Conformational study of the 1,2,3-propanetriol (glycerol) in the channel of the aquaglyceroporin GlpF

Journal of Molecular Structure: THEOCHEM 850 (2008) 21–31 www.elsevier.com/locate/theochem

Conformational study of the 1,2,3-propanetriol (glycerol) in the channel of the aquaglyceroporin GlpF Alain Porquet

a,b,*

, Montserrat Filella

a,c

a SCHEMA, 92 rue Principale, L-6990 Rameldange, Luxembourg Alpine Institute of Environmental Dynamics, L’Entropierre, 108 rue du Puy, F-38660 La Terrasse, France Department of Inorganic, Analytical and Applied Chemistry, University of Geneva, 30 Quai Ernest-Ansermet, CH-1211 Geneva 4, Switzerland b

c

Received 4 April 2007; received in revised form 9 October 2007; accepted 10 October 2007 Available online 24 October 2007

Abstract The X-ray structure of the aquaglyceroporin GlpF protein refined by Fu et al. [D. Fu, A. Libson, L.J.W. Miercke, C. Weitzman, P. Nollert, J. Krucinski, R.M. Stroud, Science 290 (2000) 481–486.] shows three glycerol molecules co-crystallized inside the channel. The conformations of these molecules have been used to study the relationship between conformation, energy balance and hydration in the hope that it will provide insight into the molecular transport mechanism in the channel. Initially, the position of the hydrogen atoms of the glycerol molecule in the three conformations was established. As the glycerol molecule progressively loses its hydration waters in its transport pathway inside the channel, the nature of the glycerol bonds changes: the geometry of the alkyl backbone adapts to the available space while the progressive dehydration is partially compensated by the formation of intramolecular hydrogen bonds. The nature of these hydrogen bonds has been established by DFT calculation of the rotation barriers of the hydroxyl groups. Finally, the influence of the intramolecular hydrogen bonds on the conformation of the alkyl backbone has been established by quantum calculations of potential energy surfaces by semi-empirical quantum calculations PM3/Zindo.  2007 Elsevier B.V. All rights reserved. Keywords: 1,2,3-Propanetriol; Glycerol; Conformation; Ab-initio calculations; GlpF

1. Introduction The first transmembrane protein responsible for the transport of glycerol (1,2,3-propanetriol) in the cells was identified a few years ago [1]. To date, a large number of proteins having the same role, gathered in a superfamily, have been discovered and studied [2–9]. The structure of the GlpF protein (glycerol facilitator) in Escherichia coli was solved by X-ray diffraction by Fu et al. [10] with a res˚ . The presence of a high concentration of olution of 2.2 A glycerol in the experimental solution made it possible to co-crystallize three molecules of glycerol inside the channel of the protein. Once the structure of the GlpF protein was * Corresponding author. Address: Department of Inorganic, Analytical and Applied Chemistry, University of Geneva, 30 Quai Ernest-Ansermet, CH-1211 Geneva 4, Switzerland. Tel.: +41 22 3796046. E-mail address: montserrat.fi[email protected] (M. Filella).

0166-1280/$ - see front matter  2007 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2007.10.021

known, the mechanisms of natural substrate conduction and of proton blocking were studied by molecular modelling [11,12]. Conduction of the substrate was shown to take place by successive formation and breakage of hydrogen bonds between the glycerol and the amino acids located on the surface of the channel. The efficiency of the conduction has been studied for polyols of different lengths [10] but the influence of the actual conformation of glycerol during its passage through the channel was not studied in detail. The conformation of glycerol has been the subject of very few studies, possibly because of its complexity. The glycerol molecule combines the high flexibility of its alkyl backbone, composed of a linear sequence of three carbons with low-energy rotation C–C bonds, with the presence of three hydroxyl groups. These groups can rotate around the C–O bonds in order to form both intramolecular and intermolecular hydrogen bonds. Hydroxyl groups can participate in hydrogen bond formation either as proton donors

