Evidences for Cooperative Resonance-Assisted Hydrogen Bonds in Protein Secondary Structure Analogs

Cooperative behaviors of the hydrogen bonding networks in proteins have been discovered for a long time. The structural origin of this cooperativity, however, is still under debate. Here we report a new investigation combining excess infrared spectroscopy and density functional theory calculation on peptide analogs, represented by N-methylformamide (NMF) and N-methylacetamide (NMA). Interestingly, addition of the strong hydrogen bond acceptor, dimethyl sulfoxide, to the pure analogs caused opposite effects, namely red- and blue-shift of the N−H stretching infrared absorption in NMF and NMA, respectively. The contradiction can be reconciled by the marked lowering of the energy levels of the self-associates between NMA molecules due to a cooperative effect of the hydrogen bonds. On the contrary, NMF molecules cannot form long-chain cooperative hydrogen bonds because they tend to form dimers. Even more interestingly, we found excellent linear relationships between changes on bond orders of N−H/N−C/C = O and the hydrogen bond energy gains upon the formation of hydrogen bonding multimers in NMA, suggesting strongly that the cooperativity originates from resonance-assisted hydrogen bonds. Our findings provide insights on the structures of proteins and may also shed lights on the rational design of novel molecular recognition systems.

Scientific RepoRts | 6:36932 | DOI: 10.1038/srep36932 indicated that this aprotic solvent can break the N− H···O = C hydrogen bond between amide molecules by forming stronger N− H···O = S hydrogen bond [40][41][42] . Thus, the infrared vibration spectroscopic properties of the two binary systems, NMF-DMSO and NMA-DMSO, are expected to be similar. But unexpectedly, we observed opposite results, which indicate different hydrogen bonding modes between NMF and NMA. The calculating results confirm this conclusion and suggest the origin of the cooperativity of hydrogen bonds is RAHB.

