Multidimensional conformational analysis of the sidechain conformers of the fully extended backbone (βL) of N-Ac-Homocysteine-NHMe; an ab initio exploratory study

Journal of Molecular Structure (Theochem) 619 (2002) 21–35 www.elsevier.com/locate/theochem

Multidimensional conformational analysis of the sidechain conformers of the fully extended form backbone (bL) of N-AcHomocysteine-NHMe; an ab initio exploratory study Aly R. Sheralya,*, Richard V. Changa, Gregory A. Chassa,b a

b

Department of Chemistry, University of Toronto, Toronto, Ont., Canada M5S 3H6 Global Institute of Computational Molecular and Materials Science (GIOCOMMS) at Velocet, 210 Dundas Street West, Suite 810, Toronto, Ont., Canada M5G 2E8 Received 15 March 2002; accepted 8 May 2002

Abstract Molecular orbital computations were carried out on the L -enantiomer of N- and C-protected homocysteine (Hcy) at the ab initio RHF/3-21G level of theory. Calculations were conducted while the Hcy backbone was relaxed in the fully extended bL (C5) conformation, in order to monitor the effects of different sidechain conformers on the overall stability of the model. q 2002 Elsevier Science B.V. All rights reserved. Keywords: Fully extended (bL or C5) homocysteine; Multidimensional conformational analysis; Ab initio MO calculations; Sidechain conformers

1. Preamble There are three sulfur-containing amino acids: methionine (Met), cysteine (Cys) and homocysteine (Hcy) (Fig. 1). The former two are incorporated into proteins at the level of translation. Though Hcy is structurally similar to a number of amino acids such as leucine (Leu), isoleucine (Ile) and Met, cells prevent the incorporation of Hcy into proteins through an editing mechanism [1]. The three sulfur-containing amino acids are interconverted via a metabolic pathway [2] (Fig. 2). Hcy is the intermediate in the conversion of Met to * Corresponding author. E-mail addresses: [email protected] (A.R. Sheraly), rj. [email protected] (R.V. Chang), [email protected] (G.A. Chass).

Cys and vice versa. Methylation of Hcy can produce Met while transulphuration of Hcy can result in the irreversible formation of Cys. Such pathways (Fig. 2) are responsible for the regulation of Met metabolism. Met formation is affected if at least one of the three essential enzymes is dysfunctional. The first is methylenetetrahydrofolate reductase (MTHFR), which is necessary to form N 5-methyltetrahydrofolate (N 5-methyl-THF) from its precursor N 5,N 10-methylenetetrahydrofolate. Hcy is methylated using N 5methyl-THF as a methyl donor. Without folate or MTHFR, Hcy cannot be converted to Met [3]. The second enzyme is Met synthase (homocysteine methyltransferase), responsible for transferring the methyl group from N 5-methyl-THF to Hcy. It is a B12 (cobalamin)-dependant enzyme. It catalyzes the transfer of a methyl group from N 5-methyl-THF to

0166-1280/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 6 - 1 2 8 0 ( 0 2 ) 0 0 3 1 0 - X

22

A.R. Sheraly et al. / Journal of Molecular Structure (Theochem) 619 (2002) 21–35

Fig. 1. N- and C-protected methionine, homocysteine and cysteine. Homocysteine is a demethylated form of methionine. Homocysteine and cysteine are related in that both their R-groups terminate with a thiol group, however, homocysteine is extended by a methylene group.

cobalamin, forming methylcobalamin, which subsequently transfers the methyl group to Hcy [4]. Therefore, deficiencies in vitamin B12 may cause a high concentration of Hcy to accumulate [5]. The third enzyme is cystathionine b-synthase, responsible for initiating the conversion of Hcy to Cys [6]. It is a pyrodoxal-50 -phosphate (PLP)-dependant enzyme. The enzyme-PLP Schiff base first reacts with serine to form a geminal (gem ) diamine intermediate, which leads to a serine-PLP Schiff base. Subsequently, an aminoacrylate-PLP Schiff base is formed, accompanied by the loss of Hþ and 2OH. Hcy, then reacts with the Schiff base to form a cystathionine-PLP Schiff base. Following this, another gem diamine is formed, which leads to the final product of cystathionine. This reaction could not proceed without PLP. Therefore, a deficiency in vitamin B6 may also result in an elevated Hcy level [7]. In addition, it may be possible for seleniumcontaining amino acids to enter this metabolic pathway. The similarity between sulfur and selenium may obscure the identity of a selenium-containing amino acid so that it may bind the active site of the enzymes responsible for this particular pathway. Analogous to the conversion of Met to Cys, selenomethionine may be converted to selenocysteine via the intermediate selenohomocysteine [8]. Hyperhomocysteinemia is an affliction that is correlated with the occurrence of vascular disease in the coronary, cerebral and peripheral vessels [9]. It is known that endothelial cells exposed to Hcy show

vessel pathology. Several hypotheses have been proposed to account for this phenomenon [10]. One suggests that Hcy participates in endothelial remodeling. The density of endothelial cells may decrease due to the activation of a matrix metalloproteinase [11]. Another recent study has shown that a high concentration of Hcy is indicative of low cell methylation, which may inhibit gene transcription, particularly genes involved in the cell cycle [12]. Consequently, a decrease in endothelial cell growth is seen. A second hypothesis proposes that a high concentration of Hcy inhibits the enzyme dimethylarginine dimethylaminohydrolase (DDAH), which is responsible for degrading asymmetric dimethylarginine (ADMA) [13]. In endothelial cells, ADMA is an inhibitor of NO synthase. Inhibition of DDAH results in an increase in the concentration of ADMA, leading to a decrease in the concentration of NO. The diatomic NO relaxes the smooth muscle in the walls of the arterioles. Yet a third hypothesis suggests that Hcy is significant in contributing to oxidative stress on endothelial cells [14]. Hcy may inhibit the expression of the glutathione peroxidase, an enzyme responsible for the reduction of a variety of hydroperoxides [15]. Equally, when Hcy auto-oxidizes to homocystine, it may be contributed to the production of reactive oxygen species, which may lead, in variety of ways, to endothelial cell damage [16]. Hypertension a consequence of vascular dysfunction is one of the leading medical concerns in North America and in the whole Western Civilization.

