O n the Dependence of Molecular Conformation on the Type of Solvent Environment: A Molecular Dynamics Study of Cyclosporin A J. LAUTZ,'

*

H. KESSLER:

W. F. van GUNSTEREN,2 H.-P. WEBER? A N D R. M. WENGER3

'Department of Physical Chemistry, University of Groningen, Nijenborgh 16, 9747 AG Groningen, The Nethcrlands, *Technixhe Universitat Munchen, 0rgan:Chem. Institut, Lichtenbergstr. 4, D-8046 Garching, F.R.G., 3 P r ~ liriical c Research, Sandoz Ltd., Basel, Switzerland

SY NOPSlS

The dependence of the conformation of cyclosporin A (CPA), a cyclic undecapeptide with potent immunosuppressive activity, on the type of solvent environment is examined using the computer simulation method of molecular dynamics (MD). Conformational and dynamic properties of CPA in aqueous solution are obtained from MD simulations of a CPA molecule dissolved in a box with water molecules. Corresponding properties of CPA in apolar solution are obtained from MD simulations of CPA in a box with carbontetrachloride. The results of these simulations in H,O and in CC1, are compared to each other and to those of previous simulations of crystalline CPA and of an isolated CPA molecule. The conformation of the backbone of the cyclic polypeptide is basically independent of the type of solvent. In aqueous solution the 8-pleated sheet is slightly weaker and the y-turn is a bit less pronounced than in apolar solution. Side chains may adopt different conformations in different solvents. In apolar solution the hydrophobic side chain of the MeBmt residue is in an extended conformation with its hydroxyl group hydrogen bonded to the backbone carbonyl group. In aqueous solution this hydrophobic side chain folds over the core of the molecule and the mentioned hydrogen bond is broken in favor of hydrogen bonding to water molecules. The conformation obtained from the MD simulation in CCl, nicely agrees with experimental atom-atom distance data as obtained from nmr experiments in chloroform. In aqueous solution the relaxation of atomic motion tends to be slower than in apolar solution.

INTRODUCTION Knowledge of molecular structure gains importance in the process of drug design. One possibility is t o use x-ray diffraction to get a picture of the molecular conformation in the solid state.' With t he introduction of high-field nmr spectrometers and the two-dimensional nmr technique,2,3 it also became possible to obtain structural information about molecular conformation in solution or in the liquid state. This provides the opportunity to study *Present address: BAYER AG Pharma Research PH-FE WII) .*)600Wuppertal 1, F.H.G. ' 1990 John Wiley & Sons, Inc. ( X C 0006-3525/90/12- 131669-19 $04.00 Biopolymers, Vol. 29, 1669-1687 (1990)

by experimental means the confonnational and dynamical behavior of a molecule in dependence of its environment. Further, computer simulation techniques offer the chance to study in detail atomic motions and molecular conformation as a function of the environment. As an example cyclosporin A (CPA), an immunosuppressive drug, consisting of 11 residues forming a cyclic peptide, has been studied. For CPA, the crystalline x-ray structure is known4 and nmr data is available: nuclear Overhauser enhancements (NOES) and J-coupling information, obtained from measurements in apolar solution (CHC1,) and in DMS0.5-7 In the latter solvent, various conformations seem t o be present. Due to the fact th a t CPA is a potent immunosuppressive drug, which has to be transported in vivo through a polar environment (H,O), it is of interest

1670

LAUTZ ET AL.

that may form hydrogen bonds are treated explicitly. The potential energy function describing the interaction between the peptide atoms and solvent molecules is the same as used in previous studiesg-13 and is described in.', I t is composed of terms representing bond stretching, bond-angle bending, harmonic (out-of-plane, out-of-tetrahedral configuration) dihedral bending, sinusoidal dihedral torsion, and van der Waals and electrostatic (coulombic) interactions. During the simulations all bond lengths are kept rigid using the SHAKE method.'"16 The water molecules are modeled by a simple rigid three-point charge model (SPC)." For the apolar solvent we used CC1, (carbontetrachloride) as a solvent. It was treated as an united atom; the chlorine atoms were incorporated into the carbon. I t has no coulombic interactions (charge equals zero) and the parameters for its Lennard-Jones interaction were taken from the literature'' [C,'iz = 75.45 x 10p3(kJ molp' nml')'/' and Cr;", = 0.5155 (kJ molp nm6)'/2]. For the different MD simulations, two initial structures were used: one was the x-ray structure (denoted by XRAY), and the other was the one obtained by a restrained dynamics simulation in vacuo' using the NOEs as distance constraints and is referred to as MDSl further on. The MD simulations in solution were performed in a periodic truncated 0ctahedr0n.l~The application of this type of

to obtain some insight in the conformational properties of CPA in aqueous solution. Here, computer simulation is the method of choice, because CPA is unsoluble in water in amounts necessary for nmr experiments. Moreover, CPA is small enough (90 atoms) to perform different simulations in various environments a t reasonable computing costs. A molecular dynamics simulation (MD) of crystalline CPA (four unit cells) and a simulation in vacuo using distance constraints obtained from NOEs to model the conformation in apolar solution have been described previously.* Here several simulations in H,O and in CC1, starting from different initial structures will be described. The simulations will be analyzed with respect to conformational differences due to the molecular environment (H,O, CCl,, crystal and vacuo). In addition, the time dependence of the motions in CPA will be examined, making use of the trajectories of the different simulations.

'

C O M P U T A T I O N A L PROCEDURE The cyclic undecapeptide cyclosporin A consists of 85 heavy atoms (Figure 1).The hydrogens attached to carbon atoms are incorporated into the latter, forming united atoms, whereas the hydrogen atoms

Me Leu 10 I

J4 L 10 Me Leu 9

L9

I

C%C ,\H3 CH I

CH3 , 7 4 3

y 2 FH3 CH-N-CH-CO-N-

3~

L

co 10 I 9

CH3 \CH-CH~-CH L / cH3

CH3-/4

I D

8

OC-CH-NI

I

A0

HO\CHA CH3

y 3

I

:H3 N-CH-(0-N-CH-CL

FH2 A

L

11

1

2

7

6

5

L Y

CH3 H

Ala

FH CH-CL b

CO- CH-N-COI

CH3

A7 Ala

L CH-N--C I

I

CH2 CH3 tH /\ CH3 CH3

L6

MeLeu 8

Sar

Abu

FH2

OI

L

8

10 I

'1

-CH -N-CO-CH I /CH \

CH3 CH3

y 3 N-CH2

4

I

N-CH3 LI I

L4 *

CH2 tH

/\

CH3 CH3

v

Val

Figure 1. Primary structure of CPA.

Leu 4

DEPENDENCE OF MOLECULAR CONFORMATION

computational box requires less solvent molecules to solvate a (spherical) solute than a cubic box. For the simulation starting from the x-ray structure in water, one CPA molecule (XRAY) was placed in the center of the computational box with the cell dimensions a = b = c = 3.66416 nm. Subsequently, the box was filled with 764 water molecules, using a minimum distance of R i = 0.23 nml2,l3 between any nonhydrogen solute and solvent atom. This simulation will be referred to as XRAYW. The same procedure was used with the MDSl structure, resulting in a box of a = b = c = 3.44972 nm, containing 632 water molecules. The simulation of this system is referred to as MDSlW. When generating the initial configurations in the Lennard-Jones solvent a value of R , = 0.39 nm was used. The x-ray structure was put in a box of size a = b = c = 5.89984 nm filled with 594 CC1, molecules, referred to as XRAYLJ, and the MDSl conformation was put into a box of size a = b = c = 5.90491 nm filled with 591 CC1, molecules, referred to as MDS1LJ. In addition, two more systems were generated that were identical to the ones described previously, except that the mass of CCl, was reduced by a factor of ten. These simulations in a low-mass solvent will be named XRAYLJLM and MDSlLJLM, respectively. The nonbonded interactions should be calculated for all atom pairs separated by more than two covalent bonds. However, to reduce computing costs a pair list cutoff radius Rcut= 0.8 nm for simulations in water and R,,, = 1.3 nm for those in the Lennard-Jones solvent was applied beyond which no nonbonded interactions were calculated. The pair list was updated every tenth MD time step. The cutoff radius R,,, is applied to centers of geometry of neutral atom groups in the peptide and to the oxygens of the water molecules in order to avoid the breaking of the charge neutrality of a group or a water molecule in case an atom-atom cutoff is applied. First all systems were relaxed by performing two cycles of energy minimization (EM).20z21During the first cycle of EM the solute was kept fixed by applying a harmonic position restraining potential, and only the solvent was allowed to move and to adapt to the solute and to the box. In the second cycle the complete system was minimized. After EM the MD simulation was started by taking the initial velocities for the atoms from a Maxwellian distribution a t 300 K. For the simulations in the low-mass Lennard-Jones solvent, the corresponding normal mass-minimized configurations were used as starting configurations for MD. The simu-

