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Molecular dynamics simulations of a simple tripeptide, N-acetyl-Pro-Gly-Phe in the crystalline states: distinction of the β-turn Type I from the Type II form
THEO CHEM ELSEVIER
Journal of Molecular Structure (Theochem) 388 (1996) 187-200
Molecular dynamics simulations of a simple tripeptide, N-acetyl-Pro-Gly-Phe in the crystalline states: distinction of the B-turn Type I from the Type II Form M i s a k o A i d a a, A k i r a N a i t o b, H a z i m e
Sait6 u
aBiophysics Division, National Cancer Center Research Institute 5-1-1, Tsuko'i Chuo-ku, Tokyo 104, Japan bDepartment of Life Science, Himeji Institute of Technology, Harima Science Garden City, Kamigori, Hyogo 678-12, Japan
Received 21 February 1996; accepted 19 March 1996
Abstract
Molecular dynamics (MD) simulations of a simple tripeptide N-acetyl-Pro-Gly-Phe in the crystalline states show that this tripeptide exhibits two different ~-tum conformations (Types I and II) in two different crystalline states. The combination of the one intramolecular and four intermolecular hydrgen bonds for each molecule in crystal plays an important role in determining a propensity to form either Type I or Type II conformation. Each of the conformations in crystals is found to be close to one of the local minima of the tripeptide itself, although more stable conformations appear in the MD simulation of the single tripeptide in vacuo. It is concluded that the conformations in crystal cannot be formed without the intermolecular interactions. The present MD simulation in one of the crystalline states demonstrates the presence of the puckering motion in the pyrrolidine ring, which is consistent with our previous finding by solid-state NMR. Keywords: Molecular dynamics; Peptide conformation; 13-Turn; Proline puckering; Crystal
1. Introduction
The 3-turn conformation is one of the important structural motifs in globular proteins, leading to globularity rather than linearity. Functional roles have been also assigned to the 3-turn form such as the site for enzymatic action [1,2]. An analysis of the X-ray crystallographic data on several globular proteins [3] reveals positional preferences for the amino acid residues to occur within the/3-turn formed by the tetrapeptide segment X1-X2-Xa-X4: the sequence of X1-Pro-GIy-X4 forms the 3-turn structure preferentially. The characteristics of the 3-turn is a hydrogen bond which is formed between the CO group of the first residue and the NH group of the fourth residue.
The 0-turn Type I has (~,XIt)2 = ( -- 60 °, - 30 °) and (CI~,xI¢)3 = ( -- 90°,0°); the 3-turn Type II has (~,ff')2 = ( - 60°,120 °) and (~,~)3 = (800,0 °) for the second and third residue of the tetrapeptide segment. Among the Pro-Gly-containing peptides, N-acetyl-Pro-Gly-Phe (N-acetyl-L-prolylglycyl-L-phenylalanine; see Fig. 1) is known to assume the 3-turn Type II conformation in the monoclinic crystal [4]. Recently, we found during the course of our solid-state NMR study [5] that this tripeptide takes also the 3-turn Type I conformation in the orthorhombic crystal, although solvent compositions for the crystalization of both types of crystals were almost the same. This small tripeptide seems to adopt different conformations depending on the intermolecular interactions in the crystal.
0166-1280/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved PII S0166-1280(96)04625-8
188
M. Aida et al./Journal of Molecular Structure (Theochem) 388 (1996) 187-200
U n
T"
/
\
c---
o
i
H--N
~
o
\
'~Ph,,
Fig. 1. Schematicrepresentationof N-acetyl-Pro-Gly-Phe. It is very interesting to reveal why these two types of conformations are present for the same molecule without involvement of any other molecules such as solvent molecule(s). In the present study, MD simulations of the tripeptide N-acetyl-Pro-Gly-Phe have been performed under the conditions of the two kinds of crystals, in order to gain insight into the stabilization mechanism of both types of the /3-turn conformations using the ab initio potentials [6] which are known to reproduce well the manner of hydrogen bonding interactions [7,8]: the use of this sort of force field is very important in view of the/3-turn conformations which are supposedly stabilized by intra- and/or inter-molecular hydrogen bonds. In fact, we arrive at the two types of the ~-turn conformations which are very similar to those of the X-ray diffraction studies [4,5]. In addition, the internal motions such as puckering motions of the pyrrolidine ring are described well by our MD simulation and consistent with the data of solid-state NMR [5]. This is the first successful MD approach to reproduce conformations of small peptides in the crystalline states to the best of our knowledge.
2. Methods Molecular dynamics calculations were performed using the KGNMD program from the MOTECC package [9] with the ab initio potentials for the solute intraand intermolecular interactions [6]. The total energy of a system is described as the sum of the solute nonbonded and the solute bonded interaction energies [9].
All the atoms are considered explicitly. In the Coulomb term, the relative dielectric constant is 1, in all cases. The equations of motion were solved using the leap-frog algorithm with a time step of 0.5 fs. All the simulations were performed within the microcanonical ensemble, maintaining constant energy, volume and number when calculating average properties. In all cases, periodic boundary conditions were applied. Two kinds of systems were simulated at 293 K in the crystallographic cells: the first system (system I) corresponds to the orthorhombic crystals [5]; the second system (system II) corresponds to the monoclinic crystals [4]. Since no solvent molecules (such as water molecules) are detected in either of the crystals experimentally, only the tripeptide molecules are taken into consideration in the conditions of the crystalline states. For each of the systems, we used the simulation box which was composed of a certain number of crystallographic cells, as will be described below, to be assured that a large enough value can be set for the cutoff radius for the non-bonded interactions. The long range Coulomb term was computed with the Ewald sum correction [10]. For the simulation of the system I, the X-ray structure [5] was used as the starting conformation. One simulation box was composed of 6 crystallographic cells: 2 cells along the a-axis, 1 cell along the b-axis and 3 cells along the c-axis. The lattice parameters are as follows: a = 10.455 A,, b = 22.93 .~ and c ~ 7.452 ,~. Four molecules per cell were placed in a crystallographic cell with the symmetry of the space group P212121. In total, 24 molecules were included in a simulation box. All these molecules were treated independently during the simulation with the periodic boundary conditions. A cutoff radius of 9.4 A was adopted with the Ewald sum correction for the long range Coulomb term. In the system II, one simulation box was composed of 18 crystallographic cells: 3 cells along the a-axis, 3 cells along the b-axis and 2 cells along the c-axis with the lattice parameters of a = 8.915 A, b = 8.458 A and c -- 13.216 A. The X-ray structure [4] was used as the starting conformation. Two molecules per cell were placed in a crystallographic cell with the symmetry of the space group P2t. In total, 36 molecules were included in a simulation box. During the simulation, they were treated as independent. The periodic boundary condition ensures that our simulation system is an
M. Aida et al./Journal of Molecular Structure (Theochem) 388 (1996) 187-200
189
a) Molecule D [
Molecule C I
i'be'
,~
/
o, -,b
IM°leculeAI
Molecule B ]
b)
,8
Fig. 2. (a) A snapshot of the tripeptides in the system I crystal during the 200 ps MD simulation. (b) A stereo view of the snapshot. Hydrogen bonds are denoted by the dotted lines.
M. Aida et aL/Journal of Molecular Structure (Theochem) 388 (1996) 187-200
190
Table 1 Torsional angles in degrees of the peptide main chain in N-Acetyl-Pro-Gly-Phe-OH system I crystal during 200 ps simulation ¢I~Fro
MD molecule A molecule B molecule C molecule D average a X-ray b type I B-turn c
-54.6 -56.9 -54.8 -56.4 -56 -76 -60
~It Pro
+ 7.9 --_ 8.2 _+ 7.8 ± 8.2
-33.4 -30.5 -32.6 -30.9 -32 -12 -30
¢I~Gly
+_ 9.1 _+ 9.8 _+ 9.6 _+ 9.7
-91.0 -90.7 -91.1 -90.8 -91 -86 -90
'ffl ely
_+ 7.4 _+ 7.5 ± 7.5 _+ 7.2
15.8 14.9 15.7 14.8 15 -4.5 0
~ Phe
_+ 9.7 _+ 9.6 _+ 9.4 _+ 9.2
-98.4 -98.5 -98.3 -98.2 -98 -83
_+ 8.3 _+ 8.1 _+ 8.0 _+ 8.0
a Averages over all the molecules in the simulation box. b Ref.[5] c Ref.[31
infinite crystal. The long range Coulomb term was computed with the Ewald sum correction with a cutoff radius of 11.5 .~. Each of the systems was equilibrated over 100 ps followed by a 50 ps run without velocity rescaling, since the average temperature remained essentially constant around 293 K. The final 200 ps simulation was used for analysis: coordinates and velocities were stored every 50 fs. For each of the system I and system II, one molecule was picked up after the MD simulation in crystal and the energy minimization was performed using the SUMSL (secant-type unconstrained minimization solver) routine [11]. The energy-minimized structures were then used as an initial structure for the MD simulation in vacuo at 293 K. The system was equilibrated during 50 ps followed by a 50 ps run without velocity rescaling, since the average temperature remained essentially constant around 293 K. The final 50 ps simulation was used for analysis: coordinates and velocities were stored every 50 fs.