A.R. Sheraly et al. / Journal of Molecular Structure (Theochem) 619 (2002) 21–35

23

Fig. 2. Metabolic pathway involving sulfur-containing amino acids. The enzymes involved in homocysteine formation and degradation are: (1) methionine synthase, (2) methylenetetrahydrofolate reductase and (3) cystathionine b-synthase.

Most of the research has focused on cholesterol as the main cause for hypertension. Yet despite this discovery and subsequent drug treatment, hypertension continues to be a leading problem. Dr McCully in his book ‘The Homocysteine Revolution’ proposes and outlines the role played by Hcy in the development of arteriosclerosis, one of the major complications in hypertension [17]. This research has led some to believe that Hcy rather than cholesterol is the primary cause of hypertension.

The rise in reactive oxygen species in hyperhomocysteinemia may lead to an increase in the expression of endothelial adhesion molecules, which may lead to a rise in the deposition of oxidized LDL particles along the vessel walls. The characterization of the conformational character of Hcy may aid in clarifying its physiological function and systemic impact. Already, some studies suggest that the D and L isomers of Hcy may have different effects on different tissue [15].

24

A.R. Sheraly et al. / Journal of Molecular Structure (Theochem) 619 (2002) 21–35

Fig. 3. Above is the structural model used for molecular computations including the N- and C-protected terminal groups. All dihedral angles that are being studied are labeled for reference. Each atom is assigned a number, as outlined by Chass et al. [26,27] to create a modular system that can be easily manipulated in an internal z-matrix during computations.

2. Introduction Hcy maintains the classical characteristics of an amino acid, consisting of an amino group, a chiral central a carbon, a carbonyl group and a sidechain. The sidechain is the demethylated form of Met, providing Hcy with similar properties to its counterpart Cys, which also contains a terminal thiol group. A

Fig. 4. A plot of f and c yield the general Ramachandran map. In general, one minima is expected to be found in each quadrant, ideally lying exactly at the center of the quadrant. Backbone dihedral rotations yielding angles between 120 and 240 result in a conformer referred to as b conformer which relates to the fully extend form of the backbone. Ideally f and c should be 180.08.

structural comparison of Met, Hcy and Cys is given in Fig. 1. For any given amino acid, up to nine possible backbone conformations are topologically probable as stable conformers when rotating the backbone dihedral angles fi and ci from 0 to 3608. The definitions of the dihedral angles are shown for the Hcy residue (Fig. 3). In accordance with the IUPAC – IUB recommendations [18 – 25], all dihedral angles were reported within 2 180.0 and 180.08 for both backbone and sidechain conformers. A traditional plot of dihedral angle rotations from 0 to 3608 about fi and ci for any amino acid diamide yields a Ramachandran map (Fig. 4). Each box, corresponds to a region in which one of the nine minima can be located. Each has been assigned an L or D subscripted Greek letter for facilitated reference indicating the axis of chirality associated with the conformational twist. L -amino acids tend to be exclusively used by organisms and thus most of the computational research is focused on uncovering the conformational characteristics of these L -enantiomers. As a mathematical representation, the energy of a peptide residue is a function of all the bond lengths, angles and of the rotation of key dihedral angles. Using the model (Fig. 3) the rotational energetic potential may be represented by the generalized

A.R. Sheraly et al. / Journal of Molecular Structure (Theochem) 619 (2002) 21–35

function:   E ¼ f ci21 ; vi21 ; fi ; ci ; vi ; fiþ1 ; x1i ; x2i ; x3i

ð1Þ

However, upon further inspection of this generalized equation, it is possible to reduce the number of variables being studied. The peptide bonds are considered to be at least semi – rigid and often found in the trans conformation, consequently all the v dihedral angles are found in the vicinity of 1808, reducing the dimensionality when considering the extent of the set of topologically probable conformers. The outcome of this reduction is shown using the following function:   E ¼ f ci21 ; fi ; ci ; fiþ1 ; x1i ; x2i ; x3i ð2Þ While ci21 and fiþ1 are also backbone dihedral angles in an amino acid diamide they are nothing more than the rotational potentials of methyl groups. Since the hydrogens on the methyl groups are all considered equivalent, and the barrier to methyl rotation is relatively low (, 3 kcal), it is possible to consider the methyl rotation contributing very little to the overall energy and therefore can be considered as a relatively constant parameter. Thus eliminating these backbone variables from the equation, again reduces the dimensionality and the function used to derive the energy of Hcy conformers, which can now be simplified to the following function:   E ¼ f fi ; ci ; x1i ; x2i ; x3i ð3Þ Returning to the Ramachandran map, a peptide with vi21 and vi ; optimized around 1808, and whose fi lies between 120.0 and 240.08 (2 120.08) and whose ci lies between 120.0 and 2 120.08, is generally classified as the b (C5) conformation. It corresponds to the fully extended backbone conformation. Ideally, the dihedral angles for the backbone would lie at the center of parameters given above corresponding to the point ðfi ; ci ¼ 180:08Þ: This is the case for glycine, but other amino acids deviate from these ideal values due to steric effects of having a bulky sidechain (relative to glycine). Generally, they may be in the vicinity of fi ¼ 21658 and ci ¼ 170:08; thus classifying it an L -enantiomer with respect to the Ramachandran plot. Taking this chirality into account, the fully extended backbone conformer is referred to as

