7894
J. Phys. Chem. B 2008, 112, 7894–7902
Estimating the “Steric Clash” at cis Peptide Bonds Simon Mathieu,† Romuald Poteau,‡ and Georges Trinquier*,‡ Laboratoire de Chimie et Physique Quantique, IRSAMC, UniVersite´ Paul-Sabatier, 31062 Toulouse Cedex 9, France, and Laboratoire de Physique et Chimie des Nano-Objets, IRSAMC, Institut National des Sciences Applique´es, 31077 Toulouse Cedex 4, France ReceiVed: NoVember 21, 2007; ReVised Manuscript ReceiVed: January 9, 2008
To account for the scarcity of cis peptide bonds in proteins, especially in nonproline (or secondary amide) cases, a steric-clash argument is often put forward, in a scheme where the R lateral chains are facing parallel one another, and the backbone is kept in an “all-trans”-like arrangement. Although such a steric conflict can be partly relieved through proper adjustment of the backbone dihedral angles, one can try to estimate its associated energy cost. To this end, quantum-chemistry approaches using a differential-torsion protocol and bond-separation-energy analyses are applied to N-ethyl propionamide CH3-CH2-CO-NH-CH2-CH3, regarded as a model capable of exhibiting Cβ · · · Cβ interaction as in alanine succession. The calculations provide an increment of 9 kcal/mol, quite close to that obtained in the nearly isostere (gsg) rotamer of n-hexane (10 kcal/mol), suggesting the local effects induced by methyl-methyl contact are similar in both cases. Analogous treatments on larger radicals as encountered in leucine or phenylalanine dimers do not change this increment much, which therefore defines the basic reference per-plaque quota to be overcome along all-cis chains. Explicit modeling indicated it can be reduced by up to a factor of 4. Introduction The vast majority of peptide bonds in peptides and proteins are in the trans conformation, or configuration, inasmuch as the amide C′-N bond maintains partial multiple-bond character. Actually, only about 0.05% of the known secondary peptide bonds sNH-COs in proteins are of cis type.1–12 The case of tertiary amides is somewhat different in that cis arrangements are here more accessible,13 as illustrated by their numerous occurrences at peptide bonds involving proline residues - these constitute about 5% of the known X-Pro junctions.3,4,12,14 These conformations can even form regular secondary structures in polyproline helices of type I (PPI).15 However, in the general case of nonprolyl secondary amides, building open or closed backbones from cis peptide units only is submitted to stringent limitations first analyzed by Pauling more than half a century ago.16 The energy difference between the cis and trans forms of the amide bond is estimated at around 2.5 kcal/mol with a barrier of 19 kcal/mol to overcome from the trans form. These results were obtained mainly from various theoretical and experimental evaluations on the parent compound N-methyl-acetamide (NMA),17 or seldom on small peptides.18 In tertiary amide links involving a proline residue (X-Pro), the cis/trans energy difference is reduced to less than 1 kcal/mol.13 As often noticed,3–5,19 under a thermodynamic equilibrium, at physiological temperatures in ViVo, these numbers would suggest a cis occurrence of about 2% for X-nonPro links, and more than 20% for X-Pro links, which is far beyond the above percentages. Possible explanations for the observed scarcity of cis amides include (i) the fact that many cis amide bonds may have been misassigned, as crystallographic refinement programs automati* Corresponding author. † Universite ´ Paul-Sabatier. ‡ Institut National des Sciences Applique ´ es.
cally refine amides as trans rotamers; (ii) importance of kinetic factors; (iii) noncovalent stabilization of trans amide forms; (iv) restrictions in conformational space, which lower the likelihood of cis amide forms. The last point singles out pure evolutionary arguments. Although there is some evidence for a physically driven stage of evolution,20–22 the selection machinery is basically governed by contingency and downstream functionality, indeed. Turning to nonPro secondary amide bonds, despite the thermodynamic preference for trans conformation, because there is a significant barrier to surmount from the opposite cis arrangement (say, 14-18 kcal/mol by virtue of the local source of the effect), one could imagine to build an oligopeptide with all peptide bonds entrapped in the cis conformation. The making of such repeated patterns is traditionally claimed to be nonviable because of the unavoidable “steric clash” that should occur between the side chains at consecutive CR carbon atoms, 1. In this view, the R lateral groups of linked (L)-aminoacids are indeed facing each other in syn position. However, this picture ignores the flagship degrees of freedom that φ and Ψ constitute in protein structure, 2, the adjustment of which could here partially relieve the constraints.
It is striking how most textbooks and courses either overlook the cis peptide-bond alternative at the freshmen level, or tend, at graduate level, to go along with this recurring steric-clash explanation. This is illustrated in Table
10.1021/jp711082d CCC: $40.75 2008 American Chemical Society Published on Web 06/11/2008
Estimating the “Steric Clash” at cis Peptide Bonds 1, which gathers quotations from a handful of books at our reach and a selection of biochemistry or protein online courses (this is, of course, nonexhaustive), further highlighting the contextsproline (P) or steric-clash argument (SCA)sin which these commentaries are made. Nearly as many items do not even mention the cis issue. Obviously, there is some oversimplification in the stericclash argument as it is often presented in this naı¨ve way. We propose in this work to try to clarify and specify what is behind this effect, and to try to assess it more quantitatively. To this end, we will use a special tool for numerical experiments and simulations of local effects in chemistry, namely the quantum-chemistry theoretical modeling. Typically, such numerical practices permit the introduction of specific or arbitrary geometrical constraints or the use of various biases for energy decomposition in order to gauge various effects under scrutiny. On another hand, the corresponding quantum computational procedures, which have benefited among others from the development of density functional theories (DFT), have now achieved a sufficient degree of reliability so that one can hope to get qualitatiVe notions emerging from the quantitatiVe treatments, providing they meet current state-of-the-art standards.