stereo view of the snapshot is shown in Fig. 2(b). During the simulation, those 24 molecules were treated independently; however, the overall X-ray structure was preserved in the crystal. Each molecule forms four intermolecular hydrogen bonds with its neighbors, as well as one intramolecular hydrogen bond. Each molecule exhibits the f3-turn type I conformation. We select a molecule arbitrarily, and it is named the molecule A. In Fig. 2, the molecules which are connected by a hydrogen bond to the molecule A are shown. The molecule A forms hydrogen bonds with the four neighbors (B, C, D and E). The molecule E, which is next to the molecule D translated by one unit along the c-axis, is not shown in Fig. 2, to avoid confusion. The average values of the torsional angles of the peptide main chain for the molecules which appear in Fig. 2 are summarized in Table 1, together with those Table 2 Intra- and intermolecular hydrogen bond average distances (.~) in N-Acetyl-Pro-Gly-Phe-OH system I during 200 ps simulation
3. Results 3.1. MD simulation of the system I The X-ray data [5] was used as an initial structure of the simulation in the crystal. As it was described in the Method, there are 24 independent molecules in the the simulation box with the periodic boundary condition. A snapshot of the molecules during the simulation in the crystal is shown in Fig. 2(a), where the hydrogen bonds are denoted by the dotted line. The
Hydrogen bond pair
Hydrogen bond distance
Oacetyl(A)-HNphe(A) Oacetyl(B)-HNphe(B) Oacetyl(C)-HNphe(C) O acetyt(D)-HNphe(D)
2.07 2.09 2.07 2.07
-+ 0.19 -+ 0.20 --- 0.19 + 0.19
HNGly(A)-Opro(B) Opro(A)-HNGIy(C) OGIy(A)-HOxt(D) HOxt(A)-O6ly(E)
2.16 2.18 1.82 1.82
~ 0.18 ~ 0.18 _+ 0.11 ± 0.10
lntramolecular
Intermolecular
M. Aida et al./Journal of Molecular Structure (Theochem) 388 (1996) 187-200
191
a) P
~.
I~°'~'e ~ I
Molecule A ]
I~olecul~ B I
::
b)
Fig. 3. (a) A snapshot of the tripeptides in the system II crystal during the 200 ps MD simulation. (b) A stereo view of the snapshot. Hydrogen bonds are denoted by the dotted lines.
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M. Aida et al./Journal of Molecular Structure (Theochem) 388 (1996) 187-200
Table 3 Torsional angles in degrees of the peptide main chain in N-Acetyi-Pro-Gly-Phe-OHsystem II crystal during 200 ps simulation cI~Pro MD molecule A molecule B molecule C molecule D average a X-ray b type II E-turn c
-47.3 -47.4 -47.2 -47.6 -47 -59 -60
- 5.8 +_ 5.6 _+ 5.7 +_ 5.6
~rPro
(I~Gly
XIIGly
112.0 -4- 7.1 112.1 _+ 7.2 112.2 _+ 7.1 112.2 +__7.3 112 128 120
89.6 --- 7.4 89.4 - 7.0 88.7 -+ 7.1 89.3 _+ 7.5 89 81 80
-10.6 -10.2 -10.4 -10.3 -10 -6 0
~ Phe _+ 9.2 _+ 9.1 --_ 8.9 __. 9.1
-100.8 - 8.1 -101.2 _+ 8.1 -100.6 +_ 7.9 -101.1 +_ 8.1 -101 -107
Averages over all the molecules in the simulation box. b Ref.[4] Ref.[3] from X-ray diffraction [5] and the standard values [3] for the/3-turn Type I. All of the independent 24 molecules exhibit very similar conformation:el, Pro = - 5 6 °, XI't pro = - 3 2 °, cbGly= -91 °, ~Gly = 15 ° and tI~ph e •ffi - 9 8 °. The characteristic feature of the /~-turn Type I is a hydrogen bond which is formed between the CO group of the first residue and the NH group of the fourth residue with (cI,,~)2 = ( - 6 0 ° , - 3 0 °) and (,I,,~)3 -- (-900,0 °) for the second and the third residues. Each of the peptides of the system I exhibits the /~-turn Type I structure and this coincides with the results from the X-ray analysis of the orthorhombic crystal. In contrast to the rather stiff conformation of the backbone for each peptide in the crystal, the rapid motion of the Phe side-chain is observed in each of the peptides during the 200 ps MD simulation in the crystal. This is consistent with the feature drawn by the thermal factors from the X-ray analysis [5]. Table 4 lntra- and intermolecularhydrogen bond distances (,~) in N-AcetylPro-Gly-Phe-OHsystem II crystal during 200 ps simulation Pair number
Pair
Hydrogen bond distance
Intramolecular Oacetyn(A)-HNphe(A) Oa~tyn(B)-HNrbe(B) Oa=tyn(D)-HNphe(D)
1.86 -+ 0.11 1.85 --- 0.11 1.86 + 0.11 1.86 -+ 0.11
OGIy(B)-HNGIy(A) Ocly(A)-HN6ny(C) Opro(A)-HOxt(D) Opro(E)-HOxt(A)
1.81 _+ 0.12 1.82 - 0.12 1.76 _+ 0.08 1.76 -+ 0.08
O acetyl(C)-nN Phe(C) Intermolecular
As is shown in Fig. 2, this/~-turn conformation of a molecule in the crystal is stabilized not only by one intramolecular hydrogen bond between acetyl O and HNph~ in each of the peptide, but also by four intermolecular hydrogen bonds: between HNGIy (A) and Opro (B), between Opro (A) and HN~Iy (C), between O~ly (A) and terminal HOxt(D), and terminal HOxt(A) and OGly (E). The intermolecular hydrogen bonds, as well as the intramolecular hydrogen bonds, are formed stably during the 200 ps simulation (Table 2). It should be emphasized that this type of/S-turn conformation is equally stabilized by both the intraand intermolecular hydrogen bond networks. 3.2. M D simulation o f the system H
The X-ray data for the peptide in the/~-turn Type II [4] was used as an initial structure of the simulation in another crystal. As was described in the Method, there are 36 independent molecules in the simulation box with the periodic boundary condition. A snapshot of the molecules during the simulation in the crystal is shown in Fig. 3(a). The stereo view of the snapshot is shown in Fig. 3(b). Each molecule forms four intermolecular hydrogen bonds with its neighbors, as well as one intramolecular hydrogen bond. The molecule A arbitarily selected is connected by hydrogen bonds with the four neighbors (B, C, D and E). The molecules D and E, which are next to the molecule A translated by one unit up and down respectively along the c-axis, are not shown in Fig. 3 to avoid confusion. The average values of the torsional angles of the peptide main chain for the molecules which appear in
M. Aida et al./Journal of Molecular Structure (Theochem) 388 (1996) 187-200
Y
8~/I~/~a
8
[3 a
Y Cy-exo - C~-endo
C y - e n d o - C[3-exo
Z1 < 0
Z1 > 0
0 >0
0 <0
Fig. 4. Schematic description of the pyrrolidine ring puckering.
Table 5 Torsional angles in the pyrrolidine ring of the molecule A in N-Acetyl-Pro-Gly-Phe-OH system I crystal Dihedral angle description ~/Pro 0 ~['r° 0
Npro-C°tpro-Cpro-Ngly Cac-Npro-Cotpro-Cpro C 6 o r o - N m - C a m - C r ~o CtSp~o-Np~o-Cap~o-Cflp~o
X1 X3
C-Ypro-C~pro-Npro-Co~pr o Npro-Co~pro-C~pro-C'Ypro C~pro-C,),pro-C~pro-Npro
X4
MD a -33.4 ± 9.1 -54.6 _ 7.9 125.7 +- 8.1 3.7 ± 9.0 6.3 + 13.7 -12.2 ± 23.6 -13.7 - 26.6 C3,-exo-Cfl-endo/ C),-endo-C/~-exo
X-ray b -12 -76 113 -8 -15 28 32 C),-endo-C/~-exo
Average values in degrees with the root-mean square deviations during the 200 ps MD simulation in crystal b Ref.[5]
Table 6 Torsional angles in the pyrrolidine ring of the molecule A in N-Acetyl-Pro-Gly-Phe-OH system II crystal
't'wo
Torsional angle description
MD a
X-ray b
N m - Cctpro-Cpro-Ngly Cac-Nm-Cotm-Cpro C/tpro-Np~o-C~m-C ~
112.0 ± 7.1 -47.3 ± 5.8 133.8 - 5.7 13.0 +- 5.7 8.7 ± 7.5 -29.5 ± 8.6 -26.9 - 10.4 C~-endo-C3,-exo
128 -59 130 10 12 -28 -30 C~-endo-C3,-exo
Ct~pro-Npro-Cotpro-C~p m C'Ypro-C~pro-Npro-Cotpro Nm-C~m-C/3m-C't m C~pro-C')'~o-CtSpro-Npro
a Average values in degrees with the root-mean square deviations during the 200 ps MD simulation in crystal b Ref.[4]
193
194
M. Aida et al.Hournal of Molecular Structure (Theochem) 388 (1996) 187-200
a)
b)
~Pro
e
-(
7
0
O
45.0
0.0"
30.0
o
15.0
-30.0
o
0.0
C m
-15.0
-60.0 0
0
-30.0
-90.0
. . . . 0.0
, .... 50.0
, .... 100.0
time
c)
, . . . . 150.0
-45.0 200.0
. . . . 0,0
i
. . . .
