Chang-Liang Sun*a,
Fu Dinga,
Yan-Li Dingb and
Yang Lic
aCenter of Physical Chemistry Test, Shenyang University of Chemical Technology, Shenyang 110142, P. R. China. E-mail: chemscl@126.com
bDepartment of Mathematics and Physics, Shenyang University of Chemical Technology, Shenyang 110142, P. R. China
cDepartment of Chemistry, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, P. R. China
First published on 3rd December 2013
The effect of water molecules upon the hydrogen-bonding cooperativity of three-stranded antiparallel β-sheet models has been studied by quantum chemical calculations at the MP2/6-311++G(3df,2p)//MP2/6-31G** level. Our calculation results indicate that the hydrogen-bonding lengths and the atom charge distribution are affected by the H2O molecules, especially for those in the same amide unit directly bonded. The hydrogen-bonding cooperativity significantly increases the binding energy of the LR or SR hydrogen-bonding ring in the three-stranded β-sheet structures and the influence is also gradually increased as more H2O molecules are added. We found that the perturbation energies are also affected as the H2O molecules are added and this supports that the cooperative enhancement is closely related to the orbital interaction. We have also found that the charge transfer among the three diglypeptides is obviously influenced by the H2O molecules.
The cooperativity of hydrogen bonds has received intensive experimental18–20 and theoretical21–38 researches. Both experimental and theoretical studies of amide clusters indicate that there is strong cooperativity in the formation of one-dimensional hydrogen-bonded chains.28,29,40,41 Dannenberg suggested the unusually large cooperative hydrogen bond in formamide chains due to the electronic effects.22,29,30,33,34 Kemp has suggested that hydrogen-bonding cooperativity contributes strongly to the formation of α-helices.36 The studies of Wu et al. indicate there is hydrogen-bonding cooperativity in both α- and 310-helices and in sheets of unnatural β-polyglycines but little or none in β-sheets of the natural α-polyglycines.23–25 Dannenberg further suggested the apparent relative absence of cooperativity in β-sheet models of polyglycine derives from the weakening and strengthening of C5 intrastrand hydrogen bonds.22,31,32 Liu et al. suggested the charge flow between the hydrogen donor and acceptor groups in the c-NMF molecule is the most important factor inducing the coopterative effect of hydrogen bond.42 The studies of Baker and co-workers suggest nonpairwise electronic effects account for half of the total cooperativity in the system of α-helix formation.43 More recently, Greef et al. carried out DFT calculations to understand the origin of the experimentally observed cooperativity in the hydrogen-bond-induced supramolecular polymerization of C3-symmetrical trialkylbenzene-1,3,5-tricarboxamides (BTAs), and their analysis demonstrated the cooperative growth of these structure is caused by electrostatic interactions and nonadditive effects brought about by redistribution of the electron density with aggregate length.44
The hydrogen-bonding cooperativity is still highly challenging especially for that in the peptide-water hydrogen-bonded systems.45–56 Karplus demonstrated the existence of a cooperative hydration effects for amidic hydrogen bonds, such as those found in peptides.55 Tsuzuki et al. demonstrated that the hydrogen-bonding cooperativity significantly increases the binding of the water with the crownophane.48 Dannenberg et al. presented density functional theory (DFT) calculations on the solvation of polyalanine α-helices in water. They found that individual water molecules cooperatively hydrogen-bond to both the C- and N-termini of the helix, which results in increases in the dipole moment of the helix/water complex to more than the vector sum of their individual dipole moments.51 Recently, Ireta has reported studies of β-sheets interactions with individual water molecules suggesting that the strengthening of water–water hydrogen bond along the solvation shell of β-sheets promotes a flat to twist transition.52 We have reported the cooperative enhancement of discrete water to the two-stranded antiparallel β-sheet models.56 In this paper we further carry out high level ab initio calculations on the discrete water binding to the three-stranded antiparallel diglypeptide β-sheet models for the quantitative evaluation of cooperative enhancement and for the purpose of understanding the origin of the enhancement.
