges, which fix the whole structure, the protein is very rigid. A large reduction of ?;OE intensities because of int’ernal movements is not probable for the p a,toms of the residue close to one of t,he disulphide bridges. There is also no evidence for any multiplicity in the conformation of R-04. Therefore in t’he n.rn.r. stru&ures these distances have to be longer than 3.5 ;I, a rather conservative lower estimate that would take into account increased flexibility of the segment (l’epermans et al., 1988). Some ot,her minor differences could be positively ident’ified between t,he two structures. A very close contact between 127, and 12N of 1.8 &A, as seen in the X-ray structure. should give rise to a strong SOE: in the 31) 90%NOE spectrum. However: this contact is weak in t)he spectrum. and consequently a longrr distanc*e is seen in t,he n.m.r. structures (Fig. 1). The difference between the n.m.r. struttures and the S-ray structure at residues 24 to 27 was noticed previously and was ascribed to the effect of crystal packing and interaction with the protease in the crystal structure (Holak et al.. 1989h). These examples show that. with the present structures. it is possible to make even small differentiations among the structures that are fully suppor?eti by the experiment,al data. (b) ~Strwtuws from thu 3D XOE-NOE inhsity umstraints or a combir~ation of the intensity and distancf, constraints

The csonclusions drawn in the previous section also hold for the structures calculated from the intensity constraints. The quality. in terms of geometry and agreement wit’h the KOE data, of the structures of (IMTI-I calculated with t)he int’ensity constraints was slightly. but noticeably. bett)er t’han t,ha.t of the structures calculated in the presence of distance constraints (Tables 3 and 4; Figs 4, 5 and 6). We have chosen t)hc structure of CMTI-T. which was refined with the relaxation matrix approach for a reference model that is the closest to the global minimum structure. For dist,ance constraints, the procedure of extracting the distances from the 31) NO&NOE cross-peaks is relatively time-consuming. as it requires a knowledge of one distance in each 3D

in Solution

167

cross-peak in order to extract the second distance. This stage is absent when working with the intensity const,raints. After an initial calibration of a few w’rsus the known distance constraints intensities (eqn (4)), the determination of the two distances in the 371 XOE--NOE peak is left t’o the caalculation itself. Within the int,ensity method. the error bounds of the distance constraints involved in the intensity constraints plays a smaller role in the final r.rn.s.d.s of the st,ructures t’han is the case when using dist,ance constraint’s directly during t.he calculat,ions. This is desirable, as t’he error bounds to the distance constraints are currently chosrn on the ba,sis of a rather subjective criteria. Another important advantage of the inbensity constraints is that the procedure is easily amenable to cbomput’er aut’omation, such as peak picking and sirnulation of the spectra. Tn fact. the cbalculation yields not only the structures, but also a simulated spectrum that) ca,n be directly compared with the experimental one (Fig. l(b)). Structures cualculated from a combination of the intensity constraints and the distance constraints (derived from peaks with 2 equal frequencies) exhibited energy and geometrical parameters t,hat were even closer t,o those of the reference CMTT-I structure. This is not surprising, as the quality of t.hr st#ru(stures increases with the increase of the number in non-trivial ronst8raints (Wiithrich. 1986). The calculation of the struct’ure of hisa.ctophilin off’rrs a practical example of an applicaation of the 311 SOE-NOE data t’o the det,erminat,ion of structures of larger proteins. Hisactophilin. an unique actin-binding prot,ein from I)ict!lostr/iurn discoiwhich dwm. is a submembraneous pH sensor. induces actin to polymerize at pH values below 7. and thus is a putative component of the signal transduction chain (Scheel et 01.. 1989). The protein has a molecaular weight of 13.5 kI)a. and its most characteristic feature-is the presence of 31 histidine residues out of 118 amino acids. Taking into ac*caount that histidine is t,he only amino acid with a pK, value close to physiological pH. the data indicate that the molecule senses the H+ c*oncentratJion 1.i~ the histidine residues and is active in its cationic form. A structural model was not previously available for the prot)ein. A superposition of the ten structures of hisactophilin is shown in Figures 7 and 8. A characteristic feature of the structures is the presence of 12 j-strands and no a-helix. The overall struct*ure can be best described as forming two four-St randed antiparallel fl-sheets and one six-stranded antiparallel ,&sheet. Figure 9 shows plots of the at)omic r.m.s. distributions for the structures. The backbone of hisactophilin within the 12 b&rands is very well determined. The t)urns and loops show greater variability. with the loop between residues 2.5 and 33 having the highest variability. Most, residues in this segment showed no KOEs in the ?\‘OE spectra. It is interesting to note that all glycines and histidines, with the exception of His3.5, His75 and His78. are lo&ed in the loops or turns whose atomic r.m.s.