1671

lations were all done at constant temperature and pressure, that is, the system was weakly coupled to a thermal bath of To = 300 K and to a pressure bath of Po = 1 atm = 0.06102 kJ mol-l nm-3, when integrating the equations of motion with a time step A t = 2 fs. This was done by applying the algorithm of Ref. 22 with a temperature relaxation time T~ = 0.1 ps (0.01 ps during the first 3 ps of the runs). The values for the isothermal compressibility p were calculated as described in Ref. 13, and (kJ mol-' nm-3)-' we obtained p = 0,7476 x for the simulations in water and = 18.52 X (kJ mol-l nmP3)-' for the simulations in CC1,. In Table I the energies and the volume of the various simulated systems are given. All simulations were performed on a one-pipe Cyber 205 supercomputer. The XRAYW simulation covered a time span of 40 ps, which took about 10 central processing unit (CPU) h. The part between 10 and 40 ps was used for analysis. For the MDSlW simulation a run of 45 ps was performed, taking about 9 h of CPU time. The final 30 ps were used for analysis. The four simulations in Lennard-Jones solvent were performed for 50 ps, using the last 40 ps for analysis. Each of those MD runs took about 2.5 CPU h. The time resolution of the trajectories used for analysis was 0.05 ps.

RESULTS General Comparison (Atomic Positions, Fluctuations)

In Table I1 the differences between the various structures of CPA are given. These are two crystalline ones (experimental XRAY and simulated MDC'), the structure modeled in vacuo using the experimentally (in CHC1,) obtained NOE distance constraints (MDSl), and the different conformations obtained from the simulations in solution (polar and apolar). The conformation in water XRAYW obtained by starting from the experimental x-ray structure shows almost the same deviation of the atomic positions from the initial (XRAY) structure as the simulated crystalline conformation MDC does. The deviations are increasing when changing the solvent into an apolar one. XRAYLJ and XRAYWLM, where the largest deviations are obtained by the simulation in the low-mass Lennard-Jones solvent. A corresponding picture is obtained when starting the simulation from the MDSl structure, the conformation obtained

1672

LAUTZ ET AL.

Table Ia Potential Energy of the XRAYW Simulation: CPA in 764 H,O Starting from the X-Ray Structurea Potential Energy (kJ mol-') Bonded Conformation

Total

Total CPA

Initial EM MD 10 ps 20 ps 30 ps 40 ps

- 24275

845

- 29458

- 226

- 32037

- 458

- 32095

- 459

- 32152

- 512

- 32292

- 416

Nonbonded

Internal

CPA-CPA

206 165

44 - 145

320 310 304 312

CPA-H,O

H,O-H,O

Volume (nm3)

595

- 25120( - 33)

- 246

- 29288( - 38)

24.6 24.6

- 99

- 679

- 31583( - 41)

- 111

- 658

- 31638( - 41)

- 122

- 694

- 31634( - 41)

- 66

- 662

- 31875( - 42)

24.9 24.7 24.6 24.8

Table Ib Potential Energy of the MDSlW Simulation: CPA in 632 H,O Starting from the MDSl Structure Potential Energy (kJ mol-') Bonded Conformation Initial EM MD 10 ps 20 ps 30 ps 40 ps 45 ps

Total 20111 X - 17134

lo4

Nonbonded

Total CPA

Internal

CPA-CPA

10669 - 210

347 226

- 120

497

403 328 319 374 332

- 26647

-

- 26651

- 516

- 26468

- 435

- 26465

- 452

- 26664

- 542

CPA-H,O

- 78

10400 - 316

- 148

- 752

- 85

- 759

- 56

- 698

112 - 109

- 714

-

- 765

H,O-H,O

Volume (nm3)

20110 x 104 27)

- 16926 ( - 26151

( - 41) ( - 42) - 26032 ( 41) 26010 ( - 41) - 26119 ( - 41) - 26326

-

-

20.5 20.5 20.5 20.6 20.6 20.6 20.7

Table Ic Potential Energy of the XRAYLJ Simulation: CPA in 594 CCI, Starting from the X-Ray Structure Potential Energy (kJ mol- I ) Bonded Conformation Initial EM MD 10 ps 20 ps 30 ps 40 ps 50 ps

Total

Total CPA

2637

- 44

- 11776

- 368

- 9029

- 227

-9115 - 8838 - 8941 9080

- 245

-

- 198 - 242 - 198

Nonbonded

Internal

CPA-CPA

206 237

44

- 294

2681

- 113

- 492

- 11410 ( -

- 101

- 433

- 131

- 431

- 117

- 415

- 116

- 426

- 142

- 382

307 317 334 300 326

CPA-CC1,

CCl,-CCl,

Volume (nrn')

19)

102.7 102.7

- 8803 ( - 15) - 8870 ( - 15) - 8640 ( - 15) - 8700 ( - 15) - 8881 ( - 15)

121.6 120.0 122.9 121.3 119.7

1673

I>EPENL)ENCE OF MOI,ECUI,AR CONFORMA'rlOK

Table Id Potential Energy of the M D S l U Simulation: CPA in 591 CC1, Starting from the MDSl Structure ~~~~

Potential Energy (kJ mol- ' ) Bonded Conformation

Total

Initial EM MD

- 9037

- 385

10 ps 20 ps 30 ps 40 ps 50 ps

Total CPA

1247

-3

8896

- 173

- 8867

- 221

- 8777

- 179

- 8790

-

-

-

8818

193 - 169

Internal 347 234 316 368 344 367 379

Nonbonded CPA-CPA

CPA-CC1,

CCl ,-CCl,

- 78

- 272

1250

187

- 432

- 8652

-

- 64

-

178 - 137 146 - 139

425

-

- 411

-

- 414

386 - 409

( - 15)

- 8723 ( -

15) -8646 ( - 15) - 8599 ( - 15) - 8603 ( - 15) ocrn,

in

Volume ( n d ) 102.7 102.7 120.6 121.2 122.6 121.5 1 0 1

A

Table Ie Potential Energy of the XRAYLJLM Simulation: CPA in 594 (Low-Mass) CCl, Starting from the X-Ray Structure Potential Energy (kJ mo1-l) Bonded Conformation MI) 1 0 ps 20 ps 30 ps 40 ps 50 ps

Total

Total CPA

Internal

- 9039

187 99 - 173 - 252 - 159

289 332 276 332 247

9048 - 8674 - 9061 -9131 -

-

-

Nonbonded CPA-CPA

CPA-CC1,

- 67

- 409

- 144

387 - 375 403 331 -

- 74 - 181

-

- 75

-

CCl,-CCl,

Volume (nm3)

- 8852

( - 15) -8810 ( - 15) - 8501 ( - 14) - 8808 ( 15) -8971(-15) -

120.4 121.1 124.1 120.6 119.9

Table If Potential Energy of the MDSlLJLM Simulation: CPA in 591 (Low-Mass) CC1, Starting from the MDSl Structure Potential Energy (kJ mol ') ~

Bonded Conformation

Total

Total CPA

Internal

204 157 - 205 - 233 - 132

306 377 351 320 353

Nonbonded CPA-CPA

CPA-CC1,

CC1,-CC1

Volume ( n d )

MI) 1 0 ps 20 ps 30 ps 40 ps 50 ps

- 8872

--

- 8967

-

- 8879 - 8930 -

8948

- 84 132 - 110 107 - 132

-

- 8668

-

-

426 402 - 446 446 - 403

- 8810 ( - 15)

-

-

- 8674

(

-

15)

( - 15)

- 8698 ( - 15) - 8766

" I n l'ahlrs la-f, t h e numbers in parentheses denote the interaction energy for one solvent molecule.