50.0
m
time
(ps)
d)
;(4
. . . .
100.0
0
7
0
45.0
45.0
30.0
30.0
15.0
15.0
0.0
0.0
-15.0
-15.0
-30.0
-30.0
-45.0
. . . . 0.0
i 50.0
. . . .
200.0
(ps)
0
c 0
. . . .
Z1
7
ol rell
| 150.0
i 100.0
. . . .
i 150.0
-45.0
. . . . 200.0
. . . . 0.0
i 50.0
. . . .
i 100.0
. . . .
i 150.0
. . . . 200.0
M. Aida et al./Journal of Molecular Structure (Theochem) 388 (1996) 187-200
Fig. 3 are summarized in Table 3, together with the data from X-ray diffraction [4]. All of the independent 36 molecules exhibit very similar conformation: ~PPro= --47 °, Xirpro -- 112°, tinGly = 89 °, XI/GIy = _10 ° and OPhe = -101°. The characteristic feature of the Type II /3-turn is a hydrogen bond which is formed between the CO group of the first residue and the NH group of the fourth residue with (¢I',xIr)2 = (-60°,120 °) and (tI',~)3 = (800,0°) for the second and the third residues. Each of the peptides of the system II takes the Type II/3-turn structure and this coincides with the results from the X-ray analysis of the monoclinic crystal. Although the backbone of each peptide is rather stiff, the 200 ps MD simulation shows the rapid motion in the Phe side-chain in the crystal. As is shown in Fig. 3, this/3-turn Type II conformation of a molecule in the crystal is stabilized by one intramolecular hydrogen bond between acetyl O and HNph¢ in each of the peptides, as well as four intermolecular hydrogen bonds: between HN~ly (A) and OGly (B), between Ooly (A) and HNGJy (C), between O p~o(A) and terminal HOxt(D), and terminal HOxt(A) and Oe~o(E). Note that the combination of the hydrogen bonding is different from the case in the system I. The average hydrogen bond lengths with the rootmean square deviations during the 200 ps MD simulation are summarized in Table 4. All the hydrogen bonds are formed stably during the 200 ps simulation.
3.3. Ring puckering of the pyrrolidine ring in the crystal The pyrrolidine ring in proline residues is known to assume a variety of different conformations in crystal structures [12]. In the system I crystal, the NMR data [5] shows that the pyrrolidine ring undergoes puckering motion between C3,-endo and C,y-exo forms (see Fig. 4). The X-ray analysis of the system II crystal shows that it adopts a mixed C~-endo-C3,-exo puckered conformation with large thermal parameters of the C3' atom [4]. The torsional angles of the pyrrolidine ring in the current MD simulations are summarized in Tables 5 and 6 for the system I and the system
195
II crystals, respectively. The history plots of some of the torsional angles for the molecule A of the system I and system II are shown in Figs. 5 and 6, respectively. For the system II crystal, the fluctuation of the pyrrolidine ring as shown in the values of the root-mean square deviations in Table 6 is rather small: the torsional angles (Table 6) observed during the 200 ps MD simulation represent well the experimentally detected values. Contrary to this, the fluctuations of the ring torsional angles are very large for the system I crystal (Table 5) and the puckering motion is observed during the 200 ps MD simulation. Fig. 5(b) and 5(d) show the history plots of 0 (C~pro-Npro-C~pro-C/~pro) and )¢1 (Npro_Cotpro_C ~ pro-C~cpro), respectively, for the system I. In the history plots, it should be noted that the signs of the torsional angles change: it means that the ring puckering occurs. The torsional angle O indicates the displacement of the a t o m C~pr o from the Npro-Cotpro-C~pro plane, while the torsional angle X1 indicates the displacement of the atom CTpro from the Npro-Cotpr o C/3pro plane. Comparing the plots for these torsional angles, it is found that the displacement of the C3'pro atom is larger than that of the CcSproatom from the Npro-Cc~pro-C/~pr o plane. Fig. 5(c) shows the X 4 (C'Ypro-C6pro-Npro-Capro) which also indicates the displacement of the atom C3'pro from the CSproNpro-Cotpr o plane. The torsional angle 0 also indicates the displacement of the atom C~p~o from the CdiproNpro-Cotpr o plane (Fig. 5(b)). It is worthwhile to point out that the displacement of the Cqcpro a t o m is significantly larger than that of the C~pro atom from the Ct~pro-Npro-Co~pr o plane (Fig. 5(b) and 5(c)). These observations show that the pyrrolidine ring in the system I crystal undergoes conformational changes between the two states, i.e., C3,-exo-C/~-endo and CT-endo-C~-exo (Fig. 4). Our solid-state NMR data suggests the existence of the ring puckering motion between the C3,-exo and C3,-endo forms in the system I (orthorhombic) crystal [5]. The observation during the current MD simulation agrees well with the experimental data. Fig. 6 shows the history plots of some torsional
Fig. 5. History plots of the torsional angles around the pyrrolidine ring of the molecule A in the system I crystal during the 200 ps MD simulation. (a) ~pro(LCac-Npro-Ctxpro-Cpro); (b) 0(LC~ipro-Npro-Cotpro-C~pro); (c) X4(LC"Ypro-Ct~pro-Npro-ftXpro); (d) xl(LNpro-Ctxpro -
C~pro-C'yp~o).
196
M. Aida et al./Journal of Molecular Structure (Theochem) 388 (1996) 187-200
a)
b)
OPro
e
,.,(
"f
~ 0.0t
45.0
-30.0
o ¢-
~= C
-60.0 '
0
0
-30.0
-90,0
.
0.0
.
.
.
i
50.0
.
.
.
.
i
time
c)
.
.
.
100.0
.
|
.
150.0
.
.
-45.0
.
200.0
. . . . 0.0
, .... 50.0
(ps)
, .... 100.0 time
;(4.
d)
(ps)
7
0
0 0
,w 10
200.0
X~
Y
A o
, . . . . 150.0
45.0
45.0
30.0
30.0'
15.0'
15.0'
0.0"
0.0"
/
C
I=
-15.0
-15.0 '
-30.0
-30.0
° 0_ 0
-45.0
-45.0 0.0
50.0
100.0
150.0
200.0
0.0
50.0
100.0
150,0
200.0
M. Aida et al./Journal of Molecular Structure (Theochem)388 (1996) 187-200
angles for the system II crystal. The situation in the system II is different from that in the system I: the puckering seldom occurs. The pyrrolidine ring in the system II is in the C/3-endo-C'r-exo state during the 200 ps MD simulation with a small fluctuation. As shown in Fig. 6, the C'y atom moves to the other side of the pyrrolidine ring once a while, but the C/3 atom does not. This tendency of the C~ atom causes the rather small fluctuation of the pyrrolidine ring in the system II, although a possibility of the ring puckering motion in the longer time scale could not be denied at present. 3.4. The tripeptide in vacuo The energy-minimized structure of the isolated tripeptide from the system I crystal is shown in Fig. 7(a); the torsional angles of the peptide main chain are ¢~Pro=--51"6°, a/Pro = --26-8°, tinGly -= -118"1°, a/Gly = 56.3 ° and ~ehe = -134.4°. The energy-minimized structure from the system II crystal is also shown in Fig. 7(b), the torsional angles of the peptide main chain are ~Pro = -48.5°, a/Pro = 106.0°, ~O~y = 134.8 °, a/~ly = -42.8° and CI~phe = -96.3 °. The former corresponds to the ~-turn Type I and the latter corresponds to the ~-tum Type II. Each of the MD simulations of the isolated peptide in vacuo starting from the energy-minimized structures gave the completely different conformations from those observed in the crystals. A 'snapshot' during the simulations is shown in Fig. 7(c): the three tight hydrogen bonds (Oacetyl-HNGly,Opro-HNpheand OGJy-HOxt) are formed in the peptide. It is emphasized that this tripeptide does not take the ~/-turn form, when it is treated as isolated in vacuo.