Figure 9. Average pairwisc atomir r.m.s. differences among the hisactophilin structures. l represents t,hr residues that are involved in /?-sheet’s; 0 represents residues of turns and loops; 1 shows the standard deviations. The superposition of t,he strurturrs wsasas in Pip. 8.

dif&rences for the backbone atoms are larger than 2.0 A (Fig. 9). Further details of the structure of hisactophilin, as well as t’he description of t,he assignments and secondary structure elements. will be presented elsewhere. Tt is clear from the presented data. however, that well-determined structures of large proteins can be obtained from the 31) NOE-NOE data even without the availability of the dihedral angle constraints. Since submission of our manuscrpt, a communcat,ion has appeared that describes a very similar approach to that of ours of a direct use of t,he 31) SO&NOE int’ensities for the structure calculations (Ronvin rt al.. 1991). The procedure described in this communication was tested on simulated n.m.r. data for an a-helix of eight residues. (c) Conclusions

We have shown that a 3D NOCKOE experiment on a protein in water provides sufficient input’ data to calculate structures that could be deemed to correspond to high resolution st’ru&ures as defined in X-ray crystallography. A large number of NOES can he extracted from the homonuclear 31) sprctrum, together with NOES that are difficult’ t)o extract from 21) R’OESY spectra. This is especially t,rue for connectivities between the side-chain Jjrotons of different residues. For the 2D spectrum, t,he aliphatic region of the NOESY spectrum is used t,o extract such connectivities; due to experimental limitations (Wiithrich, 1986), this requires a spertrum of protein dissolved in 2H20. In the 311 NO%

X’OE spectrum in H,O. t.hc SOEs between thta aliphatic J)rotons can be observed at, unique ;IrrlitI(b J>rot,on frequ(~ncir~s;. The oJ)timurn approach for reJjroduc:ing t,he strrrc*~ tural cbontent of the 31) NO&SOE cross-J)eak is t hta usage of the PI) pseudoenergy potential of rqn (9). which represents the intensity of the cross-peak. The difference bet,ween the caJculat,ed and obsrrvetl 31) NOE-SOE: intensitv is t,hrn used directly as a driving fi)rc:r on co-ordinates of it Jjrotcill in thtb structure c~alcutation. The direct use of thch NOB intensities avoids the t ransformat.ion of SOE intensities into dist)ances. whic*h is i ime-c~otrsurrli11~ and introduces targer errors in thca distancatl caom&aints. because of t.he inclusion of an additional step that involves scaling thr data. As 1he drtermination of t,he two distances involved in thch 31) NOE-SOF: ?ross-J)eak is left to the caalculat ion itself, the error bounds to the tlist,ancet caonsi)raints involved in the intensity const,raint,s J)lag a smntlcr role in the final r.m.s.d.s of‘ the structures than is I hfa case when using distance (Lonstraints direcat Jy during the calculations. \Vr thank Redmond Bernstein for his contribution to thr softwarcl drvrlopmrnt,. This work was supported by A researrh grant from the J~undrsministeri~lrll fiir Forschung und Tecxhnologir ((irant, no. OSIH!)O9A) and from t,hr I)eutsch Forsc~hurlgsKemeinsc~haft ( f’rojrcts Ho-l Z69jl 1. Shl-dO4/%4 and SFR dO7). .J.O. has trcscstla recipient of a fellowship from the, Humboldt Foundation

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n.m.r.

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Edited b?J P. JC. Wrighf