( - 15)

121.2 119.9 121.3 120.6 120.2

1674

LAUTZ ET AL.

Table I1 Atomic Positional Differences"zhof Various Conformations of CPA All atoms XRAY ( M W MDSl XRAYW XRAYLJ XRAYLJLM MDSlW MDSlLJ MDSlLJLM

C, atoms XRAY (MDC) 0.030 0.060 0.180 0.059 0.096 0.117 0.139 0.195 0.181

0.170 0.036 0.068 0.094 0.127 0.188 0.173

MDSl 0.090 0.090 0.170 0.148 0.142 0.101 0.047 0.041

XRAYW XRAYLJ XRAYLJLM MDSlW MDSlLJ 0.037 0.022 0.083 0.068 0.092 0.119 0.185 0.170

0.049 0.044 0.049 0.040 0.055 0.086 0.160 0.144

0.07 1 0.064 0.056 0.064 0.035 0.073 0.149 0.138

0.090 0.085 0.039 0.079 0.044 0.037 0.116 0.106

0.097 0.095 0.019 0.092 0.058 0.056 0.037

MDSlLJLM 0.089 0.087 0.015 0.083 0.050 0.053 0.036 0.011

0.026

"All differences are given in nanometers. hThe configurations have been translated such that the centers of mass coincide, and in addition, a rotational least-squares fit of the C, atomic positions has been performed.

on the basis of the NMR measurements in apolar (CHC1,) solvent. The structures ( M D S l U and MDSlLJLM) in Lennard-Jones solvent do not deviate much from the initial MDSl structure. However, when changing the solvent into water (MDSlW) the deviation from the MDSl structure increases by more than a factor of 2. The deviation of the atomic positions of the C, atoms from the starting conformation MDSl is still not large (0.039 nm), which indicates that the backbone conformation has not changed much. But including the side-chain atoms one finds a deviation of all atoms of 0.101 nm, which indicates that a drastic change in side-chain conformations must have occurred, especially if one compares the numbers with those obtained from the simulations in Lennard-Jones liquid. Here the deviations from the initial MDSl structure in both simulations MDSlLJ and MDSlLJLM are less than 0.02 nm for the C, atoms and less than 0.05 nm for all atoms. This indicates that the structure obtained in vacio using the NOE information as atom-atom distance constraints resembles a stable conformation quite well when simulating without the constraints but including the solvent. The fluctuations of the atomic positions (Table 111) are for all simulations of the same order of magnitude. The isotropic atomic positional fluctuations are, in all simulations, especially for the side chains, slightly larger than those obtained from the experimental B factors corresponding to the x-ray structure. Also, the amplitude of the fluctuations of the side-chain atoms seems to increase slightly when changing the solvent from polar to apolar. The fluctuations of the MDSl structure are comparable to those obtained in apolar solution without atom-atom NOE distance constraints. All sim-

ulations show a much larger anisotropy compared to the crystallographic B factors (Table IIIb). The x-ray refinement procedures tend to underestimate the mobility and anisotropy of mobile atoms2, Comparison of the Simulations Starting from the NMR Structure in Solution

As mentioned before, the simulated structures in apolar solvent (MDSlLJ and MDSlLJLM) resemble the structures obtained from a simulation including atom-atom distance restraints in vacuo (MDS1) quite well. The backbone dihedrals (G, and w ) are given in Table IVa for the MDS1, MDSlW, MDSlLJ, and MDSlLJLM structures together with their rms fluctuations in brackets. The dihedral angles of the MDSlLJ and MDSlLJLM structures resemble those of the MDSl within the rms fluctuations. Only for the MDSlW structure do a few dihedrals (1-MeBmt G, +; 2-Abu w ; 4-MeLeu +; 5-Val @; 7-Ala c$, +; Il-MeVal w ) differ by more than 10". Comparing the side-chain dihedrals (Table IVb) one finds that the MDSlLJ and MDSlLJLM conformations correspond to the MDSl one (Figure a), except for IO-MeLeu, which adopts without atom-atom distance constraints the conformation observed in the x-ray structure, and 4-MeLeu, which has a slightly different conformation. Yet the difference is smaller than the rms fluctuation. The l-MeBmt side chain exhibits the same extended conformation sticking into the solvent as determined by nmr and the previous simulation.' Only in the MDSlLJ simulation does x4 undergo a complete rotation. Starting the simulation in water from the MDSl structure, a dramatic conformational change occurs in the l-MeBmt side chain. I t

+

1)E:PENI)ENCE OF MOLECULAR CONF’ORMATlON

Table I11 Atomic Fluctuationsa of Various Conformations of CPA (a) Root Mean-Square Fluctuationsb Backbone

(Me)-Leu Side Chains

Conformation

All

N

Ca

C

0

ca

c,

XRAY (MDC) XRAYW XRAYLJ XRAYLJLM MDSlW MDSlLJ MDSlLJLM MDS 1

0.051 0.054 0.052 0.050 0.055 0.063 0.067 0.068 0.069

0.044 0.031 0.033 0.030 0.042 0.037 0.040 0.040 0.041

0.044 0.032 0.036 0.032 0.045 0.040 0.042 0.042 0.045

0.044 0.031 0.034 0.031 0.043 0.039 0.041 0.041 0.043

0.050 0.049 0.053 0.047 0.062 0.092 0.062 0.060 0.062

0.053 0.047 0.0,52 0.046 0.071 0.079 0.067 0.067 0.072

0.061 0.07 1 0.065 0.068 0,091 0.073 0.098 0.100 0.089

c61

0.070

0.112 0.105 0.104 0.130 0.106 0.130 0.131 0.133

‘62

0.067 0.111 0.087 0.1 11 0.127 0.098 0.148 0.149 0.122

(b) Ratio of Smallest and Largest Fluctuationbzc Backbone

(Me)-Leu Side Chains

Conformation

All

N

Ca

C

0

cp

C~

XRAY (MDC) XRAYW XRAYLJ XRAYLJLM MDSl W MDSlLJ MDSlLJLM MDSl

0.75 0.44 0.44 0.44 0.41 0.38 0.39 0.36 0.38

0.78 0.54 0.55 0.54 0.42 0.45 0.43 0.40 0.45

0.74 0.53 0.53 0.50 0.40 0.43 0.40 0.38 0.41

0.75 0.57 0.57 0.55 0.46 0.44 0.45 0.44 0.46

0.76 0.40 0.44 0.41 0.42 0.37 0.43 0.43 0.42

0.83 0.41 0.36 0.38 0.29 0.35 0.36 0.27 0.29

0.80 0.33 0.31 0.31 0.29 0.26 0.25 0.25 0.30

~

c61

c62

0.62 0.35 0.30 0.32 0.33 0.34 0.43 0.35 0.31

0.81 0.40 0.41 0.28 0.35 0.29 0.29 0.32 0.31

~~

aAll fluctuations are given in nanometers. bThe configurations have been translated such that the centers of m a s coincide, and in addition, a rotational least-squares fit of the C, atomic positions has been performed. ‘The ratio of the smallest t o longest principal axis of the anisotropic fluctuation ellipsoids.

