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B: Biophysical Chemistry and Biomolecules
Quantum Mechanics Study on Hydrophilic and Hydrophobic Interactions in the Trivaline-Water System Giuseppe Lanza, and Maria A. Chiacchio J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b00833 • Publication Date (Web): 27 Mar 2018 Downloaded from http://pubs.acs.org on March 30, 2018
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Quantum Mechanics Study on Hydrophilic and Hydrophobic Interactions in the Trivaline-Water System Giuseppe Lanza* and Maria A. Chiacchio Dipartimento di Scienze del Farmaco, Università di Catania, Viale A. Doria 6, Catania 95125, Italy
ABSTRACT With the aim to elucidate hydrophobic effects in the unfolded state of peptides DFT-M062X computations on the Val3H+⋅nH2O (n up to 22) clusters have been accomplished. As far as the main chain is concerned, four conformers with a β-strand or/and polyproline type II conformations, PPII, (indicated as β-β, β-PPII, PPII-β and PPII-PPII) have been found changing the φ and ψ angles. For bare peptide the side chain (isopropyl) of each residue can independently take on three different orientations with negligible effects on energetics. The great isopropyl spatial separations in β-β and β-PPII conformers allow for the construction of synergic and extensive water-water and water-peptide H-bonding in the minimal hydration Val3H+⋅22H2O models without significant steric encumbrance. Conversely, due to the proximity of the isopropyl of the central residue with the other two, some restrictions in the water shell construction around the peptide become evident for the PPII-PPII conformer and the number of energetically accessible structures decreases. This is indicative of correlated motion involving isopropyls and
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backbone mediated by water molecules, the origin of the nearest neighbor effects. Comparing the thermodynamic data of Ala3H+⋅22H2O and Val3H+⋅22H2O what emerges is that both hydration enthalpy and entropy drive the β-strand stability of the latter.
1. INTRODUCTION Hydrophilicity and hydrophobicity are the two faces of the peptide and protein properties. Both these competitive/complementary features play a crucial role in protein structure and function.1-4 Statistically, residues with a highly hydrophobic side chain often constitute the core of a protein, whereas hydrophilic residues point outwards, forming the biomolecule surface. Many biochemical functions occur on the outside shell of proteins, thus the protein surface binds water molecules and mainly drives interactions between protein-protein, receptor-ligand, enzymesubstrate, enzyme-inhibitor and so on. Clearly, the hydrophilic and hydrophobic region separation of a protein is not well defined and some residues with a non-polar side chain occur on the surface with an aliphatic chain in direct contact with the solvent. This becomes particularly important for small proteins, i.e. peptides, where the surface-area-to-volume ratio is very high and a dynamic ensemble of secondary structures becomes possible. Although the interactions between polar groups and water molecules are energetically favorable and the site-specific coordination is comprehensible enough, the solvent water interactions with aliphatic chains are puzzling due to their inability to form hydrogen bonding or favorable electrostatic interactions.1-4 In the classic view of the hydrophobic effect, the weak water-hydrocarbon attractive van der Waals forces are of comparable strength to hydrocarbon-hydrocarbon and it is generally assumed
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to have little influence on the solvent structure, even though hydrocarbons exclude water molecules from the volumes they occupy.5 If this volume is small, water molecules surround the hydrocarbon side chain, forming a cage also known as water clathrate structure. The water molecules in direct contact with non-polar groups maintain H-bonding interactions with other water molecules (∆H∼0) but they lose rotational and translational degrees of freedom (∆S Leu, Trp, Phe, Met > Val, Ile has been proposed, thus suggesting that PPII propensity can be related to side chain hydrophobicity.33-42 Since the PPII conformation stability mainly depends on explicit water coordination to the peptidic polar groups, the small side chain of alanine does not interfere with backbone solvation. The bulky-branched valine and isoleucine side chains shield the backbone from the solvent in the PPII conformation, reducing their propensities toward this structure. Instead, residues containing only one non-hydrogen substituent attached to their β carbon, result in intermediate propensities.33,34
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Recently, we reported a protocol to evaluate hydration effects on molecular properties by means of ab initio quantum mechanics methods for atomic interactions along with a bottom-up approach for the water shell construction around the peptide.24-28 The full quantum mechanics allow us to evaluate the peptide-water and water-water forces through an accurate and an unbiased way at the limit of current computational implementation. The stepwise water shell construction allows us to draw optimal hydrogen bonding water networks in which the water molecules are bonded to the hydrophilic groups of the peptide. In this way, the water shell experiences the structural changes and the heterogeneity of the peptide surface, thus providing useful information on the intimate solute-solvent contacts. This procedure has been successfully applied to alanine, dialanine and trialanine in various protonation state, obtaining encouraging results in terms of molecular structure and thermodynamic functions.24-28 Because of the biochemical importance of hydrophobic effects and their not well-understood nature, it becomes interesting to see which kind of information our protocol could provide in a representative peptide with highly hydrophobic residues, the cationic trivaline Val3H+. Trivaline has been largely studied from an experimental point of view and all these researches mainly suggest predominance of a fully extended conformation in contrast to what has been found for other tripeptides for which the polyproline type II helix is the most abundant conformation.15-17,37,42 2. CALCULATION METHODS The geometries were optimized using the DFT-M06-2X level employing the 6-31+G* basis set and including implicitly solvent effects (M062X/6-31+G*/PCM=WATER).43,44 The grid mesh in integral evaluation was settled to the “Integral(UltraFineGrid)” and in few cases it was necessary to improve computation stability to the “Integral(SuperFineGrid)” option. Minima were characterized evaluating the hessian matrix and the associated harmonic vibrational frequencies.