25

bL with the assigned subscript L to indicate that it is an L -enantiomer. This work seeks to explore all the possible sidechain conformations of Hcy while the backbone is in its fully extend or bL (C5) conformation. As such, fi and ci can now also be considered as separate from the energy equation. Thus the number of variables being systematically investigated can be reduced to the final equation:   EbL ¼ f x1i ; x2i ; x3i ð4Þ Each of these variables was examined for all its probable conformers and its influence on and coupling with the parameters from the initial equation (e.g. Eq. (1)) were monitored and reported in this study. The total energy and relative hydrogen bonding and charge-transfer interactions were explored and documented. By uncovering the factors that influence the stabilization of the molecule it may become more possible to understand and predict the mechanisms that use Hcy as an intermediate in biomedically important reactions and pathways.

3. Method An acetyl group was attached to the N-terminus and a methylamide group was attached to the Cterminus of the central Hcy residue, in order to simulate the Ca of the neighboring residues and to conserve the Ca – CO – NH – Ca polypeptide backbone structure. By adding the N- and C-protecting groups, the effects of the neighboring Ca’s on the central Hcy residue is being considered even though Hcy is not one of the amino acid residues used to synthesize polypeptides. Input files were constructed using an internal coordinates system. By convention a standardized and modular numbering system was employed to number the Hcy model, as outlined by a set of rules previously outlined [26,27]. The atoms of the acetyl group were numbered first completing the ði 2 1Þ residue, followed by the Hcy residue numbered along the peptide backbone. The sidechain was then numbered along the sidechain backbone heavy atoms into the peptide backbone, from the Ca to the thiol group. The next module to be numbered was the methyl-amide attached to the Hcy, which correspond

26

Table 1 Optimized sidechain conformers of N-Ac-L -homocysteine-NHMe at RHF 3-21g level of theory ci21

vi21

fi

ci

x1i

x2i

x3i

viþ1

fiþ1

Energy (Hartrees)

Relative energy (kcal mol21)

Stabilization energy (kcal mol21)

gþgþgþ gþgþa gþgþg2 g þ agþ g þ aa g þ ag2 g þ g 2 gþ gþg2a g þ g 2 g2 ag þ gþ ag þ a ag þ g2 aagþ aaa aag2 ag 2 gþ ag 2 a ag 2 g2 g 2 g þ gþ g2gþa g 2 g þ g2 g 2 agþ g 2 aa g 2 ag2 g 2 g 2 gþ g2g2a g 2 g 2 g2

178.1673 177.9245 178.4768 177.994 178.7861 179.1257 2 173.623 2 174.0908 2 170.5301 179.1741 178.9071 Not found 2 179.9766 2 179.8994 2 179.5325 Not found Not found Not found 70.2367 70.0572 55.0296 177.9633 177.4596 177.3704 177.2267 Not found 178.0621

177.0354 177.0131 176.7312 177.0525 177.5245 177.6627 2 177.0654 2 178.6123 2 176.8605 178.5166 178.3338

2 166.646 2 167.6426 2 163.9125 2 166.3754 2 164.4377 2 164.0078 2 170.0654 2 159.1653 2 168.6455 2 164.8397 2 164.3475

164.8789 166.5391 166.6712 169.9252 167.6728 166.8975 163.8809 159.4039 159.9018 157.0245 158.3439

59.401 61.2387 53.6739 58.1239 57.2105 56.434 77.9359 58.4138 56.8059 2 179.8285 176.245

89.6303 97.3759 80.9231 179.4914 178.5887 2 178.6835 2 63.6331 2 80.7348 2 90.1129 54.2325 57.8965

73.9298 2 170.9304 2 81.9321 65.8045 178.7791 2 68.346 81.271 2 150.0299 2 64.4241 49.4869 180.0767

174.7108 174.6549 176.0455 178.182 177.7103 178.0286 177.7732 176.8996 176.8406 179.3523 2 179.9803

135.7084 135.7316 134.3966 118.6169 119.3627 117.6216 117.5931 118.0114 117.9634 113.2972 115.7914

2 924.488703869 2 924.488459031 2 924.491371495 2 924.495558521 2 924.491101406 2 924.491618254 2 924.487778161 2 924.488708471 2 924.489147095 2 924.493473750 2 924.491067043

2 0.919 2 0.765 2 2.593 2 5.220 2 2.423 2 2.748 2 0.338 2 0.922 2 1.197 2 3.912 2 2.402

2 3.44 2 3.29 2 5.12 2 7.72 2 4.95 2 5.27 2 2.86 2 3.44 2 3.72 2 6.28 2 4.92

179.6566 179.747 179.6411

2 162.6271 2 161.6619 2 164.115

152.9711 153.3918 155.9708

2 174.8227 2 174.0912 2 172.9371

176.8372 177.8758 178.312

66.7445 179.3918 2 64.4883

178.8912 178.1185 178.3887

114.3714 122.1919 113.9786

2 924.488531428 2 924.487238622 2 924.489197098

2 0.811 0.000 2 1.228

2 3.34 2 2.52 2 3.75

178.9401 178.3551 169.924 173.4579 173.279 173.1341 173.2725

2 149.4802 2 147.0874 2 139.507 2 143.0578 2 144.4651 2 143.215 2 149.0084

161.4517 163.4172 165.1692 165.1534 165.9333 165.4163 165.6667

2 59.5719 2 56.8023 2 56.4242 2 55.9174 2 58.8159 2 58.1277 2 72.4171

90.2953 90.695 101.7531 2 175.2501 2 172.2342 2 170.7902 2 64.3386

65.7808 170.7067 2 63.4872 71.1088 2 177.8754 2 67.935 92.4867

177.985 177.0969 177.2015 177.1064 177.1873 177.2004 177.8622

117.9024 116.7688 117.342 117.6704 117.7723 117.8011 118.1294

2 924.487740702 2 924.488150845 2 924.487278235 2 924.489924649 2 924.489636687 2 924.490182973 2 924.495612748