J. Phys. Chem. B, Vol. 112, No. 26, 2008 7895 equivalent question arises when n-hexane is taken in a conformation with the central C-C-C-C bonds in synperiplanar position and the terminal methyl groups in a synclinal gauche position.24 The proposed method will therefore consist of (i) calculating the energy difference between these two forms cc and tt of n-hexane (see Figure 2), both sustaining a coplanar arrangement of their H-C1-C2-C3-C4-H inner frame, 4; (ii) calculating the energy difference between the two forms syn and anti of n-butane, for which, in principle, no geometry constraint is needed, as both forms are basically stationary points on the potential energy surface;25 (iii) subtracting the latter from the former, to get a differential increment reflecting the steric hindrance or “steric clash” occurring between the two facing bonds C1-CT and C4-CT, in turn mirroring that occurring between two methyl side chains at cis peptide bonds in a priori arrangements such as 1 or 2.
Differential Torsion We postulate that a reasonable estimate of the energy increment due to a steric clash as in 1 lies in the energy required for the rearrangement of dimethyl NMA, alias N-ethyl propionamide (NEP), from its trans,trans-form (tt) to its cis,cis-form (cc) (see Figure 1),23 minus that of the trans-to-cis rearrangement of NMA, in order to remove the CR · · · CR interaction and keep only the through-space interaction between the two facing CR-Cβ bonds. In so doing, the synclinal gauche orientations of both MeC1C′N and MeC4NC′ sequences are preserved, conferring the demanded all-else-being-equal character to the measure. Because the cc form, and to a lesser extent the tt form, are far from being real minima on the corresponding potential energy surfaces, a restriction is needed somewhere to keep these geometrical arrangements in place. To this end, we will impose the constraint of maintaining an all-trans coplanar arrangement of the H-C1-C′-N-C4-H atoms of the NMA skeletons in both forms, 3. Under such a minimal constraint, the two terminal methyl groups are now enforced to basically face each other as do the R groups in 2, while keeping the possibility to use various degrees of freedom to minimize the repulsion. A key point, here, is that their involvement will necessarily remain limited owing to the above constraint in conjunction with incontrovertible tetrahedral arrangements at C1 and C4.
In a somewhat simpler context, let us illustrate and apply the procedure in the hydrocarbon series, where a nearly
The corresponding results for n-hexane are given, at three levels of calculations, in Table 2, top, for the energies, and Table 3 for main optimized geometrical parameters.26 The energy difference between the two forms of n-butane corresponds to the “eclipsed barrier” known to be around 5.6-5.8 kcal/mol from various explorations of the corresponding torsional potential in n-butane.27 Since the cc/tt difference amounts to 15-17 kcal/mol, the sought steric repulsion increment (SRI) adds up to about 10-11 kcal/mol. This number seems reasonable regarding two parallel C-C σ bonds facing each other at a distance hardly above the sum of organic van der Waals radii. We next go to the amide system, for which the calculated energy differences are given in Table 2, bottom, and the main optimized geometrical parameters are listed in Table 4. As mentioned, the energy difference between the two forms of NMA is rather well documented around 2.5 kcal/mol. Because of the absence of symmetry along the C1C′NC4 frame, perfect planarity is here no longer guaranteed. For consistency, we forced it in both trans and cis forms, even though relaxed geometries are not perfectly planar, particularly in the cis form, where the two methyl groups must arrange at best (therefore asymmetrically) their facing CH bonds. In these conditions, the cis-trans energy difference in NMA is calculated as being around 2 kcal/mol, which is about half-the n-butane rotational barrier. Since the cc/tt energy difference now lies at 11-12 kcal/ mol, the SRI comes out to 9-10 kcal/mol, a value quite close to the above hydrocarbon case. The steric-clash generated by methyl lateral chains in a dialanine junction such as 1 or 2 is therefore estimated by this method at 9-10 kcal/mol, which thus singles out a typical Cβ · · · Cβ interaction. We shall discuss in a later section to which extent this indicator reflects other R lateral chains or how it should be modulated accordingly.
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TABLE 1: Examples of How the cis-trans Issue in Peptide Bonds Is Accounted for, When Addressed in Some Textbooks (a-i), Research Books (j-l) and On-Line Courses (m-dd). The Proline (P) or Steric-Clash Argument (SCA) Context Is Indicated, with Further Mention about the Presence of an Explicit Steric-Clash Scheme (SCS) such as Scheme 2 refs
excerpts
P
SCA
SCS
a
In the cis conformation, these groups [the two R-carbons] are on the same side of the peptide bond. Almost all peptide bonds in proteins are trans. This preference for trans over cis can be explained by the fact that steric clashes between groups attached to the R-carbon atoms hinder formation of the cis form but do not occur in the trans configuration. By far, the most common cis peptide bons are X-Pro linkages.
0
0
0
b
Peptide groups, with few exceptions, assume the trans conformation, in which successive CR atoms are on opposite sides of the peptide bond joining them. This is partly a result of steric interference, which causes the cis conformation to be ∼8 kJ/mol less stable than the trans conformation (this energy difference is somewhat less in peptide bonds followed by a Pro residue, and, in fact, ∼10% of the Pro residues in proteins follow a cis peptide bond, whereas cis peptides are otherwise extremely rare).