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Implicit solvent effects were modeled using the polarized continuum method (PCM) adopting a 78.36 dielectric constant for water as implemented in the G09 program.45 To improve energetics and to reduce intermolecular basis set superposition error, single point energy at the optimized geometries was performed using the more accurate aug-cc-pVTZ basis set. The computed electronic energies were corrected for zero-point vibrational and thermal energies and entropies to obtain enthalpy and free energy changes at 298 K (∆G°298). 3. RESULTS AND DISCUSSION 3.1. Methodological approach for water shell construction. Solvation is a collective phenomenon that is hard to be treated through quantum chemical procedures.46,47 Nevertheless, application of the solvent reaction field model for implicit solvent effects and the explicit inclusion of a significant number of water molecules has provided a reliable way to understand and rationalize main hydration effects.24-28 In this bottom-up approach, the shell hydration is constructed following the "fundamental economic law" of constrained optimization, by which the greatest possible peptide-water interaction is sought minimizing the number of explicit water molecules. Constraints, i.e. the set of conditions for the variables that have to be satisfied, are derived from basic chemical properties of water and hydrophilic groups of peptide previously described.23-26 They can be briefly summarized in the following way: a) water molecule can form two H-bonds as an acceptor and two as a donor at the best coordination, the N-H is an H-bond donor while >CO forms two H-bonds as an acceptor; b) clusters and wires of water molecules surround peptide alternating donor/acceptor H-bonds to increase their synergy and realize the highest density packing; c) the size of the bridging water network should avoid strained cyclic
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structures; d) the dipole of water molecules should align in the opposite directions of the huge dipole of charged peptide. Because water molecules have a great tendency to clump together to form energetically favored compact clusters,47 the number of peptide-water and water-water Hbonds formed must be checked with great attention to make various conformations of each hydrated model energetically comparable (the inventory criterion). 3.2. The van der Waals forces. In our previous studies on alanine, dialanine and trialanine in various protonation states, the side chain (methyl) occupies a modest amount of space; therefore, its interactions with hydration network and methyl-methyl are less extended.24-28 Conversely, the large volume of isopropyls in the Val3H+ makes these interactions significant and the peptide conformation strongly depends on them. In order to better clarify the magnitude of water-alkyl and alkyl-alkyl interactions it is useful to explore two prototypes the H2O⋅CH4 and the CH4⋅CH4 that along with the other well known water-water and water-peptide polar groups interactions can give an estimation of all forces present when a peptide is immerged in an aqueous environment. In the most stable configuration, the H2O⋅CH4 system shows a plane symmetry element, the water acts as an H-bond "donor" (Figure 1) with the HOH---CH4 and H2O---CH4 distances of 2.65 and 3.37 Å, respectively, and a stabilization energy of -0.6 kcal mol-1. A potential energy curve for the water-methane interaction was obtained for selected H2O---CH4 distances optimizing all of the other geometrical parameters. It shows that water-methane interaction is weakly attractive for distances longer than 3 Å, while for shorter distances it becomes repulsive. Previous computations48 reported interaction energy ranging from -0.6 to -0.9 kcal mol-1 and
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H2O---CH4 distance of about 3.5 - 3.6 Å, while gas-phase microwave measurements49 suggested a zero‐point center‐of‐mass separation of 3.7024 Å between the two subunits.
Figure 1. Molecular structures of the H2O⋅CH4 and the CH4⋅CH4 systems and related electronic energy curves (solid and dashed line, respectively). The interaction energies were obtained for selected H2O---CH4 and CH4---CH4 distances optimizing all the other geometrical parameters. The potential energy curve for the methane-methane along the H4C---CH4 distance shows a shallow minimum (-0.4 kcal mol-1, Figure 1) at 3.54 Å with three C-H bonds of each molecule in a staggered configuration (D3d symmetry). The interaction is weakly attractive for distances longer than 3.2 Å while for shorter distances it becomes repulsive. These data agree well with higher level computations which predicted a D3d symmetry structure with -0.51 kcal mol-1 stabilization energy and equilibrium distance of 3.27 Å.50
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There are large regions where water-alkyl and alkyl-alkyl contacts are favourable. However, these interactions are considerably less efficient than water-water and water-peptide polar groups for which a single H-bond formation produces an energy gain of about one order of magnitude higher (-5 kcal mol-1).24 This is in agreement with the recent view about relative importance of hydrophilic versus hydrophobic interactions proposed by Ben-Naim1 and for small peptides, hydrophobic effects can be seen as a perturbation of the vast and strong H-bond matrix. 3.3. The bare trivaline. The trivaline conformation can be described by the standard ψN, φcentral, ψcentral and φC backbone dihedral angles and by the three N-Cα-Cβ-Hγ dihedral angles involving the side chain (χN, χcentral and χC) as reported in Figure 2 (the "central" subscript refers to central residue while "N" and "C" indexes refer to N- and C-terminal residues, respectively). In the unfolded conformation, the main chain can take on four structures namely β-β, β-PPII, PPII-β and PPII-PPII as experimentally and computationally reported for the unfolded state of trialanine.18,19,25 In these conformations both the ψN and ψcentral torsional angles have values around 150°, while the φcentral and φC have values are around -143° and -62° for β and PPII residue conformations, respectively. The three isopropyl groups can rotate independently and each of them can assume three distinct minima corresponding to a staggered conformation in which the Cα substituents are at maximum distances of the Cβ substituents. Therefore, each main chain conformation has 27 different orientations of the isopropyl groups corresponding to χ values of about -60°, 60° and 180°. These structures are labeled with the alphabetic letters (A, B, C, . . . Y, Z, AA). The χN, χcentral and χC values in starting geometry optimization of the A structure were placed at -60°, -60° and -60° while the B and C starting geometries are obtained
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increasing the χN by 120° and 240°, respectively. The successive structures are obtained looping over χcentral and χC as schematically reported in the following nested loops.