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through their hydrogen atoms or as proton acceptors through their oxygen atoms. The orientation of these hydroxyl groups drastically modifies the energy level of the different glycerol conformations by formation or breakage of the hydrogen bonds. According to the nature of the medium, glycerol molecules will modify their conformation either to facilitate the interaction with neighbouring molecules or to form intramolecular bonds. Only the most stable conformation in the solid state is known with certainty. For the other states (liquid, gaseous phase and semi-crystalline), published studies, both experimental and theoretical, remain contradictory [13]. In the absence of specific interactions between the aquaglyceroporins and their natural substrates, this transport pathway may facilitate the intrusion of exogenous compounds in the cells. For instance, the GlpF protein has been identified as being responsible for the transport of poly-hydroxylated compounds of As(III) and Sb(III) into cells [14]. A detailed knowledge of glycerol conformations is needed in any study on the mimicry between natural and exogenous substrates. Unfortunately, the current information is limited: (i) Existing X-ray diffraction data [10] provide information on the alkyl backbone but none concerning the orientation of the hydroxyl groups because the positions of hydrogen atoms cannot be observed by X-ray diffraction. (ii) The resolution of X-ray diffraction data of the experimental structures of glycerol molecules frozen during the transport process through the GlpF ˚ ; this resolution level is suitable channel is at best of 2.0 A for a protein, but not for small molecules such as glycerol. (iii) Data on the close interactions between glycerol molecules and the GlpF protein, available on the web site of the EMBL-EBI Institute [15] and discussed by Fu et al. [10] for two of the three glycerol molecules in the GlpF channel, are not enough to define with certainty the positions of the hydrogen atoms of the glycerol molecules because their environment includes water molecules that, like the hydroxyl groups, can alternatively act as proton donors or acceptors or even as both simultaneously. In this study, first, the positions of the hydrogen atoms of the glycerol molecules in the conformations observed experimentally have been established by performing quantum calculations based on the published crystallographic structure. The hydrogen atoms of the glycerol molecules, of the amino acids in interaction with glycerol molecules and of the neighbouring water molecules were taken into account in this step. Second, the rotation barriers of the hydroxyl groups have been calculated for a conformation of the alkyl backbone with three hydroxyl groups located on the same side of the plane formed by the carbons. The objective of these calculations was to establish the intramolecular nature of the hydrogen bonds and to study the influence of two of the hydroxyl groups on the rotation of the third one and, in particular, of the disturbance created by an intramolecular hydrogen bond on the rotation barrier of a neighbour hydroxyl group. Finally, the influence of the formation of intramolecular hydrogen bonds

on the conformation of the alkyl backbone was studied. For this purpose, three potential energy surfaces (PES) were calculated by semi-empirical quantum calculations PM3/Zindo. The three PES correspond to three orientations of the hydroxyl groups having one, two or no intramolecular hydrogen bonds. 2. Methods 2.1. Definition of the conformation of the glycerol molecule The conformations of glycerol are defined by five dihedral angles: d1 [O1–C1–C2–O2] and d2 [O2–C2–C3–O3] for the alkyl backbone and v1 [H1–O1–C1–C2], v2 [H2–O2– C2–H] and v3 [H3–O3–C3–C2] that define the orientations of the O1–H1, O2–H2 and O3–H3 bonds (Fig. 1). The dihedral angles d1 and d2 present three characteristic states: gauche+ (g+), trans (t) and gauche (g) and the dihedral angles v1, v2 and v3 present four states: synclinal (s), gauche+ (g+), trans (t) and gauche (g). The combination of these states gives 576 possible conformations for glycerol [16]. The glycerol molecule does not present any chiral carbon. However, the substitution of one of the terminal hydroxyl groups involves the chirality of the central carbon. This is the reason why the representation of the conformations in the figures will always be pro-S: the central O2H2 group oriented towards the front and the O1H1 group on the left-hand side. The symmetry of the glycerol molecule is reduced by the presence of intramolecular hydrogen bonds. Depending on its conformation and the disposition of the OH groups, intramolecular hydrogen bonds can be formed. If the three oxygen atoms are located on the same side in relation to the plane formed by the alkyl backbone, the number of hydrogen bonds can be at most equal to three. The hydrogen bonds can be oriented either clockwise (O1–H1ÆÆÆO2, O2–H2ÆÆÆO3 and O3–H3ÆÆÆO1) or counter-clockwise (O1–H1ÆÆÆO3, O3–H3ÆÆÆO2, O2–H2ÆÆÆO1). If one of the oxygen atoms is not located on the same side as the others, only one or two intramolecular hydrogen bonds can be formed but the formation of intermolecular hydrogen bonds will be favoured. The three glycerol molecules co-crystallized in the channel of the GlpF protein carry the residue numbers 661, 662 and 663 in the structure file identified under the reference 1FX8 in the Brookhaven protein database [17]. This H2 H1

O1

χ2

δ

H

1

χ1

C1

H

C2

O2

δ

H

2

O''3

C3

χ3

H3

H

H

Fig. 1. Atoms and dihedral angles used to define the conformation of the glycerol molecule.

