1351
J . Phys. Chem. 1989, 93, 1351-1357
Conformational Studies of Neuroactive Ligands. 2. Solution-State Conformations of Acetylcholine K. Jeff Wilson,$ Philippe Derreumaux,t Gerard Vergoten,? and Warner L. Peticolas* Department of Chemistry and Institute of Chemical Physics, University of Oregon, Eugene, Oregon 97403 (Received: May 20, 1988)
The Raman spectra of the acetylcholine (ACh) cation in aqueous and organic solvents have been obtained as a function of temperature. A comparison of these solution spectra has been made to Raman spectra obtained from crystals where the conformation has been determined from X-ray diffraction. This comparison indicates that two distinct methylene rocking vibrations are present in solution. The most reasonable interpretation of these spectra is that the two methylene rocking populations are due to at least two distinct conformations of the ACh cation in solution. Molecular mechanics and normal-coordinate calculations are used in conjunction with the experimentally observed vibrational spectra of ACh in solution to obtain the values of the torsional angles that produce the lowest internal potential energy and the best agreement between calculated and observed Raman frequencies. The results of this approach indicate that the ACh cation in solution exists in conformations centered about two loci defined by four torsional angles along the chain. These two loci are at the values of ( T ~ T, ] , T ~ T, ~ equal ) to (180°, 160°, 300°, 1 8 0 O ) and (180°, 260°, 280°, 180°), respectively.
TABLE I: Conformations of ACh from Previous Studies
Introduction
7"
In the previous paper of this series,' a molecular-crystalline force field was developed for crystalline acetylcholine (ACh) bromide that accurately reproduced all of the vibrational frequencies. Several Raman active vibrational bands were noted that appear to be useful as indicators of the conformation of the cation in the chloride, bromide, and iodide crystals. The work reported here describes the development of a simplified version of the crystalline force field in which intermolecular crystalline interactions are removed and the frequencies of the ACh cation are calculated from the conformation of the isolated molecule. In past years, several investigators have proposed, on the basis of theoretical calculations alone, various conformations of ACh as having the lowest energy and therefore being the most probable to be found either in vacuum or in solution.24 Table I contains the results of several of these studies. Interestingly, these calculations did not include experimental data obtained from measurements on the ACh cation in solution in the refinement of the parameters used. Concurrent with, but independent of, these theoretical investigations, several N M R spectroscopic studies were reported on solutions of the ACh cation, and solution conformations were deduced using N M R coupling constant^;^-'^ several of these results are also in Table I. Although such studies can yield useful information, there are potential problems with the conformations derived from the N M R data. The relationship(s) between conformation and N M R coupling constants are based on assumptions that have not been proven for the exact compound in question (in this case ACh). Furthermore, the meaning of such a conformation is not always clear. The time scale of a N M R measurement does not allow for the determination of rapidly changing conformations that are almost certainly present in molecules such as ACh that have low potential energy barriers to one or more torsional rotations. For such molecules, the N M R data may give a time average of two or more different conformations. Inspection of Table I shows the relatively large dif, between the various ferences in the values of T ] and T ~especially theoretical studies. In this paper we include observed Raman frequencies as experimental parameters in a sequential molecular mechanicsnormal-coordinate analysis in order to locate the conformations that, in addition to being at a potential energy minima (as determined by molecular mechanics (MM) methods), also possess Present address: Faculty of Pharmacy, University of Lille, Lille, France. *Present address: Department of Biochemistry, University of Virginia School of Medicine, Charlottesville, VA 22908.
0022-3654/89/2093-1351$01.50/0
-175 -174
180
71
193 79 83 180 165 162
105 172
118
77
85 78 89 78
180.0
180.0
-76.0
180.0 180.0
-75.4
179.8 -73.6 -72.2
trans
trans
180.0
60.0 -80.0
120.0
180.0" 180.0"
theoretical theoretical
85 75 90 85
180.0
180.0" 180.0'
172.9 174.3
70
80
180.0
178.0
method ref X-ray chloride 16 X-ray bromide 16 X-ray iodide 17 X-ray perchlorate 17 X-ray resorcylate 17 X-ray resorcylate 17 X-ray bitartrate 17 X-ray Br402U 17 X-ray Br402U 17 theoretical 2 theoretical 2 theoretical 2 theoretical 2
7%
171 -.I74
180.0 180.0
NMR
gauche gauche gauche (assumed ?) 76.0 78.0
179.0 177.0
-102.0 160.0 80.0"
gauche 150.0 180.0 60.0
-75.0
90.0 a
274.0 172.0 60.0 100.0
NMR NMR NMR 172.0 173.0
theor vacuo theor aqueous theor vacuo theor aqueous NMR
180.0"
theoretical I3C N M R
8 3 3 7 9 10 4 4
5 5 11 6 12
60.0
Assumed value.