Figure 2. Stereopairs of CPA in apolar solution MDSlLJ (open lines) and the nmr structure of MDSl (filled lines). The polypeptide chain is shown with the residue sequence numbers running clockwise; the residue on top is 3-Sar, the one a t thc bottom 9-MeLeu.

1675

1676

LAU'I'Z ET AL.

Table IVa Backbone Dihedrals for Various CPA Conformationsa

4 1. MeBmt @ o

4 2. Abu

@ o

4 3. Sar

@ w

4 4. MeLeu @ w

4 5. Val

+ w

$ 6. MeLeu @ w

4 7. Ala

@ w

4 8. D-Ala

@

o

J, If. MeLeu

@ w )I

10. MeLeu @ w

4 11. MeVal

@ w

XRAY

XRAYW

XRAYLJ

XRAYLJLM

MDSl

MDSlW

MDSlLJ

MDSlLJLM

-84 123 -175 -120 89 -178 73 -129 173 -99 21 180 112 126 167 -90 99 -165 -82 52 179 87 124 - 166 -119 99 -5 -138 64 -167 -102 125 173

-99 (8.4) 96 (13.7) 180 (7.8) -lO6(17.3) 106 (11.4) -176 (9.9) 56(11.6) -121 (11.5) 173 (7.9) -107 (10.0) 36 (18.4) -177 (6.2) 118 (18.6) 121 (11.5) 167 (8.5) -94(10.7) 98 (13.6) -171 (6.7) -97 (20.3) 87 (15.7) 175 (7.1) 68 (17.4) - 122 (11.3) - 178 (7.7) -128 (9.0) 119 (11.8) 18 (12.8) -119 (9.0) 98 (8.0) -159 (6.9) -129 (7.7) 114 (9.3) 176 (6.7)

-101 (8.2) 86 (12.3) - 173 (7.1) -92 (14.8) 101 (10.2) -168 (9.1) 53 (10.6) -119 (9.9) 174 (8.1) -108 (9.4) 39 (16.7) -179 (6.6) -112 (16.7) 121 (9.0) 173 (7.1) -95 (10.5) 95 (11.2) -174 (6.8) -91 (13.1) 74 (12.2) 176 (6.3) 78 (12.7) 122 (9.8) - 175 (7.1) -136 (10.8) 110 (8.8) - 10 (10.0) -122 (7.3) 98 (8.9) -160 (8.6) -124 (7.4) 98 (10.4) - 166 (10.2)

-108 (9.3) 83 (13.3) - 174 (7.4) -98(18.3) 107 (13.9) 172 (10.9) 57 (10.3) -122 (11.8) 173 (9.5) -109 (10.8) 45 (17.6) -178 (7.4) - 111 (17.9) 117 (9.7) 172 (8.8) -100(12.3) 92 (10.8) -178 (7.1) -88 (12.4) 70 (13.9) 179 (7.2) 72 (14.7) - 124 (10.4) -176 (8.3) -131 (10.8) 114 11.3) - 13 11.9) - 123 (9.2) 98 (8.8) - 160 (9.0) - 121 (8.2) 91 (9.2) - 155 11.5)

- 100 (10.8)

- 114 (10.3)

95 (11.0) 178 (6.7) -85(15.5) 97 (8.9) 159 (8.6) 57 (9.6) -116 (9.9) 169 (7.5) -113 (9.6) 33 (18.3) 176 (6.8) -89 (21.6) 120 (9.6) 180 (8.9) -90 (11.0) 96 (11.1) -179 (6.1) -90 (14.2) 66 (12.7) 178 (6.9) 80 (17.2) - 128 (10.9) 177 (7.4) -132 (9.8) 113 (13.0) - 11 (15.0) -121 (11.4) 100 (11.0) 165 (10.9) - 123 (7.6) 104 (11.5) 172 (11.9)

82 (16.3) - 179 (7.2) -81 (17.4) 107 (11.9) 170 (10.5) 56 (10.9) -117 (9.9) 168 (8.1) -116 (9.3) 54 (17.9) 180 (6.8) - 112 (18.7) 116 (9.4) 178 (7.7) -94 (9.9) 105 (12.9) 180 (7.7) - 112 (17.3) 80 (15.9) 178 (6.3) 79 (16.6) - 132 (9.8) - 171 (7.3) -136 (8.2) 108 (10.0) - 14 (11.5) - 115 (9.0) 106 (11.7) -160 (7.1) - 123 (7.6) 94 (10.9) - 156 (12.4)

101 (8.6) 88 (15.7) 178 (8.5) -81 (17.2) 96 (9.0) - 157 (8.6) 55 (9.6) -119(12.9) 168 (8.5) -114 (11.1) 50 (26.4) 177 (8.8) -98 (24.0) 119(10.1) -177 (9.3) -92 (9.8) 92 (12.5) 180 (7.3) -92 (13.8) 69 (12.4) 180 (6.8) 71 (14.3) - 125 (10.1) -176 (7.5) -128 (9.8) 114 (10.7) - 13 (11.1) - 122 (8.5) 96 (9.4) 156 (10.7) -121 (7.9) 99 (11.2) 164 (14.5)

-98 (11.6) 89 (13.1) 177 (7.2) -81 (12.7) 97 (8.9) 158 (7.0) 56 (9.9) -120(11.6) 168 (8.4) -114 (11.4) 47 (23.6) 178 (7.3) -99 (22.0) 120 (8.4) - 178 (7.8) -93 (9.5) 92 (12.1) -179 (7.3) -91 (13.4) 68 (14.8) 179 (6.4) 74 (15.0) - 125 (11.0) -176 (7.8) -129(10.4) 114 (11.6) 13 (17.2) - 124 (11.4) 95 (9.6) 160 (15.3) - 121 (9.0) 103 (13.7) 173 (18.8)

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

a,

I'he rms fluctuations are given in parentheses. Units in degrees.

changes its conformation to the one observed in t h e crystal structure (Figure 3, folding back to the backbone due t o the unfavorable hydrophobic interactions of its lipophilic side chain, which can bury itself in the hydrophobic pocket of the backbone formed by the j?-pleated sheet. Hydrogen bonding strongly determines the secondary structure of proteins and peptides. As a hydrogen-banding criterion, the following has been used: T h e hydrogen-acceptor distance d, . . . A should be less than 0.25 nm and the donor D-H .. .A acceptor angle 0 larger than 90". If one compares the pattern of the two simulations in apolar solvent (Table Va, b) one observes the same hydrogen-bonding pattern. However, compared to t'le onc . obtained by the atom-atom distance restrained d j 9amics simulation in vacuo (MDSl), one finds that two hydroge? bonds in the

&pleated sheet (2-Abu-5-Val and 7-Ala-11MeVal) show a lower occupancy (about 20-30%) in apolar solution. The two y-turns between 2-Abu11-MeVal and 7-Ala-5-Va1, found in the previous MDSl simulation," show a higher occupancy in apolar solution indicating an even stronger bending of the two turn regions of CPA along a n axis through the C, atoms of 1-MeBmt and 6-Meleu. However, the simulation in water MDSlW yields a quite different picture (Table VI). The hydrogen bond of the 1-MeBmt side-chain hydroxyl group t o its own carbonyl is completely gone due to the rotation of the side chain around x1 and taken over by water (Table VII). The hydrogen bonds of the ,&pleated sheet are weaker than in the apolar solvent; only the 5-Val-2-Abu hydrogen bond shows the same occupancy as in the MDSlLJ and MDSlLJLM simulations. The ten-