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numbering system will be used in this article to distinguish the three structures. According to the classification limited to the dihedral angles d1 and d2, the conformations of these three molecules are (66.45, 62.45) (42.74, 50.06) and (56.81, 70.91), respectively. 2.2. Quantum calculations, energy profiles and potential energy surfaces Quantum calculations were carried out with the programme Gaussian03 revision B.01 [18] running on a PC equipped with a 3215 Mz x86 based INTEL processor. Geometry optimization, energy scan and single point energy calculations were performed with a functional with three parameters including the functionals of local exchange, exchange of Becke and exchange of Hartree– Fock, combined to the functional of local correlation (VWN), gradient-corrected according to Lee, Yang and Parr, usually known under the acronym B3LYP [19,20] and using the effective-core potential of the Stuttgart–Dresden group SDD [21–23]. Some calculations (glycerol molecule with protein environment and PES) were performed with a semi-empirical PM3/Zindo method [24]. Values of the dihedral angles and total and relative energies for the three glycerol molecules inside de GlpF channel are shown in Table 1. 2.3. Initial structures of the molecular systems glycerol-GlpF The coordinates of the atoms belonging to the amino acids of the environment of the glycerol molecules ‘661’, ‘662’ and ‘663’ were extracted from the 1FX8 file. In order to get a suitable termination of the protein segments, the Table 1 Dihedral angles v1, v2 and v3 and total and relative energies for the three glycerol molecules inside the GlpF channel B3lyp/SDD

v1/

v2/

Glycerol 661 In vacuum In water In protein interior (e = 5) In protein interior (e = 20) In GlpF*

174.9 162.5 167.7 166.6 124.4

69.1 64.4 64.1 63.1 16.8

48.3 58.6 55.7 58.2 82.9

344.7486 17.06 344.7757 0.03 344.7757 0.04 344.7758 0.00 344.7259 31.30

Glycerol 662 In vacuum In water In protein interior (e = 5) In protein interior (e = 20) In GlpF*

48.3 60.6 57.5 59.8 64.1

69.0 58.4 60.4 58.5 10.9

174.9 169.8 170.3 168.4 73.7

344.7486 18.20 344.7776 0.00 344.7775 0.06 344.7776 0.00 344.713 40.53

Glycerol 663 In vacuum 82.7 In water 68.4 In protein interior (e = 5) 72.1 In protein interior (e = 20) 69.3 In GlpF* 179.4

84.4 71.3 76.4 72.0 86.2

51.1 61.2 58.5 60.9 65.3

344.7494 18.26 344.7785 0.00 344.7783 0.09 344.7785 0.01 344.7288 31.11

*

See protocol in Section 2.

v3/

Escf/ Hartree

DEscf/ kcal/mol

23

carbon Ca, and the carbonyl group of a supplementary N-terminal residue, and the Ca and the amine group of a supplementary C-terminal were also extracted. The environment of the glycerol molecule ‘661’ is formed by four water molecules numbered 383, 354, 360 and 372 of the Thr137-Tyr138-Pro139-Asn140-Pro141-His142 and Gly195-Pro196-Leu197 segments. The environment of the glycerol molecule ‘662’ includes two water molecules, 330 and 349, and the segments Thr198-Gly199-Phe200Ala201, Ala205-Arg206-Asp207 and Ile47-Trp48-Gly49. For the glycerol ‘663’ molecule, only one water molecule, the 349, and the segments Ala65-His66-Leu67-Asn68-Pro69 and Met202-Asn203-Pro204 remain. The carbon atoms Ca at the end of the segments were completed with hydrogen atoms to be transformed into methyl groups. The histidine His66 has a labile hydrogen atom whose pKa in water is around 6. Therefore the hypothesis that its imidazol group is deprotonated was made. However this imidazol group of histidine His66 is not in direct, or even indirect, contact with the glycerol molecules; it is oriented towards the interior of the protein and not towards the surface of the channel. Thus, its protonation state has a minor influence on the conformation of the molecules of glycerol. 2.4. Determination of the position of the hydrogen atoms in the molecular systems glycerol-GlpF First, the optimization of the geometry of the molecular systems (glycerol molecule, protein segments and water molecules) was carried out at a semi-empirical level PM3/Zindo. During this optimization, only the hydrogen atoms could move freely. This optimization makes it possible to position in a suitable way a large number of hydrogen atoms that play mainly a secondary role (e.g., hydrogen atoms of the methyl groups located at the end of the protein segments; hydrogen atoms of carbons Ca; amide groups). However, this optimization does not guarantee the correctness of the position of the hydrogen atoms which can form hydrogen bonds within the molecular system (e.g., hydrogen atoms of the hydroxyl groups of glycerol, of water molecules and of certain side chains of the amino acids on the surface of the channel). In a second step, and in order to define the best orientation, the energy profiles of the rotation barriers were calculated for the hydrogen atoms of the hydroxyl groups of the glycerol molecules that present several orientations. The optimization of the positions of the hydrogen atoms was then renewed in order to relax the ensemble. This second phase can be repeated as many times as needed. 2.5. Potential energy surfaces (PES) and conformation of the alkyl backbone Three PES were established from semi-empirical calculations PM3/Zindo of 5329 (73 · 73) single point ener-