calculated Raman frequencies in agreement with the observed frequencies. Both the energy minima calculation and the nor( I ) Derreumaux, P.; Wilson, K. J.; Vergoten, G.; Peticolas, W. L. J. Phys. Chem., preceding paper in this issue. (2) Liquori, A. M.; Damiani, A.; De Coen, J. L. J. Mol. Biol. 1968, 33, 445. ( 3 ) Pullman, B.; Courriere, P.; Coubeils, J. L. Mol. Pharm. 1971, 7, 397. (4) Weintraub, H. J.; Hopfinger, A. H. Jerusalem Symp. Quanrum Chem. Biochem. 1974, 7, 131. ( 5 ) Beveridge, D. L.; Radna, R. J.; Schnuelle, G.W.; Kelly, M. M. Jerusalem Symp. Quantum Chem. Biochem. 1974, 7, 153. (6) Gelin, B. R.; Karplus, M. J. Am. Chem. SOC.1975, 97, 6996. (7) Partington, P.; Feeney, J.; Burgen, A. S. V. Mol. Pharm. 1972.8, 269. (8) Cushley, R. J.; Mautner, H. G. Tetrahedron 1970, 26, 2151. (9) Mautner, H. G.; Dexter, D. D.; Low, B. Nature (London),New Biol. 1972, 238, 87. (10) Terui, Y . ; Ueyama, M.; Satoh, S.; Tori, K. Tetrahedron 1974, 30, 1465. (1 1) Lichtenberg, D.; Kroon, P.; Chan, S.J . Am. Chem. SOC.1974, 96, 5934. (12) Cassidei, L.; Sciacovelli, 0. J. Am. Chem. SOC.1981, 103, 933.
C2 1989 American Chemical Society
1352 The Journal of Physical Chemistry, Vol. 93, No. 4,1989 TABLE II: Local-Symmetry Force Constants for the Acetylcholine Cation” Bond Stretching Force Constants name value i name value i name value 10 C4-N 4.3484 44 SS C5 4.9100 24 DSC3 4.7877 8 C5C4 5.3530 26 TSCl 5.0407 25 DS’C3 4.7857 7 01C5 4.9210 31 DSCl 4.7877 52 TSC7 4.6240 4 C601 5.2750 32 DS‘C1 4.7857 54 DSC7 4.7620 2 C 6 4 2 11.6600 33 TSC2 5.0407 55 DS’C7 4.7700 3.2520 39 DSC2 4.7877 12 TS(N) 4.6290 1 C6C7 4.7000 41 DS‘CZ 4.7857 17 DSN 4.2880 51 ASC4 4.9230 21 TSC3 5.0407 14 DS’N 4.2690 48 S S C 4 4.7000 47 ASC5 Angle Bending Force Constants i name value i name value i name value 84 ‘C4C501 1.5210 105 DD N 1.2500 81 R O C 5 0.7600 99 C5C4N 0.9610 108 DD‘N 1.0600 87 SC C4 0.4710 71 C601C5 1.4210 137 D R C 1 0.6610 74 SC C5 0.4400 64 C7C601 0.9930 122 C R C 2 0.6610 129 S D C 1 0.5667 67 C7C602 1.5050 110 DR N 1.0530 116 SD C2 0.5667 135 DDC1 0.4510 138 DR’C1 0.6643 124 SD C3 0.5667 136 DD’ C1 0.4580 123 DR’ C2 0.6643 56 SDC7 0.3630 120 DD C2 0.4510 127 D R C 3 0.6610 102 SD N 1.0220 121 DD’C2 0.4580 128 DR‘ C3 0.6643 96 TW C4 0.4580 125 DD C3 0.4510 60 D R C 7 0.6090 82 TW C5 0.5760 126 DD’C3 0.4580 61 DR’C7 0.6040 90 W A C 4 0.5620 0.4250 77 WA C5 0.6610 58 DDC7 113 DR’N 1.0550 59 DD’C7 0.4040 93 RO C4 0.6000