2 0.315 2 0.572 2 0.024 2 1.685 2 1.504 2 1.847 2 5.254

2 2.84 2 3.09 2 2.55 2 4.21 2 4.03 2 4.37 2 7.78

176.0637

2 163.7051

168.7741

2 69.5556

2 77.685

179.4346

117.5487

2 924.493348745

2 3.834

2 6.28

2 105.561

A.R. Sheraly et al. / Journal of Molecular Structure (Theochem) 619 (2002) 21–35

Sidechain conformer

A.R. Sheraly et al. / Journal of Molecular Structure (Theochem) 619 (2002) 21–35

27

Fig. 5. A plot of all the relative energies (in kcal mol21) for each of the sidechain conformers relative to the aaa conformer of bL homocysteine which was found to have the lowest stabilization energy. Note that N.F ¼ not found, applies to those conformers that were not found to exist at the RHF/3-21G level of theory with the backbone in the fully extended or bL conformation.

to the ði þ 1Þ residue. For each module all heavy atomic nuclei were numbered prior to the H also present in that module. Fig. 3 shows the model used for this study and with the inherent atomic numbering system described. The resultant input file was used as a starting point in two successive and iterative process of GAUSSIAN 98 [28] cycles to bring about a geometry optimization at the ab initio level RHF/3-21G of ‘found’ AM1 semi-empirical minima. These optimizations, involved the sidechain torsional angles being systematically varied so all possible conformation could be tested and calculated. All optimized structures were fully relaxed along all bonds, angles and dihedrals.

4. Results and discussion Calculations were carried out in such a way that the trans –trans ðvi21 ; vi ø ^180:08Þ isomer was maintained while the backbone was relaxed in its fully extend or bL (C5) form. Each of the three x dihedral angles in the sidechain was expected to have three minima (g þ , a, g 2 ). Multidimensional conformation analysis (MDCA) would yield 33 ¼ 27 topologically probable MDCA conformers as input for the calculations. A total of 22 conformers were successfully optimized at the RHF/3-21g level of theory. The optimized backbone results can be compared to those of other mono-peptide diamide models computed using ab initio methods that were also N- and C-protected such as Gly [29 – 35], Ala [29 – 35], Ser [36 –38], Phe [39,40] and most relevantly, Cys [41] and Met.

The optimized dihedral angles and the relative energies are shown in Table 1. The total energy for each conformation is reported in hartrees while the relative energies and stabilization energies are given in kcal mol21 using the conversion factor of 627:51 kcal mol21 ¼ 1 hartree. Comparatively, the most stable sidechain for Hcy in its bL backbone conformation is the g 2 g 2 g þ orientation. In addition, the ag þ g 2 , ag 2 g þ , ag 2 a, ag 2 g 2 and the g 2 g 2 a conformers were not found. The most probable reason for the ag 2 X (X ¼ gþ; a, g 2 ) gap could be due to the fact that the sulfur atom was positioned very close to the nitrogen of the ði þ 1Þ residue causing repulsion between the electron clouds. The aaa conformer was chosen as a reference when calculating the relative energy as it represents the fully extended sidechain conformation. A graph has been constructed to represent the relative energies (Fig. 5). Hydrogen bonding may occur between the thiol sidechain group and the various carbonyl and amino groups present in the backbone in Hcy. Backbone – backbone hydrogen bonding is also a factor that must be considered. Since there are several groups that can interact, they have been classified by type according to the atoms that participate in the interaction (Fig. 6). There are eight different types of hydrogen bonding that can occur in Hcy, two of which are solely backbone –backbone interactions while the remaining six are sidechain – backbone interaction. In Fig. 6, type A to type F illustrate the backbone – sidechain hydrogen bonds while type G and H demonstrate the backbone –backbone hydrogen bonding common to all polypeptide chains. Clearly not all interactions will

28

A.R. Sheraly et al. / Journal of Molecular Structure (Theochem) 619 (2002) 21–35

Fig. 6. A visual representation of all possible intramolecular interactions in homocysteine. Type A to Type F show backbone-sidechain hydrogen bonding while Type G, H show backbone–backbone hydrogen bonding. Type I to L interactions outline the ability of sulfur to host a charge transfer interaction.

Table 2 A summary of the intramolecular homocysteine interactions existing in the bL backbone Classification of type of interaction according to Fig. 6

Type of hydrogen bonding interaction

Participating atoms

Cut-off criteria ˚) (A

Distance ˚) (A

g þ g þ gþ gþgþa g þ g þ g2

Type H Type H Type H Type A Type H Type H Type H Type H Type A Type E Type H Type H Type H Type D Type H Type D Not found Type H Type H Type H Not found Not found Not found Type H Type E Type H Type H Type H Type H Type H Type H Type B Not found Type H Type D

Backbone–Backbone Backbone–Backbone Backbone–Backbone Backbone–Sidechain Backbone–Backbone Backbone–Backbone Backbone–Backbone Backbone–Backbone Backbone–Sidechain Backbone–Sidechain Backbone–Backbone Backbone–Backbone Backbone–Backbone Backbone–Sidechain Backbone–Backbone Backbone–Sidechain