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gies, each one corresponding to d1 and d2 values ranging between 0 and 360 by steps of 5. Each PES was characterised by the values of the dihedral angles v1, v2 and v3 that remained fixed during these calculations. In the first PES, all the hydroxyl groups pointed towards the exterior so as to avoid the formation of intramolecular hydrogen bonds. In the second PES, the initial orientation of the O2–H bond allowed, depending on the value of d1, the formation of a hydrogen bond with the oxygen O1. In the third PES, in addition to the hydrogen bond O2–HÆÆÆO1, the orientation of the bond O3–H also allowed, depending on the values taken by dihedral angle d2, the formation of a second hydrogen bond (O3–HÆÆÆO2) with the oxygen O2. For the three PES, the value of v1 was always of 180, thus directing the O1H1 group outside. This layout does not allow the observation of conformations including three intramolecular hydrogen bonds. The conformations corresponding to remarkable points (global and local minima) are presented graphically. The same range of colours is used for the different energy values in order to be able to compare visually the topology of the three PES. 2.6. Energy profiles of the dihedral angles v1, v2 and v3 – Nature of the intramolecular bonds Two series of energy profiles corresponding to the rotation of the hydroxyl groups of the glycerol molecule were calculated in order to study the nature of the intramolecular bonds and the influence of the neighbour OH groups (Fig. 2). The first series corresponds to the rotation of groups in terminal positions: O1H1 and O3H3 groups. Since, by symmetry, the energy profile of the rotation of both groups is identical, only the rotation around the O1H1 group was studied. The second series corresponds to the rotation of the central O2H2 group. Dihedral angles v1 or v2 changed by steps of 5 between 180 and 180, thus providing 73 single point energies in order to establish the energy profile of the rotation barrier under consideration. By fixing the dihedral angles d1 and d2 at 0, the alkyl backbone remained rigid and the conformation allowed the three hydroxyl groups to be oriented on the same side of the alkyl backbone. Calculations were carried out according to two levels of theory: semi-empirical PM3/Zindo and B3lyp/SDD. The energy profiles obtained by semiempirical calculations are rather similar to those obtained according to the B3lyp/SDD method. However, the semiempirical barriers are clearly lower than the B3lyp/SDD ones. Only the results obtained by the B3lyp/SDD method will be presented and discussed in this article. For each of the two series, five profiles, noted 2a to 2e and 2f to 2j, were calculated. For each profile, the orientation of one or two hydroxyl groups that remain fixed is selected so as to influence the neighbour groups. For the profiles 2a and 2f: the hydroxyl groups are directed towards the exterior so as to avoid any interaction

between hydroxyl groups. For the profile 2a, v2 = 0 and v3 = 180 and for the profile 2e, the value of v1 and v3 is 180. For the profiles 2b and 2g: the O3H groups are oriented towards O1H. For the profile 2b, v2 is 0 and v3 = 60 and for the profile 2e, v1 = 180 and v3 = 60. This orientation of the O3H3 group does not correspond to the formation of a hydrogen bond O3–HÆÆÆO1 because the conformation of the rigid alkyl backbone does not allow the two groups to be close enough. For the profiles 2c and 2h: One of the fixed OH groups is oriented towards the other group in order to form the hydrogen bond O3–HÆÆÆO2, present throughout the calculation of the energy profile. For the profile 2c, v2 = 0 and v3 = 0 and for the profile 2h, v1 = 180 and v3 = 0. The energy profiles 2d, 2e, 2i and 2j are combinations of the previous cases. For the profiles 2d and 2i: a hydrogen bond, either O2–HÆÆÆO3 or O1–HÆÆÆO2, and the orientation of the O3H3 groups towards O1H are always present. For the profile 2d, v2 = 120 and v3 = 60 and for the profile 2i, v1 = 0 and v3 = 60. For the profiles 2e and 2j: two hydrogen bonds are present. For the profile 2e, v2 = 120 and v3 = 0 and they form the bonds O2–HÆÆÆO1 and O3–HÆÆÆO2, both oriented counter-clockwise. For the profile 2j, v1 = 0 and v3 = 0, forming the bonds O1–HÆÆÆO2 and O3–HÆÆÆO2, both oriented in opposite directions. In order to evaluate the influence of the neighbouring OH groups on the energy profile of a rotamer, calculations were carried out by maintaining the specific interactions of the OH neighbour groups. This could be carried out in all the cases except for the rotation of the OH central group in the presence of two hydrogen bonds (profile 2j). In order to form two hydrogen bonds, the OH central group has to participate in both hydrogen bonds because no hydrogen bond can be formed between two OH final groups in this conformation of the alkyl backbone. Therefore the rotation of the mid OH group necessarily involves the breakage of one of the two hydrogen bonds. Calculations were carried out in order to maintain the specific interactions. During these calculations, only one degree of freedom (dihedral angle v1 or v2) is modified. This is the reason why ‘steric clashes’ are observed when the hydrogen atoms of the hydroxyl groups are too close or overlap. These conformations correspond to highenergy conformations and are not realistic under normal conditions. 3. Results and discussion 3.1. Determination of the positions of the hydrogen atoms in the molecular systems glycerol-GlpF The environments of the three glycerol molecules during their passage through the channel of the GlpF protein are shown in Fig. 3. The situation of the atoms corresponds to