0
0
c
Two conformations are theoretically possible with CR atoms at positions either cis or trans. [. . .] The trans form is energetically favored and thus prevails for all amino acids in proteins. For proline, the peculiar structure of which creates constraints within the protein, the trans position remains dominant in coiled proteins (94% of proteins are in this form), while the cis position becomes the dominant form in uncoiled proteins. (English translation)
0
d
Because of the double-bond nature of the peptide bond, the conformation of the peptide group is restricted to one of two possible conformations, either trans or cis. In the trans conformation, the two R-carbons of adjacent amino acid residues are on opposite sides of the peptide bond and at the opposite corners of the rectangle formed by the planar peptide group. In the cis conformation, the two R-carbons are on the same side of the peptide bond and are closer together. The cis and trans conformations arise during protein synthesis when the peptide bond is formed by joining amino acids to the growing polypeptide chains. The two conformations cannot be interconverted by rotation around the peptide bond once it has formed. The cis conformation is less favorable than the extended trans conformation because of the steric interference between the side chains attached to the two R-carbons atoms. Consequently, nearly all peptide groups in proteins are in the trans conformation. Rare exceptions occur, usually at bonds involving the amide nitrogen of proline, for which the cis conformation creates only slightly more steric interference than the trans conformation.
0
e
While the trans peptide linkage is usual, the cis-peptide linkage, which is ∼8 kJ/mol less stable than the trans linkage, also occurs in proteins quite often. The nitrogen atom is usually but not always from proline.
0
f
Unlike other peptide bonds in proteins, for which the trans isomer is highly favored (by a factor of about 1000), proline residues favor the trans form in the preceding peptide bond by a factor of only about 4.
0
g
These peptide bonds are virtually planar units which are mostly in trans configuration. (English translation)
h
The partial double-bond character of the peptide bond is sufficient to prevent rotation around the C-N bond, at physiological temperatures; this sets in a same plane the six atoms involved in the peptide bond [. . .]. Given the freedom of rotation around the CR-C and CR-N bonds, there exist only two possible configurations around the peptide bond [. . .]. In the trans configuration, the polypeptide chain spreads from one to the other opposite corners of the rectangular plane encompassing the atoms of the peptide bond. In the cis configuration, the two CR atoms of neighboring amino acid residues are closer to one another. This rapprochement leads to a spatial steric repulsion between the two lateral chains of the two R carbons, making the cis configuration less favorable than the trans one. This is why almost all amino acid residues in proteins are linked together in the trans configuration. Nevertheless, in bonds involving proline, the cis configuration is as much likely as the trans one because the amide nitrogen is here part of a ring. (English translation).
i
The peptide-bonded NH and CO in virtually all known structures had essentially identical dimension and adopted a planar trans conformation. [. . .] An important aspect of polypeptide structures is that the amide bond usually occurs in the planar trans conformation.
j
The third bond of the backbone, the peptide bond, is constrained to be planar, in either the cis or trans form (ω ) 0 or 180°); the trans form is the more stable, unless the next residue is Pro.
0
k
The conclusion can be drawn that the cis form is relatively improbable and will arise only as a variation on the central theme of protein conformation. A cis conformation can be expected to arise whenever its presence makes possible favorable intramolecular interactions with energy great enough to counterbalance the instability of this isomer. [. . .] The above observations suggest that both trans and cis proline conformations may exist in proteins, with a bias toward the trans conformation which may be negated by the immediate molecular environment of the proline group. Because of the high energy of the cis conformation in polypeptide systems, except in pyrrolidine peptide links, and because trans conformations form the basis for most protein model structures, in the following discussion we shall for simplicity disregard the potential appearance of cis conformations.
0
0
0
0
0
Estimating the “Steric Clash” at cis Peptide Bonds
J. Phys. Chem. B, Vol. 112, No. 26, 2008 7897
TABLE 1: Continued refs
excerpts
P
SCA
l
Owing to the fact that the C-N bond is a partial double bond, the peptide-bond group is planar and able to exist in the two forms. The trans configuration is preferred in most of the proposed structures of proteins, e.g., the R-helical structure. The cis form is generally less likely, owing to steric hindrance.
m
Proline is virtually the only amino acid which may adopt a stable cis structure, because of the small energy difference between cis and trans forms (it has two carbons linked to the nitrogen). The preferred conformations of proline are Ψ ) 160° and φ ) -75° for the cis configuration; a repeat of prolines in cis gives a polyproline helix of type I or PPI. The PPI helix is right-handed. [. . .] No PPI helix has ever been met in proteins yet. (English translation)
0
n
The peptide bond nearly always has the trans configuration since it is more favorable than cis, which is sometimes found to occur with proline residues. As can be seen above, steric hindrance between the functional groups attached to the CR atoms will be greater in the cis configuration. [. . .] However for proline residues, the cyclic nature of the side chain means that both cis and trans configurations have more equivalent energies. Thus proline is found in the cis configuration more frequently than other amino acids. The ω torsion angle of proline will be close to 0 degrees for the cis configuration, or most often, 180 degrees for the trans configuration.
0
o
Due to the peptide bond’s partial double-bond character, the ω angle is restrained to values near 0 (cis-peptide) and 180 degrees (trans-peptide). Cis-peptides are relatively rare and usually (but not always) occur if the next residue is a proline.
0
p
Trans: R carbons on opposite sides of the amide bond. Cis: R carbons on the same side of the amide bond. [. . .] Almost all peptide bonds in proteins are trans because of steric clashes of side groups. [. . .] By far the most common cis peptide bonds are those involving proline (X-Pro) where there is less steric difference between both forms.
0
0
q
Two possible configurations: cis and trans. Trans is energetically more favorable. But 10% of prolines in proteins are in cis configuration. Serines and other aminoacids in sites of dynamic character may find themselves in cis configuration to “preload” the enzyme with energy for catalysis. [. . .] Configurational aspects trans vs cis: trans (φ ) Ψ ) 180°, ω ) 180°), cis (φ ) Ψ ) 180°, ω ) 0°), a rare configuration (∼10% of Pro). (English translation)
0
0
r
In general, the R-carbons on adjacent amino acids are in a trans configuration. [. . .] The peptide bond is nearly always in a trans configuration since the steric hindrance of side chains is greater for a cis configuration.
s
The planarity of the peptide bond restricts to 180 degrees in very nearly all of the main chain peptide bonds. In rare cases ) 10 degrees for a cis peptide bond which usually involves proline.
