Comparison of the NMR solution structures of cyclosporin A determined by different techniques

.IOURRAI.

OF MAGNETIC

RESONANCE

92, 468-479

( 1991 )

Comparison of the NMR Solution Structures of Cyclosporin A Determined by Different Techniques RUTH PACHTER, Russ B.ALTMAN, Star$~rd

Magntctic

Resonance

Received

JERZYCZAPLICKI,PANDOLEGJARDETZKY*

Lahorutory.

Stunfi,rd

University.

April

23, 1990; revised

October

Smfi,rd.

(hlifi,rnia

04305-5055

25, 1990

An evaluation and comparison of the NMR solution structures of cyclosporin A are presented in this study. A new structure has been calculated by the probability filtered estimate (PROFILE) technique using new NMR data, in addition to the previously reported data. The mean structure, along with explicit estimates of uncertainty in the position of each atom, satisfies the NMR constraints but does not imply a unique structure. A comparison of this structural calculation with models obtained with other computational methods shows large variations in the Ramachandran angles ( C#J.#). These differences are explained on the basis of both the calculated uncertainty in backbone atomic coordinates and the cooperative motion of the backbone dihedral angles. Q 1991 Academic PW. IX

The potent immunosuppressive drug cyclosporin A (GA) is a cyclic undecapeptide which consists of the following sequence of amino acids: cyclo( -MeBmt i-L-AbuSar-L-MeLeu-L-Val-L-MeLeu-L-Ala-D-Ala-L-MeLeu-L-MeVal ’ ‘- ). ’ Its crystal structure is known ( l), and in addition, a structural model has been obtained on the basis of the NMR data ( 1, 2). Although the structures derived from X-ray and NMR analyses were found to be similar (I ), differences were observed for the side-chain conformations of MeBmt ’ and MeLeu lo. Specifically, the X, for the X-ray structure was found to be -168” for MeBmt’, while the NMR value is 60”. and the X1 (Xray) for MeLeu ‘” was - 165”, while the x1 (NMR) is -60”. Also, an additional hydrogen bond { N8-He . -08 } within D-Ala8 was postulated on the basis of the NMR experiments ( I ) . Further structural determinations have been carried out with molecular dynamics ( MD) simulations (3), distance geometry DISMAN calculations (4), and molecular mechanics (5) using either the X-ray or the NMR data. The solution structure of CsA has also been solved by applying a systematic conformational search method (6), in which a rigid model of the molecule is built from fragments having reasonable geometries. NMR distance constraints are then used to constrain the search, and angles 4, II/ are incrementally rotated within a range of plausible values to find the set of possible conformations. Recently, the PROFILE (probability.filtered estimate) methodology was introduced by Altman and Jardetzky ( 7) for protein solution structure determination. This method * .To whom correspondence should be addressed. t Permanent address: Institute of Molecular Physics, Polish Academy of Sciences, Poznan. Poland. ’ Where Abu. MeBmt, and Sar represent n-aminobutyric acid, (4R)-4-[ (E)-2-butenyll-4,N-dimethylL-threonine, and N-methylglycine, respectively. 0022-2364/Y

I $3.00

468

STRUCTURE

OF CYCLOSPORIN

A

469

uses principles of Bayesian probability to sequentially refine estimates of the mean position and the variance of each atom, thus providing a set of atomic positions consistent with the applied constraints, as well as an explicit quantification of the uncertainty in atomic position for each segment of the protein. The technique was shown to perform well in deriving a structure from NMR data (8). Moreover. in contrast to DISMAN (4), our program uses both distance and dihedral angle input constraints directly and is therefore suitable also for an application to a cyclic peptide consisting of nonstandard amino acids such as the CsA molecule. In the present study PROFILE has been applied to an investigation of the solution structure of cyclosporin A using the original NMR data (I) and a more extensive set of nuclear Overhauser effect constraints obtained experimentally in this laboratory. The results are compared to structural models obtained with other methods. METHOD