DEPENDENCE OF MOLECULAR CONFORMATION

1677

Table IVb Side Chain Dihedrals for Various CPA Conformations" XRAY

x1

XRAYW

XRAYLJ

x4 x5 x1

-166 -167 (7.9) -170 (7.3) 73(11.0) 72 (10.1) 74 173 (11.5) - 172 (11.5) - 179 - 126 - 153 (26.6) - 155 (26.4) 179 (8.0) 179 (8.0) - 175 48(27.2) -178 -114 (45.7)

x2 x1 x1 xZ

-51 - 54 -51 -176 - 177

7. Ala 8. ~ - A l a 9. MeI,eu x1

- 54

- 70

- 63

- 77

1. MeHmt

xz x3

2. Abu 3. sar 4. MeLeu x1 5. Val 6. MeLeu

10. MeLeu 11. MeVal

x2 x1 xZ x1

-80 (15.3)

-83 (18.6) (43.8) -61 (12.2) -59 (11.6) - 170 (9.3) - 168 (9.5) - 141 (31.1) - 130 (31.2) - 103 (43.0)

- 127

(13.1) - 147 (35.3) (18.0) - 153 (19.9) -163 -169 (9.7) -166 (9.5) - 169 - 164 (12.9) - 154 (26.7) -53 -61 (14.5) -56 (10.8)

XRAYLJLM - 170 (8.4)

71 (12.2) - 168 (12.7) - 158 (37.4) 179 (8.1) - 88 (38.5) - 75

(19.1) (33.9) -60 (11.3) - 167 (13.0) - 116 (30.5) - 87

- 90

(35.2) (30.8) - 169 (10.4) - 158 (21.3) -57 (12.6) - 93

MDSl

MDSlW

-67 (9.7) - 151 (25.3) 139 (48.6) 163 (48.6) - 119 (37.6) - 141 (36.0) 180 (48.9) - 175 (54.0) 180 (8.0) 180 (8.1) - 93 (41.9) - 125 (50.1) - 79

(10.5) (22.7) -63 (10.3) - 173 (14.0) - 133 (30.4) - 80

- 72

(14.8) (34.3) - 118 (35.7) -80 (13.5) -60 (8.9) - 96

-75 (10.5) - 72 (14.7) -61 (9.2) - 169 (13.0) - 145 (32.0)

- 75

(17.3) (30.3) - 91 (22.1) - 84 (22.0) -55 (9.7) - 97

MDSlU

MDSlLJLM

-68 (9.3) 164 (18.6) - 90 (26.7) - 94 (29.9) 180 (52.2) - 11 (184.7)b 180 (7.9) 180 (7.8) - 123 (48.7) - 104 (49.4) - 64

(8.8)

- 168 (14.6)

114 (42.8)

- 103 (37.2)

- 115 (48.7)

115 (47.1) (10.4) - 168 (10.6) 136 (33.8)

-

-66 (9.6) - 169 (10.7) - 131 (33.6)

77 (20.9) (31.2) - 160 (22.3) - 148 (35.4) -58 (10.3) -

- 95

-

- 65

- 96

(39.7)

- 111 (39.3) -

165 (9.9)

- 157 (27.4) - 59

(10.4)

* T h e rnis fluctuations are given in parentheses. Units in degrees bI)uring the simulation a 360' rotation occurred.

dency of forming y-turns is much less pronounced in water than In apolar solvent. The 2-Abu-11MeVal hydrogen bond is occupied only to 22% occupied and the 7-Ala-5-Val hydrogen bond is completely gone. However all carbonyl oxygens of CPA are icvolved in hydrogen bonds with water hydrogens, whereas only three polar hydrogens act a s a donor (Table VII): 1-MeBmt-OH, 2-Abu-NH,

and ~ - D - A ~ ~ - N The H .picture of the occurrence of water-solute hydrogen bonds (Table VII) resembles qualitively quite well the one obtained by accessible surface area calculation^^^ (H. P. Weber, unpublished results). In Ref. 8 the MDSl structure was derived by a MD simulation in vacuo, using a n atom-atom distance restraining term in the potential energy

Figure 3. Stereopairs of CPA in water MDSlW (open lines) and the structure in apolar solution MDSlLJ (filled lines).

1678

LAUTZ ET AL.

Table V (a) Hydrogen Bonds" of CPA in CCl, (MDSlLJ Simulation) Donor

Acceptor

1-Mebmt 0 - H 2-Abu N-H 2-Abu N-H 5-Val N-H 7-Ala N-H 7-Ala N-H 8-D-Ala N-H

1-MeBmt 0 5-Val 0 11-MeVal 0 2-Abu 0 5-Val 0 11-MeVal 0 6-MeLeu 0

&..A

0.279 0.31 1 0.298 0.300 0.299 0.314 0.301

d H ...A

O(D-H ... A)

occ.

129 150 129 154 129 159 141

87 30 58 65 49 49 60

0.206 0.222 0.225 0.209 0.227 0.220 0.217

(b) Hydrogen Bonds" of CPA in Low-Mass CC1, (MDSlLJLM Simulation) Donor

Acceptor

1-Mebmt 0 - H 2-Abu N-H 2-Abu N-H 5-Val N-H 7-Ala N-H 7-Ala N-H 8 - ~ - A l N-H a

1-MeBmt 0 5-Val 0 11-MeVal 0 2-Abu 0 5-Val 0 11-MeVal 6-MeLeu

4,.. . A 0.281 0.309 0.300 0.303 0.299 0.311 0.301

d H .. .A

@(I)-H .. . A )

occ.

128 151 129 155 128 158 140

90 36 52 73 47 56 66

0.210 0.220 0.227 0.2 11 0.229 0.218 0.218

"Distances d in nanometers, angles 0 in degrees, and occupancies (Occ.) in percents.

function, which forced the molecule to satisfy the experimentally determined NOE distance constraints. One finds in the M D S l U structure only five violations of the experimentally determined distances (out of a total of 58). The result is given in Table VIII. The violations are not larger than 13%,which is comparable to the error of about lo%, being inherent in distance determination using nmr. The largest violations occur in the 10-MeLeuside chain, which rotated during the simulation (Table I n ) , causing these violations. However, the overall conformation obtained by the simulations in apolar solution resembles quite well the one obtained in vacuo including the atom-atom NOE constraints, which indicates that this previously obtained structure is a stable conformation.

Comparison of the Simulations Starting from the X-Ray Structure in Solution with the XRAY and (MDC) Structures

The backbone dihedral angles (+, 4 , and a) are given in Table IVa for the experimental x-ray structure and the simulated structures in the different solvents. For most of the dihedral angles the rms fluctuation (given in parentheses) is larger than the difference between x-ray and the simulated ones. Thus the backbone conformation remained quite stable and close to the x-ray one, independent of the type of solvent. The same observation holds for the side chains (Table I n ) , which adopt on average the same conformations as in the x-ray structure. Only for 9-MeLeu is a slightly different conformational deviation from the x-ray structure observed, but this was also observed in the previous simulation of four unit cells

Table VI Hydrogen bonds" of CPA in H,O (MDSlW Simulation) Donor

Acceptor

2-Abu N-H 2-Abu N-H 5-Val N-H 7-Ala N-H 8-D-Ala N-H

5-Val 0 11-MeVal 0 2-Abu 0 11-MeVal 0 6-MeLeu 0

a

d u . .. A 0.309 0.305 0.298 0.314 0.304

d H ...*

0.223 0.231 0.211 0.220 0.228

O(D-H . . .A)

occ.

147 130 148 159 133

23 28 72 54

Distances d in nanometers, angles 0 in degrees, and occupancies (Occ.) in percents.

