Cooperativity in Amide Hydrogen Bonding Chains. A Comparison between Vibrational Coupling through Hydrogen Bonds and Covalent Bonds. Implications for Peptide Vibrational Spectra

Polarisation effects on the H-bond acceptor properties of sulfonamides

The strengths of H-bonding interactions in networks are affected by cooperativity between the interacting sites. Compounds with an intramolecular H-bond between a sulfonamide NH group and pyridine nitrogen were used to measure the magnitude of cooperative effects on intermolecular H-bonding interactions with the sulfonamide oxygen. X-ray crystallography and 1H NMR experiments confirm the presence of the intramolecular H-bond and show that it is maintained in the 1 : 1 complex formed with perfluoro-tert-butanol (PFTB) in n-octane solution. Association constants for formation of 1 : 1 complexes with PFTB were determined using UV/Vis absorption titrations for a series of compounds equipped with different pyridine groups. Substituents on the pyridine were used to tune the strength of the intramolecular H-bond and investigate the effects on the strength of the intermolecular H-bond. Electron-donating groups on the pyridine that increase the strength of the intramolecular H-bond were found to increase in the strength of the intermolecular interaction with PFTB. The results were used to determine the H-bond acceptor parameters, β, for the sulfonamide oxygen group, and the values show a linear relationship with the value of β for the pyridine nitrogen. The slope of this relationship corresponds to the cooperativity parameter, κ, which is +0.16. The positive cooperativity observed in H-bonded sulfonamides is comparable to the value measured previously for the amide group (κ = +0.20).

Negative cooperativity in the formation of H-bond networks involving primary anilines

Networks of H-bonds can show non-additive behaviour, where the strength of one interaction perturbs another. The magnitude of such cooperative effects can be quantified by measuring the effect of the presence of an intramolecular H-bond at one site on a molecule on the association constant for formation of an intermolecular H-bond at another site. This approach has been used to quantify the cooperativity associated with the interaction of a primary amine with two H-bond acceptors. A series of compounds that have an intramolecular H-bond between an aniline NH2 group and a pyridine nitrogen were prepared, using polarising substituents on the pyridine ring to vary the strength of the intramolecular H-bond. The presence of the intramolecular interaction was confirmed by X-ray crystallography in the solid state and NMR spectroscopy in n-octane solution. UV-vis absorption titrations were used to measure the association constants for formation of an intermolecular H-bond with tri-n-butyl phosphine oxide in n-octane. Electron-donating substituents on the pyridine ring, which increase the strength of the intramolecular H-bond, were found to decrease the strength of the intermolecular H-bond between the aniline and the phosphine oxide. The results were used to determine the H-bond donor parameters for the anilines, α, and there is a linear relationship between the values of α and the H-bond acceptor parameter of the pyridine group involved in the intramolecular H-bond, β. The slope of this relationship was used to determine the cooperativity parameter (κ = -0.10), which quantifies the negative allosteric cooperativity between the two H-bonding interactions. Calculated molecular electrostatic potential surfaces of the anilines quantitatively reproduce the experimental result, which suggests that effects are electrostatic in origin, either due to polarisation of the NH bonds or due to secondary electrostatic interactions between the two H-bond acceptors.

Polarisation effects on the H-bond acceptor properties of secondary amides

H-bonding interactions in networks are stabilised by cooperativity, but the relationship between the chemical structures of the interacting functional groups and the thermodynamic consequences is not well-understood. We have used compounds with an intramolecular H-bond between a pyridine H-bond acceptor and an amide NH group to quantify cooperative effects on the H-bond acceptor properties of the amide carbonyl group. 1H NMR experiments in n-octane confirm the presence of the intramolecular H-bond and show that this interaction is intact in the 1 : 1 complex formed with perfluoro-tert-butanol (PFTB). UV-vis absorption titrations were used to measure the relationship between the association constant for formation of this complex and the H-bond acceptor properties of the pyridine involved in the intramolecular H-bond. Electron-donating substituents on the pyridine increase the strength of the intermolecular H-bond between PFTB and the amide. There is a linear relationship between the H-bond acceptor parameter β measured for the amide carbonyl group and the H-bond acceptor parameter for the pyridine. The cooperativity parameter κ determined from this relationship is 0.2, i.e. β for an amide carbonyl group is increased by one fifth of the value of β of an acceptor that interacts with the NH group. This result is reproduced by DFT calculations of H-bond parameters for the individual molecules in the gas phase, which implies that the observed cooperativity can be understood as polarisation of the electron density in the amide π-system in response to formation of a H-bond. The cooperativity parameter κ measured for the secondary amide H-bond donor and H-bond acceptor is identical, which implies that polarisation of an amide mediates the interaction between an external donor or acceptor in a reciprocal manner.