A. Porquet, M. Filella / Journal of Molecular Structure: THEOCHEM 850 (2008) 21–31

25

Fig. 2. Conformational potential energy profiles of the glycerol molecule calculated with the B3lyp/SDD quantum method. Dihedral angles d1 and d2 are fixed to 0. In the first columns at the left-hand side: v (one of the external OH groups) changes between 0 and 360 by steps of 2. In the columns at the right-hand side: v 0 (central OH group) changes between 0 and 360 by steps of 2. From (a) to (e): five different arrangements of other OH groups. The energy in the x-axis is relative to the lower energy of the curve. Energy values at the bottom of the curves correspond to the difference between the lowest value of the minima of the 10 studied arrangements. Energy values are expressed in kcal/mol.

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that of the structure obtained by X-ray diffraction, except for the hydrogen atoms whose position was obtained according to the optimization protocol described in this article. The distances between the atoms involved in the hydrogen bonds formed by the glycerol molecules are shown in Fig. 3. For the glycerol molecule ‘661’, the least advanced in the transport process in the channel, the number of water molecules of hydration is the highest one. The most external O1H1 hydroxyl group is still located in a network of hydrogen bonds with three water molecules (354, 360 and 383). They separate the hydroxyl group from the amino acids of the GlpF protein. The oxygen atom O3 only shows an indirect interaction with the protein via a bridging water molecule (372). The only direct link of the glycerol with the wall of the channel is made through the carbonyl of Pro139. The ‘662’ molecule presents more direct interactions with the protein. The functions O1H1 and O2H2 are chelated by the guanidinium group of Arg206 on one side and by the carbonyl groups of the Gly199 and Phe200 residues on the other. The side chains of the Phe200 and Trp48 residues are located on the side opposed to these two amino acids. This situation clearly illustrates the amphiphilic character of the channel. The ‘662’ glycerol molecule is only in contact with two water molecules placed in front and behind it in the direction of conduction in the channel. The ‘663’ glycerol molecule, the most advanced in the channel, has practically lost all hydration waters. Only one water molecule (349) remains. This water molecule is shared with the glycerol molecule following it in the channel. The nature of the bonds of the glycerol molecules ‘663’ and ‘662’ with the protein are very different. The interactions involve asparagines Asn68 and Asn200. Each one points one hydrogen atom of their carboxamide group

towards the oxygen atoms O1 and O2 of the glycerol. The third hydroxyl group (O3H3) of the glycerol interacts with the carbonyl group of the His66. Contrary to the two previous glycerol molecules, the situation of the ‘663’ glycerol molecule offers the possibility of forming an intramolecular hydrogen bond. This bond is relatively weak since the OÆÆÆH ˚ . This molecule also presents a different distance is of 2.48 A conformation of the alkyl backbone (g+, g+) instead of (g+, g) for ‘661’ and ‘662’. This situation is particularly interesting because the glycerol molecule uses two of its characteristics to pass the narrower region of the channel: (i) From the steric point of view, the geometry of the alkyl backbone is adapted to the available space. (ii) From the energy point of view, the destabilization caused by the progressive dehydration is partially compensated by the formation of an intramolecular hydrogen bond. The optimization of the geometry of the glycerol molecule ‘661’ in its explicit environment of the channel of the GlpF protein gives values of the dihedral angles v1, v2 and v3 of 82.9, 16.8 and 121.4. All these values correspond to the global minima obtained by the individual analysis of the rotation of the three dihedral angles v1, v2 and v3. For the glycerol molecule ‘662’, the optimization gives: 159.0; 6.5 and 63.4. The v1 value obtained by optimization under constraint corresponds to a local minimum where the O1H1 function forms a hydrogen bond with the water molecule 330. The global minimum (v1  80.0) corresponds to an interaction of the O1H1 group with the carbonyl of Gly199. After v1 being modified accordingly, the second optimization converges to a value of v1 = 73.7 which corresponds to the global minimum of v1. From the energy point of view, this modification involves a decrease of 7.89 kcal/mol of the energy level. The modification of v1 disturbs the organization of the other OH groups without leading to a significant

Fig. 3. PM3/Zindo optimized structures of the three glycerol molecules shown in their own proteinic environment: ‘661’ at the left-hand side, ‘662’ in the middle and ‘663’ at right-hand side (description in the Section 2). Specific hydrogen bonds are shown with dot lines.