Molecular modeling theory. In the PROFILE program, the structural molecular model of a protein consisting of N atoms is described by a list of the mean positions (the so-called state vector x) and the covariance matrix C(x). In general, C(x) contains the linear dependence of atomic coordinates on one another based on the known constraints. The elements of C for any two atoms M, N are symmetric submatrices C,, which describe the relationship between the positions of atoms M and N. The diagonal of the covariance matrix [C,,] describes the extent of three-dimensional uncertainty ( a$, uf , a:, in addition to off-diagonal terms) in the position of an atom M. Experimental distance and dihedral angle measurements z are represented by nonlinear functions of the state vector h(x) and an assumed additive variance v (a function of the experiment which produces the data). Given this information, a sequential linear estimator for the minimum variance estimate of the state is obtained using the extended Kalman filter for nonlinear measurement functions ( 9). x(+)

= x(-)

+ K{z

- h(x(-))}

and

C(+)

= C(-)

- KHC(-),

[l]

where ( -) signifies a previous structural representation, which is sequentially updated (+). The criterion for the choice of the Kalman estimator gain matrix K of a weighted scalar sum of the = C(-)HT(HC(-)HT + v}- ’ is the minimization diagonal elements of the error covariance matrix C. The term within the inverse in the expression for K represents the variance of the observed measurement (C( z ) = C( h(x)) + v). The first-order Taylor approximation of C(h(x)) is HCHT, where H is the derivative of the data model, h, and HT is the transpose of H. The extended Kalman filter approach is used to obtain higher-order nonlinear filters. e.g.. by an iterative procedure,

x(+11,= x(-J + Kli{z - [h(x(+)k-1) + H(x(-) - x(+)x-1)1)

121

with a similar expression for C( +)k for any iteration k. This iterative procedure is carried out for each of the distance and dihedral angle constraints. However, since the filter is not optimal in the nonlinear case, residual inaccuracies may still result. Therefore, the mean positions obtained after all data are introduced are used for another cycle (I) of updating. The covariance matrix is reset to its initial large value in order to allow the atoms freedom to move in response to the constraints, and all measure-

470

PACHTER

ET

TABLE NOE No. I 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

Values

Residue

Group

I. MeBmt

N-CH, N

2. Abu

3. Sar

4. MeLeu

AL.

I

in Cyclosporin

A NOE

with

2w. 7w, 16~. 55w, 56~. 58w*. 60~. 61w Iw, 3m*, 5~. 7m, low, Ilm. 12m, 31~. 35w, 37w, 58w* 2m*, 7w. 8w. IOs*. I Iw. 38~ 5m*, 7w*, 8s*, 9s*, I Iw. l2w* 2w, 4m*, 7m*, 8m*, 9m*. 57w* 8m*, 9m*, 20m*, 35w* lw, 2m. 3w. 4w*, 5m*. SW. 3 I w 3w, 4s*, 5m*, 6m*. 7w 4s*, 5m*, 6m* 2w, 3s*, llw, l2w*, 18m*. 27m* 2m, 3w. 4w, low, 12w*, 6lw 2m. 4w*. low*. 1 lw*. 14m. l5m 12m. 16~ l2m, 16~. 31~ Iw, l4w, 15~. 17s*, l8m 16s* lOm*, 16m, 2lw, 25w, 27w, 28w, 6Ow 2Os*, 21s*, 23m, 25w, 27w* 6m*, 19s*, 2lw*, 23w*. 30~ 18w, 19s*. 2ow* 19m, 2Ow*