On the Short-Range Nature of Cooperativity in Hydrogen-Bonded Large Molecular Clusters

The variation in the hydrogen bond (HB) strength has considerable consequences on the physicochemical properties of molecular clusters. Such a variation mainly arises due to the cooperative/anti-cooperative networking effect of neighboring molecules connected by HBs. In the present work, we systematically study the effect of neighboring molecules on the strength of an individual HB and the respective cooperativity contribution toward each of them in a variety of molecular clusters. For this purpose, we propose a use of a small model of a large molecular cluster called the spherical shell-1 (SS1) model. This SS1 model is constructed by placingg the spheres of an appropriate radius centered on X and Y atoms of the X-H···Y HB under consideration. The molecules falling within these spheres constitute the SS1 model. Utilizing this SS1 model, the individual HB energies are calculated within the molecular tailoring approach-based framework and the results are compared with their actual counterparts. It is found that the SS1 is a reasonably good model of large molecular clusters, providing 81-99% of the total HB energy estimated using the actual molecular clusters. This in turn suggests that the maximum cooperativity contribution toward a particular HB is due to the fewer number of molecules (in the SS1 model) directly interacting with two molecules involved in its formation. We further demonstrate that the remaining part of the energy or cooperativity (∼1 to 19%) is captured by the molecules falling in the second spherical shell (SS2) centered on the hetero-atom of the molecules in the SS1 model. The effect of increasing size of a cluster on the strength of a particular HB, calculated by the SS1 model, is also investigated. The calculated value of the HB energy remains unchanged with the increase in the size of a cluster, emphasizing the short-ranged nature of the HB cooperativity in neutral molecular clusters.

H-bond cooperativity: polarisation effects on secondary amides

Formation of a H-bond with an amide carbonyl oxygen atom increases the strength of subsequent H-bonds formed by the amide NH, due to polarisation of the bond. The magnitude of this effect has been quantified by measuring association constants for the formation of 1 : 1 complexes of 2-hydroxylbenzamides with tri-n-butyl phosphine oxide. In 2-hydroxybenzamides, there is an intramolecular H-bond between the phenol OH group and the carbonyl oxygen atom. Comparison of the association constants measured for compounds with and without the 2-hydroxy group allows direct quantification of the effect of the intramolecular H-bond on the H-bond donor properties of the amide NH group. Substituents were used to modulate the strength of the intramolecular and intermolecular H-bonds. The presence of an intramolecular H-bond increases the strength of the intermolecular H-bond by more than one order of magnitude in n-octane solution. The increase in the H-bond donor parameter used to describe the amide NH group is directly proportional to the H-bond donor parameter of the phenol OH group that makes the intramolecular H-bond. These polarisation effects will lead to substantial cooperativity in complex systems that feature networks of non-covalent interactions, and the measurements described here provide a quantitative basis for understanding such phenomena.

Formation of an intramolecular phenol-amide H-bond leads to a dramatic increase in the H-bond donor strength of the amide NH group. Polarisation of the amide group is directly proportional to the polarity of the phenol H-bond donor.

Tracking the Amide I and αCOO- Terminal ν(C=O) Raman Bands in a Family of l-Glutamic Acid-Containing Peptide Fragments: A Raman and DFT Study

The E-hook of β-tubulin plays instrumental roles in cytoskeletal regulation and function. The last six C-terminal residues of the βII isotype, a peptide of amino acid sequence EGEDEA, extend from the microtubule surface and have eluded characterization with classic X-ray crystallographic techniques. The band position of the characteristic amide I vibration of small peptide fragments is heavily dependent on the length of the peptide chain, the extent of intramolecular hydrogen bonding, and the overall polarity of the fragment. The dependence of the E residue's amide I ν(C=O) and the αCOO- terminal ν(C=O) bands on the neighboring side chain, the length of the peptide fragment, and the extent of intramolecular hydrogen bonding in the structure are investigated here via the EGEDEA peptide. The hexapeptide is broken down into fragments increasing in size from dipeptides to hexapeptides, including EG, ED, EA, EGE, EDE, DEA, EGED, EDEA, EGEDE, GEDEA, and, finally, EGEDEA, which are investigated with experimental Raman spectroscopy and density functional theory (DFT) computations to model the zwitterionic crystalline solids (in vacuo). The molecular geometries and Boltzmann sum of the simulated Raman spectra for a set of energetic minima corresponding to each peptide fragment are computed with full geometry optimizations and corresponding harmonic vibrational frequency computations at the B3LYP/6-311++G(2df,2pd) level of theory. In absence of the crystal structure, geometry sampling is performed to approximate solid phase behavior. Natural bond order (NBO) analyses are performed on each energetic minimum to quantify the magnitude of the intramolecular hydrogen bonds. The extent of the intramolecular charge transfer is dependent on the overall polarity of the fragment considered, with larger and more polar fragments exhibiting the greatest extent of intramolecular charge transfer. A steady blue shift arises when considering the amide I band position moving linearly from ED to EDE to EDEA to GEDEA and, finally, to EGEDEA. However, little variation is observed in the αCOO- ν(C=O) band position in this family of fragments.