All possible 108 minima were found on the Born-Oppenheimer surface (Tables S1-S4) and these structures spread in a narrow energy range (∼3 kcal mol-1, Figure 2). The relative energy of various minima shows a periodic behavior and the structures A, D, G, J, M, P, S, V and Y, characterized by χN ∼ -50°, are slightly more stable than the others. In these geometries, the two isopropyl methyls of the N-terminal amino acid points away from the ammonium group minimizing their steric interactions. Furthermore, the four curves show a low energy drift for the structures S-AA, which are characterized by the χC ∼ 180° and the S, V and Y structures are generally the most stable for the four peptidic conformations. Due to the alternance from one side to the other side of the isopropyls along the backbone, the minimal C---C distance between isopropyls is never less than 4 Å; therefore, side-chains interactions are weakly attractive (Figure 1) and there is no steric hindrance. In other words, in spite of the bulkiness near to the backbone, there is no restriction in the conformations the main-chain can adopt. Furthermore, the rotational barriers are rather modest (∼4 kcal mol-1), so the Cα-Cβ bonds are free to rotate.
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Figure 2. Relative electronic energy for the bare Val3H+ in the β-β, β-PPII, PPII-β and PPII-PPII backbone conformations (solid line, dashed, dashed-dotted and dotted lines, respectively) changing the isopropyl orientations. The β-β_A structure has been assumed as a reference. 3.4. Hydrating the β-β β conformer. The water shell construction around the cationic trivaline starts adding water molecules to the charged ammonium group and proceeds along the backbone until a complete hydrogen bonded water network surrounds the peptide. The geometry optimization of the Val3H+⋅10H2O, Val3H+⋅14H2O, Val3H+⋅18H2O, and Val3H+⋅22H2O trivalinewater complexes were successfully performed for the fully-extended (β-β), polyproline type II helix (PPII-PPII) and the mixed β-PPII conformations. Furthermore, for each peptide-water structure various conformations of the isopropyl groups were considered, thus about one hundred minimal searches were successfully performed. Because of the huge computational efforts in analyzing the various isopropyl orientations, the PPII-β conformer has been presently overlooked, nevertheless, the most prominent features are already present in the other inquired conformers.
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Even though the partially hydrated models give important information for the heuristic construction of solvation shell around the β-β conformation (some results are listed in Tables 1 and S5), the more significant results can be gathered from the fully H-bonded peptidic hydration, the Val3H+⋅22H2O model, and we will focus our attention on this. In the 22H2O_β-β model the peptide polar groups lie in two well separated regions, thus the hydration shell consists of two indipendent water networks, with 12 molecules placed in the up and 10 placed in the down regions (Figure 3). They start at the charged terminal -NH3+ group, which acts as a donor of three H-bonds, and links all other polar groups, realizing the best synergic water network and optimal peptide-water interactions. The model structure is equal to what has been previously reported for the Ala3H+⋅22H2O system25,26 and overall 12 peptidewater and 23 water-water H-bonds are formed with a significant energy gain (-163±1 kcal mol-1 Table 1). Ten conformations of the side chains were proved (Tables 1 and S5) and all of them maintain the shape of the water network with the exception of the G conformation for which a >C=O--H2O H-bond of the N-terminal residue is lost and an extra H2O---H2O H-bond is formed. The particular orientation of the central residue (χcentral∼180°) drives the H2O far from the carbonyl group and the G, H and I structures will not be further considered. For A-F structures the Nterminal and the central isopropyls orientations (χN and χcentral) have been systematically explored while the C-terminal isopropyl orientation were explored for some selected cases (J, K and S structures). At this stage of hydration there is no important limitation to the isopropyls dispositions and water network and, probably, many other structures with different side chain conformations could be obtained with the present solvent molecules arrangement. The nine
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22H2O_β-β conformers lie in a narrow energy range (∆E=-163±1 kcal mol-1) and only a modest greater stability is noted for the S structure. The Val3H+⋅22H2O complex formation is slightly more exoenergetic than the one found for the less hydrophobic trialanine (∆E=-160.2 kcal mol-1, Table 1), thus the bulk side chains do not reduce the efficiency of the hydration of charged and polar groups, rather they introduce weak favorable interactions between side chains and water network.
Figure 3. Selected molecular structures of the Val3H+⋅22H2O complex in the β-β and β-PPII peptide conformations.
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Table 1. Formation energies (∆E, kcal mol-1) of the Val3H+·nH2O (n=10, 14, 18 and 22) complexes at the M06-2X/aug-cc-pVTZ/PCM using the M06-2X/6-31+G*/PCM optimized geometries. They were computed relative to the Val3H+ (in the β-β_A conformation) and “n” isolated water molecules. Data for the Ala3H+·22H2O complex are reported for comparison. Val3H+ PPII-PPII β-β β-PPII 10H2O A -75.1 -75.0 -73.4 B -75.1 -75.4 -75.9 C -74.7 -75.6 -77.8 D -76.2 -76.6 E -76.0 -78.5 F -75.4 -79.3 G -73.9 H -76.1 I -77.8 J -73.5 S -73.8 14H2O A -104.8 -104.9 -101.8 B -105.3 -105.2 -105.0 C -104.8 -106.4 -107.1 D -107.3 E -109.1 F -109.1 G -105.2 H -107.7 I -108.5 J -104.6 -103.9 S -104.9 -100.9 18H2O A -136.9 -137.1 -133.4 B -136.7 -137.8 -136.6 C -136.0 -138.2 -137.2 D -139.5 E -141.2 F -140.3 G -137.5 H -140.0 I -140.8 J -136.9 -135.9 S -137.4 -133.3 22H2O A -163.0 -167.2 -167.7 B -162.7 -167.9 -169.7 C -162.2 -167.2 -169.8 D -164.3 -170.2 -172.5 E -163.2 -168.8 -173.6 F -163.5 -169.5 -173.2 G -170.3 H -171.0
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I J K S Ala3H+⋅22H2O
-172.4 -163.2 -161.9 -165.1 -160.2
-166.8 -166.8 -167.4 -165.7
-171.2
3.5. Hydrating the β-PPII conformer. The hydration shell over the β-PPII conformer is similar to that found for the β-β conformer, as far as the N-terminal and central residues concern with well separated up and down water networks (Figure 3). However, because of the carboxylic group rotation, the water molecules come closer, the up and down arrangements merge and an extra water-water H-bond is formed with respect to those found in the 22H2O_β-β model. (12 peptide-water and 24 water-water). The water shell differs slightly from the ones previously reported for cationic trialanine,25,26 because a different connection occurs between water molecules in the >CO central residue and carboxylic region, even though, the overall number of formed H-bonds is equal. By changing the isopropyls orientation, ten structures were optimized (A-G, J, K and S, Tables 1 and S6). Analogously to the 22H2O_β-β model, the G conformer loses a >C=O---H2O H-bond of the N-terminal residue and an extra H2O---H2O H-bond is formed. The other nine structures maintain the solvent molecules arrangement with optimal peptide-water interactions. Excluding the structures with the χcentral ∼ 180° angle, many other geometries could be optimized by changing the isopropyl orientations; however, the studied set is representative enough. In spite of the various isopropyls orientations, the structures are close in energy (∆E=-168±2 kcal mol-1), indicative of modest steric effects in building the 22-water-molecule network. The formation energy of the partially hydrated peptide (Val3H+⋅nH2O, n=10, 14 and 18) in the β-β and β-PPII conformations are similar because the hydration concerns the common β-strand region, while an