N7 – H11· · ·O10 N7 – H11· · ·O10 N7 – H11· · ·O10 S15 –H16· · ·O10 N7 – H11· · ·O10 N7 – H11· · ·O10 N7 – H11· · ·O10 N7 – H11· · ·O10 S15 –H16· · ·O10 S15 –H16· · ·N21 N7 – H11· · ·O10 N7 – H11· · ·O10 N7 – H11· · ·O10 N21 –H24· · ·S15 N7 – H11· · ·O10 N21 –H24· · ·S15

2.60 2.60 2.60 2.60 2.60 2.60 2.60 2.60 2.60 2.60 2.60 2.60 2.60 3.05 2.60 3.05

2.089 2.082 2.113 2.445 2.110 2.127 2.136 2.159 2.532 2.971 2.228 2.185 2.145 2.763 2.124 2.715

Backbone–Backbone Backbone–Backbone Backbone–Backbone

N7 – H11· · ·O10 N7 – H11· · ·O10 N7 – H11· · ·O10

2.60 2.60 2.60

2.167 2.163 2.145

Backbone–Backbone Backbone–Sidechain Backbone–Backbone Backbone–Backbone Backbone–Backbone Backbone–Backbone Backbone–Backbone Backbone–Backbone Backbone–Sidechain

N7 – H11· · ·O10 S15 –H16· · ·N21 N7 – H11· · ·O10 N7 – H11· · ·O10 N7 – H11· · ·O10 N7 – H11· · ·O10 N7 – H11· · ·O10 N7 – H11· · ·O10 S15 –H16· · ·O4

2.60 2.60 2.60 2.60 2.60 2.60 2.60 2.60 2.60

2.209 2.749 2.214 2.165 2.176 2.166 2.166 2.128 2.319

Backbone–Backbone Backbone–Sidechain

N7 – H11· · ·O10 N21 –H24· · ·S15

2.60 3.05

2.109 2.833

g þ agþ g þ aa g þ ag2 g þ g 2 gþ

gþg2a g þ g 2 g2 ag þ gþ ag þ a ag þ g2 aagþ aaa aag2 ag 2 gþ ag 2 a ag 2 g2 g 2 g þ gþ g2gþa g 2 g þ g2 g 2 agþ g 2 aa g 2 ag2 g 2 g 2 gþ g2g2a g 2 g 2 g2

A.R. Sheraly et al. / Journal of Molecular Structure (Theochem) 619 (2002) 21–35

Sidechain conformers with bL backbone

29

30

A.R. Sheraly et al. / Journal of Molecular Structure (Theochem) 619 (2002) 21–35

Fig. 7. (A) Shows the isodesmic reaction used to calculate the stabilization energy. Both glycine (Gly) and homocysteine (Hcy) were in the bL conformation. Below each reactant and product are the names of the compound and the energy in hartrees. These constants were used in the stabilization equation. The stabilization energy for each homocysteine conformer was calculated using the energy from Table 1. (B) Outlines the specific equation used to calculate the stabilization energy. All results were converted into kcal mol21 using the conversion factor 627:51 kcal mol21 ¼ 1 hartree and are shown graphically in Fig. 8.

occur in each conformer, but generally the greater the strength of interaction involved the more stable the conformer. A hydrogen bond between the ði 2 1Þ oxygen and the ði þ 1Þ amide hydrogen as shown in type H, is unique to the gL and gD backbone conformers, shown for the sake of completeness as only bL conformers were investigated in this study. While it is theoretically possible for an extremely ˚, weak hydrogen bond to exist at lengths of up to 5 A more concrete cut-off criteria were chosen when reporting hydrogen bonding (Fig. 6) for each specific type of hydrogen bonding interaction. Using these cut-off criteria, hydrogen bonding for each conformer shown in Table 2. A second form of interaction between the sidechain and the backbone is possible when studying Hcy, involving charge-transfer interaction inherent to the thiol group. Sulfur, being a third period atom on the periodic table, has the ability to accept electrons in its empty 3d orbital, overcoming the limitation of bonding to two constituents which is imposed on its smaller oxygen counterpart. In Hcy the thiol group present in the sidechain, can interact with the carbonyl carbon or oxygen of the backbone to create an additional stabilizing force. This feature can also be manifested in the related peptide residue, Cys [41]. Using the model (Fig. 3) four possible charge-transfer interactions can exist (Fig. 6). Type I and J represent structures in which the sulfur and carbonyl oxygen interact, while type K and L represent structures in which the sulfur and carbonyl carbon interact.

However, like all other interactions, distance between the electron donor and acceptor must lie at least slightly below the range determined by the sum of their van der Waal radii to be considered a stabilizing force. Just as was uncovered with the bL conformer of Cys, no charge-transfer interactions were found in ˚ [41]. The closest Hcy using the cutoff point of 3.25 A distance was observed in the g 2 g 2 g þ conformer ˚ between the sulfur and the with a distance of 3.37 A ði 2 1Þ residue carbonyl (type I, Fig. 6) and ˚ between the g þ g þ g 2 with a distance of 3.49 A sulfur and the (i) residue carbonyl (type J, Fig. 6) (values not shown). While this particular stabilizing force was not present in the bL conformers of Hcy, does not necessarily mean that this interaction has no role in stabilization of other Hcy backbone conformations. Stabilization energy as presented in (Table 1) is a measure of the stabilization or destabilization exerted by the sidechain on the backbone relative to a sidechain containing only a hydrogen atom, as in the case of Gly. It is possible to compare Hcy to Gly using the isodesmic reaction as outlined in Fig. 7(A) [42, 43]. Using the bL conformer of Gly as a reference for the bL Hcy, propanethiol (CH3 – CH2 – CH2 – SH) in its fully extended (aaa ) form was isodesmically coupled with bL Gly to produce methane and bL Hcy. Fig. 7 also lists the energy for each of the substances used below the reactant, except for Hcy whose specific conformational energies were used as shown in Table 1. The equation used to derive the stabilization energy