4. Discussion
Proline is contained in many biologically important peptide sequences [13-15]. Proline is a unique amino acid since its a-nitrogen atom is a part of the pyrrolidine ring, and it imposes strong restraints on the conformation of a peptide chain. The conformational
197
energy of a proline residue is known to depend largely on the value of a/. For an isolated proline residue there are two minima around a/Pro = -55° and a/Pro = +145 ° [16]. In the current simulations of N-acetyl-Pro-GlyPhe crystal, the average values are a/P~o = -32 ° and a/pro = +112 ° for the system I crystal (~-turn Type I) and system II crystal (~/-turn Type II), respectively, as shown in Tables 1, and 3. The observed a/Pro values in two different crystalline states correspond to the energetically favored values, as far as the conformation of a proline residue is concerned. In both crystals I and II, the same number of hydrogen bonds are formed firmly during the 200 ps simulation with the different combination. The torsional angles of the peptide in the crystal I (Table 1) are consistent with those of the/3-turn Type I during the 200 ps simulation, whereas those of the crystal II (Table 3) are in the form of the /3-turn Type II. These are in good agreement with the experimental X-ray data [4,5]. We therefore concluded that the two types of the ~-turn forms were correctly reproduced by the MD simulation under the condition that the correct numbers of the intramolecular as well as intermolecular hydrogen bond networks were taken into account. On the contrary, MD simulation of the isolated peptide in vacuo gave a completly different form (Fig. 7(c)) than the one experimentally derived. A number of local minima exist for a flexible peptide, as far as a single molecule is concerned. It is worthy of note that the energy-minimized conformations of the tripeptide (Fig. 7(a) and (b)) are close to those found in the system I crystal (Fig. 2) and the system II crystal (Fig. 3), respectively. This result indicates that the conformation of the flexible peptide in crystal is close to one of the local minima of the peptide, although it is completely different from those found in the MD simulation of the isolated peptide in vacuo (Fig. 7(c)). It is interesting to note that both of the intrinsic structural feature of the peptide itself and the inter-molecular hydrogen bonding interactions play important roles in determining the conformation of the peptide in crystal. It is noticeable that the pyrrolidine ring of the system I crystal undergoes the puckering motions as
Fig. 6. History plots of the torsional angles around the pyrrolidine ring of the molecule A in the system II crystal during the 200 ps MD simulation. (a) ~pro(LCac-Npro-Capro-Cpro); Co) O(LC~)pro-Npro-Cotpro-C~pro);(c) x4(LC'Ypro-C~pro-Npro-Cotpro); (d) xl(LNpro-Cotpro-C
~pro--C'ym).
198
M. Aida et al./Journal of Molecular Structure (Theochem) 388 (1996) 187-200
manifested from the present M D simulation, although no such m o t i o n appears in the system II crystal: the time scale of the ring puckering m o t i o n o f the former is in the order o f 10 -x° to 10 -11 s b e t w e e n the
C3,-exo-CB-endo and C3,-endo-CB-exo conformations, where the amplitude of the displacement of the C3' is larger than that of the CB, as demonstrated in Fig. 5. The presence or absence of such motion can
a)
b)
c) 02
o.~ "(3
©
Fig. 7. (a) A stereo view of the energy-minimized structure of the molecule A from the system I crystal. (b) A stereo view of the energyminimized structure of the molecule A from the system II crystal. (c) A stereo view of one snapshot of the peptide during the MD simulation in vacuo.
M. Aida et al./Journal of Molecular Structure (Theochem) 388 (1996) 187-200
be probed by the 13C spin-lattice relaxation times (T1) which are sensitive to the motions in the order of 10 -8 to 10 -1° s. The specific reductions of the T1 values of both C/8 and C',/carbon signals in Pro residues (1-3 s) as in collagen, (Pro)n, Ala-Pro-Gly, etc., compared with those of other carbons (10-20 s), were explained in terms of the ring puckering motion between the conformations of the C3,-exo-C/~-endo and C',/-endoC/3-exo in the solid-state [17]. It was shown that the T 1 values for Pro C~ and C3, of cyclo(Gly-Pro-D-Ala) were of the order of 3 s, and the estimated correlation time of the puckering motion was 1.2 x 10 -11 S [18]. This is comparable to the result of the present simulation. Our previous NMR study of N-acetyl-Pro-GlyPhe in orthorhombic crystal [5] showed the broadened 13C resonance line of the C3' carbon signal caused by the interference with the decoupling frequency, and the correlation time for the ring-puckering in Nacetyl-Pro-Gly-Phe was estimated to be in the order of 10 -4 to 10 -5 s. It should be noted that the estimation of the correlation time in NMR study depends on the models used in the analysis, and it is likely that some concerted motion of the molecules in crystal might be related in this case. The present 200 ps MD simulation is too short to represent concerted motions of the molecules in crystal. No experimental data for the relaxation parameters for the system II crystal (monoclinic) is available at present, in spite of our continued effort to crystallize the peptide in this crystalline form, although the present MD simulation predicts no ring puckering motions in this crystalline form. What is the origin of the difference of the puckering motions between the system I and II crystals? It is worth noting that the Owo (i.e., Cac-Npro-Cotpr o Cprn) in the system I crystal (Fig. 5(a)) fluctuates largely during the 200 ps simulation, although the Oproin the system II crystal (Fig. 6(a)) does not. In either of the systems, the acetyl O atom is involved in the intramolecular hydrogen bond with the HNph e atom and the Ovro atom is involved in the inter-molecular hydrogen bond. As shown in Tables 2, and 4, however, the hydrogen bond distances from Orro atoms in the system I crystal (HNGIy(A) - Opro(l) and Opro(A)HN~Iy(C)) are longer than those in the system II crystal (Owo(A)-HOxt(D) and Or~o(E)-HOxt(A)). The rather loose hydrogen bonds in the system I crystal allows the CI'proto fluctuate and the large amplitude in fluctuation of the Opro brings about the puckering
199
motion of the pyrrolidine ring. In the system II crystal, the tight hydrogen bond networks including Opro atoms do not allow the fluctuation of the Oprotorsional angle and this smaller fluctuation of the Oproprevents from puckering of the pyrrolidine ring. Finally, it is worthwhile to point out that the present MD simulations for N-acetyl-Pro-Gly-Phe reproduced successfully the two types of the /3-turn conformations, as far as the hydrogen-bond networks were correctly taken into account under the conditions of the crystalline states. No solvent molecules (such as water molecules) are detected in either of the crystals experimentally: there is no solute-solvent interactions in the present crystals. Our MD simulations treated the tripeptide molecules in the crystal conditions, and reproduced the conformations of the tripeptide in the crystals. In addition, the dynamical features of the side-chain motions of the phenyl ring and in the pyrrolidine ring were drawn from the MD simulation. Since the hydrogen bonding interactions play an important role in determining the conformations and the dynamical features of the peptides in crystal, it is critical to use the force field which is able to represent the distance and angle dependencies of the hydrogen bonding intereractions. Our set of ab initio potentials derived from the ab initio MO calculations [6] is very suitable for the study of the present purpose [7,8].
Acknowledgements The numerical calculations were carded out on the IBM/RS6000 Powerstations at the National Cancer Center Research Institute and on the SP2 at the computer center of the Institute for Molecular Science. This work was supported in part by a Grant-in Aid for Priority Area (07208230) from the Ministry of Education, Science and Culture, Japan.
References [1] S.K. Brahmachari and V.S. Ananthanarayanan, Proc. Natl. Acad. Sci. U.S.A.,76 (1979)5119. [2] J.G. Beely, Biochem. Biophys. Res. Commun., 76 (1977) 1051. [3] P.Y. Chou and G.D. Fasman, J. Mol. Biol., 115 (1977) 135.
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[4] S.K. Brahmachari, T.N. Bhat, V.Sudhakar, M.Vijayan, R.S. Rapaka, R.S. Bhatanagar and V.S. Ananthanarayanan, J. Am. Chem. Soc., 103 (1981) 1703. [5] A. Naito, K. Nishimura, S, Kimura, S. Tuzi, M. Aida, N. Yasuoka and H. Saito, J. Phys, Chem., 100 (1996) 14995. [6] M. Aida, G. Corongiu and E. Clementi, Int. J. Quantum Chem., 42 (1992) 1353. [7] M. Aida, Bull. Chem. Soc. Jpn., 66 (1993) 3423. [8] M. A.ida, J. Mol. Struct. (Theochem.), 311 (1994) 45. [9] G. Corongiu, M. Aida, M.F. Pas and E. Clementi, in E. Clementi (Ed.), Modern Techiniques in Computational Chemistry: MOTECC-91, ESCOM, Leiden, 1991, Chapter 21. [10] S.W. De Leeuw, LW. Perran and E.R. Smith, Proc. Roy. Soc. (London), A373 (1980) 27.
[11] J.E. Dennis, D.M. Gay and R.E. Welsch, ACM Trans. Math. Software, 7 (1981) 369. [12] G. Kartha and G.Ambaby, Acta Crystallogr., Sect. B, B31 (1975) 2035. [13] M.W. MacArthur and J.M. Thornton, J. Mol. Biol., 218 (1991) 397. [14] G. Vanhoof, F. Goossens, I. de Meester, D. Hendriks and S. Scharp6, FASEB J., 9 (1995) 736. [15] P.R. Schimmel and P.J. Flory, J. Mol. Biol, 34 (1968) 105. [16] K.A. Williams and C.M. Deber, Biochemistry, 30 (1991) 8919. [17] H. Saito and M. Yokoi, J. Biochem. (Tokyo), 111 (1992) 376. [18] S.K. Sarkar, D.A. Torchia, K.D. Kopple and D.L. VanderHart, J. Am. Chem. Soc., 106 (1984) 3328.