5. Val

6. MeLeu

7. Ala

8. D-Ala

9. MeLeu

18~. 19~. 26w*, 27w, 28m 25w*. 27~. 28~. 29w*, 3Ow* lOm*, 18~. 19w*. 25~. 26~. 28w*. 29w* 18~. 25m, 26~. 27w* 26w*, 27w*. 3Ow 2Ow, 26w*, 29~. 52w, 58~ 2w. 7w, 15w, 33m*, 34w*. 36w, 37m. 52m* 33m*, 34w*, 35w 3lm*, 32m* 3lw*, 32w*. 35w*, 36w*. 4Ow 2w, 6w*, 32~. 34w*, 4Ow 31w, 34w*. 37w 2w, 31m. 36~. 38w*, 39w*, 57w 3w, 37w*, 39m*. 4Ow 37w*, 38m* 34w, 35~. 38~. 4lw*, 42w*. 57~ 4Ow*, 42m*. 43m, 57w 4Ow*, 41m* 41m, 45w, 46~. 52w, 59w 45s*, 46m*, 47w*, 49w, 51m. 54w, 55w 43w, 44s*, 46m*, 47m*, 51m, 57w 43w, 44m*, 45m* 44w*. 45m*, 57w 52w 44w

STRUCTURE

OF CYCLOSPORIN

471

A

TABLE l-Continued No.

Residue

Group

NOE with

10. MeLeu

N-CH,

51m 44m. 45m, 50m, 52m*, 53m*. 54~ 3Ow, 31m*, 43~. 48w, 51m*, 53m*. 57m 5 lm*, 52m* 44~. 51w, 55w*. 56w* 1w, 44w. 54w* lw, 54w* 5w*, 37w, 40~. 41~. 45~. 47w, 52m. 58w. 59~. 61m lw*, 2w*. 30~. 57~. 59w*. 6Ow*. 61m 43~. 57~. 58w*. 6Ow*, 6 1m* lw, 18~. 58w*. 59w* lw, 1lw. 57m. 58m, 59m*

i(l) P (2)

1 1. MeVal

6 (1) 6 (2) N-CH3

58

59 60 61

; Y (1) Y (2)

JV?)fe.The NOE values from the spectrum with 300 ms mixing time are shown. Those NOES that appear in the 50 ms spectrum are denoted with an asterisk. The letters s. m, w qualify a given peak as strong, medium, or weak, correspondingly. For easy reference, the NOES between each proton pair are given for both of the protons involved.

merits are reintroduced into the system for each of these doubly iterated cycles. The successive I cycles are repeated until all of the constraints are satisfied to within a preset threshold of standard deviations. Computational details. The consecutive numbering of the backbone constituents in CsA follows the sequence [N&H; (or CH3 pseudoatom;) 2)~C,J( H,,rl)(C,i2)C,&-OJ] , for each of the 11 amino acids i, so that all N-H and Q-H hydrogen atoms are explicitly used. A pseudoatom representation was used, however, for the N-methyl backbone groups, as well as for all side-chain -CH3, -CH2, -CH, and -OH groups, and their numbering is sequential from residues 1 to 11. A total of 60 atoms and 4 1 pseudoatoms which constitute CsA were assigned initial random mean coordinates with a variance of 49 A2. These coordinates were subsequently refined by PROFILE using all of the available NMR experimental distance and dihedral angle data, as well as the chemical covalent distance information. “ Experimental NMR information ” consists of 52 ( or 93 ) distance and 55 dihedral angle constraints derived from Ref. ( 1 ), as follows. (i) 47 NOE effects (Fig. 6 in Ref. ( I )) with the appropriate corrections made for pseudoatoms: NOE effects larger than 5% were assigned a somewhat shorter mean distance. An additional 4 1 NOE constraints were derived from the data in Table 1. The calculations were performed both with the full set of 88 NOE distances (a) and with the original experimental data ( 1) only (b) . The use of pseudoatoms renders it necessary to apply a larger variance to the NOE distances ( 1.1 A’ ) ( 10). (ii) Trans isomerism about all amide bonds (w = 180” ) excluding the cis peptide bond (w = 0”) about MeLeu lo and MeLeu ” : The o angles were assigned a variance of 25’ * . (iii) { N-H * . -0 1 hydrogen bonds ( =2.9 A, variance = 0.5 A2) involving the following atoms: 8-35: 13-30; 43-77; 42-50; 50-56. (iv) Side-chain conformations: MeBmt’: XI = 60”, x2 = 60”, X3 = 180”, X4 = 240”, X5 = 180”; Abu*: X, = 180”; MeLeu4: X1 = -6O”, X2 = 180”, X3 = -60”: ValS: Xl