Wilson et al. TABLE 111: Initial Geometries for the Acetylcholine Cation Taken as the Average of the Chloride, Bromide, and Iodide Crystal Valuesa** Bond Lengths
i
Out-of-Plane Bending Force Constant name value OPB C=O 0.2790 Dihedral Torsion Force Constants value i name value i name
i 139
i name value 140 Y C4N 0.1817 143 Y NC3 0.4188 145 Y C501 0.1460 141 Y NC1 0.4188 144 Y C4C5 0.1500 147 Y C6C7 0.0680 142 Y NC2 0.4188 146 Y 01C6 0.1460 Mixed/Off-Diagonal Force Constants i name value i name value 6 C602/C-O 0.9390 9 C4C5/OC5 0.4270 11 C4NiC5C4 0.3730 5 C6C7-C-0 0.3580 0.4340 0.1570 3 C6C7/C=O 100 CCN/C4N 0.1700 101 CCN/C5C4 0.2420 85 CCOIC4C5 0.1170 66 CCOlC6C7 65 CCOlC602 -0.3500 0.1940 70 CCO2C6C7 86 CCOlOlC5 0.4160 68 CCO2C601 69 CCO2C602 -0.1940 -0.6790 72 COC/OlC5 73 COC/C601 0.2870 0.2770 62 DDC7DRC7 -0.0800 106 DDN/DSN -0.1900 109 DD’NDS’N 107 DDN/SDN -0.01 10 -0.1910 115 DR‘DD‘N 63 DR’7C6C7 -0.0500 0.0280 114 DR‘DS‘ N 0.0280 0.1920 111 DRNDDN 112 DRN DSN 0.0860 0.1920 42 DS‘2DS‘l DS’2DSf3 43 0.0860 0.0860 40 DSC2DSC3 20 DSN/C4N -0.0047 0.0055 16 DS‘N/C4N 18 DSN/DS’N 19 DSNTSN 0.0056 -0.3400 15 DS’NITSN -0.0456 -0.0170 95 R04R05 94 R04TW5 0.0660 148 S33 S38 0.0000 149 s 33 s43 150 S38 S43 0.0000 0.0000 88 SC4/C4N -0.1330 89 SC4/C5C4 -0.1150 75 s c c 5 c 5 c 4 -0.1640 -0.0120 76 SCC501C5 134 SDl/DSN -0.0020 133 SDlIDS’N 0.0237 132 DSl/TSN -0.2840 117 SD2/DSN -0.0020 SD2IDS’N 118 -0.2840 0.0237 119 SD2JTSN 131 SD3/DSN -0.0020 -0.2840 130 SD3/TSN 57 SDC7C6C7 -0.2380 0.1400 104 SDN/C4N 0.1340 103 SDNTSN 0.5040 49 SSC4C4N 50 s s c 4 c 5 c 4 0.4530 0.4460 45 s s c 5 c 5 c 4 0.6320 46 s s c 5 0 1 c 5 -0,2248 28 TSClDSN 29 TSCIDS’N -0.0013 0.0650 27 TSClTSC3 30 TSC 1TSN -0.2248 36 TSC2DSN 0.3180 37 TSCZDS’N 34 TSC2TSCl -0.0013 0.0650 35 TSC2TSC3 38 TSC2TSN 0.0650 0.3 180 22 TSC3/DSN -0.2248 23 TSC3/TSN 0.3 180 53 TSC7C6C7 0.3800 13 TSN/C4N 0.2230 98 TW4 R 0 5 97 TW40TW5 -0.0660 0.0690 83 TW/RO 5 91 WA4/C4N 0.0830 -0.3200 92 WA4/C5C4 79 WA/C5C4 0.2780 -0.2760 80 WA/OlC5 78 WA/SC 5 0.3720 -0.0247 ‘Units: mdynjA for stretching and stretching-stretching, mdyn .&/rad2 for bending, torsion, and bending-bending, and mdyn/rad for stretchingbending.