Journal of Molecular Structure (Theochem) 388 (1996) 187-200
Molecular dynamics simulations of a simple tripeptide, N-acetyl-Pro-Gly-Phe in the crystalline states: distinction of the B-turn Type I from the Type II Form M i s a k o A i d a a, A k i r a N a i t o b, H a z i m e
Sait6 u
aBiophysics Division, National Cancer Center Research Institute 5-1-1, Tsuko'i Chuo-ku, Tokyo 104, Japan bDepartment of Life Science, Himeji Institute of Technology, Harima Science Garden City, Kamigori, Hyogo 678-12, Japan
Received 21 February 1996; accepted 19 March 1996
Abstract
Molecular dynamics (MD) simulations of a simple tripeptide N-acetyl-Pro-Gly-Phe in the crystalline states show that this tripeptide exhibits two different ~-tum conformations (Types I and II) in two different crystalline states. The combination of the one intramolecular and four intermolecular hydrgen bonds for each molecule in crystal plays an important role in determining a propensity to form either Type I or Type II conformation. Each of the conformations in crystals is found to be close to one of the local minima of the tripeptide itself, although more stable conformations appear in the MD simulation of the single tripeptide in vacuo. It is concluded that the conformations in crystal cannot be formed without the intermolecular interactions. The present MD simulation in one of the crystalline states demonstrates the presence of the puckering motion in the pyrrolidine ring, which is consistent with our previous finding by solid-state NMR. Keywords: Molecular dynamics; Peptide conformation; 13-Turn; Proline puckering; Crystal
1. Introduction
The 3-turn conformation is one of the important structural motifs in globular proteins, leading to globularity rather than linearity. Functional roles have been also assigned to the 3-turn form such as the site for enzymatic action [1,2]. An analysis of the X-ray crystallographic data on several globular proteins [3] reveals positional preferences for the amino acid residues to occur within the/3-turn formed by the tetrapeptide segment X1-X2-Xa-X4: the sequence of X1-Pro-GIy-X4 forms the 3-turn structure preferentially. The characteristics of the 3-turn is a hydrogen bond which is formed between the CO group of the first residue and the NH group of the fourth residue.
The 0-turn Type I has (~,XIt)2 = ( -- 60 °, - 30 °) and (CI~,xI¢)3 = ( -- 90°,0°); the 3-turn Type II has (~,ff')2 = ( - 60°,120 °) and (~,~)3 = (800,0 °) for the second and third residue of the tetrapeptide segment. Among the Pro-Gly-containing peptides, N-acetyl-Pro-Gly-Phe (N-acetyl-L-prolylglycyl-L-phenylalanine; see Fig. 1) is known to assume the 3-turn Type II conformation in the monoclinic crystal [4]. Recently, we found during the course of our solid-state NMR study [5] that this tripeptide takes also the 3-turn Type I conformation in the orthorhombic crystal, although solvent compositions for the crystalization of both types of crystals were almost the same. This small tripeptide seems to adopt different conformations depending on the intermolecular interactions in the crystal.
0166-1280/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved PII S0166-1280(96)04625-8
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M. Aida et al./Journal of Molecular Structure (Theochem) 388 (1996) 187-200
U n
T"
/
\
c---
o
i
H--N
~
o
\
'~Ph,,
Fig. 1. Schematicrepresentationof N-acetyl-Pro-Gly-Phe. It is very interesting to reveal why these two types of conformations are present for the same molecule without involvement of any other molecules such as solvent molecule(s). In the present study, MD simulations of the tripeptide N-acetyl-Pro-Gly-Phe have been performed under the conditions of the two kinds of crystals, in order to gain insight into the stabilization mechanism of both types of the /3-turn conformations using the ab initio potentials [6] which are known to reproduce well the manner of hydrogen bonding interactions [7,8]: the use of this sort of force field is very important in view of the/3-turn conformations which are supposedly stabilized by intra- and/or inter-molecular hydrogen bonds. In fact, we arrive at the two types of the ~-turn conformations which are very similar to those of the X-ray diffraction studies [4,5]. In addition, the internal motions such as puckering motions of the pyrrolidine ring are described well by our MD simulation and consistent with the data of solid-state NMR [5]. This is the first successful MD approach to reproduce conformations of small peptides in the crystalline states to the best of our knowledge.
2. Methods Molecular dynamics calculations were performed using the KGNMD program from the MOTECC package [9] with the ab initio potentials for the solute intraand intermolecular interactions [6]. The total energy of a system is described as the sum of the solute nonbonded and the solute bonded interaction energies [9].
All the atoms are considered explicitly. In the Coulomb term, the relative dielectric constant is 1, in all cases. The equations of motion were solved using the leap-frog algorithm with a time step of 0.5 fs. All the simulations were performed within the microcanonical ensemble, maintaining constant energy, volume and number when calculating average properties. In all cases, periodic boundary conditions were applied. Two kinds of systems were simulated at 293 K in the crystallographic cells: the first system (system I) corresponds to the orthorhombic crystals [5]; the second system (system II) corresponds to the monoclinic crystals [4]. Since no solvent molecules (such as water molecules) are detected in either of the crystals experimentally, only the tripeptide molecules are taken into consideration in the conditions of the crystalline states. For each of the systems, we used the simulation box which was composed of a certain number of crystallographic cells, as will be described below, to be assured that a large enough value can be set for the cutoff radius for the non-bonded interactions. The long range Coulomb term was computed with the Ewald sum correction [10]. For the simulation of the system I, the X-ray structure [5] was used as the starting conformation. One simulation box was composed of 6 crystallographic cells: 2 cells along the a-axis, 1 cell along the b-axis and 3 cells along the c-axis. The lattice parameters are as follows: a = 10.455 A,, b = 22.93 .~ and c ~ 7.452 ,~. Four molecules per cell were placed in a crystallographic cell with the symmetry of the space group P212121. In total, 24 molecules were included in a simulation box. All these molecules were treated independently during the simulation with the periodic boundary conditions. A cutoff radius of 9.4 A was adopted with the Ewald sum correction for the long range Coulomb term. In the system II, one simulation box was composed of 18 crystallographic cells: 3 cells along the a-axis, 3 cells along the b-axis and 2 cells along the c-axis with the lattice parameters of a = 8.915 A, b = 8.458 A and c -- 13.216 A. The X-ray structure [4] was used as the starting conformation. Two molecules per cell were placed in a crystallographic cell with the symmetry of the space group P2t. In total, 36 molecules were included in a simulation box. During the simulation, they were treated as independent. The periodic boundary condition ensures that our simulation system is an
M. Aida et al./Journal of Molecular Structure (Theochem) 388 (1996) 187-200
189
a) Molecule D [
Molecule C I
i'be'
,~
/
o, -,b
IM°leculeAI
Molecule B ]
b)
,8
Fig. 2. (a) A snapshot of the tripeptides in the system I crystal during the 200 ps MD simulation. (b) A stereo view of the snapshot. Hydrogen bonds are denoted by the dotted lines.
M. Aida et aL/Journal of Molecular Structure (Theochem) 388 (1996) 187-200
190
Table 1 Torsional angles in degrees of the peptide main chain in N-Acetyl-Pro-Gly-Phe-OH system I crystal during 200 ps simulation ¢I~Fro
MD molecule A molecule B molecule C molecule D average a X-ray b type I B-turn c
-54.6 -56.9 -54.8 -56.4 -56 -76 -60
~It Pro
+ 7.9 --_ 8.2 _+ 7.8 ± 8.2
-33.4 -30.5 -32.6 -30.9 -32 -12 -30
¢I~Gly
+_ 9.1 _+ 9.8 _+ 9.6 _+ 9.7
-91.0 -90.7 -91.1 -90.8 -91 -86 -90
'ffl ely
_+ 7.4 _+ 7.5 ± 7.5 _+ 7.2
15.8 14.9 15.7 14.8 15 -4.5 0
~ Phe
_+ 9.7 _+ 9.6 _+ 9.4 _+ 9.2
-98.4 -98.5 -98.3 -98.2 -98 -83
_+ 8.3 _+ 8.1 _+ 8.0 _+ 8.0
a Averages over all the molecules in the simulation box. b Ref.[5] c Ref.[31
infinite crystal. The long range Coulomb term was computed with the Ewald sum correction with a cutoff radius of 11.5 .~. Each of the systems was equilibrated over 100 ps followed by a 50 ps run without velocity rescaling, since the average temperature remained essentially constant around 293 K. The final 200 ps simulation was used for analysis: coordinates and velocities were stored every 50 fs. For each of the system I and system II, one molecule was picked up after the MD simulation in crystal and the energy minimization was performed using the SUMSL (secant-type unconstrained minimization solver) routine [11]. The energy-minimized structures were then used as an initial structure for the MD simulation in vacuo at 293 K. The system was equilibrated during 50 ps followed by a 50 ps run without velocity rescaling, since the average temperature remained essentially constant around 293 K. The final 50 ps simulation was used for analysis: coordinates and velocities were stored every 50 fs.