0
t
Another important feature of the peptide bond is that the alpha CR at opposite ends of the rectangle are usually trans to each other (on opposite sides of the C-N bond in the peptide bond). This trans arrangement of the CR’s is sterically favored by a factor of 1000/1 for all peptide bonds except X-Pro. Pro, which is a cyclic amino acid, is sterically restricted. The link above, which also shows the X-Pro bond, clearly shows that both the trans and cis forms of the X-Pro bonds are hindered to a similar extent. In X-Pro bonds in proteins, the trans/cis ratio found in proteins is 4/1.
0
u
The amide group will prefer to have all atoms connected to it in the same plane as the amide bond (no rotation). This can result in a cis or trans configuration. Due to steric and electronic reasons the trans configuration is the predominant form for the amide bond. Figure 3 shows the two possible planar configurations. Note the steric clash between the side chain groups in the cis form.
V
Like any double bond, rotation about the peptide bond angle ω is restricted, with an energy barrier of ∼3 kcal/mol between cis and trans forms. These two isomers are defined by the path of the polypeptide chain across the bond. Successive R-carbons in the chain (i, i + 1) are on the same side of the bond in the cis isomer as opposed to the staggered conformation of the trans isomer. For all amino acids but proline, the cis configuration is greatly disfavored because of steric hindrance between adjacent side chains. Ring closure in the proline side chain draws the β-carbon away from the preceding residue, leading to lower steric hindrance across the X-pro peptide bond. In most residues, the trans to cis distribution about this bond is about 90/10, but with proline, the trans to cis distribution is about 70/30.
w
Nearly all peptide groups in proteins are in the trans conformation.
x
The configuration of the peptide bond can be either trans or cis. Almost all protein aminoacid residues adopt the trans configuration, in which steric repulsion is minimal. (English translation)
y
Trans peptide groups are more stable. Peptide groups assume trans conformation (i.e., CR atoms are on opposite sides of the peptide bond joining them). Reason: partly due to steric hindrance which causes the cis conformation to be less stable than the trans by 8 kJ/ mol. But peptide bonds followed by a Pro residue are slightly more stable than that. So, about 10% of Pro residues in proteins follow a cis peptide bond (whereas this is extremely rare for other amino acids).
0
z
Peptide group can have two possible conformations, trans or cis. cis conformation is less favorable due to steric interference of side chains. Nearly all peptide groups in proteins are in trans conformation (proline is the exception, it often introduces kinks in polypeptide chain).
0
aa
The peptide links are planar; strong double-bond character; isomerization of the peptide linkages s-trans, s-cis; trans favored; cis: bump. (English translation)
SCS
0
0
0
0
0
0
0
0
0
0
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TABLE 1: Continued refs
excerpts
P
bb
These limitations force CR carbons on either side of the peptide bond to be, with few exceptions, trans to each other (opposite sides of the peptide bond). cis configuration is rare; steric hindrance is greater. Trans is much more stable (sterically favored).
cc
Most peptide bonds prefer overwhelmingly to adopt the trans isomer (typically 99.9% under unstrained conditions), chiefly because the amide hydrogen (trans isomer) offers less steric repulsion to the preceding CR atom than does the following CR atom (cis isomer). By contrast, the cis and trans isomers of the X-Pro peptide bond are nearly isosteric (i.e., equally bad energetically); the CR (cis isomer) and Cδ atoms (trans isomer) of proline are roughly equivalent sterically. Hence, the fraction of X-Pro peptide bonds in the cis isomer under unstrained conditions ranges from 10-40%.
0
dd
The partial double bond renders the amide group planar, occurring in either the cis or trans isomers. In the unfolded state of proteins, the peptide groups are free to isomerize and adopt both isomers; however, in the folded state, only a single isomer is adopted at each position (with rare exceptions). The trans form is preferred overwhelmingly in most peptide bonds (roughly 1000:1 ratio in trans:cis populations). However, X-Pro peptide groups tend to have a roughly 3:1 ratio, presumably because the symmetry between the CR and Cδ atoms of proline makes the cis and trans isomers nearly equal in energy
0
SCA
SCS
0
a Berg, J. M.; Tymoczko, J. L.; Stryer, L. Biochemistry , 6th ed.; Freeman: New York, 2007; Chapter 2, p 38. b Voet, D.; Voet, J. G. Biochemistry, 3rd ed.; John Wiley & Sons: New York, 2004, p 220. c Kamoun, P.; Lavoine, A.; de Verneuil, H. Biochimie et Biologie Mole´culaire; Medecine-Sciences Flammarion: Paris, 2003. d Horton, H. R.; Moran, L. A.; Ochs, R. S.; Rawn, D. J.; Scrimgeour, K. G. Principles of Biochemistry, 3rd ed.; Prentice-Hall/Pearson Education: Upper Saddle River, NJ, 2002; p 87. e Metzler, D. E. Biochemistry. The Chemical Reactions of LiVing Cells, 2nd ed.; Harcourt/Academic Press: San Diego, 2001; Vol. 1, p 56. f Mathews, C.E.; van Holde, K. E.; Ahern, K. G. Biochemistry, 3rd ed.; Addison Wesley Longman, Inc.: San Francisco, 1999; pp 162, 188. g Lippard, S.; Berg, J. Principes de Biochimie Mine´rale; De Boeck: Brussels, 1997. h Rawn, J. D. Traite´ de Biochimie; De Boeck-Wesmael: Brussels, 1990; p 76. i Cantor, C. R.; Schimmel, P. R. Biophysical Chemistry; Freeman: San Francisco, 