A.R. Sheraly et al. / Journal of Molecular Structure (Theochem) 619 (2002) 21–35

31

Fig. 8. The relative stabilization energies for the reaction converting bL glycine to bL homocysteine. Note that N.F ¼ not found, applies to those conformers that were not found to exist at the RHF/3-21G level of theory with the backbone in the fully extended or bL conformation.

is also shown in Fig. 7(B). A resulting negative stabilization energy indicates a stabilization effect while a positive energy indicates a destabilizing effect. Fig. 8 plots the stabilization energy for each conformer. From Fig. 8 it is clear that the sidechain has a stabilizing effect for each of the existing conformers as expected. Cys and Hcy are very similar in structure as shown in Fig. 1 and it is expected that similar geometry should exist for these structures. The only difference between Cys and Hcy is the additional methylene group before the terminal thiol. Cys was also analyzed using the RHF 3-21g level of theory using the N- and C-protected model [41]. It is of some interest to note that the sidechain aa structure for Cys was not found [41] while the aag þ , aaa and aag 2 structures were all found in Hcy. It is possible that this extension of the additional methylene group placed the large sulfur atom far enough from the backbone to allow it to occupy a stable positioning compared to Cys, allowing all three possible conformers to exist. Comparatively, the aaa for Hcy was the most unstable of all the bL sidechain conformers, which tends to agree with the Cys findings. One interesting feature that was noted after all the computations were completed was that when x1i was placed in the g 2 position, the f1i of the Hcy consistently deviated some 308 from the optimum value of 1808 resulting in values around 2 1408 (Table 1). This peculiar feature was more distorted in Cys when x1i was in the g 2 position, as the f1i were calculated to be between 2 1208 (g 2 g þ ) and 2 1388 (g 2 a ) [41]. Besides this trend, no other odd features were noted when comparing all the sidechain conformations for the bL conformers.

Due to the similar features between the sidechain structures between Cys and Hcy, a chart was created to compare their conformers. However, since Hcy contains an extra methylene group and thus an extra x rotation, it is not meaningful to directly compare dihedral angles. Instead of comparing the ordered x rotations of the sidechain, a comparison of rotations containing similar atomic makeup could provide more insight on the overall conformational properties. Fig. 9 is a diagrammatic plot of the dihedral x1i (Ca – Cb dihedral) verse the dihedral representing the thiol rotation in Hcy and Cys. In the case of Cys, the thiol rotation is x2i (Cb – SH) while in Hcy the rotation is x3i (Cg – SH). Since Hcy has an additional dihedral rotation x2i (Cb– Cg), it is necessary to incorporate this information into the diagram as well because each Cys conformer will have three Hcy analogues. This is shown as three subdivisions of each of the nine larger quadrants in Fig. 9. Thus each smaller rectangle represents a possible conformation that x2i from the Hcy residue can occupy (g þ , a, g 2 ). The black dots represent structures that were found in Hcy and thus rectangles missing a black dot indicate structures not found in Hcy. The structures found in Cys are represented by the shaded gray quadrants and thus structures not found in Cys are not shaded and remain white. For the most part the data, as expected, matches for Hcy and Cys. Roughly the same percentage of conformers were found for Cys (7/9) [41] and Hcy (22/27). Comparatively in Cys, of the ag þ , aa and ag 2 , only the aa conformer failed to converge. The most probable explanation for this finding was that hydrogen bond between the amino hydrogen and the sulfur were formed in the ag þ and ag 2 conformers,

32

A.R. Sheraly et al. / Journal of Molecular Structure (Theochem) 619 (2002) 21–35

Fig. 9. (A) Both cysteine (Cys) and homocystiene (Hcy) sidechain dihedral angles are labeled. x1i in both cases represent the dihedral angle formed between the a carbon of the backbone and the b carbon of the sidechain. However, the thiol dihedral angle is represented by x2i in Cys, while it is represented by x3i in Hcy. Thus a direct comparison of dihedral angles would be less meaningful and thus a comparison of dihedral angles based on participating atoms would be more relevant. (B) x1i verse the thiol dihedral (x2i in Cys, x3i in Hcy) conformers were comparatively plotted to examine the similarities between the two residues. x1i is labeled on the bottom axis. For reference, the atoms participating in the dihedral rotation have been referenced. Note that Z is either the S in Cys or the g carbon in Hcy. The thiol dihedral is labeled along the left axis, x2i in the case of Cys, x3i in the case of Hcy. The atoms participating in the dihedral rotation have also been referenced. Note that Y is the a carbon in the case of Cys, while it is the b carbon in Hcy. However, since Hcy has an additional dihedral angle, x2i composed of the b carbon and g carbon in the sidechain, each Cys conformer will have three Hcy analogues. This information is incorporated in the chart by subdividing each of the nine larger quadrants in to three smaller rectangles each corresponding to a different x2i conformer of Hcy. These x2i conformers for Hcy are labeled on the right axis. Shaded quadrants indicate conformers found in Cys, and thus white quadrants indicate the absence of a stable conformer in Cys. Rectangles containing a black dot indicate conformers found in Hcy, and thus rectangles without any black dot indicate the absence of a stable conformer in Hcy.