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conformational change. The values of the dihedral angles v1, v2 and v3 finally obtained are 73.7, 10.9 and 64.1. The optimization of the glycerol molecule ‘663’, which does not present the same conformation of the alkyl backbone, converges towards the values 179.4, 86.2 and 65.3. This conformation is in agreement with the individual analysis of the rotation barriers of the dihedral angles v1, v2 and v3. However, the structure obtained shows an intramolecular bond O2–HÆÆÆO3 corresponding to a distance HÆÆÆO3 of ˚ . To favour this bond, the hydrogen contiguous to 2.35 A O3 points in opposite direction to the carbonyls of the Ala65 and His66 residues. The analysis of the rotation barrier of v3 shows a local minimum energetically very close to the global minimum corresponding to a value of v3, around 100 and allowing the formation of a hydrogen bond with the carbonyl of His66. This bond is formed to the detriment of the intramolecular bond O2–H2ÆÆÆO3 by reducing the overlapping of the corresponding molecular orbitals. Geometry optimization starting with a value of v3 around 100 converges towards 97.1. This reorganization of the weak interactions allows a decrease of 2.02 kcal/mol, a reorientation of v2, giving 61.4 instead of 86.2, the lengthening of the intramolecular connection O2–H2ÆÆÆO3 ˚ . Therefore, the selected conformation correto 2.48 A sponds to 179.4, 61.4 and 97.1.

27

This analysis of the environment of the glycerol molecules is in agreement with that provided by Fu et al. [10] for the glycerol molecules ‘662’ and ‘663’. The analysis of the molecule ‘661’ has not been published. The single point energy calculation of the conformations of the molecules of glycerol ‘661’, ‘662’ and ‘663’ carried out at the B3lyp/SDD level gives values of 344.7258828, 344.7129926 and 344.7288912 a.u., respectively. 3.2. PES of the dihedral angles d1 and d2 – Conformation of the alkyl backbone The symmetry of the molecule is easily recognized in the topology of the representation of the PES corresponding to the conformation of glycerol without intramolecular hydrogen bonds (Fig. 4). The map presents an energy maximum for an eclipsed conformation (240, 120) of the O1H1 and O3H3 groups. This conformation is the most unfavourable one due to the proximity of the free pairs of the oxygen atoms O1 and O3. The global minimum corresponds to the conformation (g+, g). In this conformation the alkyl backbone is entirely extended and allows the maximum separation of the hydroxyl groups from each other. However, the topology of the map shows that it is easy to attain

Fig. 4. Potential energy surfaces of the dihedral angles d1 and d2 of glycerol without intramolecular hydrogen bonds. The hydrogen atoms of the hydroxyl groups are all oriented towards the outside. The map has been prepared from the PM3/Zindo energies calculated for 5329 (73 · 73) conformations. Dihedral angles d1 and d2 lie between 0 and 360 and change by 5 steps.

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A. Porquet, M. Filella / Journal of Molecular Structure: THEOCHEM 850 (2008) 21–31

the conformations (g+, t) or (t, g) by passing an energy barrier of the order of 1–2 kcal/mol. These conformations are practically as stable as the global minimum, only 0.15 kcal/mol separate them. Conformations (g+, g+) and (g, g) also present local minima at +1.66 kcal/mol and can only be reached by passing a barrier of about 4–6 kcal/mol. Once this region of the conformational space reached, the structure of glycerol can also take a conformation (t, g+) or (g, t) but these regions do not imply minima and can only be transitory states. The region (g, g+) is particularly high in energy, at least 7–8 kcal/mol higher than the global minimum. This region corresponds to conformations including the three hydroxyl groups on the same side of the carbon plane. This region is disadvantaged by the high repulsion of the free pairs of the oxygen atoms that are closer in these conformations. By imposing a value of 120 to the dihedral angle v2, glycerol presents an intramolecular hydrogen bond O2– H2ÆÆÆO1. Broadly, the aspect of the map remains unchanged (Fig. 5). The maximum for the conformation (240,120) is still present and the regions of low-energy correspond to the same conformations. However a detailed examination shows that some elements change: the global minimum has shifted and corresponds to the conformation (g+, t) and no longer to (g+, g). This conformation, although

remaining relatively low in energy, no longer corresponds to a local minimum. This value of v2 favours the conformations d1 as g and d2 as g+. The local minimum of conformation (g+, g+) shifts from +1.67 to +0.43 kcal/mol and that of conformation (g, g) shifts from +1.65 to +1.28 kcal/mol. The regions (t, g+) and (g, t) emerge as rather stable local minima, +1.54 and +0.67 kcal/mol. The region (g, g+) becomes more accessible, in particular by the conformation (0, 60) side. On the other hand, the barriers to pass from (g+, g+) to (g+, t) and from (g+, g) to (t, g) become more difficult to cross, 3–4 kcal/mol, narrower and they increase their height appreciably. The formation of this possible intramolecular hydrogen bond causes the partial loss of the symmetry of the map. The aspect of the map is completely modified if the dihedral angles v2 and v3 are simultaneously modified in order to form two possible intramolecular hydrogen bonds. This reflects the loss of symmetry of the glycerol molecule (Fig. 6). The conformational topology becomes relatively simple: there is a single region of low-energy which is primarily centred around conformation (g+, g). This region is surrounded by barriers very high in energy, one corresponding to conformations where the value of v2 is 120, beyond 10–15 kcal/mol, and the other corresponding to v1 = 240, at least 4–6 kcal/mol. Theses are due to steric