Results
IR spectra of N−H stretching modes. Attenuated total reflection Fourier transform infrared spectroscopic (ATR-FTIR) technique was employed to get original infrared spectra. As shown in Fig. 2A, red shift  Scientific RepoRts | 6:36932 | DOI: 10.1038/srep36932 (19.1 cm −1 ) of the N− H stretching infrared absorption was recorded when introducing DMSO into NMF, while blue shift (5.9 cm −1 ) was observed in the case of NMA as in Fig. 2C. It should be noted that deuterated DMSO (DMSO-d 6 ) was used in the measurements to avoid overlap of methyl C− H stretching vibration peaks between amide and DMSO.
The infrared spectral data have been analyzed by excess spectroscopy [43][44][45][46] as shown in Fig. 2B,D. Clearly, we see opposite features of the excess spectra in the N− H stretching region. In NMF-DMSO-d 6 system, for each concentration, the negative peak is on the high wavenumber side (around 3380 cm −1 ) and the positive peak is on the low wavenumber side (about 3260 cm −1 ). In NMA-DMSO-d 6 system, the feature is just reversed: the negative (or positive) peak is on the low (or high) wavenumber side. These results imply the apparent different interaction modes of the two analog molecules in interacting with DMSO. Furthermore, both positive and negative peak positions in the excess spectra are relatively fixed, suggesting that the self-associating complex of NMF and NMA, as well as the newly formed complexes between NMF/NMA and DMSO, are stable 45 .
IR spectra of C = O stretching modes. As for C = O bond, which is the main proton acceptor group in the two analogs, the ordinary and excess IR spectra are shown in Fig. 3. The peak positions of C = O stretching vibration mode in both NMF and NMA are blue-shifted with adding DMSO-d 6 . This is expected, because C = O The excess IR spectra in the C = O stretching vibration region are shown in the lower panels in Fig. 3. As can be seen in the figure, the positions of both positive and negative peaks are fixed, in agreement with the results shown in Fig. 2. A feature worth of reminding is that multiple negative peaks are seen in Fig. 3D, which suggests that populations of different self-association structures of NMA would decrease with increasing concentration of DMSO-d 6 . On contrast, the excess peaks of NMF in Fig. 3B are similar to a simple two-state transformation situation 45 . Optimized amide complexes by quantum chemical calculations. The hydrogen bonds involving N− H are classified as red-shifted hydrogen bonds 47,48 , thus the red-and blue-shift of ν(N− H) in the two binary systems indicate the strengthening and weakening of the hydrogen bonds. To reveal the different relative energy relationships of self-associating amides and amide-DMSO complexes in the two systems, we turned to quantum chemical calculations. Selected average hydrogen bond energy E and configurations of representative complexes are shown in Fig. 4. For the self-association of NMA, due to the steric effect of the methyl groups, the associating complexes tend to choose linear configuration. Continuous increase in the absolute value of E from NMA dimer to hexamer implies the cooperativity of the related hydrogen bonds. In the case of NMF, two conformers, cis-and trans-NMF, exist in pure liquid. According to literature 49   Dashed arrows indicate the energy change of different complexes with adding DMSO to NMF (grey color) or NMA (black color). In the configurations, only − N− H···O = C− units are drawn in the ball-stick model, and N, H, O, C atoms are shown in blue, white, red, and grey balls, respectively. The numbers labeled in the models are the hydrogen bond lengths, and the unit is Å. All the NMF are trans-conformers without specific notification.
As can be seen in Fig. 4, the energy level of NMF-DMSO complex is between the trimer and dimer of NMF. Because we observed red-shift of ν(N− H) upon addition of DMSO into NMF, the dominant species in the binary mixtures are either monomers or non-cooperative dimers. This is in agreement with the conclusions in literature 50 . In the case of NMA, the energy level of NMA-DMSO complex is also between the trimer and dimer of NMF. However, because blue-shift of ν(N− H) upon addition of DMSO into NMA was observed, we conclude that the dominant species in the binary mixtures are oligomers of NMA, larger than dimers. Very importantly, these oligomers are cooperative, namely there is an extra energy gain upon formation of longer hydrogen bonding chains. Further, the oligomers of NMA from hexamer (or even larger ones) to trimer would dissociate upon addition of DMSO to NMA, which could be the reason of multiple-negative-peak feature in the excess spectra of Fig. 3D. It is noteworthy that the presence of cooperativity in the hydrogen bond network of NMA makes it a better model to peptides/proteins than NMF.
Taking the picture of Fig. 4 in mind, we may predict that diluting NMF and NMA with an inert solvent, for example CCl 4 , will result in blue shift of ν(N− H), because the diluting processes in both cases would cause the weakening of the hydrogen bonding interaction among the amide molecules. Our ATR-FTIR experiments supported the prediction ( Figure S4). Likewise, the parallel blue shifts of ν(C = O) shown in Fig. 3C can be explained easily, as the diluting processes of the two amides by DMSO only concern with the breaking of the carbonyl-involved hydrogen bonds. The hydrogen bonds between the carbonyl groups and the methyl groups of DMSO, if there are any, are very weak and can be ignored. Now we address the important issue, the origin of cooperativity of hydrogen bonds, by taking NMA as the model system. Following the discussion above, we learnt that the bond strength of N− H or C = O in the non-cooperative case (NMA-DMSO and NMA-CCl 4 mixtures) is stronger than that in the cooperative hydrogen bonding associates (pure NMA). This means that the cooperative process weakens the strength of these bonds, which is in line with the resonance effect showing in Fig. 1. Inspired by this, we calculated the average bond orders (BOs) of C = O, N− H and C− N in different NMA self-associating complexes using the natural bond orbital (NBO) analysis method 51 . Not surprisingly, resonance between peptide bond structure and enol-like structure has already existed in NMA monomer, where the bond orders of C = O, N− H and C− N bonds are 1.658 (< 2), 0.794 (< 1), and 1.197 (> 1), respectively. What surprises us is the perfect linear relationships between the average hydrogen bond energies and the changes on bond orders of the three covalent bonds forming the resonance structures, as shown in Fig. 5. In