![]() | ||
Fig. 1 Optimized geometry for the three-stranded antiparallel diglypeptide β-sheet models at the MP2/6-31G** level. |
Throughout our studies, the binding energies are calculated by supermolecular approach. For example, the binding energy of LR hydrogen-bonding ring in complex B can be obtained by eqn (1). Where E(BSSE)total hydrogen-bonding tetramer is the binding energy of the total hydrogen-bonding tertamer, E(BSSE)upper diglypeptide−H2O hydrogen-bonding dimer is the binding energy of the hydrogen-bonding dimer formed by the upper diglypeptide and H2O molecule, and E(BSSE)middle-lower diglypeptide hydrogen-bonding dimer is the binding energy of middle and lower diglypeptide hydrogen-bonding dimer. Both the hydrogen-bonding tetramer and two dimers contain more than one fragment, so all of the binding energies of them are subject to basis set superposition error (BSSE). In this paper, BSSE correction is estimated using the counterpoise (CP) method of Boys and Bernardi.63 The interaction energy calculated by eqn (1) also contains other van der Waals interaction as dispersion or induction as well as possible repulsive interactions, electrostatic contributions and others. Nevertheless, the interaction energy is taken as an estimate of the hydrogen bond energy in this paper.
ELR = E(BSSE)total hydrogen-bonding tetramer − E(BSSE)upper diglypeptide−H2O hydrogen-bonding dimer − E(BSSE)middle-lower diglypeptide hydrogen-bonding dimer | (1) |
The geometry optimizations for the antiparallel diglypeptide β-sheet models are carried out at the MP2/6-31G** level. The geometrical structures are optimized with a plane of symmetry (Cs) symmetry restraints.22,23 All of the electronic energies of the hydrogen-bonding complexes are obtained by performing B3LYP/6-31+G** and MP2/6-311++G(3df,2p) basis sets based on the optimized geometrical structures. The CP correction for basis set superposition error was incorporated using the single point a posteriori method rather than via optimization on the CP-corrected potential energy surfaces (CP-OPT) due to the excessive CPU time required.64 The natural bond orbital analysis (NBO) is carried out using the NBO package included in the Gaussian 03 suite of program.65,66 All the ab initio calculations are carried out in vacuum, thus they correspond to the intrinsic properties.
![]() | ||
Fig. 2 Optimized geometries at the MP2/6-31G** level for the three-stranded sheet structures with one H2O molecule. |
![]() | ||
Fig. 3 Optimized geometries at the MP2/6-31G** level for the three-stranded sheet structures with two H2O molecules. |
![]() | ||
Fig. 4 Optimized geometry at the MP2/6-31G** level for the three-stranded sheet structures with four H2O molecules. |
A | B | C | D | E | F | G | H | I | J | ||
---|---|---|---|---|---|---|---|---|---|---|---|
r(H(1)⋯O(1)) | 1.907 | 1.886 | 1.879 | 1.913 | 1.903 | 1.883 | 1.885 | 1.857 | 1.908 | 1.858 | |
r(H(2)⋯O(2)) | 1.882 | 1.892 | 1.869 | 1.882 | 1.882 | 1.893 | 1.870 | 1.881 | 1.882 | 1.881 | |
r(H(3)⋯O(3)) | 2.148 | 2.145 | 2.150 | 2.146 | 2.116 | 2.111 | 2.147 | 2.144 | 2.117 | 2.112 | |
r(H(4)⋯O(4)) | 2.104 | 2.107 | 2.104 | 2.085 | 2.080 | 2.081 | 2.084 | 2.104 | 2.069 | 2.067 | |
The binding energy between upper and middle diglypeptides | B3LYP/6-31+G** | −16.66 | −17.47 | −17.62 | −16.61 | −16.82 | −17.37 | −17.53 | −18.12 | −16.71 | −18.20 |
0.00 | −0.81 | −0.96 | 0.05 | −0.16 | −0.71 | −0.87 | −1.46 | −0.05 | −1.54 | ||
MP2/6-311++G(3df,2p) | −20.36 | −20.69 | −21.28 | −20.30 | −20.54 | −20.83 | −21.20 | −21.61 | −20.43 | −21.70 | |
0.00 | −0.33 | −0.92 | 0.06 | −0.18 | −0.47 | −0.84 | −1.25 | −0.07 | −1.34 | ||