rn
HQ CQ HA HB HC CC
CQ NQ CA CB CC NQ
r,,
CB OS
0.9897 1.5018 0.9975 1.0267 0.9749 1.5103
1.4334 1.1908 1.3682 1.4834 1.4917
o c os c
C CA CB C C
Bond Angles a0
HQ HQ CQ CQ NQ NQ CC HC CC
CQ HQ CQ NQ NQ CQ NQ cc C C CB CC HC CB H B C C CB CB
os
a0
109.65 109.26 109.49 109.39 1 17.08 105.89 110.47 108.81 111.70
H C CC HC H B CB HB H B CB OS CB OS C
109.87 107.06 108.51 115.59 123.00 126.67 111.31 107.50 110.30
os c
0 0 C CA C CA H A H A CA H A OS C CA
Dihedral Andes X X X X
CQ NQ CC CB
NQ X CC X CB X OS X
x o s c x
X C C A X
n
d
3 3 3 3 2 3
0.0 0.0 0.0 0.0 180.0 0.0
Out-of-Plane Angle C
n 0
CA OS 0
d 0.0
“Bond lengths in A and angles in degrees. bAtom-type definitions: HQ, hydrogens bound to C1, C2, or C3; HA, hydrogens bound to C4; HB, hydrogens bound to C5; HC, hydrogens bound to C7; 0, carbonyl oxyge, 0 2 ; OS, ester oxygen, 0 1 ; NQ, quaternary nitrogen, N; CQ, methyl carbons bound to quaternary nitrogen, C1, C2, or C3; CA, methylene carbon C4; CB, methylene carbon, C5; CC, acetyl methyl carbon, C7; C, carbonyl carbon, C6; X, any atom.
TABLE IV: CHARMM Nonbonded Parametersa atom type HQ CQ NQ
cc
HC CB HB
os
C
0 CA HA
Emin,kcal/mol -0.0290 -0.0947 -0.2271 -0.0947 -0.0095 -0.0947 -0.0095 -0.1682 -0.0947 -0.1682 -0.0947 -0.0095
Where D , = Rmin,i+ Rminjand E , =
Rmim A 0.950 1.726 1.524 1.726 1.410 1.726 1.410 1.480 1.726 1.480 1.726 1.410
+ ifminJ.
mal-coordinate analysis (NCA) are performed with respect to each of the four main torsional angles ( 7 , , - ~ ~of) the ACh cation. A search then is made for overlapping minima: a minima in the molecular potential energy and a minima in the difference between the observed and calculated frequencies. Such overlapping minima correspond to the most probable conformations of the ACh cation in a given physical state. This approach is not completely novel. In addition to the energy minimization noted above,*” it should also be noted that Shimanouchi used the NCA of several specific rotational isomers as a means of determining the conformation of molecules such as pentane in the liquid state.I3 Krimm, Scheraga, and their co( I 3) Shimanouchi, T. Vibrational Spectroscopy and Its Chemical Applicorions; University of Tokyo: Bunkyo-ku, Tokyo, Japan, 1977.
The Journal of Physical Chemistry, Vol. 93, No. 4, 1989 1353
Solution Conformations of Acetylcholine
5Cb. 0
60b. 0
800.0 90h 0 10ob. 0 1 1 Wovenumber
70R. 0
0
Figure 1. Classical Raman spectra of (a) crystalline acetylcholine bromide, (b) aqueous acetylcholinebromide, and (c) crystalline acetylcholine chloride from 500 to 1100 cm-'.