Understanding the influence of low-frequency vibrations on the hydrogen bonds of acetic acid and acetamide dimers

Low-frequency vibrations coupled to high-frequency modes are known to influence the hydrogen bond strengths in a weakly interacting dimer.

Label-free nanometer-resolution imaging of biological architectures through surface enhanced Raman scattering

Label free imaging of the chemical environment of biological specimens would readily bridge the supramolecular and the cellular scales, if a chemical fingerprint technique such as Raman scattering can be coupled with super resolution imaging. We demonstrate the possibility of label-free super-resolution Raman imaging, by applying stochastic reconstruction to temporal fluctuations of the surface enhanced Raman scattering (SERS) signal which originate from biomolecular layers on large-area plasmonic surfaces with a high and uniform hot-spot density (>10¹¹/cm², 20 to 35 nm spacing). A resolution of 20 nm is demonstrated in reconstructed images of self-assembled peptide network and fibrilated lamellipodia of cardiomyocytes. Blink rate density is observed to be proportional to the excitation intensity and at high excitation densities (>10 kW/cm²) blinking is accompanied by molecular breakdown. However, at low powers, simultaneous Raman measurements show that SERS can provide sufficient blink rates required for image reconstruction without completely damaging the chemical structure.

"Additive" cooperativity of hydrogen bonds in complexes of catechol with proton acceptors in the gas phase: FTIR spectroscopy and quantum chemical calculations

Experimental study of hydrogen bond cooperativity in hetero-complexes in the gas phase was carried out by IR-spectroscopy method. Stretching vibration frequencies of O-H groups in phenol and catechol molecules as well as of their complexes with nitriles and ethers were determined in the gas phase using a specially designed cell. O-H groups experimental frequency shifts in the complexes of catechol induced by the formation of intermolecular hydrogen bonds are significantly higher than in the complexes of phenol due to the hydrogen bond cooperativity. It was shown that the cooperativity factors of hydrogen bonds in the complexes of catechol with nitriles and ethers in the gas phase are approximately the same. Quantum chemical calculations of the studied systems have been performed using density functional theory (DFT) methods. It was shown, that theoretically obtained cooperativity factors of hydrogen bonds in the complexes of catechol with proton acceptors are in good agreement with experimental values. Cooperative effects lead to a strengthening of intermolecular hydrogen bonds in the complexes of catechol on about 30%, despite the significant difference in the proton acceptor ability of the bases. The analysis within quantum theory of atoms in molecules was carried out for the explanation of this fact.

H-Bonding Cooperativity Effects in Amyloids: Quantum Mechanical and Molecular Mechanics Study

The cooperativity effects have been evaluated on three model systems, the formamide, (formylamino)acetamide and amyloidic-layer oligomers with an increasing size of the monomer units (6, 13 and 214 atoms). In the last model, each layer is a dimer of the amino-acid sequence GNNQQNY in one-letter amino-acid abbreviations. The series of oligomers for each model system of up to six monomers have been constructed. For the calculation of the strength of a particular H-bond formed between various sub-oligomers within an oligomer, different wave function, density functional and semi-empirical quantum mechanical methods as well as empirical force fields have been used. Semi-empirical methods are found to be a reasonable compromise between accuracy and computational cost. These methods are able to describe the cooperativity effects with an accuracy almost comparable to that of the ab initio methods. On the contrary, the empirical force-field methods for all of the model systems mostly failed to describe the H-bonding cooperativity effects properly. Based on the results obtained in this work, we recommend using semi-empirical methods. For the systems where this is impossible, we agree to use polarizable force fields with some reservations. Generally, the more flexible the oligomer chain is (the less steric the repulsion or rigid motifs are), the larger the cooperativity that can be achieved. With the increasing number of monomers in a sequence connected via H-bonds, the cooperativity effects appear to be growing, but relatively soon (at 3–4 monomer units) they tend to become saturated.