The binding energy between lower and middle diglypeptides | B3LYP/6-31+G** | −4.82 | −5.34 | −4.82 | −5.09 | −5.31 | −5.57 | −5.05 | −5.10 | −5.38 | −5.68 |
0.00 | −0.52 | 0.00 | −0.27 | −0.49 | −0.75 | −0.23 | −0.28 | −0.56 | −0.86 | ||
MP2/6-311++G(3df,2p) | −8.80 | −8.88 | −8.81 | −9.06 | −9.35 | −9.38 | −9.06 | −8.88 | −9.46 | −9.56 | |
0.00 | −0.08 | −0.01 | −0.26 | −0.55 | −0.58 | −0.26 | −0.08 | −0.66 | −0.76 | ||
Total binding energy of the three-stranded sheet structures | B3LYP/6-31+G** | −21.48 | −22.82 | −22.44 | −21.70 | −22.13 | −22.94 | −22.59 | −23.22 | −22.09 | −23.89 |
0.00 | −1.34 | −0.96 | −0.22 | −0.65 | −1.46 | −1.11 | −1.74 | −0.61 | −2.41 | ||
MP2/6-311++G(3df,2p) | −29.16 | −29.57 | −30.09 | −29.36 | −29.89 | −30.22 | −30.26 | −30.49 | −29.88 | −31.25 | |
0.00 | −0.41 | −0.93 | −0.20 | −0.73 | −1.06 | −1.10 | −1.33 | −0.72 | −2.09 |
A | B | C | D | E | F | G | H | I | J | |
---|---|---|---|---|---|---|---|---|---|---|
q(H(1)) | 0.4742 | 0.4768 | 0.4775 | 0.4738 | 0.4748 | 0.4773 | 0.4770 | 0.4803 | 0.4744 | 0.4805 |
q(O(1)) | −0.8384 | −0.8416 | −0.8415 | −0.8373 | −0.8403 | −0.8436 | −0.8404 | −0.8450 | −0.8392 | −0.8460 |
q(H(2)) | 0.4761 | 0.4750 | 0.4776 | 0.4762 | 0.4761 | 0.4750 | 0.4776 | 0.4764 | 0.4761 | 0.4764 |
q(O(2)) | −0.8305 | −0.8274 | −0.8369 | −0.8307 | −0.8303 | −0.8273 | −0.8371 | −0.8334 | −0.8304 | −0.8332 |
q(H3)) | 0.4834 | 0.4840 | 0.4835 | 0.4824 | 0.4851 | 0.4858 | 0.4826 | 0.4842 | 0.4844 | 0.4852 |
q(O(3)) | −0.7880 | −0.7888 | −0.7879 | −0.7855 | −0.8018 | −0.8027 | −0.7855 | −0.7889 | −0.7998 | −0.8009 |
q(H(4)) | 0.4809 | 0.4805 | 0.4810 | 0.4856 | 0.4826 | 0.4822 | 0.4858 | 0.4807 | 0.4869 | 0.4867 |
q(O(4)) | −0.8103 | −0.8089 | −0.8118 | −0.8139 | −0.8108 | −0.8095 | −0.8155 | −0.8104 | −0.8139 | −0.8141 |
E(n(O(1)) → σ*(H(1)–N(1))) | 14.41 | 15.65 | 16.02 | 14.12 | 14.68 | 15.89 | 15.67 | 17.42 | 14.44 | 17.45 |
E(n(O(2)) → σ*(H(2)–N(2))) | 15.32 | 14.80 | 16.23 | 15.34 | 15.32 | 14.77 | 16.18 | 15.61 | 15.33 | 15.57 |
E(n(O(3)) → σ*(H(3)–N(3))) | 6.71 | 6.80 | 6.67 | 6.72 | 7.51 | 7.63 | 6.69 | 6.82 | 7.45 | 7.59 |
E(n(O(4)) → σ*(H(4)–N(4))) | 7.66 | 7.59 | 7.68 | 8.21 | 8.34 | 8.29 | 8.25 | 7.67 | 8.70 | 8.73 |
As shown in Table 1, the hydrogen-bonding lengths of r(H(1)⋯O(1)), r(H(2)⋯O(2)), r(H(3)⋯O(3)), and r(H(4)⋯O(4)) in complex A without water molecule participate are 1.907 Å, 1.882 Å, 2.148 Å, and 2.104 Å, respectively. As one or more H2O as proton donor or acceptor bond to the outside N–H or CO, the hydrogen-bonding lengths obviously become shorter, especially those in the same amide unit. For example, the r(H(1)⋯O(1)) in complex B is 1.886 Å, which is shorter by 0.021 Å than that in complex A. The four hydrogen-bonding lengths in complex J are 1.858 Å, 1.881 Å, 2.112 Å, and 2.067 Å, respectively, which are obviously shorter than those in complex A.
It can be seen from Table 1 that the binding energies calculated by B3LYP/6-31+G** are obviously weaker than those from MP2/6-311++G(3df,2p) calculations. However, the relative energies calculated by the two methods are similar. For example, the total binding energies of complex A and J calculated by B3LYP/6-31+G** are −21.48 and −23.89 kcal mol−1. The calculation results by MP2/6-311++G(3df,2p) are −29.16 and −31.25 kcal mol−1, which are obviously stronger than those by B3LYP/6-31+G**. However, the energy difference between complex A and J calculated by MP2/6-311++G(3df,2p) is −2.09 kcal mol−1, which is similar to the value of −2.41 kcal mol−1 by B3LYP/6-31+G**. We also can find that the tendency of energies changes is not influenced by computational methods. So the further discussions are only based on MP2 calculation results.