1980; Part I, pp 91, 254. j Creighton, T. F. In Protein Engineering; Oxender, D.L, Fox, C. F., Eds.; A. R. Liss, Inc.: New York, 1987; Chapter 7 (Protein folding), p 83. k Schellman, J. A.; Schellman, C. In The Proteins. Composition, Structure and Function, 2nd ed.; Neurath, H., Ed.; Academic Press: New York, 1964; Vol. II, Chapter 7 (The conformation of polypeptide chains in proteins), pp 8, 9. l Linderstrom-Lang, K. U.; Schellman, J. A. In The Enzymes, 2nd ed.; Boyer, P. D., Lardy, H., Myrback, K., Eds.; Academic Press: New York, 1959; Vol. 1, Chapter 10 (Protein structure and enzyme activity), p 446. m Internet course on Biochimie des Prote´ines (BCM-514); Universite´ de Sherbrooke (http://pages.usherbrooke.ca/bcm-514-bl/2b.html). n Internet course on The principles of protein structure; Birkbeck College, University of London, 1996 (http://www.cryst.bbk.ac.uk/PPS95/course/3_geometry/peptide2.html). o Practical Model Validation; EMBO Bioinformatics course; Uppsala, 2001 (http://alpha2.bmc.uu.se/embo2001/modval/03.html). p Biochemistry for Biomedical Materials: The Molecular Design of Life; Manchester University (http://personalpages.manchester.ac.uk/staff/R.Ulijn/biochemistry/Biochem05lecture_4.ppt#318,18,Diapositive 18). q Mode´lisation Mole´culaire; Universite´ de Provence, Marseille (http://biologie.univ-mrs.fr/upload/p199/1_MM.pdf). r Introduction to Biochemistry and Molecular Biology, Course BCH 4024, Lecture 3, University of Florida (http://faraday.ufbi.ufl.edu/∼thmareci/bch4024/lecture3.pdf). s Principles of Protein Structure, ComparatiVe Protein Modeling and Visualization, Chapter 1, Swiss-model server, Expasy (http://swissmodel.expasy.org/course/ text/chapter1.htm). t Understanding Protein Conformation, Biochemistry Online, Chapter 2, College of Saint Benedict, Saint John’s University (http://employees.csbsju.edu/hjakubowski/classes/ch331/protstructure/olunderstandconfo.html). u Ramachandran Plots. Amino Acid Configuration in Proteins, Chemistry 351 (http://www.upei.ca/∼chem352/Resources/Tutorials/Ramachandran.doc.pdf). V Primary Structure, Secondary Motifs, Tertiary Architecture, And Quaternary Organization, Proteins, Chapter 1: Protein structure; Section 1, Princeton University (http://www.biophysics.org/ education/carey.pdf). w Course Amino Acids and the Primary Structure of Proteins, Erskine College (http://acad.erskine.edu/facultyweb/smith/ OrganicChemII/ProteinsforOrganic.ppt; http://acad.erskine.edu/facultyweb/smith/BiochemI/Powerpoints/3DProteinstructure.ppt). x Chimie Supramole´culaire - Supramolecular Chemistry, University of Southampton U.K., (http://pages.usherbrooke.ca/ydory/pdf/BCM_300_04.PDF). y Undergraduate course, lecture note 8A2, University of Winnipeg, Department of Chemistry (http://chemistry.uwinnipeg.ca/meze/pdf/ 3502Notes_8A2_ProteinStruct_Oct20_05.pdf). z Amino Acids and Peptides, Biology 2315, lecture notes, Chapter 3, Langara College (http://www.langara.bc.ca/biology/mario/Biol2315notes/biol2315chap3.html). aa Chimie Bio-Organique, Mode´lisation Mole´culaire. Introduction (http://www.mapageweb.umontreal.ca/schmitza/Pr%C3%A9sentation3.pdf). bb Peptides and Proteins, Lectures 8, CHM333, Purdue University, College of Science, Department of Chemistry (http://www.chem.purdue.edu/courses/chm333/Fall%202005/Fall%202005%20Lectures/Fall%202005%20Lecture%208.pdf). cc Wikipedia encyclopedia (english), “Proline” item (http://en.wikipedia.org/wiki/Proline). dd Wikipedia encyclopedia (english), “Peptide bond” item (http://en.wikipedia.org/wiki/Peptide_bond).
Bond Separation Energies We now turn to a practice frequently used in theoretical chemistry, which consists of using an isodesmic reaction to determine a bond separation energy (BSE). This energy increment reflects the change in thermodynamic stability that a given bond undergoes when it changes its environment. It is defined from an isodesmic reaction, where, by definition, each member contains the same number of atoms and kind of bonds. In the case of the C-C bonds in NEP, the corresponding isodesmic reaction writes:
CH3-CO-NH-CH3 (cis) + 2 CH3-CH3 f CH3-CH2-CO-NH-CH2-CH3 (cc) + 2 CH4 (1) Again, let us first illustrate the purpose in the simpler case of n-hexane, where our isodesmic equation writes:
CH3-CH2-CH2-CH3 (syn) + 2 CH3-CH3 f CH3-CH2-CH2-CH2-CH2-CH3 (cc) + 2 CH4 (2) On the right-hand side of the equation, the two terminal C-C bonds are in the hindered position, while on the left-hand side, the two C-C bonds under attention are totally free in the ethane context. Note, however, that the coupling involves not only this steric interaction, but it also includes all other electronic effects such as delocalization or hyperconjugation effects, and this procedure does not allow one to discriminate between them all. However, because of the localized character of σ C-C bonds, and the weak extent of hyperconjugation in saturated hydrocarbons, one can bet that, in such a case, the BSE obtained from equation (2) is a good indicator of steric hindrance in n-hexane (cc).28 This is actually observed, as illustrated in Table 5, top. At the DFT(B3LYP) level, this BSE is calculated at 9.7 kcal/mol, a value nearly identical to the index obtained from the above differential-torsion procedure
Estimating the “Steric Clash” at cis Peptide Bonds
J. Phys. Chem. B, Vol. 112, No. 26, 2008 7899 TABLE 2: Calculated Relative Energies for the Constrained Rotamersa model system molecule hydrocarbons
n-hexane n-butane
amides
NEP NMA
a
Figure 1. The two constrained rotamers of N-ethyl propionamide (NEP) calculated in the differential-torsion procedure.