Discussion
By comparing the behavior of two similar molecules, N-methylformamide and N-methylacetamide, in forming hydrogen bonds with an aprotic molecule, dimethylsulphoxide, we have been fortunate to observe opposite shifting of the N− H stretching absorption bands. This allows us to state that N-methylacetamide is a better molecular model in studying peptide bonds, particularly when the issue of cooperative hydrogen bonds in proteins/peptides is under concern. Frequently, formamide and N-methylformamide are used as the model molecules. For example, Dannenberg 12 and Wu's groups 17 once used formamide to study the cooperativity in amide hydrogen bonding chains. Although it is almost perfect to perform quantum chemical calculations using the small molecule, the two N− H bonds in the molecule provide too many possibilities in forming hydrogen bonds with another molecule. As a result, it is virtually impossible to expect the simple linear arrangement of the molecule in a real sample. This could be an important reason that no experimental work has been reported in testing these studies. The replacement of one N− H bond by N− CH 3 reduces such possibilities. But the derived molecule, N-methylformamide, is still not perfect. On the one hand, the carbonyl groups in real peptides connect with alkyl groups, while in N-methylformamide it bonds with a hydrogen atom. This gives the C− N bond more freedom to rotate, causing cis-and trans-conformers. On the other hand, the cis-conformers would terminate the extension of hydrogen bond chains (see SI for details). Different from these two molecules, N-methylacetamide has been shown to be the best model molecules among these derivatives. This is because the repulsion between the two methyl groups allows only trans-conformers of this molecule and thus favors the extension of hydrogen bond chains.
Regarding the origin of the cooperativity of the hydrogen bonds in proteins/peptides, our work suggests that it is the resonance of the amide. The perfect linear relationships between the interaction energy and bond order changes of the three key covalent bonds, C = O, N− H and C− N, strongly support this conclusion. Zhao and Wu used quantum chemical calculations to study the hydrogen bond energies of formamide self-associations 17 . They found that introduction of a medium (methanol) to the hydrogen bonding network in gas phase markedly reduced the cooperative energy, and thus proposed that the main reason of cooperativity is electrostatic interaction. Qualitatively speaking, we think the resonance-origin and electrostatic interaction-origin is not contradictory. This is because that resonance of the amide structure will cause redistribution of charges in the concerned molecules and thus will exert an influence on the electrostatic interactions. Similarly, we can also use the resonance model to explain the idea of van der Waals interaction-origin proposed by Hua et al. 18 , because the charge redistribution from the enol-like resonance structures would put an effect on the dipole moments of the molecules and thus will affect the van der Waals interaction, as we just explained. Actually, the amide molecules discussed here are all neutral. Under this circumstance, diploe-dipole interaction and electrostatic interaction are the same in nature.
To sum up, we report the experimental evidences on the cooperativity of hydrogen bonds in NMA in this work. Compared with other amides, such as the popular formamide and N-methylformamide, only N-methylacetamide prefers to forming long chain structure, which makes it a better model molecule to peptides/ proteins. We discovered perfect linear relationships between the average changes on the bond order of C = O, N− H, and C− N and the average hydrogen bond energies in various associates of NMA, which are consistent with the bond strength changes revealed by infrared experiments. We thus conclude that the origin of the cooperativity is the resonance of the peptide bonds in the hydrogen bonding network of proteins. The findings of this work may inspire the understanding of some biochemical processes and rational design of functional materials using cooperative hydrogen-bond strategies.

Methods
Chemicals. DMSO  Excess Infrared Spectroscopy. The theory of excess infrared spectroscopy has been described in detail elsewhere 43,44,46 . Briefly, an excess infrared spectrum is defined as the difference between the spectrum of a real solution and that of the respective ideal solution under identical conditions. The working equation in calculating the excess infrared spectrum of a binary system is as follows: where A is the absorbance of the mixture, d is the light path length or the penetration depth in the case of ATR measurements, C 1 and C 2 are molarities of the two components, x 1 and x 2 are mole fractions of components 1 and 2, and ε ⁎ 1 and ε ⁎ 2 are molar absorption coefficients of the two components in their pure states, respectively.

Quantum Chemical Calculations.
All calculations were carried out using the Gaussian 09 package 53 .
The geometries (isolated single molecules, their self-associates and complexes) were first optimized in gas phase using B3LYP method with 6-31+ + G** basis set. Then the energy, vibrational frequency, electrostatic surface potential and the natural population analysis (NPA) charge were calculated at the same level. The B3LYP functional has been successfully and extensively used to study the hydrogen bonding interactions in amide-containing systems 3,12,17,[54][55][56][57] . Electrostatic surface potentials of NMF, NMA, and DMF are calculated first to determine the possible hydrogen bonding sites between molecules. Then we searched possible structures for dimers of NMA, NMF and DMA. Totally 21 conformers were optimized and 9 stable conformers were obtained. Among the 9 stable conformers, we picked up the most stable conformers to represent the dimers of NMA, NMF and DMA. Their energies are shown in Fig. 4. For NMF, in agreement with the work of Cordeiro 41 , the most stable self-associating structures are dimer and trimer, and we repeated their calculation. For NMA, we added a single NMA to an optimized NMA dimer, and changed the position of the NMA. We have optimized 7 conformers, and 4 stable conformers were obtained. Similar method was applied to the calculation of tetramer and other self-associating structures. The primary structure of an oligomer was created by adding a monomer to the (n − 1) oligomer structure and then optimized by Gaussian. Average hydrogen bond energy E was calculated by the interaction energy of each complexes divided by the number of hydrogen bonds. Energy zero points were set at the energies of individual molecules. All the optimized geometries were recognized as local energy minima with no imaginary frequency. The natural population analysis was done with the nature bond orbital (NBO) method 44 . Meanwhile, the basis set superposition error (BSSE) correction 58 was performed for obtaining accurate interaction energies.