stereo view of the snapshot is shown in Fig. 2(b). During the simulation, those 24 molecules were treated independently; however, the overall X-ray structure was preserved in the crystal. Each molecule forms four intermolecular hydrogen bonds with its neighbors, as well as one intramolecular hydrogen bond. Each molecule exhibits the f3-turn type I conformation. We select a molecule arbitrarily, and it is named the molecule A. In Fig. 2, the molecules which are connected by a hydrogen bond to the molecule A are shown. The molecule A forms hydrogen bonds with the four neighbors (B, C, D and E). The molecule E, which is next to the molecule D translated by one unit along the c-axis, is not shown in Fig. 2, to avoid confusion. The average values of the torsional angles of the peptide main chain for the molecules which appear in Fig. 2 are summarized in Table 1, together with those Table 2 Intra- and intermolecular hydrogen bond average distances (.~) in N-Acetyl-Pro-Gly-Phe-OH system I during 200 ps simulation
3. Results 3.1. MD simulation of the system I The X-ray data [5] was used as an initial structure of the simulation in the crystal. As it was described in the Method, there are 24 independent molecules in the the simulation box with the periodic boundary condition. A snapshot of the molecules during the simulation in the crystal is shown in Fig. 2(a), where the hydrogen bonds are denoted by the dotted line. The
Hydrogen bond pair
Hydrogen bond distance
Oacetyl(A)-HNphe(A) Oacetyl(B)-HNphe(B) Oacetyl(C)-HNphe(C) O acetyt(D)-HNphe(D)
2.07 2.09 2.07 2.07
-+ 0.19 -+ 0.20 --- 0.19 + 0.19
HNGly(A)-Opro(B) Opro(A)-HNGIy(C) OGIy(A)-HOxt(D) HOxt(A)-O6ly(E)
2.16 2.18 1.82 1.82
~ 0.18 ~ 0.18 _+ 0.11 ± 0.10
lntramolecular
Intermolecular
M. Aida et al./Journal of Molecular Structure (Theochem) 388 (1996) 187-200
191
a) P
~.
I~°'~'e ~ I
Molecule A ]
I~olecul~ B I
::
b)
Fig. 3. (a) A snapshot of the tripeptides in the system II crystal during the 200 ps MD simulation. (b) A stereo view of the snapshot. Hydrogen bonds are denoted by the dotted lines.
192
M. Aida et al./Journal of Molecular Structure (Theochem) 388 (1996) 187-200
Table 3 Torsional angles in degrees of the peptide main chain in N-Acetyi-Pro-Gly-Phe-OHsystem II crystal during 200 ps simulation cI~Pro MD molecule A molecule B molecule C molecule D average a X-ray b type II E-turn c
-47.3 -47.4 -47.2 -47.6 -47 -59 -60
- 5.8 +_ 5.6 _+ 5.7 +_ 5.6
~rPro
(I~Gly
XIIGly
112.0 -4- 7.1 112.1 _+ 7.2 112.2 _+ 7.1 112.2 +__7.3 112 128 120
89.6 --- 7.4 89.4 - 7.0 88.7 -+ 7.1 89.3 _+ 7.5 89 81 80
-10.6 -10.2 -10.4 -10.3 -10 -6 0
~ Phe _+ 9.2 _+ 9.1 --_ 8.9 __. 9.1
-100.8 - 8.1 -101.2 _+ 8.1 -100.6 +_ 7.9 -101.1 +_ 8.1 -101 -107
Averages over all the molecules in the simulation box. b Ref.[4] Ref.[3] from X-ray diffraction [5] and the standard values [3] for the/3-turn Type I. All of the independent 24 molecules exhibit very similar conformation:el, Pro = - 5 6 °, XI't pro = - 3 2 °, cbGly= -91 °, ~Gly = 15 ° and tI~ph e •ffi - 9 8 °. The characteristic feature of the /~-turn Type I is a hydrogen bond which is formed between the CO group of the first residue and the NH group of the fourth residue with (cI,,~)2 = ( - 6 0 ° , - 3 0 °) and (,I,,~)3 -- (-900,0 °) for the second and the third residues. Each of the peptides of the system I exhibits the /~-turn Type I structure and this coincides with the results from the X-ray analysis of the orthorhombic crystal. In contrast to the rather stiff conformation of the backbone for each peptide in the crystal, the rapid motion of the Phe side-chain is observed in each of the peptides during the 200 ps MD simulation in the crystal. This is consistent with the feature drawn by the thermal factors from the X-ray analysis [5]. Table 4 lntra- and intermolecularhydrogen bond distances (,~) in N-AcetylPro-Gly-Phe-OHsystem II crystal during 200 ps simulation Pair number
Pair
Hydrogen bond distance
Intramolecular Oacetyn(A)-HNphe(A) Oa~tyn(B)-HNrbe(B) Oa=tyn(D)-HNphe(D)
1.86 -+ 0.11 1.85 --- 0.11 1.86 + 0.11 1.86 -+ 0.11
OGIy(B)-HNGIy(A) Ocly(A)-HN6ny(C) Opro(A)-HOxt(D) Opro(E)-HOxt(A)
1.81 _+ 0.12 1.82 - 0.12 1.76 _+ 0.08 1.76 -+ 0.08
O acetyl(C)-nN Phe(C) Intermolecular
As is shown in Fig. 2, this/~-turn conformation of a molecule in the crystal is stabilized not only by one intramolecular hydrogen bond between acetyl O and HNph~ in each of the peptide, but also by four intermolecular hydrogen bonds: between HNGIy (A) and Opro (B), between Opro (A) and HN~Iy (C), between O~ly (A) and terminal HOxt(D), and terminal HOxt(A) and OGly (E). The intermolecular hydrogen bonds, as well as the intramolecular hydrogen bonds, are formed stably during the 200 ps simulation (Table 2). It should be emphasized that this type of/S-turn conformation is equally stabilized by both the intraand intermolecular hydrogen bond networks. 3.2. M D simulation o f the system H
The X-ray data for the peptide in the/~-turn Type II [4] was used as an initial structure of the simulation in another crystal. As was described in the Method, there are 36 independent molecules in the simulation box with the periodic boundary condition. A snapshot of the molecules during the simulation in the crystal is shown in Fig. 3(a). The stereo view of the snapshot is shown in Fig. 3(b). Each molecule forms four intermolecular hydrogen bonds with its neighbors, as well as one intramolecular hydrogen bond. The molecule A arbitarily selected is connected by hydrogen bonds with the four neighbors (B, C, D and E). The molecules D and E, which are next to the molecule A translated by one unit up and down respectively along the c-axis, are not shown in Fig. 3 to avoid confusion. The average values of the torsional angles of the peptide main chain for the molecules which appear in
M. Aida et al./Journal of Molecular Structure (Theochem) 388 (1996) 187-200
Y
8~/I~/~a
8
[3 a
Y Cy-exo - C~-endo
C y - e n d o - C[3-exo
Z1 < 0
Z1 > 0
0 >0
0 <0
Fig. 4. Schematic description of the pyrrolidine ring puckering.
Table 5 Torsional angles in the pyrrolidine ring of the molecule A in N-Acetyl-Pro-Gly-Phe-OH system I crystal Dihedral angle description ~/Pro 0 ~['r° 0
Npro-C°tpro-Cpro-Ngly Cac-Npro-Cotpro-Cpro C 6 o r o - N m - C a m - C r ~o CtSp~o-Np~o-Cap~o-Cflp~o
X1 X3
C-Ypro-C~pro-Npro-Co~pr o Npro-Co~pro-C~pro-C'Ypro C~pro-C,),pro-C~pro-Npro
X4
MD a -33.4 ± 9.1 -54.6 _ 7.9 125.7 +- 8.1 3.7 ± 9.0 6.3 + 13.7 -12.2 ± 23.6 -13.7 - 26.6 C3,-exo-Cfl-endo/ C),-endo-C/~-exo
X-ray b -12 -76 113 -8 -15 28 32 C),-endo-C/~-exo
Average values in degrees with the root-mean square deviations during the 200 ps MD simulation in crystal b Ref.[5]
Table 6 Torsional angles in the pyrrolidine ring of the molecule A in N-Acetyl-Pro-Gly-Phe-OH system II crystal
't'wo
Torsional angle description
MD a
X-ray b
N m - Cctpro-Cpro-Ngly Cac-Nm-Cotm-Cpro C/tpro-Np~o-C~m-C ~
112.0 ± 7.1 -47.3 ± 5.8 133.8 - 5.7 13.0 +- 5.7 8.7 ± 7.5 -29.5 ± 8.6 -26.9 - 10.4 C~-endo-C3,-exo
128 -59 130 10 12 -28 -30 C~-endo-C3,-exo
Ct~pro-Npro-Cotpro-C~p m C'Ypro-C~pro-Npro-Cotpro Nm-C~m-C/3m-C't m C~pro-C')'~o-CtSpro-Npro
a Average values in degrees with the root-mean square deviations during the 200 ps MD simulation in crystal b Ref.[4]
193
194
M. Aida et al.Hournal of Molecular Structure (Theochem) 388 (1996) 187-200
a)
b)
~Pro
e
-(
7
0
O
45.0
0.0"
30.0
o
15.0
-30.0
o
0.0
C m
-15.0
-60.0 0
0
-30.0
-90.0
. . . . 0.0
, .... 50.0
, .... 100.0
time
c)
, . . . . 150.0
-45.0 200.0
. . . . 0,0
i
. . . .