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energy gain of about 5 kcal mol-1 is obtained once the PPII hydration occurs in the Val3H+⋅22H2O system. This is mainly due to a better coordination of the water molecules around the residue with the PPII conformation as reported for dialanine and trialanine. Also for the βPPII conformer the Val3H+⋅22H2O complex formation is slightly more exoenergetic than the one found for the less hydrophobic trialanine (∆E=-165.7 kcal mol-1, Table 1). Again the bulk side chains do not reduce the efficiency peptide-water interactions at the present hydration stage. The 22H2O_β-PPII_A, 22H2O_β-PPII_J, and 22H2O_β-PPII_S are characterized by the same orientation of isopropyl in N-terminal and central residues (χN∼ -60 and χcentral∼ -60°), while the isopropyl of C-terminal assumes the three possible orientations (χC∼ -60, 60 and 180°, respectively). For the 22H2O_β-PPII_J structure, the isopropyls of the central and C-terminal residues point away from each other and a water wire that connects the >NH and >CO groups of the C-terminal residue can settle between them (Figure 3). For the 22H2O_β-PPII_A and 22H2O_β-PPII_S, the isopropyl of central and C-terminal residues lie close to each other and the smallest H---H contact is about 2.7 Å, thus to connect the >NH and >CO groups of the Cterminal residue the water wire must climb this region. In the present case the water wire is long enough to climb this steric encumbered region without significant perturbation of the entire water network and the three enquired structures have comparable energies. 3.6. Hydrating the PPII-PPII conformer. For the PPII-PPII conformer the peptidic polar groups are not sorted into two well defined regions and the isopropyls lie in between them. Furthermore, gyration radius of the PPII-PPII conformer is smaller than others, thus the handcraft water shell construction is more elaborate and important side chain effects are present also for the partially hydrated model complexes.
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Figure 4. Selected molecular structures of the Val3H+⋅nH2O (n=10, 14, 18, and 22) complexes in the PPII-PPII peptide conformation. In the 10H2O_PPII-PPII model there is the complete hydrophilic groups hydration of the Nterminal and central residues (Figure 4). Data show significant energy differences among the structures obtained rotating isopropyls N-terminal and central residues (Tables 1 and S7). The five structures characterized by the same N-terminal's isopropyl orientation (χN∼ -60°, 10H2O_PPII-PPII_A, D, G, J, and S) are less stable than others (about 4 kcal mol-1) because the three-molecule water chain which connects ammonium and the carbonyl of the central residue is not long enough to optimally circumscribe the two methyls of the N-terminal isopropyl. To
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accommodate repulsive water-side chain interactions, the isopropyl must move from the best orientation obtained for the bare peptide so that the χN angle goes from -56° of the bare peptide to -73° of the hydrated structures (Tables S4 and S7). Also the two sets of structures B, E, H (χN ∼60°) and C, F, I (χN∼ -170°) show a modest energetic separation and the latter are about 1.5 kcal mol-1 more stable. For the latter, both methyls of N-terminal isopropyl point away from the three-molecule water chain, reducing the peptide-water repulsive interactions. Of course, it is possible to enlarge the water chain and remove this strain, but this will push away solvent molecules from the peptidic main chain. The orientation of the isopropyl of the central residue also affects the peptide-water complex stability, in particular if one of its methyls (sets A-C and G-I) or the hydrogen atom (D-F) point toward the two-molecule water bridge that connects the >NH and >CO groups of the central residue. Thus, the A-C and G-I structure sets are isoenergetic, while the D-F set is 3 kcal mol-1 more stable (Table 1). Overall, the 10H2O_PPII-PPII_E and 10H2O_PPII-PPII_F are the most stable. Comparing these data with those obtained for the β-β and β-PPII main chain conformations it is evident that the β→PPII rearrangement of the central residue causes an energy gain (up to 3 kcal mol-1) for structures without strain, while for strained structures there is an energy loss (up to 3 kcal mol-1) in spite of the favorable peptide-water electrostatic interactions in the residue with the PPII conformation. For the 14H2O_PPII-PPII and 18H2O_PPII-PPII models, the partial and full hydration of the C-terminal hydrophilic groups occurs. The structure/energy analysis shows a scenario similar to that described for the 10H2O_PPII-PPII model and the E, F and I rotamers of the 14H2O_PPII-
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PPII and 18H2O_PPII-PPII are the most stable. Even though the second residue with the PPII conformation is hydrated, there is no significant energy gain with respect to hydrated β-β and βPPII conformers, since the better peptide-water electrostatic interactions are in part canceled by the repulsion with the side chain. To complete the five-water-molecule cluster over the carboxylic group, twenty water molecules are sufficient, but to form the 22H2O_PPII-PPII model, a two-molecule water bridge connecting "up" and "down" water networks is added. This bridge can be placed in various positions, but we have chosen to put it close to the isopropyl of the C-terminal residue. However, this choice poses some limits to the side chain rotation, the J-R (χC∼180°) and S-AA (χC∼ 60°) structures cannot be optimized without destroying the water network. Other water arrangements could be analyzed; however, it is clear that placing χC∼ 180° or χC ∼60°, the C-terminal isopropyl shields the peptidic main chain from the water approach. The A-I (χC∼ -60°) structures were successfully optimized, forming the same peptide-water and water-water H-bonds as the ββ and β-PPII conformers. The formation energy data of the 22H2O_PPII-PPII_(A-I) structures show noticeable differences (up to 7 kcal mol-1) confirming the presence of important water-side chain steric repulsions due to the N-terminal and central isopropyl. The greater stability of the 22H2O_PPIIPPII_E and 22H2O_PPII-PPII_F structures is essentially due to the particular arrangement of water molecules and isopropyl chains, which allows for the optimization of hydrophilic interactions and minimizes hydrophobic ones. These two structures are ∼8 and ∼3 kcal mol-1 more stable than the best 22H2O_β-β, and 22H2O_β-PPII conformers respectively, indicating that side chains reduce the energy gain once both residues assume PPII conformation.