w o r k e r ~anticipated l ~ ~ ~ ~ part of our theoretical approach in that they calculated the energy minima of oligopeptides and then the normal modes for these minima. It is of interest to note that their vibrational analysis was carried out independently of their MM calculation. We will discuss the advantages of such computational independence below. We have performed the first systematic calculation on any molecule on which both the vibrational normal coordinates and potential energy minima are obtained over a complete set of torsional coordinates using essentially the same force field. This method permits the selection of the physical conformation from the theoretically possible (local potential energy minima) conformations. The method that we have used is free from the disadvantages mentioned earlier. A comparison of the Raman spectra obtained from different types of crystals with different conformations (see Table I) allows one to determine experimentally whether or not any of the Raman bands are sensitive to differences in conformation. NCA permits the assignment of these modes to specific vibrational displacements. The conformationally sensitive bands may be used as marker bands for unknown conformations in solution. Since Raman scattering occurs on the time scale of molecular vibrations, the Raman spectra contain information on all of the different conformations that are present in solution at any given time. Materials and Methods
Acetylcholine Preparation. All acetylcholine salts were commercially obtained (Sigma; acetylcholine-d9 bromide from MSD Isotopes), recrystallized by vapor diffusion of diethyl ether into saturated ethanolic solutions of the particular salts, and dried in vacuo (20 Torr) to constant mass in an Abderhalden device over boiling chloroform. Raman Spectroscopy. Crystalline samples were prepared by selecting a single large crystal of the salt and grinding it to a fine powder under a dry nitrogen atmosphere. The powder was loaded (14) Maxfield, F. R.; Bandekar, J.; Krimm, S.; Evans, D. J.; Leach, S . J.; Nemethy, G.; Scheraga, H. A. Macromolecules 1981, 14, 997. ( 1 5 ) Naik, V. M.; Krimm, S.; Denton, J. B.; Nemethy, G.; Scheraga, H. A. Int. J . Pept. Protein Res. 1984, 24, 613.
75b. 0
80d. 0
85b. 0
95b 0
gob. 0
Wovenumber
Figure 2. Raman spectra of aqueous ACh versus temperature: (a) 5, (b) 15, (c) 25, (d) 35, (e) 45, (0 55, and (g) 65 i C .
75 0 ,
,
,
,?,
,J
800. , 0
Wovenumber 850.0
goo. o,
,
,
95 '. 0 ,
Figure 3. Raman spectra of ACh in acetonitrile at (a) 15, (b) 40, and (c) 75 o c .
into a borosilicate melting point capillary tube and sealed with paraffin wax. Aqueous samples were prepared by dissolving enough crystalline acetylcholine bromide, chloride, or iodide in dilute aqueous hydrohalogenic acid (pH 4.5-5.5) to give a concentration from 50 to 900 mM and were used immediately. In order to minimize hydrolysis of aqueous ACh samples at temperatures above 20 OC, these spectra were obtained by flowing an ice-cold solution (via a syringe pump and microbore tubing) through a water bath at the desired temperature and into the thermostated sample capillary; then the solution was disposed of. This method exposed the sample to elevated temperatures for less
1354 The Journal of Physical Chemistry, Vol. 93, No. 4, 1989
Wilson et al.
380
a 300
240
a
al
-0
BO
I20
1.30
240
380
300
Taul (degrees) 380
b
300
240
h
VI
u al
&
-
180
al
5 N
120
3 k
BO
0
BO
120
I80
240
360
300
Taul (degrees) 380
C 300
h
240
a al
&
1.30
al
a
Y
N
120
2 -i 60
0
0
80
120
180
240
380
300
Taul (degrees)
Taul (degrees)
+
Figure 4. Contour plots of T I versus TZ versus (a) bond stretching angle bending potential energy; (b) dihedral torsional energy; (c) van der Waals + electrostatic potential energy; (d) molecular potential energy.
+ out-of-plane bending potential
Solution Conformations of Acetylcholine than 1 min, while allowing continuous spectroscopic sampling. Nonaqueous solution samples were prepared as saturated solutions at -10 OC in the desired solvent. Classical Raman spectra were taken using the 514.5-nm line of a Spectra Physics argon ion laser with 85 mW of power at the sample. The Raman signal was collected and dispersed through a Spex 1301 double monochromator and measured with a cooled ITT 401 3 photomultiplier tube. The monochromator and photon-counting electronics were interfaced to a Hewlett-Packard 98 16 technical computer which recorded the signal and controlled the monochromator wavenumber and sample temperature. Slits were 75 pm, which corresponds to an instrumental resolution of 1-3 cm-' (at 3700-100 A cm-I). Unless otherwise noted, the temperature of the samples was kept at 15.0 OC. Signal averaging was used to improve the signal-to-noise ratio of the spectra. Calibration of frequencies were made with an neon lamp. Where necessary, solvent bands were removed by subtracting the spectrum of the pure solvent. Computational Methods. The atom designations, atom numbering, displacement coordinate definitions, and force constant designations are the same as those used previously.' For our molecular mechanics calculations, we used the computer program CHARMMI* (CONVEX C-1 version 20.3 from Polygen Co.). This program approximates the potential energy V of a system as
The Journal of Physical Chemistry, Vol. 93, No. 4, 1989 1355 24, 0
L.