In complex A, the binding energy of LR hydrogen-bonding ring between the upper and middle diglypeptides is −20.36 kcal mol−1 calculated by MP2/6-311++G(3df,2p) and the SR hydrogen-bonding ring between the lower and middle diglypeptides is −8.80 kcal mol−1. The total binding energy of LR and SR is −29.16 kcal mol−1. When one H2O molecule acting as proton donor bond to the outer CO of the upper diglypeptide (complex B), the binding energy of LR is −20.69 kcal mol−1, which is 0.33 kcal mol−1 stronger than that in complex A. It means that the cooperative enhancement is about 0.33 kcal mol−1 as the H2O molecule added. The binding energy of SR is −8.80 kcal mol−1, which is influenced slightly. In complex C, the O atom of H2O molecule serves as proton acceptor and bonds to the outside N–H of the upper diglypeptide, while the two H atoms of H2O molecule serves as proton donor and bonds to the outside C
O simultaneously. The interaction energy of LR is −21.28 kcal mol−1. The cooperative enhancement by the H2O molecule to the binging energy is about −0.92 kcal mol−1. In complex D and E, one H2O as proton donor or acceptor bonds to the down diglypeptide. It can be seen from Table 1 that the binding energy of the three-strands β-sheet models is also influenced as the H2O molecule added, especially for the binding energy of SR.
In complex F, there are two H2O molecules: one as proton donor bonds to the outer CO of the upper diglypeptide and the other one as proton acceptor bonds to the outer N–H of the lower diglypeptide. The cooperative enhancement by the two H2O molecules to the binging energy is as large as −1.06 kcal mol−1 (0.47 kcal mol−1 of LR and 0.58 kcal mol−1 of SR). In complex H, the two H2O molecules are both bond to the upper diglypeptide. We can find that the cooperative enhancement by the two H2O molecules to LR is 1.25 kcal mol−1. Similarly, when the two H2O molecules are both bonded to the lower diglypeptide (complex I), the cooperative enhancement to SR is 0.66 kcal mol−1. In complex J, four H2O molecules are bonded to the upper diglypeptide and lower diglypeptide simultaneously. It can be seen in Table 1 the cooperative enhancement to LR is 1.34 kcal mol−1, which is slightly stronger than the value of 1.25 kcal mol−1 in complex H. Similarly, the cooperative enhancement to SR 0.76 kcal mol−1 is also slightly stronger than that in complex I. It means that the hydrogen-bonding cooperativity is mutual enhancement by the two H2O molecules bonding to the upper diglypeptide and the two bonding to the lower diglypeptide.
In the study of two-stranded sheet structures, we have found that the atom charge distributions are obviously affected by the addition of H2O molecules and the cooperative enhancement is closely related with the orbital interaction. From Table 2, one can see that the electrostatic charges of the H and O atoms in three-stranded sheet structures are also obviously affected by H2O molecule adding. For example, the q(H(1)) is 0.4742e and the q(O(1)) is −0.8384e in complex A. The values in complex B, F, H, and J which one H2O molecule bonded to the outer CO of the upper diglypeptide are 0.4768e and −0.8416e, 0.4773e and −0.8436e, 0.4803e and −0.8450e, 0.4805 and −0.8460. Furthermore, the values of q(H(1)), q(O(1)), q(H(2)), q(O(2)), q(H(3)), q(O(3)), q(H(4)), and q(O(4)) in complex A are 0.4742e, −0.8384e, 0.4761e, −0.8305e, 0.4834e, −0.7880e, 0.4809e, and −0.8103e. The values in complex J are 0.4805e, −0.8460e, 0.4764e, −0.8332e, 0.4852e, −0.8009e, 0.4867e, and −0.8141e, which are obviously more positive and negative charges than those in complex A.