11

D E P E N D E N C E OF MOLECULAR CONFORMATION

1679

Table VII (a) Hydrogen Bonds" of Water-CPA (MDSlW Simulation) Donor

Acceptor 1-MeBmt O,, 1-MeBmt 0 2-Abu 0 3-sar 0 4-MeLeu 0 5-Val 0 6-MeLeu 0 7-MeLeu 0 8-D-Ala 0 9-MeLeu 0 10-MeLeu 0 11-MeLeu 0

OW-H OW-H OW-H OW-H OW-H OW-H OW-H OW-H OW-H OW-H OW-H OW-H

CI!H,,,*

CI!II,.,A

0.301 0.297 0.299 0.298 0.294 0.308 0.292 0.205 0.287 0.295 0.295 0.289

O(D-H.. .A)

OCC.

149 136 148 144 144 140 140 149 154 138 142 131

44 119 52 77 150 15 125 96 87 101 119 60

0.214 0.220 0.213 0.215 0.211 0.228 0.212 0.292 0.196 0.217 0.213 0.217

(b) Hydrogen Bonds" of CPA-Water (MDSlW Simulation) Donor

Acceptor

1-MeBmt O,,-H 2-Abu N-H 8-D-Ala N-H

ow ow ow

~~

'11

... A

',,...A

0.278 0.304 0.301

@(D-H*..A)

OCc.

131 150 146

101 32 80

0.212 0.215 0.216

~

a Distances d in nanometers, angles 0 in degrees, and occupancies (Occ.) in percents. Occupancies larger than 100%indicate multiple hydrogen bonds.

of CPA.' The 1-MeBmt side chain adopted in the apolar solution simulations the same conformation as observed by x-ray diffraction and showed no tendency t o move to the extended conformation detected by nmr and established by simulations starting from the MDSl structure in apolar solvent. This suggests that there are two possible conformations for the 1-MeBmt side chain, which are both stable in lipophilic environment. Comparing the two simulations in apolar solvent XRAYLJ and XRAYLJLM, one obtains a different picture of the hydrogen-bonding pattern (Table IX). In the XRAYLJ simulation the hydrogen bonds of the /3-pleated sheet are nicely retained with occupancies of about 80%. Also the two y-turns

observed in the (MDC) and MDSl structures are found in this simulation. However, the 2-Abu-11MeVal hydrogen bond is much more pronounced than the 7-Ala-5-Val one. In addition, one finds two more hydrogen bonds, one between 5-Val and 3-Sar, and one within the 5-Val residue. The last type of hydrogen bond forms a five-membered ring, but only limited experimental evidence for such structures exist so far.25-27 In the XRAYLJLM simulation, using the reduced mass Lennard-Jones liquid, one observes a breaking up of the P-pleated sheet, and the occupancies of 2-Abu-5-Val and 7-Ala-11-MeVal are reduced by almost 50%. The y-turn formed by 2-Ala and 11-MeVal is still present; however, the 7-Ala-5-Val hydrogen bond is not present any-

Table VIII Atom- Atom Distance Violations of CPA (MDSlLJ Simulation)'

1-MeBmt C,H 1-MeBmt CsH 7-Ala NH 9-MeLeu C,H 9-MeLeu C,H

7-Ala NH 2-Abu NH 8-Ala NH 10-MeLeu CslH 10-MeLeu C,H

0.350

0.369

0.019

0.350

0.384

0.034

0.350 0.450 0.350

0.366 0.515 0.372

0.016 0.065 0.022

'reXr!is the experimentally determined distance and rsimis the average distance obtained from the simulation. All distances are given in nanometers.

1680

LAUTZ E T AL.

Table IX (a) Hydrogen Bondsa of CPA in CCI, ( X R A Y U Simulations) Donor 2-Abu N-H 2-Abu N-H 5-Val N-H 5-Val N-H 5-Val N-H 7-Ala N-H 7-Ala N-H 8-D-Ala N-H

Acceptor 5-Val 0 11-MeVal 0 2-Abu 0 3-sar 0 &Val 0 5-Val 0 11-MeVal 0 6-MeLeu 0

&...A

0.303 0.296 0.297 0.307 0.274 0.303 0.305 0.301

d~ . . . A

O(D-H . . .A)

occ.

147 126 151 135 99 125 157 140

71 52 80 15 14 17 90 62

0.216 0.227 0.207 0.228 0.240 0.236 0.212 0.218

(b) Hydrogen Bonds" of CPA in Low-Mass CC1, (XRAYLJLM Simulation) Donor

Acceptor

1-Mebmt 0 - H 2-Abu N-H 2-Abu N-H 5-Val N-H 5-Val N-H 7-Ala N-H 8-D-Ala N-H

10-MeLeu 0 5-VM 0 11-MeVal 0 2-Abu 0 3-sar 0 11-MeVal 0 6-MeLeu 0

&...A

0.288 0.312 0.298 0.296 0.305 0.316 0.300

dti...A

O(D-H . . . A )

occ.

132 150 130 153 135 159 140

12 38 49 68 18 48 66

0.213 0.223 0.225 0.206 0.226 0.222 0.217

"Distances d in nanometers, angles 0 in degrees, and occupancies (Occ.) in percents.

more. The 5-Val-3-Sar hydrogen bond is also found in this simulation, but in addition one observes to a small extent a hydrogen bond between the 1MeBmt hydroxyl hydrogen and the carbonyl oxygen of 10-MeLeu. The hydrogen-bond pattern of the simulation in water (XRAYW) (Table X) is the same as obtained by the simulation in Lennard-Jones liquid. The P-pleated sheet is nicely stable during the simulation. The y-turn pattern is less pronounced and comparable to the (MDC) structure. In addition we find here also the 5-Val-3-Sar and the hydrogen bond within 5-Val as before. All carbonyl oxygens of CPA act as acceptors for hydrogen b n d s with water hydrogens (Table XI). But 5-Val-0' and 11-MeVal-0' show a very low

H-bond occurrency, less than 10%. Only two polar hydrogens 1-MeBmt-OH and 8 - ~ - A l a - N act 3 to a considerable amount as donors to water oxygens. The picture of the occupancies of hydrogen bonds formed with water resembles the results obtained by accessible surface area calculation^^^ of the x-ray structure well (H. P. Weber, unpublished results).

General Comparison of the Solvent Simulations

Even if the dihedral angles seem to resemble the backbone conformation of the x-ray structure, it turns out that due to the fluctuations, the hydrogen-bonding pattern indicates rather different con-

Table X Hydrogen Bondsa of CPA in H,O (XRAYW Simulation) Donor

Acceptor

2-Abu N-H 2-Abu N-H 5-Val N-H 5-Val N-H &Val N-H 7-Ala N-H 7-Ala N-H 8-D-Ala N-H

5-Val 0 11-MeVal 0 2-Abu 0 3-sar 0 &Val 0 5-Val 0 11-MeVal 0 6-MeLeu 0

4).. . A 0.304 0.299 0.293 0.307 0.274 0.301 0.297 0.295

d~ ... A

0.214 0.230 0.203 0.228 0.239 0.234 0.206 0.217

O(D-H.. . A )

occ.

152 125 151 136 100 125 153 135

82 22 85 15 18 13 92 44 ~

"Distances d in nanometers, angles 0 in degrees, and occupancies (Occ.) in percents.

DEPENDENCE OF MOLECULAR CONFORMATION

1681

Table XI (a) Hydrogen Bonds’ Water-CPA (XRAYW Simulation) Donor OW-H OW-H OW-H OW-H OW-H OW-H OW-H OW-H OW-H OW-H OW-H OW-H

Acceptor

dD,,,A

dH,,,A

O(D-H.. .A)

Occ.