472

PACHTER

ET

TABLE Dihedral

Angles

Residue I

b

1

2 3 4 5a 5b

6 3

1 2 3 4 5a 5b

6 4

1

2 3 4 5a 5b

6 5

1 2 3 4 Sa 5b

6 6

I 2 3 4 5a Sb

6

Bonds

in GA”

(degrees)

dJ

X-ray structure MD of X-ray structure NMR model MD of NMR model PROFILE a

6 Conformational 2

angles

Structure 1 2 3 4 5

2

and Hydrogen

a. Backbone

AL.

search

-86 -91 -84 -100 -105 -128 -89

[-SO

-121 -108 -121 -85 -19 -119 ~ 135 [-90

ic

to -1301b

123 105 122 95 159 154 135 [IO0

to -150p

90 100 92 97 93 87 105 [IO0

72 59 70 57 81 71 60’

w 175 -~I78 176 178 178 179

to 1601” 176 180 -. 178 159 179 180 to 1 lo]*

-127 -117 -127 -116 -121 -146 -140’

173 171 173 169 -178 -173

-100 -107 -101 -113 -63 -56 -90’

21 31 23 33 .- 7 14 20 [- 10 to 401*

180 -179 179 176 176 167

-112 -119 -115 -89 -135 -119 -85

166 163 166 180 178 175

to -LOO]*

126 121 130 120 105 131 149 [90 to 1801h

-164 174 -165 -179 -178 m-169

to -150]*

101 108 89 96 110 97 92 [30 to 1801h

-89 -86 -94 -90 -96 -137 -121

[-70

[-80

STRUCTURE

OF TABLE

a. Backbone Residue 7

I 2 3 4

-83 -91 -95 -90 -91 -93 -89

5a 5b 6 I

2 3 4 5a 5b 6 1

2 3 4 Sa Sb 6 II

5a 5b 6

1

1

2 3 4 Sa 5b

ti

il 51 61 53 66 55 51 45 [40 to 701 h

to ~901~

to 170]b

-176 -117 -157 -118 I65 -177 ~162 [-I50

to -1801h

101 121 98 II3 70 X0 104 [loo

-139 -119 -154 -121 -133 -144 -133

to ~1401~

h3 94 6, 100 40 58 I I3 [50 to 150)~

to ~ 1501*

126 II6 125 103 123 I15 IO3 [40 to 190]h

b. Side-chain Structure

(degrees)

-117 -121 --IO2 --I32 --95 -101 -126 [---90 to -170]h

[--80

m-101 -129 -103 m-123 ~136 -104 -109 [-80

I

2 3 4

Residue

[-80

88 70 144 80 151 151 158 [I50

I

2 3 4

10

angles 9

5b 6

9

473

A

2-Continued

Structure

5a

8

CYCLOSPORIN

angles

to I lO]b

(degrees)

Xl

X2

xi

~168 -172 hOd -67 86 76

77 x9 60 I63 87 60

178 I56 180 -I I9 I71 I75

X4 I28 15 120 175 --II6 -I I5

17X

17’) ! x0 ! 80 I74 179

474

PACHTER TABLE

Residue 2

Structure 1

2 3 4 5a 5b

1 2 3 4 5a 5b 1

2 3 4 Sa 5b

6

1

2 3 4 5a 5b

9

1 2 3 4

X3

-178 -

-51 -134 -60 -80 ~61 ~46

--I78 -150 180 125 174 179 -52 -95 ~60 -79 -62 -79 -174 180 176 174 -178 ~163 180 -173 -178 -175

180 -179 -165 -51 -51 -60 -63 ~60 -47 -178 -128 180 -133 180 159

5b

-165 -169 -60d -118 -48 -59

-167 -152 180 -80 175 -170

1

-178

-51 ~62 -60 -67 -72 ~60

1

2 3 4 5a

II

x2

180 -

5b

2 3 4 5a 5h

AL.