A.R. Sheraly et al. / Journal of Molecular Structure (Theochem) 619 (2002) 21–35

˚ , respectively with distances around 2.58 and 2.80 A [41]. Thus breaking this interaction to attain the aa conformer may have been unfavorable and prevented it from stabilizing in that potential minima. In Hcy there are nine different possible sidechain conformers in which x1i resides in the a orientation because x2i can occupy three potential minima (g þ , a, g 2 ) and similarly x3i can also occupy three potential minima (g þ , a, g 2 ), so therefore 3 £ 3 ¼ 9 distinct conformers. Of the five conformers not found in Hcy, four of them had x1i in the a orientation. While it is not clear why four of the nine possible conformers failed to successfully stabilize, it appears that repulsive forces (dipole –dipole) contributed to their destabilization. Also as noted earlier, steric interference and crowding of the sulfur and ði þ 1Þ nitrogen atoms in to a small region of space could have been a cause for the absence of the ag 2 X (X is x3i ¼ gþ; a, g 2 ) conformers of Hcy. Although these results were produced at the RHF/3-21G level of theory, their merit as a stepping stone to higher level of theory is valid and has been proven effective for modeling peptides. The RHF/321G level of theory does not accurately take into account the electronic interactions and thus this stands as the main source of error. It is also known that the RHF/3-21G level of theory does not employ enough Gaussian functions to describe all the valence electrons in third period atoms such as phosphorous and sulfur. Thus there may be a limitation with respect to the reliability of the van der Waal interactions and thus the conformers found. However, by calculating all the conformers at lower levels of theory and then bringing these results up to more extensive basis sets, it is possible to save computational time. Generally it is assumed that conformers not existing at lower levels of theory do not exist at higher more rigorous levels of theory. Thus by eliminating those conformers that still do not exist, early in the study at lower levels of theory, less computational time is spent searching for these conformers that do not exist at higher levels of theory.

5. Concluding remarks The completion of all the bL conformers provides

33

an outline for Hcy backbone and sidechain groupings. When referring to the Ramachandran map (Fig. 4) the bL represents only one of the nine possible backbone conformations. A full study of the entire surface at a level of theory such as RHF/3-21G would provide a more detailed outline as to the behavior of Hcy. There are 8 additional backbone orientations each having 27 possible sidechain conformations making a total of 8 £ 27 ¼ 216 still remaining to be calculated. However, dipole – dipole repulsion tends to restrict or eliminate some of these potential backbone conformations. Such a trend has been noted in Cys [41], in which both the eL and aL do not exist. Thus by analogy, applied to Hcy, the number of computations can be reduced by 2 £ 27 ¼ 54 conformers resulting in potentially 162 remaining conformers. The most informative quadrant to study would be those conformers with the Hcy backbone relaxed in the gL and gD regions. Finally, beyond the mapping of Hcy conformers on the potential energy hypersurface (PEHS), these results can be used in computing larger, complex structures also involved in the Met degradation pathway as shown in Fig. 2. Most importantly would be to compute the conformational structures for S-adenosylhomocysteine, the demethylated form of SAM.

Acknowledgments This work was supported by grants from Velocet Communications Inc., Toronto, Ont., Canada and the National Science Foundation (EPS-0091900), USA. The authors thank Graydon Hoare for database management, network support and software and distributive processing development. A special thanks is extended to Andrew M. Chasse, Steve M. Scopa and Christopher M. Andrews for their development of novel scripting and coding techniques, which facilitate a reduction in the number of CPU cycles needed. The pioneering advances of Kenneth P. Chasse, in all composite computer-cluster software and hardware architectures, are also acknowledged. David C.L. Gilbert and Adam A. Heaney are also thanked for CPU time.

34

A.R. Sheraly et al. / Journal of Molecular Structure (Theochem) 619 (2002) 21–35

References [1] H. Jakubowski, Translational incorporation of S-nitrosohomocysteine into protein, J. Biol. Chem. 275 (29) (2000) 21813–21816. [2] D. Voet, J.G. Voet, Biochemistry, Second ed., Wiley, New York, 1995, p. 739. [3] A.B. Guttormsen, P.M. Ueland, I. Nesthus, O. Nygard, J. Schneede, S.E. Vollset, H. Refsum, Determinants and vitamin responsiveness of intermediate hyperhomocysteinemia ($40 mmol/l): the Hordaland homocysteine study, J. Clin. Investig. 98 (9) (1996) 2174–2183. [4] V. Bandarian, K.A. Pattridge, B.W. Lennon, D.P. Huddler, R.G. Matthews, M.L. Ludwig, Nat. Struct. Biol. 9 (2002) 53–56. [5] L.A. Afman, N.M.J. Van der Put, C.M.G. Thomas, J.M.F. Trijbels, H.J. Blom, Reduced vitamin B12 binding by transcobalamin II increases the risk of neural tube defects, QJM 94 (3) (2001) 159–166. [6] S. Dayal, T. Bottiglieri, E. Arning, N. Maeda, M.R. Malinow, C.D. Sigmund, D.D. Heistad, F.M. Faraci, S.R. Lentz, S.R. Lentz, Endothelial dysfunction and elevation of S-adenosylhomocysteine in cystathionine [beta]-synthase-deficient mice, Circ. Res. 88 (11) (2001) 1203– 1209. [7] J.V. Woodside, J.W.G. Yarnell, D. McMaster, I.S. Young, E.E. McCrum, A.E. Evans, K.F. Gey, D.L. Harmon, A.S. Whitehead, Vitamin B6 status, MTHFR and hyperhomocysteinaemia, QJM 90 (8) (1997) 551– 552. [8] Z.S. Zhou, A.E. Smith, R.G. Matthews, L -selenohomocysteine: one-step synthesis from L -selenomethionine and kinetic analysis as substrate for methionine synthases, Bioorg. Med. Chem. Lett. 10 (21) (2000) 2471– 2475. [9] M. Ward, Homocysteine, folate, and cardiovascular disease, Int. J. Vitam. Nutr. Res. 71 (3) (2001) 173 –178. Review. [10] O. Stanger, M. Weger, W. Renner, R. Konetschny, Vascular dysfunction in hyperhomocyst(e)inemia. Implications for atherothrombotic disease, Clin. Chem. Lab. Med. 8 (2001) 725–733. Review. [11] A. Miller, V. Mujumdar, L. Palmer, J.D. Bower, S.C. Tyagi, Reversal of endocardial endothelial dysfunction by folic acid in homocysteinemic hypertensive rats, Am. J. Hypertens. 15 (2 pt 1) (2002) 157 –163. [12] H. Wang, X. Jiang, F. Yang, G.B. Chapman, W. Durante, N.E. Sibinga, A.I. Schafer, Cyclin A transcriptional suppression is the major mechanism mediating homocysteine-induced endothelial cell growth inhibition, Blood 99 (3) (2002) 939 –945. [13] M.C. Stuhlinger, P.S. Tsao, J.H. Her, M. Kimoto, R.F. Balint, J.P. Cooke, Homocysteine impairs the nitric oxide synthase pathway: role of asymmetric dimethylarginine, Circulation 104 (21) (2001) 2569– 2575. [14] J.C. Chambers, P.M. Ueland, M. Wright, C.J. Dore, H. Refsum, J.S. Kooner, Investigation of relationship between reduced, oxidized, and protein-bound homocysteine and vascular endothelial function in healthy human subjects, Circ. Res. 89 (2) (2001) 187–192. [15] N. Weiss, Y.Y. Zhang, S. Heydrick, C. Bierl, J. Loscalzo, Overexpression of cellular glutathione peroxidase rescues