1-MeBmt OYl 1-MeBmt 0 2-Abu 0 3-sar0 4-MeLeu 0 5-Val 0 6-MeLeu 0 7-MeLeu 0 8 - ~ - A l0 a 9-MeLeu 0 10-MeLeu 0 11-MeLeu 0

0.307 0.294 0.293 0.296 0.296 0.295 0.289 0.300 0.306 0.298 0.217 0.302

0.227 0.215 0.221 0.217 0.213 0.209 0.214 0.218 0.216 0.220 0.291 0.221

141 140 133 138 145 147 135 142 153 138 134 138

120 121 42 96 126 5 114 82 86 115 109 3

(b) Hydrogen Bonds’ CPA- Water (XRAYW Simulation) Donor 1-MeBmt Oy,-H 2-Abu N-H 7-Ala N-H 8-D-Ala N-H

Acceptor

dD.,,A

ow ow ow ow

0.279 0.312 0.311 0.306

dH,,,A

0.205 0.225 0.222 0.224

O(D-H .A)

OCC.

138 146 149 142

99 4

+.

1

50

a Distances d in nanometers, angles 0 in degrees, and occupancies (Occ.) in percents. Occupancies larger than 100% indicate multiple hydrogen bonds.

formations. Comparing the two simulations in water starting from the x-ray structure and from the nmr-structure MDS1, one gains a different pattern. As mentioned before the P-pleated sheet is nicely retained in the XRAYW simulations, while it is opened up in the MDSl simulation. One also finds much more internal hydrogen bonds in the XRAYW than in the MDSlW simulation. The CPA molecule behaves in the XRAYW simulation like a drop of oil in water, which is also indicated by the lower amount of hydrogen bonds with water (Table XI) compared to the MDSlW simulation. This effect may be due to the fact that the MDSl conformation is much more “open” in the beginning of the simulation due to the extended 1-MeBmt side chain, before it starts moving to the backbone, whereas in the XRAY structure the P-sheet is somehow shielded by this folded side chain right from the beginning. If one compares the simulations in Lennard-Jones liquid, then the simulation starting from the MDSl structure shows almost no effect to the mass of the solvent used in the simulations (Table IV). Both simulations give the same picture of the opened /%pleated sheet, which is also observed in the water simulation and a higher occupancy of the y-turns compared to the MDC, MDS1, MDSlW, and XRAY simulation in solution.

However comparing the two simulations starting from the x-ray structure in apolar solvent, the pattern of hydrogen bonds is changed when the mass of the Lennard-Jones liquid is reduced. The simulation in the heavy mass liquid (XRAYLJ) gives the same results (Table IXa) as observed in the x-ray structure, the MDC, or XRAYW simulation for the P-sheet, but there are additional hydrogen bonds concerning the 5-Val carbonyl oxygen that are not observed in the MDSl Lennard-Jones simulations. If the mass of the solvent is reduced (XRAYLJLM), one observes the same effect of the opening of the /%pleated sheet, as it results from the MDSl simulations in apolar and polar solution. Another interesting feature is the folding of the 1-MeBmt side chain forming with its hydroxyl group an internal hydrogen bond to 10-MeLeu-0’. In all the other simulations performed in apolar solvent the hydroxyl group was not involved in a hydrogen bond a t all. The MD simulations starting from different starting structures in the same solvent (either water or Lennard-Jones) do not lead to exactly equal average conformations. This is due to the limited length (40-50 ps) of the simulations. In order to obtain accurate statistics on the relative populations of various conformations in solution, much longer MD simulations are required. However, the

1682

LAUTZ ET AL.

0

0

0

0

01

'0

.oo

1

.oo

2

1

.oo

3.00

T I M E [PSI

4

.oo

1

5

.oo

01

'0.00

1

I

.oo

1

1

3 .oo

2 .oo

T I M E [PSI

1

4 .OO

1

5.00

(b)

(a)

Figure 4. Atomic positional fluctuation autocorrelation functions of the MDSl simulation of CPA. (a) Thin line: 5-Val-C,; thick line: 9-MeLeu-C,. (b) Thin line: 4-MeLeu-C,,; thick line: 9-MeLeu-C,,.

0 0

0 0

0 0

..-

\

LI) 0

00

0 .so

I

I

.oo

1

.so

T I M E [PSI

I

2 .oo

I

2.50

0

'I 00

1

0 .so

1

1

.oo

1

I

.so

T I M E [PSI

(C)

Figure 5. Atomic positional fluctuation autocorrelation functions of the crystal simulation (MDC) of four unit cells consisting of 16 CPA molecules (thin line: molecule 1; thick line; molecule 8. (a) 5-Val-C,, (b) 9-MeLeu-C,, (c) 4-MeLeu-Csl, and (d) 9-MeLeu-C8,.

1

2 .OD

1

2 .so

DEPENDENCE OF MO1,ECULAH CONFORMATION

results presented here may give an impression of the conformational changes that can be observed within a few tens of picoseconds.

where time averaging is denoted by ( . . . ) and i is the atom index. The correlation functions for the fluctuation is determined by8

Dynamics

The type of solvent environment of a solute may not only influence its equilibrium conformation, but may also effect its dynamics. Therefore the time evolution of the atomic positional fluctuations for the different MD simulations have been examined using correlation functions28.29.For the analysis the first part of the trajectories of the previous MDSl (vacuo) and MDC simulation (crystal, simulation of four unit cells)' was used. From the trajectories the time series of the atom positional fluctuations were calculated:

hr,( t ) = ri( t ) - (ri(t ' ) ) t .

1683

+ t ' ) . Ari(t')),.

Ci( t ) = (Ar,( t

(2)

For estimating the relaxation time r of a given atomic fluctuation correlation function, the initial decay was approximated by an exponential function. Assuming that the internal motions of a peptide or protein can be interpreted with the aid of a simple harmonic Langevin equation [30,31], one can calculate the friction coefficient 4 , if T aiid the mean square displacement (Ar') are known: 3rk,T /=

(1)

(3)

(ar">

0

ln 0

I

I

I

0

0 0

%o

I

0

2

!

.oo

4

1

I

.oo

6 .OO

TINE (c)

[PSI

8

I

.oo

Ib .oo

'0 .oo

2

I

.oo

I

4 .oo TIME

6.00

[PSI

(4

Figure 6. Atomic positional fluctuation autocorrelation functions of the simulations of CPA in water (thin line: XRAYW thick line: MDS1W. (a) 5-Val-C,, (b) g-MeLeu-C,, (c) 4-MeLeu-C,, , and (d) 9-MeLeu-C,, .

I

e .oo

I

10 .oo

1684

LAUTZ ET AL.

0 0

0 0

-1

oj-.-..'0 .oo

I

2

.oo

4

I

I

.oo

6.00

TINE

00

2'. 00

4 ' . 00

8

I

.oo

1

10.00

01

'0'. 00

,

2.00

8'. 00

Ib.00

TIflE [PSI (C)

00

2'. 00

I

.oo

TIME

[PSI

6'. 00

4

6.00

.oo

1

I 0 .OD

[PSI

6'. 0 0

4'.00

TIME

8

[PSI

8 .oo

10.00

(d)

Figure 7. Atomic positional fluctuation autocorrelation functions of the simulations of CPA in the heavy mas apolar solution (thin line: XRAYLJ; thick line: MDSlLJ). (a) 5-Val-C,, (b) 9-MeLeu-C,, (c) 4-MeLeu-C,,, and (d) 9-MeLeu-C,, .