I-Continued

-58 -94 -60 ~72 ~63 -64

5a

10

Xl

ET

180 167 163

172

177 157

58 60 60 37 -59 -100 -60 -96 ~62 ~61 73 60 64 54

X4

ys

STRUCTURE

OF

TABLE

1 2 4 5a’ 5b’

N2H.. 2.84 2.95 3.10 2.81 2.99

.05

N5H.. 3.02 2.89 3.00 2.91 2.88

.02

475

A

2--Continued

c. Hydrogen-bond Structure

CYCLOSPORIN

distance N,H..

(A) .O,,

2.98 2.96 3.06 3.24 3.15

NsH.. 2.90 3.01 3.01 2.95 2.91

.06

NBH.

. .OR

2.67 2.57 2.92

a Note that the angles for structures 1 and 3 were taken from Ref. (I), whereas the corresponding angles given in Ref. (3) were taken from the coordinates of the crystal and NMR mode1 built structures. * The dihedral angle range in brackets contains those found in the conformational search (6). ‘These dihedral angles were not rotated in the conformational search (6). d The angle predicted on the basis of NMR data is different from that in the crystal structure. ’ These are the mean PROFILE positions: in all cases the differences with other structures are within the final standard deviation of the calculated distance.

= 180”, xZ = -60”; MeLeu6: X, = 180”, x2 = 180”, x3 = 60”; MeLeu’: X, = -60”. x2 = 180”, x3 = 60”: MeLeu”: X, = -60”; x2 = 180”; x3 = 60”; MeVal”: X, = 180”, x2 = -60”. (v) NOE effects and vicinal NH-C,(H) coupling constants supporting a set of (4, $) angles given in ( 1 ), which we used as a starting point to be consistent with the (4, 1c/)range of a 0 sheet, but with a large variance (625” 2). “Covalent chemical distance information” of bond lengths and all possible distances implied by bond angles was used, i.e., a total of 262 distance constraints, with a variance of 0.1 A2 assigned to distances in the backbone, and a larger uncertainty (0.5 A”) assumed for pseudoatom distances within side chains. The PROFILE algorithm updates the structural model as shown in Eq. [2] for a maximum of three k iterations for each of the distance or dihedral angle constraints. with a threshold of 0.1 standard deviation for the termination of the iterative procedure. In addition, a van der Waals check is used at the end of each cycle 1. A van der Waals distance constraint is introduced when the system detects two atoms violating the van der Waals distance. At the end of each cycle, all of the constraints are sorted according to the corresponding error evaluated from the updated structure, so that the constraints with the worst errors are applied first in the next cycle. All computations of the doubly iterated Kalman filter procedure were carried out using the vectorized parallelized program PROTEAN-part II ( 11) on a Stardent minisupercomputer. One cycle of a PROFILE calculation for this size problem requires a few CPU minutes of Stardent computer time. NMR spectroscopy. The sample of cyclosporin A used in our NMR studies was obtained as a gift from the Department of Cardiac Surgery of Stanford University. Five milligrams of CsA was dissolved in 0.5 cc of deuterated chloroform (99.8% D). The concentration of CsA in the prepared sample was about 8.3 mA4 and sufficed to obtain a strong NMR signal. All proton spectra were recorded at 300 K on an AM-500 Bruker NMR spectrometer equipped with an Aspect 3000 computer. The parameters for J-resolved spectra were

416

PACHTER

ET AL.