50.0
m
time
(ps)
d)
;(4
. . . .
100.0
0
7
0
45.0
45.0
30.0
30.0
15.0
15.0
0.0
0.0
-15.0
-15.0
-30.0
-30.0
-45.0
. . . . 0.0
i 50.0
. . . .
200.0
(ps)
0
c 0
. . . .
Z1
7
ol rell
| 150.0
i 100.0
. . . .
i 150.0
-45.0
. . . . 200.0
. . . . 0.0
i 50.0
. . . .
i 100.0
. . . .
i 150.0
. . . . 200.0
M. Aida et al./Journal of Molecular Structure (Theochem) 388 (1996) 187-200
Fig. 3 are summarized in Table 3, together with the data from X-ray diffraction [4]. All of the independent 36 molecules exhibit very similar conformation: ~PPro= --47 °, Xirpro -- 112°, tinGly = 89 °, XI/GIy = _10 ° and OPhe = -101°. The characteristic feature of the Type II /3-turn is a hydrogen bond which is formed between the CO group of the first residue and the NH group of the fourth residue with (¢I',xIr)2 = (-60°,120 °) and (tI',~)3 = (800,0°) for the second and the third residues. Each of the peptides of the system II takes the Type II/3-turn structure and this coincides with the results from the X-ray analysis of the monoclinic crystal. Although the backbone of each peptide is rather stiff, the 200 ps MD simulation shows the rapid motion in the Phe side-chain in the crystal. As is shown in Fig. 3, this/3-turn Type II conformation of a molecule in the crystal is stabilized by one intramolecular hydrogen bond between acetyl O and HNph¢ in each of the peptides, as well as four intermolecular hydrogen bonds: between HN~ly (A) and OGly (B), between Ooly (A) and HNGJy (C), between O p~o(A) and terminal HOxt(D), and terminal HOxt(A) and Oe~o(E). Note that the combination of the hydrogen bonding is different from the case in the system I. The average hydrogen bond lengths with the rootmean square deviations during the 200 ps MD simulation are summarized in Table 4. All the hydrogen bonds are formed stably during the 200 ps simulation.
3.3. Ring puckering of the pyrrolidine ring in the crystal The pyrrolidine ring in proline residues is known to assume a variety of different conformations in crystal structures [12]. In the system I crystal, the NMR data [5] shows that the pyrrolidine ring undergoes puckering motion between C3,-endo and C,y-exo forms (see Fig. 4). The X-ray analysis of the system II crystal shows that it adopts a mixed C~-endo-C3,-exo puckered conformation with large thermal parameters of the C3' atom [4]. The torsional angles of the pyrrolidine ring in the current MD simulations are summarized in Tables 5 and 6 for the system I and the system
195
II crystals, respectively. The history plots of some of the torsional angles for the molecule A of the system I and system II are shown in Figs. 5 and 6, respectively. For the system II crystal, the fluctuation of the pyrrolidine ring as shown in the values of the root-mean square deviations in Table 6 is rather small: the torsional angles (Table 6) observed during the 200 ps MD simulation represent well the experimentally detected values. Contrary to this, the fluctuations of the ring torsional angles are very large for the system I crystal (Table 5) and the puckering motion is observed during the 200 ps MD simulation. Fig. 5(b) and 5(d) show the history plots of 0 (C~pro-Npro-C~pro-C/~pro) and )¢1 (Npro_Cotpro_C ~ pro-C~cpro), respectively, for the system I. In the history plots, it should be noted that the signs of the torsional angles change: it means that the ring puckering occurs. The torsional angle O indicates the displacement of the a t o m C~pr o from the Npro-Cotpro-C~pro plane, while the torsional angle X1 indicates the displacement of the atom CTpro from the Npro-Cotpr o C/3pro plane. Comparing the plots for these torsional angles, it is found that the displacement of the C3'pro atom is larger than that of the CcSproatom from the Npro-Cc~pro-C/~pr o plane. Fig. 5(c) shows the X 4 (C'Ypro-C6pro-Npro-Capro) which also indicates the displacement of the atom C3'pro from the CSproNpro-Cotpr o plane. The torsional angle 0 also indicates the displacement of the atom C~p~o from the CdiproNpro-Cotpr o plane (Fig. 5(b)). It is worthwhile to point out that the displacement of the Cqcpro a t o m is significantly larger than that of the C~pro atom from the Ct~pro-Npro-Co~pr o plane (Fig. 5(b) and 5(c)). These observations show that the pyrrolidine ring in the system I crystal undergoes conformational changes between the two states, i.e., C3,-exo-C/~-endo and CT-endo-C~-exo (Fig. 4). Our solid-state NMR data suggests the existence of the ring puckering motion between the C3,-exo and C3,-endo forms in the system I (orthorhombic) crystal [5]. The observation during the current MD simulation agrees well with the experimental data. Fig. 6 shows the history plots of some torsional
Fig. 5. History plots of the torsional angles around the pyrrolidine ring of the molecule A in the system I crystal during the 200 ps MD simulation. (a) ~pro(LCac-Npro-Ctxpro-Cpro); (b) 0(LC~ipro-Npro-Cotpro-C~pro); (c) X4(LC"Ypro-Ct~pro-Npro-ftXpro); (d) xl(LNpro-Ctxpro -
C~pro-C'yp~o).
196
M. Aida et al./Journal of Molecular Structure (Theochem) 388 (1996) 187-200
a)
b)
OPro
e
,.,(
"f
~ 0.0t
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o ¢-
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.
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.
.
.
i
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.
.
.
.
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.
.
.
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.
|
.
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.
.
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.
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. . . . 0.0
, .... 50.0
(ps)
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(ps)
7
0
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,w 10
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, . . . . 150.0
45.0
45.0
30.0
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15.0'
15.0'
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° 0_ 0
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-45.0 0.0
50.0
100.0
150.0
200.0
0.0
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150,0
200.0
M. Aida et al./Journal of Molecular Structure (Theochem)388 (1996) 187-200
angles for the system II crystal. The situation in the system II is different from that in the system I: the puckering seldom occurs. The pyrrolidine ring in the system II is in the C/3-endo-C'r-exo state during the 200 ps MD simulation with a small fluctuation. As shown in Fig. 6, the C'y atom moves to the other side of the pyrrolidine ring once a while, but the C/3 atom does not. This tendency of the C~ atom causes the rather small fluctuation of the pyrrolidine ring in the system II, although a possibility of the ring puckering motion in the longer time scale could not be denied at present. 3.4. The tripeptide in vacuo The energy-minimized structure of the isolated tripeptide from the system I crystal is shown in Fig. 7(a); the torsional angles of the peptide main chain are ¢~Pro=--51"6°, a/Pro = --26-8°, tinGly -= -118"1°, a/Gly = 56.3 ° and ~ehe = -134.4°. The energy-minimized structure from the system II crystal is also shown in Fig. 7(b), the torsional angles of the peptide main chain are ~Pro = -48.5°, a/Pro = 106.0°, ~O~y = 134.8 °, a/~ly = -42.8° and CI~phe = -96.3 °. The former corresponds to the ~-turn Type I and the latter corresponds to the ~-tum Type II. Each of the MD simulations of the isolated peptide in vacuo starting from the energy-minimized structures gave the completely different conformations from those observed in the crystals. A 'snapshot' during the simulations is shown in Fig. 7(c): the three tight hydrogen bonds (Oacetyl-HNGly,Opro-HNpheand OGJy-HOxt) are formed in the peptide. It is emphasized that this tripeptide does not take the ~/-turn form, when it is treated as isolated in vacuo.