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3.7. Energetics. The increase in strength of the peptide-water bonds and therefore of the vibrational frequencies, on passing from the extended to the PPII conformation for each residue, produces two effects: i) an increase in zero-point energy, and ii) the reduction of particle mobility with a consequent decrease in standard molar entropy. Table 2 lists the relative enthalpy, entropy and Gibbs free energy of various structures for the Val3H+⋅22H2O model. The inclusion of zero point and thermal correction to enthalpy does not significantly alter the relative stability for the various structures and only a modest reduction of exothermicity (about 1 kcal mol-1 with respect to the electronic energy, Table 1) is observed on passing from fully-extended to β-PPII and PPII-PPII conformers. The enthalpic preference for the β-PPII and PPII-PPII conformers for the trivaline model is less pronounced than the one computed for the Ala3H+⋅22H2O complex, especially for the latter (Table 2). Entropy has a more marked effect in determining the final stability of the three conformers (Table 2). The β-β conformer has the highest value of standard molar entropy and it slightly depends on the isopropyl conformations (-3±4 cal mol-1 K-1). A significant entropy reduction is observed once one (-16±4 cal mol-1 K-1) or two residues (-23±2 cal mol-1 K-1) adopt the polyproline arrangement. This reduction is much more marked than the one obtained for trialanine and it is caused by the geometrical constraints of the water network imposed by the isopropyl groups. All the structures analyzed with the β-β conformation have comparable Gibbs free energy and hence are similarly accessible, while the rotamers of the PPII-PPII conformer show significant different accessibility. A rough estimation of the effect of the various accessible structures can be
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obtained averaging thermodynamic functions over the Boltzmann population using the 27 optimized structures (Table 2). Table 2. Calculated Relative Enthalpy, Entropy, and Gibbs Free Energy at 298 K (∆H°298 and ∆G°298, kcal mol-1; ∆S°298, cal mol-1K-1) for the Val3H+·22H2O Complexes in the β-β, β-PPII and PPII-PPII backbone conformations and several side-chain conformations. Data for the Ala3H+·22H2O complex and experimental results for the Ala3H+ are reported for comparison. ∆H°298 Val3H+·22H2O
a
∆S°298
∆G°298
β-β
β-PPII
PPII-PPII
β-β
β-PPII
PPII-PPII
β-β
β-PPII
PPII-PPII
A
0.0
-2.6
-3.9
0.0
-21.6
-22.4
0.0
3.8
2.8
B
0.1
-3.7
-5.8
0.8
-11.1
-22.8
-0.1
-0.4
1.0
C
0.7
-2.9
-6.4
1.1
-16.3
-18.9
0.4
2.0
-0.7
D
-1.2
-6.3
-8.5
-5.3
-15.8
-23.8
0.4
-1.6
-1.4
E
0.1
-5.0
-9.6
1.8
-10.7
-26.0
-0.4
-1.8
-1.9
F
0.1
-5.6
-9.7
-8.5
-15.3
-19.7
2.6
-1.0
-3.8
G
-
-
-6.4
-
-
-23.4
0.6
H
-6.9
-23.4
0.1
I
-8.6
-22.1
-2.0
J
0.2
-2.6
-8.0
-13.7
2.6
1.5
K
1.4
-2.4
-2.0
-16.3
2.0
2.2
S
-2.0
-3.1
-5.6
-19.4
-0.4
2.7
Thermal averagea
-1.6
-5.9
-9.5
-4.9
-15.2
-21.8
0.2
-1.4
-3.0
Ala3H+·22H2O
0.0
-5.1
-10.7
0.0
-5.4
-14.2
0.0
-3.5
-6.4
Ala3H+ Exper.b
0.0
−2.5
−7.4
0.0
−7.1
−20.1
0.0
-0.4
-1.4
Ala3H+ Exper.c
0.0
−2.9
−6.8
0.0
−10.7
−22.7
0.0
0.3
0.0
Boltzmann thermally averaged thermodynamic quantities. bFrom ref 19. cFrom ref 18.