spectral width in F?, 4504.5 Hz. in F,, 39.06 Hz; data size in FZ. 8K, in F,, 128 points: t, increment, 12.8 ms; acquisition time, 909 ms; matrix size for processing in F2, SK, in F, , 1K. For COSY spectra the parameters were spectral width in F2, 4504.5 Hz, in F,, 4504.5 Hz; data size in F2, 2K, in F,, 512 points; acquisition time, 227 ms; t, increment, 111 ys; TPPI phasing scheme during acquisition; matrix size for processing in F,, 4K, in F, , 4K. COSY spectra optimized for long-range couplings were recorded with the delay 200 ms after each 90” pulse. NOESY spectra were recorded for mixing times of 50, 100, and 300 ms, with parameters the same as those for COSY. The parameters that were constant for all spectra were 4 s relaxation delay and 16 scans, preceded by 2 dummy scans. In all cases a sine-bell window was used in both dimensions and spectra were symmetrized. NMR spectra allowed for unambiguous assignment of proton signals to particular residues of the molecule. The three NOESY spectra, recorded with mixing times of 50, 100, and 300 ms, made it possible to distinguish direct NOE peaks from those resulting from spin-diffusion effects. The NOES are summarized in Table 1. There are 74 intra- and 60 inter-NOES in Table 1, and thus the set of NOES reported here is larger than the one reported by Kessler et al. (I) by 43 intra- and 34 inter-NOES. RESULTS

AND DISCUSSION

The PROFILE (double-iterated Kalman filter) methodology was used with distance and dihedral angle information supplied by experimental NMR data to obtain a highresolution structure of the CsA cyclic molecule. A total of 126 and 97 cycles (I) were utilized in the a and b computations of CsA, respectively, thus reducing the initial average and maximum errors of 3 1 and 535 standard deviations (SD) to 0.35 and 2.7 SDS, and 0.25 and 2.6 SDS, with most of the distance constraints reproduced to within less than 1.O SD (the final errors are shown in Figs. la and 1b. Clearly, the structural features with regard to both the backbone and the side chains of the CsA peptide as reproduced by PROFILE are in good agreement with the NMR data.

FIG 1. The final PROFILE errors (in standard deviations) for structures (a) 5a and (b) 5b.

STRUCTURE

OF

CYCLOSPORIN

477

A

Tables 2a and 2b summarize the (4, $, w) and X angles, respectively, for six structural models: 1, X-ray structure (1); 2, MD of X-ray structure (3); 3, model built from NMR data (1); 4, MD of NMR model (3); 5, PROFILE a and b; 6, average angles, as well as the range of angles, from a systematic conformational search (6). Table 2c lists the calculated {N-(H) . - - 0 } hydrogen-bond distances whenever available. The same NMR information (1) was used to generate structures 3, 4, 5b, and 6 of CsA. while additional NOE effects were used to derive Sa. Although relatively large differences exist between dihedral angles $,1c, of all of the NMR-derived structures (3-6 ) . these angles are consistent with the p region in the Ramachandran contour diagram (see Fig. 2 for the three solution structures 3, 4, and 5a). The largest differences ( -40” ) between our 5a and the NMR structure derived by model building (3) occur for the I$ angles of residues Abu2 and MeLeu4 and the $ angle of MeBmt ’ , while variations of >50” between 5a and the molecular dynamics simulated structure (4) are shown for II, of MeBmt i and D-Ala*. Interestingly, large differences are shown also between the NMR-derived molecular model (3) and the MD structure (4) for the DAla’ amino acid (4 angle). However, the PROFILE calculations predict the variance for the N, C,, and C backbone atoms in CsA to be in the range of 0.7- 1.1 A’, which, in turn, may be consistent with such large variations in the angles 9, +. This is the result of the mathematical dependence of a dihedral angle measurement (h(x)) on x which is more sensitive to small variations in x than the distance function. The dihedral angles $,1c/of 5a are mostly consistent with the range of angles given by 6, and deviations from the non-fixed angles range established by the systematic conformational search ( 6 ) are found only for 4 of Val 5 and # of MeLeu’ . The average absolute deviation of the o angle from 180”/0” in the PROFILEgenerated structures ( Aw( a) = 2.1 o and Aw( b) = 4.5’ ) is smaller than that in structures I-4, which compute comparable values of 7.8”, 7.4”, 9.8”, and 7.1”. respectively. In

NMR model(3) MD of (3) PROFILE (54

*e -180 -180

-120

I -60

,

1 0

.