formal B3LYPb MP2b MP2c rearrangement tt f cc anti f syn ∆(∆E ) tt f cc trans f cis ∆(∆E )
15.4 5.7 9.8 11.0 2.3 8.8
17.0 6.0 11.0 12.4 2.3 10.1
16.5 5.7 10.8 11.6 1.8 9.8
In kcal/mol. b 6-31G** basis set. c 6-311++G(2d,p) basis set.
basis set. In this worst case, it is clear that only the difference ∆(BSE) is the significant indicator for the steric clash, as the BSE alone here carries more causes than the steric repulsion alone. This will prove to be even more conspicuous with the amide systems. The BSE calculated for NEP, corresponding to reaction (1), are listed in the mid part of Table 5. The BSE for the (cc) form, is calculated at only 6 kcal/mol, a value more than 2-kcal/mol lower than the increment obtained from the above differentialtorsion procedure. The π-scheme at C′-N allows significant hyperconjugation to take place with the terminal C1-CT and C4-CT bonds, which favors their synclinal gauche conformations with respect to C′-N, and comes to decrease their mutual repulsive effect. This stabilizing effect also occurs in the (tt) form and it appears to be even more pronounced at the MP2 level. In the extreme, the MP2/6-311++G(2d,p) level gives a BSE of only 4 kcal/mol for the (cc) form, and as much as -6 kcal/mol for the (tt) form, on a stabilizing side. Again we tend to trust the DFT results more than the MP2 ones, which are known to somewhat overestimate this stabilizing effects. Even more than in the preceding hydrocarbon case, the difference between the two BSE is the significant index, and again, this difference appears to converge satisfactorily to the value of 9-10 kcal/mol. Discussion
Figure 2. The two constrained rotamers of n-hexane calculated in the differential-torsion procedure.
(9.8 kcal/mol). In concomitance, the BSE obtained for the relatively unhindered (tt) form of n-hexane is quite small, and of negative sign, reflecting small hyperconjugation of the terminal CC bonds with the carbon central frame. Note that, by construction, the difference (cc) - (tt), noted ∆(BSE) in Table 5, is necessarily identical to the above-discussed ∆(∆E) in Table 2. In Table 5, one can see that the MP2 level of description seems to overestimate the conjugation effects with respect to the DFT level, a trend even more pronounced with the larger
Geometries. Interesting features can be seen from Tables 3 and 4. From (tt) to (cc), which geometrical parameters will distort more in order to somewhat soothe the steric constraint? For n-hexane, these are the C2-C3 central bond length (+0.04 Å), and the C1C2C3 and C2C3C4 central-frame valence angles (+12°). On NEP, equivalent changes occur, although to a somewhat different extent: C′-N increases by +0.01 Å, and C1C′N and C′NC4 increase by +8° and +14°, respectively. In both cases, the valence angles at C1 and C4 also increase by 4-5°. An amazing detail, tiny but significant as coming up from the three levels of description, is the small dissymmetry exhibited by the terminal methyl groups in (cc) n-hexane. Whereas the (tt) form has Ci symmetry, the (cc) form could have, by construction, a Cs symmetry. It slightly distorts from it as shown by the dissimilar values of the parameters associated to each CT. This is further mirrored by the corresponding dihedral angles CTC1C2C3 and C2C3C4CT, not given in Table 3, which differ from 1–3° according to the level of description. The same trends are observed on NEP, but in this case, no symmetry would advocate the strict equivalence of the terminal methyl groups. The BSE for the totally relaxed forms are given in Table 5, bottom. For n-hexane, the absolute minimum is calculated as being 1.5-2 kcal/mol below the constrained tt form. As expected, this preferred form corresponds to an all-staggered all-antiperiplanar (or “all-trans”) conformation, so that this lowering reflects the energy required for turning the terminal methyl groups into
7900 J. Phys. Chem. B, Vol. 112, No. 26, 2008
Mathieu et al.
TABLE 3: Calculated Main-Frame Bond Lengths and Bond Angles for the Constrained Hydrocarbonsa B3LYPb
MP2b
anti
syn
∆
C1sC2 C2sC3 C1C2C3 C1 · · · C4
1.531 1.534 113.3 3.931
1.534 1.561 116.8 2.946
+ 0.003 + 0.028 + 3.5 - 0.985
C1sC2 C3sC4 C2sC3 C1sCT C4sCT C1C2C3 C2C3C4 C2C1CT C3C4CT C1 · · · C4 CT · · · CT
1.539
1.545 1.546 1.573 1.536 1.536 126.9 127.2 118.6 119.2 3.436 3.437
+ 0.006 + 0.007 + 0.038 + 0.002 + 0.002 + 12.1 + 12.4 + 3.6 + 4.2 - 0.539 - 2.117
a
1.535 1.534 114.8 115.0 3.975 5.554
MP2c ∆
anti
syn
∆
n-butane 1.524 1.528 1.525 1.551 112.9 116.4 3.904 2.911
+ 0.003 + 0.026 + 3.5 - 0.993
1.526 1.526 112.7 3.902
1.530 1.553 116.2 2.903
+ 0.004 + 0.027 + 3.5 - 0.999
n-hexane (tt/cc) 1.531 1.535 1.539 1.526 1.562 1.526 1.529 1.532 114.4 125.6 126.6 114.4 117.1 119.2 3.944 3.373 5.492 3.333
+ 0.005 + 0.008 + 0.035 + 0.003 + 0.006 + 11.2 + 12.2 + 2.7 + 4.8 - 0.572 -2.160
1.531
1.536 1.539 1.563 1.532 1.537 125.5 126.0 117.1 118.6 3.359 3.295
+ 0.005 + 0.008 + 0.036 + 0.004 + 0.009 + 11.3 + 11.8 + 3.0 + 4.5 - 0.582 - 2.187
anti
syn
1.527 1.528 114.2 114.1 3.941 5.482
In angstro¨ms and degrees. b 6-31G** basis set. c 6-311++G(2d,p) basis set.