The quantum chemical investigations show that the covalent interaction from a nonbonding orbital of the acceptor atom to the antibonding σ* molecular orbital of the donor group should be a significant ingredient of the hydrogen bonding energies.67–69 So we applied the NBO second-order perturbation analysis to calculate the second-order stabilization energy of nonbonding orbital of the acceptor O atom to the antibonding σ* molecular orbital of the donor group H–N. The obtained perturbation energies due to n(O(1)) → σ*(H(1)–N(1)), n(O(2)) → σ*(H(2)–N(2)), n(O(3)) → σ*(H(3)–N(3)), and n(O(4)) → σ*(H(4)–N(4)) orbital interactions are listed in Table 2. As shown in Table 2, the perturbation energies are obviously affected as the H2O molecules bonded, especially for those in the same amide unit directly bonded by the H2O molecules. For example, the perturbation energies of n(O(1)) → σ*(H(1)–N(1)) in complex B is 15.65 kcal mol−1, which is enhanced by 9% from 14.41 kcal mol−1 of complex A. In complex J, the value of 17.45 kcal mol−1 is increased by 21% from complex A. As listed in Table 2, the perturbation energies due to n(O(1)) → σ*(H(1)–N(1)), n(O(2)) → σ*(H(2)–N(2)), n(O(3)) → σ*(H(3)–N(3)), and n(O(4)) → σ*(H(4)–N(4)) orbital interactions in complex A are 14.41 kcal mol−1, 15.32 kcal mol−1, 6.71 kcal mol−1, and 7.66 kcal mol−1. As four H2O molecules bonded, the values are changed to 17.45 kcal mol−1, 15.57 kcal mol−1, 7.59 kcal mol−1, and 8.73 kcal mol−1. These results further support the conclusion that the perturbation energies make a certain contribution to the cooperative enhancement of the β-sheet models.
We have also investigated the effect of the charge transfer among the three diglypeptides of the β-sheet structures. The net charges of the upper, middle and lower diglypeptides are listed in Table 3. In complex A, the net charges of the three diglypeptides are −0.0002e, 0.0009e and −0.0007e, respectively. Therefore, the three-stranded sheet structure is electric neutrality. In complex B, one H2O molecule acting as proton donor bond to β-sheet structure and the net charge of the upper diglypeptide that directly bonded by the H2O molecule is 0.0118e. The net charge of middle diglypeptide changes from 0.0009e to 0.0027e and the value for the lower diglypeptide changes slightly. The total net charge of the three-stranded sheet structure is 0.0141e. It means that the electronic charge transfer from the three-stranded sheet structure to the H2O molecule. In complex E, one H2O molecule acting as proton acceptor bonds to the lower diglypeptide. The total net charge of the three-stranded sheet structure is −0.0193e which means the electronic charge transfer from the H2O molecule to the three-stranded sheet structure.
A | B | C | D | E | F | G | H | I | J | |
---|---|---|---|---|---|---|---|---|---|---|
Net charges of the upper diglypeptide | −0.0002 | 0.0118 | −0.0191 | 0.0002 | −0.0006 | 0.0115 | −0.0186 | −0.0056 | −0.0003 | −0.0055 |
Net charges of the middle diglypeptide | 0.0009 | 0.0027 | 0.0010 | 0.0016 | 0.0004 | 0.0021 | 0.0018 | 0.0032 | 0.0012 | 0.0036 |
Net charges of the lower diglypeptide | −0.0007 | −0.0004 | −0.0007 | 0.0222 | −0.0191 | −0.0186 | 0.0221 | −0.0004 | 0.0041 | 0.0041 |
Total net charges of three-stranded sheet structures | 0.0000 | 0.0141 | −0.0187 | 0.0240 | −0.0193 | −0.0054 | 0.0053 | −0.0028 | 0.0049 | 0.0022 |
It is interesting to note that there is an additive property for the total net charge of the three-stranded sheet structure. For example, the total net charge of complex F is −0.0054e, which is close to the summation of complex B and E −0.0052e. The value 0.0053e of complex G is close to the value of C plus D. The sum of D and E is 0.0047e, which is also close to the value 0.0049e of I. However, it is exceptional for H. The total net charge of H is −0.0028e, but the sum of B and C is −0.0046e. In complex H, the two H2O molecules are both bonded to the same outside CO. The carbonyl O atom serves as a proton acceptor in three separate hydrogen bonds simultaneously, which would tend to weaken each. So the cooperative effect of the two H2O molecules in complex H is weaker than the sum of B and C.17 It is also the reason why the total net charge of complex J is close to the sum of complex H and I but not close to the sum F and G, and neither close to the sum of B, C, D and E.
Footnote |
† Electronic supplementary information (ESI) available: The geometrical coordinates of the ten three-stranded antiparallel diglypeptide β-sheet models optimized at the MP2/6-31G** level. See DOI: 10.1039/c3ra45892j |
This journal is © The Royal Society of Chemistry 2014 |