Fig. 5. Potential energy surfaces of the dihedral angles d1 and d2 of glycerol with one intramolecular hydrogen bond. The other hydrogen atoms of the O1H1 and O3H3 hydroxyl groups are oriented towards the outside. The map has been prepared from the PM3/Zindo energies calculated for 5329 (73 · 73) conformations. Dihedral angles d1 and d2 lie between 0 and 360 and change by 5 steps.

A. Porquet, M. Filella / Journal of Molecular Structure: THEOCHEM 850 (2008) 21–31

effects: the first to the overlapping of hydrogen atoms of hydroxyl groups, and the second to the overlapping between one hydrogen atom of an hydroxyl group with an hydrogen atom of the alkyl backbone. These situations are an artifact because they are the result of the method of calculating the PES which allows only the dihedral angles taken as variables to change. This gives sometimes nonrealistic conformations. However, this map shows that the glycerol molecule still preserves a high conformational freedom, even when two intramolecular hydrogen bonds are possible. Also noteworthy is the particularly favourable situation when v1 is between 60 and 70. The structure presents then four minima for v2 equal to 0, 60, 200 and 300. They are the minimum global and local, located at +1.46, +0.83 and +0.18 kcal/mol, respectively, with an energy barrier less than 1 kcal/mol. 3.3. Energy profiles of the dihedral angles v1, v2 and v3 – Nature of the intramolecular bonds As discussed in Section 2.6, Fig. 2 shows the conformational energy profiles of the glycerol molecule calculated with the B3lyp/SDD quantum method. The profiles 2h and 2e show the lowest minima of all the profiles. The corresponding conformation shows two intramolecular hydro-

29

gen bonds O3–H3ÆÆÆO2 and O2–H2ÆÆÆO1. The difference of 0.02 kcal/mol between profiles 2h and 2e results from the fact that the dihedral angle v2 is fixed at 120. This value does not correspond exactly to the minimum for profile 2e which is closer to 118, the value taken by v2 in the profile 2h. Both hydrogen bonds are not exactly identical. The groups O1H1 and O2H2 are collinear while the groups O3H3 and O2H2 form a bend of about 120. This difference is observed at the energy level by analyzing the sequence of profiles 2a, 2e on the one hand and of profiles 2h and 2f on the other. The minima of profiles 2a and 2e are characterised by the absence or the presence of a hydrogen bond formed between the hydrogen atom of the central O2H2 group and the oxygen of a terminal group O1H1 or O3H3. This difference is identical for the profiles 2h and 2f. From an energy point of view, this results in a difference of 10.51 and 11.24 kcal/mol, respectively. The minimum of the profile 2a corresponds to the presence of the hydrogen bond O1–H1ÆÆÆO2, the intermediate state (+10.77 kcal/mol and v1 = 354) not presenting this bent intramolecular bond. The minimum of the profile 2f corresponds to the presence of the hydrogen bond O2–H2ÆÆÆO1 and the maximum (+10.09 kcal/mol and v2 = 0) does not present this intramolecular bond. The energy contribution of these two

Fig. 6. Potential energy surfaces of the dihedral angles d1 and d2 of glycerol with two intramolecular hydrogen bonds, O2–H2ÆÆÆO1 and O3–H3ÆÆÆO2. The hydrogen atom of the O1H1 hydroxyl group is oriented towards the outside. The map has been prepared from the PM3/Zindo energies calculated for 5329 (73 · 73) conformations. Dihedral angles d1 and d2 lie between 0 and 360 and change by 5 steps.

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A. Porquet, M. Filella / Journal of Molecular Structure: THEOCHEM 850 (2008) 21–31

Fig. 7. Three types of hydrogen bonds present in different conformations of the glycerol molecule.