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The populations, pi, of each conformer can be evaluated as
e
pi =
−
∆Ei RT
27
∑e
−
∆Ei RT
i =1
(1)
where ∆Ei is the electronic energy difference between the ith structure and the structure with the lowest energy, corrected with zero-point vibrational energy.47 The thermally averaged quantities (enthalpy, entropy and Gibbs free energy) for each main-chain conformer is given by the relation
X
298
9
= ∑ p j X 298 j j =1
(2)
The ∆H° and ∆S° show that both make PPII-PPII conformation less favored for trivaline residues when compared to trialanine. Therefore, if for trialanine ∆G° shows a clear preference for the PPII conformation, this is not so obvious for trivaline (Figure 5). Because of the limitation in both the hydration model and electronic structure methods, the present data have a semiquantitative value and more elaborate techniques are desirable for a more reliable prediction on the ∆G°. More accurate modeling would further disadvantage the PPII and make it definitively less stable than the β, as suggested by experimental data.16,17
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Figure 5. Energy differences between the β-β and PPII-PPII conformers for the bare and hydrated Ala3H+ and Val3H+ peptides. Present computational results are in agreement with DFT calculations on the energetics of the β=PPII central residue transformation in GlyXxxGly peptides (Xxx = Ala, Leu, Val, and Ile) considering explicitly ten water molecules and the polarizable continuum water model.29 They found the dominant role of backbone hydration in stabilizing the PPII conformation of residues in water. Furthermore, they found that both energy and entropy depend on the Cβ-branching. 3.8. Comparison with experimental data. The structure of trivaline has been widely studied by several authors through various spectroscopic techniques. In agreement with present results, all experiments support a greater propensity towards the extended β-strand conformation with respect to trialanine although quantitatively there are some differences. In an earlier study, Schweitzer-Stenner et al.,15 by means of polarized visible Raman, FTIR, VCD and UVCD spectroscopies studied cationic, anionic and zwitterionic trivaline. For all three protonation states they suggest the dominance of a single configuration with a mixture of about 90% β-strand and
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10% PPII at room temperature. Graf et al.,16 using experimental NMR measurements combined with molecular dynamics computations, derived a ratio of β/PPII of 52/29 for the specific central residue in cation along with a noteworthy contribution of α-helix (19%). Schweitzer-Stenner et al.,17,42 reinterpreted their spectroscopy data along with NMR measurements and they reported a ratio β/PPII 68/16 while the remaining fraction is the contribution from 310-helix (10%) and inverse γ-turn. Kallenback et al.32 developed an integrated bayesian approach combining Graf’s NMR coupling constants16 and molecular dynamics. Conversely, they suggested that the most dominant conformation for trivaline has the central residue in the PPII conformation with a population ratio of 10/50, while the remaining fraction is the contribution from various αhelices.32 Large sets of data on several host-guest peptides have been reported with the aim to define a PPII propensity scale of various amino acid residues.33-42 All experimental sources agree on the PPII propensity reduction on passing from alanine-based peptides to valine ones even though quantitatively some differences are noted on molar fractions. From these data it also emerges that PPII propensity is context-dependent and, for example, comparison between GlyValGlyH+ and Val3H+ reveals that the terminal valines reduce the PPII propensity of the central valine residue, confirming the present correlation between the backbone hydration and the sterically-demanding side chain (vide infra).37,42 As far as the numerical values of the ∆H° and ∆S° are concerned, the qualitative temperaturedependent analysis on the Val3H+ suggests that the PPII contribution disappears at higher temperatures.15 This indicates negative ∆H° and ∆S° values for the β→PPII transformation in full agreement with present results.
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The data reported for specific central residue β→PPII transformation in the GXG peptides show a consistent reduction (more negative values) of both ∆H° and ∆S° upon replacing alanine with valine (Table 3).38 Conversely, estimated residue-averaged thermodynamic quantities for the AcXXNH2 (X=Ala and/or Val, Table 3) peptides show a small increase (less negative values) in both ∆H° and ∆S° upon replacing alanine with valine.51,52 The same trend is observed for alanine and valine in the GAVG peptide.53 Furthermore, for the central residue β→PPII transformation in Ala3, ∆H° and ∆S° become more than double than those obtained for GAG, still indicating that thermodynamic functions strictly depend on the framework where the inquired residue is placed. Table 3. Experimental enthalpy (kcal mol-1) and entropy (cal mol-1 K-1) for the β→PPII conformational transformation in specific residue (in bold) of tri- and tetrapeptides and averaged residue in protected dipeptides. ∆H° ∆S°
a
GAGa
-2.4
-5.5
GVGa
-9.6
-32.5
AAAb
-5
-13
GAVGc
-0.9
-3.6
GAVGc
-0.7
-2.7
AcAANH2d
-4.93
-14.0
AcAVNH2d
-4.48
-13.3
AcVANH2d
-4.54
-13.4
AcVVNH2d
-4.13
-13.1
From ref 38. bFrom refs 18 and 19. cFrom ref 53 dFrom refs 51 and 52.
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3.9. Neighboring residue effect on peptide backbone conformation. The comparison of structural and energetic data for the Ala3H+⋅(H2O)22 and Val3H+⋅(H2O)22 complexes indicates a lower efficiency of the peptide-water H-bonding in trivaline when the residues are in the PPII conformation. Thus, the main effect stabilizing PPII is reduced by the concurrence of the sterically demanding Cβ-branching side chains. Furthermore, the trivaline backbone hydration is modulated by the relative orientation of isopropyls when the residues are in the PPII conformation, i.e. there is an high correlation between isopropyl orientations and backbone hydration. All these data are indicative of conformational dependent nearest neighbor interactions mediated by water.54 The relevance of a correlation between backbone and side-chain motions has been recently highlighted in molecular dynamic simulations for conformational entropy evaluation in native↔denaturate transformation of ubiquitin.55 Accounting for this correlated motions, through the use of joint probability distributions, Sosnick et al. 55 found that the loss of backbone entropy in the unfolded process is three- to four larger than the side-chain contribution. Solvent-mediated interactions are ubiquitous in biology and technological processes. Their characteristics depend on the surface chemical details, which can become very complex for amphiphiles.54,56 Less familiar is the neighboring residue effect on peptide backbone conformation. This phenomenon was proven by Penkett et al.57 for a highly unfolded 130-residue protein. They provided evidence of individual residues having distinct main-chain conformational preferences, which depend not only on the amino acid constituents but also on the neighboring residues in the sequence. There are various recent experimental reports that further support the nearest neighbor effects. Among them, particular important were the large
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changes of conformational propensities observed in the conformational distributions of “GxyG” host–guest peptides in aqueous solution: GDyG, GSyG, GxLG, GxVG, where x/y=A, K, L, V.53 Statistical analysis over a large body of structures, using the explicit φ,ψ angles obtained from a PDB-based "coil library" (data only for residues not involved in intramolecular hydrogen bonded secondary structure)58 showed a strong PPII conformation preference for all amino acids and underlined the importance of the local amino acid sequence in determining the conformational preference. Furthermore, it was found that the magnitude of the nearest effects depends on neighbor type, with the largest effects for the β-branched and aromatic residues.58 These results were confirmed combining calculated and measured residual dipolar couplings for chemically denatured apomyoglobin, staphylococcal nuclease and eglin C.58 Other NMR, CD, and molecular dynamics simulations studies of all the 400 blocked dipeptides (AcXXNH2) do not present significant neighboring peptide interaction effects on the backbone conformational distribution.51,52 However, the presence of only two side chains greatly reduces their water-mediated correlated motion. The nearest neighbors phenomenon represents a breakdown of the polymer theory treatment developed by Flory et al.59 (the random coil theory), in which it is assumed that no nonlocal interactions along the peptidic chain occur and the φ,ψ torsion angles of a given residue are independent on the orientation of adjacent residues (isolated pair hypothesis).59 In this assumption, the free energy is given as a sum of the conditional hydration of individual residues. However, the presence of significant nearest neighbors interactions in highly hydrophilic sidechains would require a subsequent refinement to include residue pairs.