a
j 12.0
b 3
t
2
1
36. 0
b
j 18.0
e
t
I
0.0 1
where r, = the ith bond length, ai,= the angle between adjacent bonds i and j , f,,k = the torsional angle formed by bonds i, j , and k (torsion about bond j ) , n, k = periodicity of the torsion angle about bond j , ai,k = angle offiset of the torsional angle about bond j , wijk = the out-of plane angle formed by bonds i, j , and k ( k out of plane of bonds i and j ) , d,, = the distance between nonbonded atoms i and j , and Ki = the force constant for stretching the ith bond, H,, = the force constant for the bending of angle ai,,Kjk = the force constant for the torsion Af,,k, wuk = the force constant for the out-of-plane bend Auifk,Q, = the residual charge on the ith atom, Dij and E , are the parameters for a Lennard-Jones potential between nonbonded atoms i andj, and Juk = an artificial force constant used to constrain the torsion about bond j . The summations are over relevant internal displacement coordinates or atom pairs for nonbonded interactions. Inspection of eq 1 reveals that it is basically a subset of the modifkd Urey-Bradley function used in the previous paper in this seriesi The only differences are in the definitioins of the van der Waals potentials; for our NCA calculations we use a Buckingham potential, while CHARMM uses a Lennard-Jones potential. We have chosen the parameters D,, and E - by successive approximation methods such that the actual values of the Lennard-Jones functions correspond as close as possible to the Buckingham functions used in the NCA calculations. The remaining values for the force constants and residual charges in eq 1 are derived from those we obtained in our previous work' and are contained in Table 11. These values are derived from the crystal force field by removing the constants due to crystalline forces and setting certain constants equal due to symmetry imposed by (relatively) free methyl rotations. Jirk was set to 1000 %, kcal/mol when applicable. The initial geometries used for the molecular mechanics calculations are the average of the geometries found the chloride, bromide, and iodide crystals of ACh'6J7 and are given in Table 111. The parameters for the CHARMM nonbonded potentials are given in Table IV. Once the torsional angles r0 through r3 have been chosen and constrained by assigning the harmonic potential (16) Svinning, T.; Sorum, H. Acta Crystallogr.. Sect. B Struct. Crystallogr. Cryst. Chem. 1975, 831, 1581. (17) Jagner, S.; Jensen, B. Acta Crystallogr., Sect. B Struct. Crystallogr. Cryst. Chem. 1911, 833, 2751.
(18) Brooks, B. R.; Bruccoleri, R. E.;Olafson, B. D.; States, D. J.; Swaminathan, S.; Karplus, M. J . Comput. Chem. 1983, 4 , 187.
0
60
I 80
I20 Tau 0
240
300
360
(degrees)
Figure 5. Graphs of molecular potential energy versus (a) T~ and (b) T,, with 7 , = 7 2 = 60° (solid line) and T~ = T~ = 180° (dashed line).
TABLE V Conformationally Sensitive Vibrations and Assignments frequency, cm-l, for ACh Y no. vibr assignt chloride bromide aqueous MeCN 17 C=O str 1733 1745 1736 1752 961 958 965 962 48 C6-0 str 955 950 952 952 49 N-C deg str 939 918 916 a 50 N-C4 str 51 C4-H rocking 878 871 877 876 847 842 837 52 C5-H rocking C5-H rocking 825 827 820 720 723 720 719 53 N-(CH,), str 646 652 646 643 54 ester deformation a
Obscured by solvent band.