Here T denotes the temperature and k , Boltzmann's constant. The atomic positional correlation functions for four representative atoms, two of which are in the P-pleated sheet, 5-Val-C, and 4-MeLeu-Csl, and two of which are in the loop region, 9-Meleu-C, and g-MeLeu-C,,, are shown in Figures 4-8. Table XI1 shows the values of the mean square fluctuations Ar2,the relaxation times r and the friction coefficients / calculated using Eq. (3). The relaxation times are between 0.2 and 6 ps, and most of them are observed in the range between 0.2 and 1.5 ps. For the vacuum simulation (MDS1) and the one in the crystalline environment (MDC) the relaxation times are generally shorter than for the other ones. For the solution simula-

tion one finds shorter values for the 5-C, atom in the P-sheet than for the 9-C, atom in the open loop. The side-chain atoms 5-C,, and 9-Cs, show generally longer relaxation times. The crystal and vacuum simulation show almost the same relaxation times. Also, the friction coefficients of the 5-C, atoms of the solvent simulation are much smaller, and of the size of the MDSl simulation, than those of the 9-C, atoms of the loop region, indicating that the latter part is much more open to the solvent than the more compact ,&sheet, which is strongly dominated by intramolecular interactions with the neighboring atoms. The correlation functions in Figures 4-8 can be separated into three classes. The first class contains correlation functions from the vacuum

1685

DEPENDENCE OF MOLECULAR CONFORMATION 0 0

0

b?oo

2

.oo

4

.oo

8

6 .OO

.oo

4 .oo TIME

2'. 00

'0'. 00

10.00

T I M E [PSI

6 .OO

.oo

10.00

8.00

10.00

8

[PSI

(a) a

0

0

0

01

'0.00

2

.oo

4

.oo

8'. 00

6 .OO

I0

T I M E [PSI

.oo

1

2

'0.00

.oo

4

1

1

.oo

6.00

T I M E [PSI

Figure 8. Atomic positional fluctuation autocorrelation functions of the simulations of CPA in the low-mass apolar solution (thin line: XRAYLJLM; thick line: MDSlLJLM). (a) 5-Val-C,,, (b) g-MeLeu-C,,, (c) 4-MeLeu-Ca,, and (d) 9-MeLeu-C8,. Table XI1

Mean Square Fluctuations, Correlation Times, and Friction Coefficients Obtained from the Correlation Functions of the Various CPA Simulations" 5-c,

Configuration

P

(*r2) .lo3

9-C,

T

P

(Ar2>

.lop4

.lo3

T

0.2 0.2 0.2 0.3 0.3 0.2 0.4 0.4 0.4

1.966 0.5596 1.968 1.044 0.7831 1.672 1.693 1.667 1.652

0.52 0.23 0.38 1.2 0.35 0.80 4.6 1.9 1.1

9-Ca1

4%

P

(Ar2) T

.lop4

0.64 0.47 0.42 5.8 2.6 1.4 1.2 6.0 2.4

0.02 0.05 0.04 0.1 0.1 0.04 0.1 0.1 0.09

P

(Ar2) T ~~

MIISI MIIC-I MIIC-H XItAYW XRAY L,,I XRAYIJLM M I S 1W MIIS1 1,J MI)SILJIAM tlr

11s.

1.201 0.6897 2.053 0.8602 0.7128 1.304 0.7956 1.200 0.9235

0.35 0.20 0.42 0.40 0.25 0.40 0.45 0.60 0.50

0.2 0.3 0.1 0.9 0.3 0.4 2.1 0.9 0.5

23.43 7.59 6.99 31.66 14.40 25.69 7.67 34.55 20.33

7

1 h c . niean square fluctuations a r e given in nm', t h e correlation times

T

20.24 5.253 7.238 6.668 12.46 22.56 11.26 12.89 22.70

0.49 0.25 0.32 0.70 2.0 1.0 1.3 0.80 2.6

0.02 0.04 0.03 0.08 0.1 0.03 0.09 0.05 0.09

in ps, and t h e friction coefficients f in k J molp nm-'

1686

LAUTZ ET AL.

(MDS1; Figure 4) and crystal (MDC; Figure 5) simulation, which show a rapid initial decay followed by large well-defined oscillations. For the MDC simulation, two different molecules out of the four unit cells containing CPA molecules have been chosen. Both display the same pattern in the correlation function. The second class contains correlation functions from the simulation in water (Figure 6) and in Lennard-Jones solvent (Figure 7). They show a rapid initial decay followed by a linear decrease. The third class contains the correlation functions from the simulations in the low mass Lennard-Jones solvent (Figure S), which show also a quite rapid initial decay followed by a linear decrease, on which a harmonic oscillation with a low amplitude is superimposed. The correlation functions in water and in Lennard-Jones solvent show both the same pattern, especially for the backbone atoms. The 5-MeLeu-C, atom shows a much faster decay than the 9-MeLeu-C, atom, indicating that the 5-C, atom is much more fixed in its position in the ,&sheet than the 9-C, atom, which is in the more flexible loop region. Even if the hydrogen-bond pattern indicates some opening, the @-sheet region remains still rather fixed. The low-mass Lennard-Jones simulation displays the same features, but more harmonic like in the MDSl and MDC simulations. In the water simulation the hydrogen-bond network of the solvent makes the surroundings quite viscous, which induces like the high mass of the Lennard-Jones solvent strong forces acting on the solute atoms. The 4-MeLeu side chain has much more freedom to move than the 9-MeLeu side chain, which is indicated by the much slower decay of the correlation function of the 4-MeLeu-C,, atom, independent of the surroundings. D ISCUSSION The molecular dynamics (MD) simulations presented in this paper give some insight in the conformation and dynamics of a small cyclic peptide and its dependence on its environment, which might be helpful in understanding the pharmaceutical action and further development of improved cyclosporin derivatives. When interpreting the results of the 40-50 ps MD simulations, one should keep in mind that the complete conformational space of the CPA molecule cannot be thoroughly searched within this selectively short time period. In apolar solvent starting from the MDSl (nmr) structure, which fits the 58 experimentally ob-

tained NOE distance constraints, the conformation also remains stable in the absence of the atomatom distance restraining interaction. This indicates that the previously obtained MDSl structure is a reasonably stable conformation. Its stability is not forced artificially by the NOE constraints. When changing the solvent from apolar to polar, the same MDSl conformation changes quite dramatically. The extended side chain of 1 residue (1-MeBmt) is moving by 120" around x1 and adopts the same conformation as observed in the x-ray structure. This observation is consistent with studies using monoclonal antibodies against specific regions of CPA. However, when simulating in apolar solution starting from the x-ray structure, the opposite change does not occur. This indicates the possibility of two stable conformations in apolar environment for CPA, although the nmr data show a strong preference of the Mebmt side chain being extended into the solvent. One should keep in mind that the 1-MeBmt side chain is crucial to the biological activity of CPA. The simulations starting from the MDSl structure in the different solvents all show an opening of the P-pleated sheet, while the x-ray structure remains stable in water and in the Lennard-Jones solvent. In water the x-ray structure adopts a much more compact conformation than the structure resulting by simulating from the initial MDSl structure. This is indicated by the opening of the &sheet, and consistent with this, by more pronounced hydrogen bonding with the water molecules. Nuclear magnetic resonance spectra of CPA in polar solvents like DMS04s7,32or ethanol/water 33 suggest that different conformers (most probably ck-trans isomers about N-methylated amide bonds) coexist in polar environment. As these conformers are in slow exchange on the nmr time scale, they are not detected within the relatively short simulation periods of 40-50 ps. The simulations of CPA in water should be much longer to obtain significant conclusions on the possible occurrence of various conformers. The present study illustrates the capacity and limitations of the technique of computer simulation when studying the dependence of molecular conformation on the environment. Differences in hydrogen-bonding patterns and side-chain torsional angle conformations can be observed, and should be related to the functional properties of the molecule, but firm conclusions on conformational variability may only be based on much longer simulations, which will become feasible with advent of even faster and cheaper computers.

DEPENDENCE OF MOLECULAR CONFORMATION

The support of the Werkgroep Supercomputer (WGS) is gratefully acknowledged. Furthermore, we want to thank SARA (Amsterdam) for its support while we used the Cyber 205 supercomputer.

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Received August 29, 1988 Accepted June 13, 1989