I 60

.

I 120

180

angles

of three

PHI

FIG. 2. Ramachandran molecule.

diagram

for the backbone

dihedral

solution

structures

of the CsA

478

hc;. 3. PROFILE uncertainty at I SD)

PACHTER

(a) stereo of the CsA

ET

view of the mean position molecule derived by NMR

AL.

and data.

(b)

uncertainty

(dran

as ellipsoids

ot

addition, the x side-chain torsional angles of our structure reproduce the experimental NMR input information well. On the other hand, relatively large deviations are found in the MD result, for which the RMS positional fluctuations obtained by averaging were calculated to be as large as 54” (Table 3B in (3)). Differences between the PROFILE-derived { N-H. . -0 } hydrogen-bond distances and those of other structures were all within the initially assigned variance of 0.5 A’. The van der Waals bounds were not relaxed to allow the possibility of hydrogen-bond formation. A comparison of the two 5a and 5b structures generated with PROFILE by using different data sets shows that they are within an average RMS deviation of 1.O A for the N, C,, and C backbone atoms and within 1.5 A when all atoms are included.

STRUCTURE

OF

CYCLOSPORIN

419

A

Note that 15 of the 41 additional NOE constraints are violated in structure 5b by more than 2.0 standard deviations. A stereo view of the refined structure Sa and its uncertainty are depicted in Figs. 3a and 3b. The important conclusion of this analysis is that several methods of NMR data analysis, including a systematic conformational search method, the double-iterated Kalman filter (PROFILE), restrained molecular dynamics, and an iterative relaxation matrix analysis ( 12), lead to very similar structures, which in this case are also consistent with the crystal structure refined by molecular dynamics. The largest variation between different computational methods is seen in the Ramachandran angles 4, $. and the variances for the coordinates of the N, C,, and C backbone atoms calculated by the PROFILE method are consistent with this variation. The analysis makes it evident that more than a single structure is compatible with the NMR data. but that the region of conformational space allowed by the set of experimental constraints is well circumscribed. ACKNOWLEDGMENTS The authors thank Dr. Garland Marshall for providing the results of his systematic mational space of CsA and Dr. Enrico Carrara for technical assistance. We also thank Inc. for use of a Titan RR02300 and R.B.A.

minisupercomputer is supported by NIH

for these calculations. GM0736.5.

This

work

search of the conforStardent Computers

was supported

by NIH

Grant

REFERENCES I.

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AND

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10. K. WOTHRICH. II.

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I?

H. KESSLER.

M. FILLETER, R. PACHTER, personal

If&

c.1101~

I)(wqrr

I. 2 19

68, 661 ( 19X5).

W. F. VAN G~NSTEREN.

6. Ci. R. MARSHALL, personal communication. 7. R. B. ALTMAN AI\;D 0. JARDETZKY. in”Methods in Enzymology” Eds.), Vol. 177, p. 2 18. Academic Press, San Diego, 1989.

‘AND A. WIDMER.

(‘GUI? Ik\ipl

I/L/. .Ilo!.

3, I95 ( IYXY).

(N. J. Oppenheimer

and T. L. James.

AND 0. JARDETZKY. J. :Mu@z. Revon. 89, 578 (1990). Estimation.” MIT Press, Cambridge. Massachusetts. 1984. AND W. BRAUN, J. ,Mol. Bid. 169, 949 ( 1983). E. CARRARA. AND 0. JARDETZKY. QCPE 10(4),

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596 ( 1990).