hydrogen bonds linked in the same direction is of 21.28 and 21.33 kcal/mol, depending on the profiles used. In the case of profile 2a, the hydrogen bond formed by rotation of the angle v1 is a bent hydrogen bond while for the profile 2f, the hydrogen bond formed is linear. Conversely, the transition from the profile 2a to the profile 2e gives a linear hydrogen bond while the transition from profiles 2h to 2f is made through the formation of a bent hydrogen bond. It can be deduced that the linear bond has slightly less energy (10.09 and 10.53 kcal/mol) than the bent bond (10.77 and 11.24 kcal/mol), with a mean difference of about 0.7 kcal/mol. In both cases, there is a very slight synergy for the formation of the second hydrogen bond of about 0.4–0.5 kcal/mol. The effect of the direction of sequence of formation of the hydrogen bonds is clearly observed in profiles 2e and 2j. As already discussed, in the minimum of the 2e profile, both hydrogen bonds are formed in the same direction, counterclockwise, while for the minimum of profile 2j, the O1–H1ÆÆÆO2 bond is formed clockwise and the O3–H3ÆÆÆO2 counter-clockwise. The conformation corresponding to the minimum of 2j is also that of the profile 2c. Destabilizations of 3.52 and 3.38 kcal/mol are respectively obtained. The orientation of one of the terminal OH groups towards the other, by imposing a value of 60 to the angle v3, causes an important disturbance of the conformations under consideration. The minima of profiles 2b, 2d and 2g are destabilized by 6.18, 7.85 and 6.48 kcal/mol, respectively. The disturbance is lower in profile 2i because of the adaptation of the orientation of the group O2H2. The value of the dihedral angle v2 is then of 76, reducing the destabilization to 2.25 kcal/mol. This antiparallel orientation of two OH bonds seems to be favourable. It is also present in the conformation of the intermediate state of the profile 2g (+5.15 kcal/mol in relation to the minimum of the profile). Depending on the relative orientation of the donor and acceptor groups, two types of hydrogen bonds can be observed in the glycerol molecule (Fig. 7). The first type (type I) is a bent hydrogen bond with a 120 angle between the O–H bonds. The overlapping of one of the molecular orbitals of one of the free pairs of the accepting oxygen with the bridging hydrogen atom is maximum. This hydro-

gen bond is the strongest one observed for glycerol (11 kcal/mol). The second type (type II) of hydrogen bond corresponds to two collinear OH groups, i.e. both OH groups are aligned. In this case, the bridging hydrogen is situated between the two molecular orbitals of the free pairs of the accepting oxygen and form a linear hydrogen bond. The overlapping of the orbitals is slightly less important than in the previous case and gives a slightly less strong bond (10.25 kcal/mol). A third type of stabilizing interaction (type III), of about 5 kcal/mol, is observed when the O–H bonds are antiparallel. In this case, there is mutual interaction, as shown in Fig. 7. References [1] S. Hohmann, S. Nielsen, P. Agre (Eds.), Aquaporins, Academic Press, San Diego, 2001. [2] Y. Fujiyoshi, K. Mitsuoka, B.L. de Groot, A. Philippsen, H. Grubmu¨ller, P. Agre, A. Engel, Curr. Opin. Struct. Biol. 12 (2002) 509–515. [3] E. Tajkhorshid, P. Nollert, M.Ø. Jensen, L.J.W. Miercke, J. O’Connell, R.M. Stroud, K. Schulten, Science 296 (2002) 525–530. [4] D. Thomas, P. Bron, G. Ranchy, L. Duchesne, A. Cavalier, J.-P. Rolland, C. Rague´ne`s-Nicol, J.-F. Hubert, W. Haase, C. Delamarche, Biochim. Biophys. Acta 1555 (2002) 181–186. [5] F. Zhu, E. Tajkhorshid, K. Schulten, Biophys. J. 83 (2002) 154–160. [6] B.L. de Groot, A. Engel, H. Grubmu¨ller, J. Mol. Biol. 325 (2003) 485–493. [7] A.D. Schenk, P.J.L. Werten, S. Scheuring, B.L. de Groot, S.A. Mu¨ller, H. Stahlberg, A. Philippsen, A. Engel, J. Mol. Biol. 350 (2005) 278–289. [8] Y. Wang, K. Schulten, E. Tajkhorshid, Structure 13 (2005) 1107– 1118. [9] S. To¨rnroth-Horsefield, Y. Wang, K. Hedfalk, U. Johanson, M. Karlsson, E. Tajkhorshid, R. Neutze, P. Kjellbom, Nature 439 (2006) 688–694. [10] D. Fu, A. Libson, L.J.W. Miercke, C. Weitzman, P. Nollert, J. Krucinski, R.M. Stroud, Science 290 (2000) 481–486. [11] M.Ø. Jensen, E. Tajkhorshid, K. Schulten, Structure 9 (2001) 1083– 1093. [12] M.Ø. Jensen, S. Park, E. Tajkhorshid, K. Schulten, PNAS 99 (2002) 6731–6736. [13] R. Chelli, F.L. Gervasio, C. Gellini, P. Procacci, G. Cardini, V. Schettino, J. Phys. Chem. A 104 (2000) 5351–5357. [14] O.I. Sanders, C. Rensing, M. Kuroda, B. Mitra, B.P. Rosen, J. Bacteriol. 179 (1997) 3365–3367.

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