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4. CONCLUSIONS The present study, explicitly treating water molecules over cationic trivaline determined at the state of the art electronic structure methods, confirms the expected low propensity to adopt polyproline type II conformation and holds several new insights. The reduced gyration radius in PPII-PPII conformation brings the highly hydrophobic side chains close to each other, preventing the optimal site specific peptide-water interactions, the essential requisite for its stabilization. Many structures for the Val3H+⋅22H2O model with PPII-PPII conformation cannot be optimized while those obtained do not have remarkable enthalpic stabilization with respect to β-strand structures conversely to what was found for trialanine. The water cluster molecules Hbonded at the peptide are locked by side chain in the PPII conformation with a noticeable entropic disadvantage. Computation/experimental comparative analysis on ∆H° and ∆S° of alanine/valine based peptides suggests that in denatured and unfolded state, they might well depend on the respective neighbors and could therefore vary between different peptides and proteins.37 Furthermore, present results confirm the previous thesis that the neighboring residue effect is determined by the solvation of the peptide backbone processes rather than by intrapeptide steric encumbrances.54
ASSOCIATED CONTENT Supporting Information: Optimized dihedral angles, for the bare Val3H+ and hydrated complexes Val3H+⋅nH2O (n=10, 14, 18, 22) in the studied conformations are in Tables S1-S7. A complete list of Cartesian coordinates of all structures presently analyzed are also reported. This material is available free of charge via the Internet at http://pubs.acs.org.”
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AUTHOR INFORMATION Corresponding Author *E-mail:
[email protected] ORCID Giuseppe Lanza: 0000-0002-8358-0885 Notes The authors declare no competing financial interest. ACKNOWLEDGMENT This work was supported by the Università di Catania within the FIR-2017 project. REFERENCES (1) Ben-Naim, A. Molecular Theory of Water and Aqueous Solutions Part I: Understanding Water; World Scientific Publishing: Singapore, 2009. (2) Blokzijl, W.; Engberts, J. B. F. N. Hydrophobic Effects - Opinions and Facts. Angew. Chem. Int. Ed. 1993, 32, 1545-1579. (3) Chandler, D. Interfaces and the Driving Force of Hydrophobic Assembly. Nature 2005, 437, 640-647. (4) Snyder, P. W.; Lockett, M. R.; Moustakas, D. T.; Whitesides, G. M. Is it the Shape of the Cavity, or the Shape of the Water in the Cavity? Eur. Phys. J. Special Topics 2014, 223, 853891.
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(5) Stillinger, F. H. Structure in Aqueous Solutions of Nonpolar Solutes from the Standpoint of Scaled-Particle Theory. J. Solution Chem. 1973, 2, 141-158. (6) Dec, S. F.; Bowler, K. E.; Stadterman, L. L.; Koh, C. A.; Sloan, E. D. Direct Measure of the Hydration Number of Aqueous Methane. J. Am. Chem. Soc. 2006, 128, 414-415. (7) Uversky, V. N. Flexible Nets of Malleable Guardians: Intrinsically Disordered Chaperones in Neurodegenerative Diseases. Chem. Rev. 2011, 111, 1134-1166. (8) Hsu, W.-L.; Oldfield, C. J.; Xue, B.; Meng, J.; Huang, F.; Romero, P.; Uversky, V. N. Dunker, A. K. Exploring the Binding Diversity of Intrinsically Disordered Proteins Involved in one-to-many Binding. Protein Sci. 2013, 22, 258-273. (9) Lim, W. A.; Richards, F. M.; Fox, R. O. Structural Determinants of Peptide-binding Orientation and of Sequence Specificity in SH3 Domains. Nature 1994, 372, 375-379. (10) Dyson, H. J.; Wright, P. E. Intrinsically Unstructured Proteins and their Functions. Nat. Rev. Mol. Cell. Biol. 2005, 6, 197-208. (11) Jardetzky, T. S., Brown, J. H.; Gorga, J. C.; Stern, L. J.; Urban, R. G.; Strominger, J. L.; Wiley, D. C. Crystallographic Analysis of Endogenous Peptides Associated with HLA-DR1 Suggest a Common, Polyproline II-like Conformation for Bound Peptides. Proc. Natl. Acad. Sc. U.S.A. 1996 93, 734-738. (12) Jensen, M. R.; Zweckstetter, M.; Huang, J.; Blackledge, M. Exploring Free-Energy Landscapes of Intrinsically Disordered Proteins at Atomic Resolution Using NMR Spectroscopy. Chem. Rev. 2014, 114, 6632-6660.