defined by J,,k, the structure (valence bond lengths and angles, out-of-plane angles, and methyl torsional angles) is energy minimized by 100 cycles of steepest descent and by 200 cycles of adopted-basis Newton-Raphson minimizations, followed by enough full-basis Newton-Raphson minimizations to zero the potential energy gradient for the constrained conformation. Then the Cartesian coordinates and potential energy terms (described by eq 1) of the minimized structure were recorded. Next, a new conformation was generated and constrained, followed by the structure minimization just described. This process was repeated incrementally throughout the conformational space defined by To through f 3 . After a complete set of optimized structures (conformations) were obtained, a NCA calculation was performed for each structure using the method described previously.' Table I1 contains the force constants used for these calculations. Results and Discussion Figure 1 shows the classical Raman spectrum of (a) crystalline acetylcholine bromide, (b) aqueous acetylcholine bromide, and (c) crystalline acetylcholine chloride from 500 to 1100 cm-l. Notice the definite presence of two bands in the 820-850-cm-'
1356 The Journal of Physical Chemistry, Vol. 93, No. 4, 1989
Wilson et al.
380
a 300
-
240
m 0 0
180
0
.e N
: c
120
BO
n
0
BO
I20
160
240
300
360
Taul ( d e g r e e s )
A
b
Taul ( d e g r e e s )
A
C
Taul ( d e g r e e s )
Figure 6. Deviation contours of calculated vibrational frequencies from (a) observed bromide crystal frequencies, (b) observed aqueous solution frequencies = 827 cm-l, and (c) observed aqueous solution frequencies with vS2 = 842 cm-I.
with
region of aqueous ACh, while crystalline acetylcholine bromide and chloride have only a single band at 825 and 847 cm-I, respectively (corresponding t? the C5 methylene rocking vibration as determined previously1). Inspection of the spectra in Figure 1 suggest that the doublet in the 820-850-~m-~region of the aqueous spectrum is due to splitting of the 825-cm-l vibration observed in the bromide crystal spectrum into two distinct populations of C5 methylene rocking vibrations. From this simple comparison of the observed spectra, we attribute the two observed populations to two solution conformations of the ACh cation. The population represented by the 827-cm-' band is due to a conformation similar to that found in the bromide crystal (7, = 79O, r 2 = 7 S 0 , and C5 methylene rocking at 825 cm-I), and the other population is due to a conformation similar to that in the chloride crystal ( 7 1 = 1 9 3 O , T~ = 85", and C5 methylene rocking at 848 cm-I). To estimate the relative energetics of these two populations, the spectrum of ACh in water was measured as a function of temperature. The results of this experiment are shown in Figure 2. As can be seen from Figure 2, the shape and relative intensity
of the doublet about 835 cm-I change only slightly in the temperature range of 0-65 OC, with a slight increase in the 840-cm-' band intensity. This suggests that the relative populations (making up the doublet) are approximately isoenergetic in water. To rule out the possibility of ACh hydrolysis being responsible for the doublet in the aqueous spectra, especially at the higher temperatures, the experiment was repeated in organic solvents, with the CH3CN results shown in Figure 3. The existence of the two C5 methylene rocking bands in CH3CN prove that the two bands are not due to hydrolysis. Also, in this solvent there is an obvious inequality between the C5 methylene rocking populations at 75 O C , with the populations becoming approximately equal at low to ambient temperatures. Similar results (two C5 methylene rocking bands) were obtained in methanol and formamide. This illustrates the effect of solvent change on the conformational energies. In order to quantitate and get a better understanding of our experimental observations, we constructed a theoretical model of the ACh cation in order to explore the theoretical energetics and
Solution Conformations of Acetylcholine vibrational structure as a function of conformation. Using established molecular mechanics we obtained the po) in Figure 4. These tential energy surfaces (for versus T ~ shown surfaces are for T~ equal to 180' and T~ equal to 180°, which we initially assumed and later determined to be the minimum energy values for these torsional angles (any small change in value for either of these torsional angles resulted in a large increase in the potential energy of the system). Figure 4 consists of contour plots of (a) the bond stretching potential plus the angle bending potential, (b) the dihedral torsional potential plus the out-of-plane bending potential, (c) the van der Waals potential plus the electrostatic potential, and (d) the total potential energy (less the constrainment energy). Notice (in Figure 4d) that there are multiple minima in the surface of near equal depth separated by barriers of varying potential. Of particular importance is the relatively low (approximately 5 kcal/mol) barrier between the two conformers (minima) at ( T ' , T ~ equal ) to (80°, 40') and (180°, 40'). This indicates that the (model) molecule spends approximately equal time in each of these conformations and has little difficulty in changing from one to the other. This supports our explanation of the experimental presence of two roughly equal populations of ACh conformations in solution. Figure 5 shows two different slices through the potential energy hypersurface: (a) potential energy versus T~ with T,, at 180' and (b) potential energy versus r0 with 7) at 180'; the solid lines represent the surface with T~ = T~ = 60' and the dashed lines represent 71 = T~ = 180'. These graphs confirm our intuitive assumption that both T~ and T3 are very close to 180' a t the potential energy minimum of our model. For the potential function used in the ) when M M calculations, there is symmetry in the ( T ~ T, ~ surface r3 is equal to 180°, meaning that the minima at (80°, 40') and (180°, 80') are mirrored by minima at (280°, 320') and (180°, 320'). After determining the optimum (minimum potential energy) structures for each conformation of the T ~ - Q surface, a NCA calculation for each conformation was performed. Since a relative few of the possible 72 normal vibrations are intimately (directly) involved with torsional changes in the molecule, we concentrated our attention on the bands previously demonstrated to show conformational sensitivity.' These vibrations, their assignments, and their observed frequencies in crystals and solutions are given in Table V. While the molecular mechanics program, CHARMM, will calculate (approximate) molecular vibrational frequencies, our experience has been that the agreement between the observed and calculated frequencies obtained using the simple M M force field is much worse than that obtained using the Urey-BradleySchimanouchi force field and the NCA methods described in ref 1. This inequity comes from two areas. The first area is the neglect of certain interactions by the M M force field that are accounted for in the NCA force field. Schimanouchi and his collaborators showed in their many papers on the normal modes of polyatomic molecules that the inclusion of these 1-3 nonbonded
The Journal of Physical Chemistry, Vol. 93, No. 4, 1989 1357 interactions in the molecular force field improved the agreement between calculated and observed frequencies as compared to simpler force fields such at those currently in use in molecular mechanics programs.13 The second area has to do with redundancies in the force field. Although the CHARMM program solves the vibrational equations in the Cartesian space (where redundancies do not explicitly exist), the problem is defined in terms of the internal (redundant) coordinates and then linearly transformed into Cartesian space. In general, the transformation from a redundant space to a nonredundant space is not linear.lg The method we use, originally developed by S c h i m a n ~ u c h i ,solves '~ the redundancy problem by utilizing nonredundant symmetry coordinates that can easily be generated from the redundant internal coordinates. In order to determine the preferred conformation of the ACh cation in various environments, maps of the average deviation (absolute difference) between the observed and calculated frequencies for the vibrations listed in Table V were made. These results are shown in the contour plots of Figure 6. Notice that there are two maps for the solution state corresponding to the two C5 methylene rocking bands in the observed spectra. It was found that regardless of the conformation, only one band corresponding mostly to a C5 methylene rocking vibration was computed in the region of 700-900 cm-I, strongly suggesting that the two bands observed in this region are due to different conformations. Notice that the plot for the deviation from the bromide frequencies accurately predicts the conformation observed by X-ray crystallography (refer to Table I). From the data presented in these plots, we conclude that the ACh cation in aqueous solution exists predominantly about two conformations at ( T ' , Q ) equal to (260°, 280') (Figure 6b) and (160°, 300') (Figure 6c). In summary, we have shown strong experimental evidence that the solution-state ACh cation exists in predominantly two conformations, based on comparisons of crystal and solution state Raman spectra. Using M M methods, we obtained a complete set of structures spanning the conformational space of the ACh cation and determined the potential energy surface for this cation. By calculating the vibrational frequencies of the ACh cation over its complete conformational space, and comparing these frequencies to those experimentally observed, we have accurately deduced the most probable conformations of the ACh cation in solution.
Acknowledgment. We thank Dr. Dan Harris and Professor Martin Karplus for helpful discussions regarding molecular mechanics (CHARMM) calculations. This work was supported by the National Science Foundation (Grant 8417199) and National Institutes of Health (Grant GM15547). Registry No. ACh, 51-84-3. (19) Crawford, Jr., B.; Overend, J. J . Mol. Spectrosc. 1964, Z2, 307.