4. Discussion
Proline is contained in many biologically important peptide sequences [13-15]. Proline is a unique amino acid since its a-nitrogen atom is a part of the pyrrolidine ring, and it imposes strong restraints on the conformation of a peptide chain. The conformational
197
energy of a proline residue is known to depend largely on the value of a/. For an isolated proline residue there are two minima around a/Pro = -55° and a/Pro = +145 ° [16]. In the current simulations of N-acetyl-Pro-GlyPhe crystal, the average values are a/P~o = -32 ° and a/pro = +112 ° for the system I crystal (~-turn Type I) and system II crystal (~/-turn Type II), respectively, as shown in Tables 1, and 3. The observed a/Pro values in two different crystalline states correspond to the energetically favored values, as far as the conformation of a proline residue is concerned. In both crystals I and II, the same number of hydrogen bonds are formed firmly during the 200 ps simulation with the different combination. The torsional angles of the peptide in the crystal I (Table 1) are consistent with those of the/3-turn Type I during the 200 ps simulation, whereas those of the crystal II (Table 3) are in the form of the /3-turn Type II. These are in good agreement with the experimental X-ray data [4,5]. We therefore concluded that the two types of the ~-turn forms were correctly reproduced by the MD simulation under the condition that the correct numbers of the intramolecular as well as intermolecular hydrogen bond networks were taken into account. On the contrary, MD simulation of the isolated peptide in vacuo gave a completly different form (Fig. 7(c)) than the one experimentally derived. A number of local minima exist for a flexible peptide, as far as a single molecule is concerned. It is worthy of note that the energy-minimized conformations of the tripeptide (Fig. 7(a) and (b)) are close to those found in the system I crystal (Fig. 2) and the system II crystal (Fig. 3), respectively. This result indicates that the conformation of the flexible peptide in crystal is close to one of the local minima of the peptide, although it is completely different from those found in the MD simulation of the isolated peptide in vacuo (Fig. 7(c)). It is interesting to note that both of the intrinsic structural feature of the peptide itself and the inter-molecular hydrogen bonding interactions play important roles in determining the conformation of the peptide in crystal. It is noticeable that the pyrrolidine ring of the system I crystal undergoes the puckering motions as
Fig. 6. History plots of the torsional angles around the pyrrolidine ring of the molecule A in the system II crystal during the 200 ps MD simulation. (a) ~pro(LCac-Npro-Capro-Cpro); Co) O(LC~)pro-Npro-Cotpro-C~pro);(c) x4(LC'Ypro-C~pro-Npro-Cotpro); (d) xl(LNpro-Cotpro-C
~pro--C'ym).
198
M. Aida et al./Journal of Molecular Structure (Theochem) 388 (1996) 187-200
manifested from the present M D simulation, although no such m o t i o n appears in the system II crystal: the time scale of the ring puckering m o t i o n o f the former is in the order o f 10 -x° to 10 -11 s b e t w e e n the
C3,-exo-CB-endo and C3,-endo-CB-exo conformations, where the amplitude of the displacement of the C3' is larger than that of the CB, as demonstrated in Fig. 5. The presence or absence of such motion can
a)
b)
c) 02
o.~ "(3
©
Fig. 7. (a) A stereo view of the energy-minimized structure of the molecule A from the system I crystal. (b) A stereo view of the energyminimized structure of the molecule A from the system II crystal. (c) A stereo view of one snapshot of the peptide during the MD simulation in vacuo.
M. Aida et al./Journal of Molecular Structure (Theochem) 388 (1996) 187-200
be probed by the 13C spin-lattice relaxation times (T1) which are sensitive to the motions in the order of 10 -8 to 10 -1° s. The specific reductions of the T1 values of both C/8 and C',/carbon signals in Pro residues (1-3 s) as in collagen, (Pro)n, Ala-Pro-Gly, etc., compared with those of other carbons (10-20 s), were explained in terms of the ring puckering motion between the conformations of the C3,-exo-C/~-endo and C',/-endoC/3-exo in the solid-state [17]. It was shown that the T 1 values for Pro C~ and C3, of cyclo(Gly-Pro-D-Ala) were of the order of 3 s, and the estimated correlation time of the puckering motion was 1.2 x 10 -11 S [18]. This is comparable to the result of the present simulation. Our previous NMR study of N-acetyl-Pro-GlyPhe in orthorhombic crystal [5] showed the broadened 13C resonance line of the C3' carbon signal caused by the interference with the decoupling frequency, and the correlation time for the ring-puckering in Nacetyl-Pro-Gly-Phe was estimated to be in the order of 10 -4 to 10 -5 s. It should be noted that the estimation of the correlation time in NMR study depends on the models used in the analysis, and it is likely that some concerted motion of the molecules in crystal might be related in this case. The present 200 ps MD simulation is too short to represent concerted motions of the molecules in crystal. No experimental data for the relaxation parameters for the system II crystal (monoclinic) is available at present, in spite of our continued effort to crystallize the peptide in this crystalline form, although the present MD simulation predicts no ring puckering motions in this crystalline form. What is the origin of the difference of the puckering motions between the system I and II crystals? It is worth noting that the Owo (i.e., Cac-Npro-Cotpr o Cprn) in the system I crystal (Fig. 5(a)) fluctuates largely during the 200 ps simulation, although the Oproin the system II crystal (Fig. 6(a)) does not. In either of the systems, the acetyl O atom is involved in the intramolecular hydrogen bond with the HNph e atom and the Ovro atom is involved in the inter-molecular hydrogen bond. As shown in Tables 2, and 4, however, the hydrogen bond distances from Orro atoms in the system I crystal (HNGIy(A) - Opro(l) and Opro(A)HN~Iy(C)) are longer than those in the system II crystal (Owo(A)-HOxt(D) and Or~o(E)-HOxt(A)). The rather loose hydrogen bonds in the system I crystal allows the CI'proto fluctuate and the large amplitude in fluctuation of the Opro brings about the puckering
199
motion of the pyrrolidine ring. In the system II crystal, the tight hydrogen bond networks including Opro atoms do not allow the fluctuation of the Oprotorsional angle and this smaller fluctuation of the Oproprevents from puckering of the pyrrolidine ring. Finally, it is worthwhile to point out that the present MD simulations for N-acetyl-Pro-Gly-Phe reproduced successfully the two types of the /3-turn conformations, as far as the hydrogen-bond networks were correctly taken into account under the conditions of the crystalline states. No solvent molecules (such as water molecules) are detected in either of the crystals experimentally: there is no solute-solvent interactions in the present crystals. Our MD simulations treated the tripeptide molecules in the crystal conditions, and reproduced the conformations of the tripeptide in the crystals. In addition, the dynamical features of the side-chain motions of the phenyl ring and in the pyrrolidine ring were drawn from the MD simulation. Since the hydrogen bonding interactions play an important role in determining the conformations and the dynamical features of the peptides in crystal, it is critical to use the force field which is able to represent the distance and angle dependencies of the hydrogen bonding intereractions. Our set of ab initio potentials derived from the ab initio MO calculations [6] is very suitable for the study of the present purpose [7,8].
Acknowledgements The numerical calculations were carded out on the IBM/RS6000 Powerstations at the National Cancer Center Research Institute and on the SP2 at the computer center of the Institute for Molecular Science. This work was supported in part by a Grant-in Aid for Priority Area (07208230) from the Ministry of Education, Science and Culture, Japan.
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[4] S.K. Brahmachari, T.N. Bhat, V.Sudhakar, M.Vijayan, R.S. Rapaka, R.S. Bhatanagar and V.S. Ananthanarayanan, J. Am. Chem. Soc., 103 (1981) 1703. [5] A. Naito, K. Nishimura, S, Kimura, S. Tuzi, M. Aida, N. Yasuoka and H. Saito, J. Phys, Chem., 100 (1996) 14995. [6] M. Aida, G. Corongiu and E. Clementi, Int. J. Quantum Chem., 42 (1992) 1353. [7] M. Aida, Bull. Chem. Soc. Jpn., 66 (1993) 3423. [8] M. A.ida, J. Mol. Struct. (Theochem.), 311 (1994) 45. [9] G. Corongiu, M. Aida, M.F. Pas and E. Clementi, in E. Clementi (Ed.), Modern Techiniques in Computational Chemistry: MOTECC-91, ESCOM, Leiden, 1991, Chapter 21. [10] S.W. De Leeuw, LW. Perran and E.R. Smith, Proc. Roy. Soc. (London), A373 (1980) 27.
[11] J.E. Dennis, D.M. Gay and R.E. Welsch, ACM Trans. Math. Software, 7 (1981) 369. [12] G. Kartha and G.Ambaby, Acta Crystallogr., Sect. B, B31 (1975) 2035. [13] M.W. MacArthur and J.M. Thornton, J. Mol. Biol., 218 (1991) 397. [14] G. Vanhoof, F. Goossens, I. de Meester, D. Hendriks and S. Scharp6, FASEB J., 9 (1995) 736. [15] P.R. Schimmel and P.J. Flory, J. Mol. Biol, 34 (1968) 105. [16] K.A. Williams and C.M. Deber, Biochemistry, 30 (1991) 8919. [17] H. Saito and M. Yokoi, J. Biochem. (Tokyo), 111 (1992) 376. [18] S.K. Sarkar, D.A. Torchia, K.D. Kopple and D.L. VanderHart, J. Am. Chem. Soc., 106 (1984) 3328.