TABLE 4: Calculated Main-Frame Bond Length and Bond Angles for NMA and NEPa B3LYPb
MP2b ∆
trans
MP2c ∆
trans
cis
cis
C1sC′ C′sN NsC4 C1C′N C′NC4 C1 · · · C4
1.524 1.370 1.451 114.4 122.6 3.814
1.521 1.371 1.452 116.1 127.3 2.927
+ + + + -
0.003 0.001 0.001 1.7 4.7 0.887
1.516 1.369 1.448 114.2 122.2 3.798
1.514 1.369 1.448 115.7 126.8 2.901
+ + + + -
C1sC′ C′sN NsC4 C1sCT C4sCT C1C′N C′NC4 C′C1 CT NC4 CT C1 · · · C4 CT · · · CT
1.530 1.367 1.463 1.537 1.532 115.3 123.3 114.1 114.0 3.843 5.468
1.532 1.378 1.464 1.540 1.536 123.7 137.0 119.5 117.5 3.310 3.374
+ + + + + + + + + -
0.002 0.011 0.001 0.003 0.004 8.4 13.7 5.4 3.5 0.533 2.094
NEP (tt/cc) 1.520 1.523 1.367 1.376 1.457 1.458 1.529 1.535 1.525 1.529 115.0 123.2 122.2 136.3 112.7 118.7 113.4 116.8 3.818 3.276 5.401 3.305
+ + + + + + + + + -
∆
trans
cis
0.002 0.001 0.001 1.5 4.6 0.897
1.516 1.366 1.451 114.4 122.7 3.804
1.513 1.366 1.451 115.7 126.2 2.886
+ + + + -
0.003 0.000 0.001 1.3 3.5 0.918
0.003 0.009 0.001 0.005 0.004 8.2 14.1 6.0 3.4 0.542 2.096
1.519 1.363 1.458 1.531 1.526 115.3 122.7 113.0 113.3 3.821 5.413
1.521 1.373 1.461 1.538 1.530 122.9 135.7 118.6 117.0 3.256 3.271
+ + + + + + + + + -
0.002 0.010 0.003 0.007 0.004 7.6 13.0 5.6 3.7 0.565 2.142
NMA
a
In angstro¨ms and degrees. b 6-31G** basis set. c 6-311++G(2d,p) basis set.
TABLE 5: Calculated Bond Separation Energies (BSE)a system
B3LYPb
MP2b
MP2c
n-hexane (cc) n-hexane (tt) ∆(BSE) N-ethyl propionamide (cc) N-ethyl propionamide (tt) ∆(BSE) n-hexane (relaxed) N-ethyl propionamide (relaxed)
9.7 -0.1 9.8 6.4 -2.4 8.8 -2.3 -4.8
8.5 -2.5 11.0 5.0 -5.1 10.1 -4.1 -7.3
6.6 -4.2 10.8 3.6 -6.1 9.8 -5.7 -8.3
a In kcal/mol. The corresponding isodesmic reactions are as follows: n-hexane: CH3-CH2-CH2-CH3 + 2 CH3-CH3 f CH3-CH2-CH2CH2-CH2-CH3 + 2 CH4; N-ethyl propionamide: CH3-CO-NHCH3 + 2 CH3-CH3 f CH3-CH2-CO-NH-CH2-CH3 + 2 CH4. b 6-31G** basis set. c 6-311++G(2d,p) basis set.
anticlinal gauche in tt. For NEP, a comparable lowering is also calculated around 2 kcal/mol. In this case, the minimum corresponds to a trans-amide frame with skewed terminal methyl groups, each to a different extent, and leading to two nearly degenerate
isomers according to their mutual relative orientation trans or cis. The CTC1C’N dihedral angle being around 150-170° (according to the isomer and the method), and the C′NC4CT being close to orthogonality at 80-100°. Generalization. This estimate should be viewed as an upper bound since mobilization of the adjustment variables that are backbone dihedral angles φ, Ψ, and to a lesser extent ω, are expected to, and actually do,29,30 partly relieve the hindrance. On the other hand, the above-calculated SRI increment represents a lower bound insofar as most nonglycine residue lateral chains are bulkier, regardless of attractive interactions that would surely take place between charged residues of opposite signs such as KE or ND combinations.31 We have further applied the differential-torsion procedure to two examples of heavier lateral chains, namely LL and FF neighboring. At the DFT level, the SRI indexes are calculated at 9.2 kcal/mol for leucine and 8.2 kcal/mol for phenylalanine, which are quite close to the value of 8.8 kcal/mol given in Table 2. The corresponding (cc) geometries are reported in Figure 3. The two sec-butyl groups
Estimating the “Steric Clash” at cis Peptide Bonds
J. Phys. Chem. B, Vol. 112, No. 26, 2008 7901
Figure 3. How the lateral chains of neighboring leucines (left) or phenylalanines (right) position one another when forced to keep syn-gauche arrangement.