[16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]

[27]

[28]

[29] [30] [31] [32] [33]

[34] [35] [36] [37] [38] [39] [40]

homocyst(e)ine-induced endothelial dysfunction, Proc. Natl Acad. Sci. USA 98 (22) (2001) 12503– 12508. R. Ragone, Homocystine solubility and vascular disease, FASEB J. 16 (3) (2002) 401–404. K.S. McCully, The Homocysteine Revolution, Keats Publishing Inc, New Canaan, Connecticut, 1997. Arch. Biochem. Biophys. 145 (1971) 405– 421. Biochem. J. 121 (1971) 577 –585. Biochemistry 9, (1971) 3471–3479. J. Biochem. 17 (1969) 193 –201. Biochim. Biophys. Acta 229 (1971) 1–17. J. Biol. Chem. 245 (1970) 1–17. J. Mol. Biol. 52 (1970) 6489–6497. Pure Appl. Chem. 40 (1974) 291 –308. ¨ . Farkas, A. G.A. Chass, M.A. Sahai, J.M.S. Law, S. Lovas, O Perczel, I.G. Csizmadia, Toward a computed peptide structure database: the role of a universal atomic numbering system of amino acids in peptides and internal hierarchy of database, Int. J. Quant. Chem. (2002) in press. M.A. Sahai, G.A. Chass, A. Perczel, S. Lovas, A. Varro, J.A. Papp, A modular numbering system of selected oligopeptides for molecular computations, Theochem (2002) in press. M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. AlLaham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart, M. HeadGordon, C. Gonzalez, J.A. Pople, GAUSSIAN 94, Revision E.2, Gaussian, Inc., Pittsburgh, PA, 1995. S.J. Weiner, V.C. Singh, T.J. O’Donnell, P.A. Kollman, J. Am. Chem. Soc. 106 (1984) 6243. A.M. Sapse, L.M. Fugler, D. Cowburn, Int. J. Quant. Chem. 29 (1986) 1241. T.C. Chean, S. Krimm, J. Mol. Struct. (Theochem) 188 (1989) 15. T.C. Chean, S. Krimm, J. Mol. Struct. (Theochem) 193 (1989) 1. A. Perczel, J.G. Angyan, M. Kajtar, W. Viviani, J.L. Rivail, J.F. Marcoccia, I.G. Csizmadia, J. Am. Chem. Soc. 113 (1991) 6256. T. Head-Gordon, M. Head-Gordon, M.J. Frish, C. Brooks, J. Pople, Int. J. Quant. Chem., Quant. Biol. Symp. 16 (1989) 311. T. Head-Gordon, M. Head-Gordon, M.J. Frish, C. Brooks, J. Pople, J. Am. Chem. Soc. 113 (1991) 5989. O. Farkas, M.A. McAllister, J.H. Ma, A. Perczel, M. Hollosi, I.G. Csizmadia, J. Mol. Struct. (Theochem) 369 (1996) 105. A. Perczel, O. Farkas, I.G. Csizmadia, Can. J. Chem. 75 (1997) 1120. O. Farkas, A. Perczel, J.F. Marcoccia, M. Hollosi, I.G. Csizmadia, J. Mol. Struct. (Theochem) 331 (1995) 27. A. Perczel, O. Farkas, I.G. Csizmadia, J. Comput. Chem. 17 (1996) 821. A. Perczel, O. Farkas, I.G. Csizmadia, J. Am. Chem. Soc. 118 (1996) 7809.

A.R. Sheraly et al. / Journal of Molecular Structure (Theochem) 619 (2002) 21–35 [41] M.A. Zamora, H.A. Baldoni, J.A. Bombasaro, M.L. Mak, A. Perczel, O. Farkas, R.D. Enriz, An exploratory ab initio study of the full conformational space of N-acetyl-L -cysteine-Nmethylamide, J. Mol. Struct. (Theochem) 540 (2001) 271–283. [42] B. Kim, G.A. Chass, Theochem (2002) in press.

35

[43] W. Viviani, J.-L. Rivail, A. Perczel, I.G. Csizmadia, J. Am. Chem. Soc. 115 (1993) 8321. [44] M.A. McAllister, G. Endredi, W. Viviani, A. Perczel, P. Csaszar, J. Ladik, J.-L. Rivail, I.G. Csizmadia, Can. J. Chem. 73 (1995) 563.