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(13) Tiffany, M. L.; Krimm, S. New Chain Conformations of Poly(glutamic acid) and Polylysine. Biopolymers 1968, 6, 1379-1382. (14) Woutersen, S.; Hamm, P. Structure Determination of Trialanine in Water Using Polarization Sensitive Two-dimensional Vibrational Spectroscopy. J. Phys. Chem. B 2000, 104, 11316-11320. (15) Eker, F.; Griebenow, K.; Schweitzer-Stenner, R. Stable Conformations of Tripeptides in Aqueous Solution Studied by UV Circular Dichroism Spectroscopy. J. Am. Chem. Soc. 2003, 125, 8178-8185. (16) Graf, J.; Nguyen, P. H.; Stock, G.; Schwalbe, H. Structure and Dynamics of the Homologous Series of Alanine Peptides: A Joint Molecular Dynamics/NMR Study. J. Am. Chem. Soc. 2007, 129, 1179-1189. (17) R. Schweitzer-Stenner Distribution of Conformations Sampled by the Central Amino Acid Residue in Tripeptides Inferred From Amide I Band Profiles and NMR Scalar Coupling Constants. J. Phys. Chem. B 2009, 113, 2922-2932 (18) Oh, K.-I.; Lee, K.-K.; Park, E.-K.; Yoo, D.-G.; Hwang, G.-S.; Cho, M. Circular Dichroism Eigenspectra of Polyproline II and β-strand Conformers of Trialanine in Water: Singular Value Decomposition Analysis. Chirality 2010, 22, E186-201. (19) Toal, S.; Meral, D.; Verbaro, D.; Urbanc, B.; Schweitzer-Stenner, R. pH-independence of Trialanine and the Effects of Termini Blocking in Short Peptides: A Combined Vibrational, NMR, UVCD, and Molecular Dynamics Study. J. Phys. Chem. B 2013, 117, 3689-3706.
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(20) Furuta, M.; Fujisawa, T.; Urago, H.; Eguchi, T.; Shingae, T.; Takahashi, S.; Blanch, E. W.; Unno, M. Raman Optical Activity of Tetra-Alanine in the Poly(L-proline) II Type Peptide Conformation. Phys. Chem. Chem. Phys. 2017, 19, 2078-2086. (21) Han, W.; Jalkanen, K.; Elstner, M.; Suhai, S. Theoretical Study of Aqueous N-acetyl-Lalanine N′-methylamide: Structures and Raman, VCD, and ROA Spectra. J. Phys. Chem. B 1998, 102, 2587-2602. (22) Poon, C.-D.; Samulski, E. T.; Weise, C. F.; Weisshaar, J. C. Do Bridging Water Molecules Dictate the Structure of a Model Dipeptide in Aqueous Solution? J. Am. Chem. Soc. 2000, 122, 5642-5643. (23) Drozdov, A. N.; Grossfield, A.; Pappu, R. V. Role of Solvent in Determining Conformational Preferences of Alanine Dipeptide in Water. J. Am. Chem. Soc. 2004, 126, 25742581. (24) Lanza, G.; Chiacchio, M. A. Ab Initio MP2 and Density Functional Theory Computational Study of AcAlaNH2 Peptide Hydration: A Bottom-up Approach. ChemPhysChem 2014, 15, 2785-2793. (25) Lanza, G.; Chiacchio, M. A. Interfacial Water at the Trialanine Hydrophilic Surface: a DFT Electronic Structure and Bottom-up Investigation. Phys. Chem. Chem. Phys. 2015, 17, 17101- 17111. (26) Lanza, G.; Chiacchio, M. A. Peptide Hydration Phenomena Through a Combined Quantum Chemical and Bottom-up Approach. Z. Phys. Chem. 2016, 230, 1373-1393.
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(27) Lanza, G.; Chiacchio, M. A. Effects of Hydration on the Zwitterion Trialanine Conformation by Electronic Structure Theory. J. Phys. Chem. B 2016, 120, 11705-11719. (28) G. Lanza, M. A. Chiacchio Quantum Mechanics Approach to Hydration Energies and Structures of Alanine and Dialanine. ChemPhysChem 2017, 18, 1586-1596. (29) Ilawe, N. V.; Raeber, A. E.; Schweitzer-Stenner, R.; Toal S. E.; Wong, B. M. Assessing Backbone Solvation Effects in the Conformational Propensities of Amino Acid Residues in Unfolded Peptides. Phys. Chem. Chem. Phys. 2015, 17, 24917-24924. (30) Ireta, J. Microsolvation Effects on the Stability of Polyalanine in Extended and Polyproline II Conformation. Int. J. Quantum Chem. 2012, 112, 3612-3617. (31) Mirkin, N. G.; Krimm, S. Water Interaction Differences Determine the Relative Energetic Stability of the Polyproline II Conformation of the Alanine Dipeptide in Aqueous Environments. Biopolymers 2012, 97, 789-794. (32) Xiao, X.; Kallenbach, N.; Zhang, Y. Peptide Conformation Analysis Using an Integrated Bayesian Approach. J. Chem. Theory Comput. 2014, 10, 4152-4159. (33) Rucker, A. L.; Pager, C. T.; Campbell, M. N.; Qualls, J. E.; Creamer, T. P. Host-guest Scale of Left-handed Polyproline II Helix Formation. Proteins 2003, 52, 68-75. (34) Chellgren, B. W.; Creamer, T. P. Short Sequences of Non-Proline Residues Can Adopt the Polyproline II Helical Conformation. Biochemistry 2004, 43, 5864-5869. (35) Eker, F.; Griebenow, K.; Cao, X.; Nafie, L. A.; Schweitzer-Stenner, R. AHA, ASA, AVA, AWA, and Zwitterionic AKA Clearly Prefer an Extended β-strand Conformation in the E region. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 10054-10059.
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