Figure 4. Calculated overall conformational map for a regular all-cis alanine tripeptide model, illustrating the possible escape towards various catchment regions (RHF/3-21G level, ω constrained to zero, contour lines from 1 to 20 kcal/mol, with steps of 2 kcal/mol).
of leucine lateral chains actually adapt their position in order to keep the iPr parts as far as possible, so that the Cβ · · · Cβ interaction embodied in the Me · · · Me model captures the essence of the repulsion, as reflected by an SRI only 0.3 kcal aboVe that of the alanine-alanine model. On the other hand, the two phenyl groups of the phenylalanine lateral chains also take up a distal position, but what is striking in this case is their perfect alignment reflecting some conjugation with the amide main frame. Because they afford this conjugation, the group effect is now slightly stabilizing, and the SRI appears to be 0.6 kcal/mol below that of the alanine-alanine model. Both cases are close, anyway. Avoidance. In a previous work on all-cis alanine tridecamers, it was shown how the dihedral angles along the backbone can work together to reduce the initial encumbrance and find efficient compromises in strain-relieved, if not strain-free, helical arrangements. This can be visualized from a “meta” Ramachandran conformational map associated with the two CR hinges of a regular alanine tripeptide model including two R carbons and three cis plaques: Me-CONH-CHMe-CONH-CHMeCONH-Me. As schematized on the calculated map drawn in Figure 4, escape from the 180/180 hindered region can lead to five possible catchment regions obtained in the present context. Combinations of these along the chain defines various kind of helices, four of which were particularly documented from explicit minimization results.30 In these constructions, the strain has been estimated to drop to about 2.5 kcal/mol per plaque, a
lower bound representing roughly one-quarter of the initial steric-tension increment. Concluding Remarks. This work has tried to measure out as directly as possible and in some absolute manner the steric repulsion generated by two facing side chains at a cis-peptide bond linking two (L-) amino acids. The estimate around 10 kcal/ mol is an amount that the system has, systematically, if not to overcome completely, at least to lessen as much as possible, for each couple of CR’s along the protein backbone. The present model only addresses one peptide plaque, therefore describing a local effect. For two cis plaques and beyond, the effect can hardly be understood as local, since neighboring cis plaques are by construction strongly coupled.30 They are thus no longer independent, unlike the φ/Ψ degrees of freedom at each CR legitimating the interest of Ramachandran maps in standard alltrans proteins – a consideration that points to the limits of the otherwise useful presently proposed indicator. While the case of all-cis polyglycine, not giving rise to Cβ · · · Cβ interaction, needs to be examined separately, explicit treatment on all-cis polyalanine open chains have shown that this energy increment can be divided by up to a factor of 4. Acknowledgment. The explicit laboratory affiliation statuses are UMR5626, CNRS, for the Laboratoire de Chimie et Physique Quantique, and UMR5215, CNRS-UPS-INSA, for the Laboratoire de Physique et Chimie des Nano-Objets. We thank the CINES and CALMIP computing centers in Montpellier and Toulouse, respectively, for generously allocating computational resources. We are grateful to Dr. Yves-Henri Sanejouand for communicating his results from the PDB analysis, and for fruitful discussions. References and Notes (1) Ramachandran, G. N.; Mitra, A. K. J. Mol. Biol. 1976, 107, 85. (2) Bairaktari, E.; Mierke, D. F.; Mammi, S.; Peggion, E. J. Am. Chem. Soc. 1990, 112, 5383. (3) Stewart, D. E.; Sarkar, A.; Wampler, J. E. J. Mol. Biol. 1990, 214, 253. (4) Weiss, M. S.; Jabs, A.; Hilgenfeld, R. Nat. Struct. Biol. 1998, 5, 676. (5) Jabs, A.; Weiss, M. S.; Hilgenfeld, R. J. Mol. Biol. 1999, 286, 291. (6) Pal, D.; Chakrabarti, P. J. Mol. Biol. 1999, 294, 271. (7) Forbes, C. C.; Beatty, A. M.; Smith, B. D. Org. Lett. 2001, 3, 3595. (8) Dugave, C.; Demange, L. Chem. ReV. 2003, 103, 2475. (9) Pahlke, D.; Leitner, D.; Wiedemann, U.; Labudde, D. Bioinformatics 2005, 21, 685. (10) For examples of biological implications of non-prolyl cis peptide bonds, see. (a) Herzberg, O.; Moult, J. O. Proteins: Struct., Funct., Genet. 1991, 11, 223. (b) Delbaere, L. T.; Vandonselaar, M.; Prasad, L.; Quail, J. W.; Wilson, K. S.; Dauter, Z. J. Mol. Biol. 1993, 230, 950. (c) Odefey, C.; Mayr, L. M.; Schmid, F. X. J. Mol. Biol. 1995, 245, 69. (d) Hennig, M.; Jansonius, J. N.; Terwisscha van Scheltinga, A. C.; Dijkstra, B. W.; Schlesier, B. J. Mol. Biol. 1995, 254, 237. (e) Xia, Z.-x.; Dai, W.-w.; Zhang, Y.-f.; White, S. A.; Boyd, G. D.; Mathews, F. S. J. Mol. Biol. 1996, 259, 480. (f) Banerjee, S.; Shigematsu, N.; Pannell, L. K.; Ruvinov, S.; Orban, J.; Schwarz, F.; Herzberg, O. Biochemistry 1997, 36, 10857. (g) Weiss, M. S.; Metzner, H. J.; Hilgenfeld, R. FEBS Lett. 1998, 423, 291. (h) Weiss,
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