A scheme for rapid prediction of cooperativity in hydrogen bond chains of formamides, acetamides, and N-methylformamides

A scheme is proposed in this article to predict the cooperativity in hydrogen bond chains of formamides, acetamides, and N-methylformamides. The parameters needed in the scheme are derived from fitting to the hydrogen bonding energies of MP2/6-31+G** with basis set superposition error (BSSE) correction of the hydrogen bond chains of formamides containing from two to eight monomeric units. The scheme is then used to calculate the individual hydrogen bonding energies in the chains of formamides containing 9 and 12 monomeric units, in the chains of acetamides containing from two to seven monomeric units, in the chains of N-methylformamides containing from two to seven monomeric units. The calculation results show that the cooperativity predicted by the scheme proposed in this paper is in good agreement with those obtained from MP2/6-31+G** calculations by including the BSSE correction, demonstrating that the scheme proposed in this article is reasonable. Based on our scheme, a cooperativity effect of almost 240% of the dimer hydrogen bonding energy in long hydrogen bond formamide chains, a cooperativity effect of almost 190% of the dimer hydrogen bonding energy in long hydrogen bond acetamide chains, and a cooperativity effect of almost 210% of the dimer hydrogen bonding energy in long hydrogen bond N-methylformamide chains are predicted. The scheme is further applied to some heterogeneous chains containing formamide, acetamide, and N-methylformamide. The individual hydrogen bonding energies in these heterogeneous chains predicted by our scheme are also in good agreement with those obtained from Møller-Plesset calculations including BSSE correction.

Ab initio calculations on C6H6···(HF)n clusters — X–H···π hydrogen bond

MP2/6–311++G(d,p) calculations on C6H6···(HF)n clusters were performed and full optimizations were carried out for systems containing up to four HF molecules (n = 4) and calculations on the systems of C6v symmetry were carried out for up to six HF molecules (n = 6). Cooperativity effects were analyzed for these molecular aggregates. It was found that F–H···π and F–H···F hydrogen bonds exist for these complexes and those interactions are enhanced as the number of HF molecules increases. The cooperativity effects cause numerous changes in geometrical, energetic, and topological parameters, the latter ones derived from the quantum theory of atoms in molecules. Various correlations between the analyzed parameters are presented. There are meaningful differences between the molecular graphs for the fully optimized complexes and those for the linear complexes of C6v symmetry (for the latter, the linear chain of HF molecules is attached to a benzene molecule acting as the Lewis base). For the linear complexes, unique bond paths connect the H-attractor of the HF molecule and the ring critical point of the benzene molecule.

A density functional theory study of vibrational coupling in the amide I band of beta-sheet models

We report the first molecular orbital/density functional theory (DFT) calculations on the vibrational frequencies involved in the amide I band of completely geometrically optimized models for beta-sheet peptides based upon (up to 16) glycine residues. These calculations use the B3LYP/D95** level of DFT. The primary means of vibrational coupling occurs through H bond, rather than through space, interactions, which is consistent with a previous report on alpha-helical polyalanines and H-bonding chains of both formamides and 4-pyridones. We decoupled the C=O stretching vibrations using selected 14C substitutions to probe the coupling mechanism and to determine "natural" frequencies for individual 14C=Os. The intermolecular H-bonding interactions affect the geometries of the amide groups. Those near the center of H-bonding chains have long C=O bonds. The C=O bond lengths correlate with these "natural" frequencies, The frequencies obtained from the DFT calculations are generally more coupled, and the most intense are more red shifted than those calculated by transition dipole coupling (TDC). TDC inverts the order of the shifted frequencies compared to DFT in several cases.

Computing protein infrared spectroscopy with quantum chemistry

Quantum chemistry is a field of science that has undergone unprecedented advances in the last 50 years. From the pioneering work of Boys in the 1950s, quantum chemistry has evolved from being regarded as a specialized and esoteric discipline to a widely used tool that underpins much of the current research in chemistry today. This achievement was recognized with the award of the 1998 Nobel Prize in Chemistry to John Pople and Walter Kohn. As the new millennium unfolds, quantum chemistry stands at the forefront of an exciting new era. Quantitative calculations on systems of the magnitude of proteins are becoming a realistic possibility, an achievement that would have been unimaginable to the early pioneers of quantum chemistry. In this article we will describe ongoing work towards this goal, focusing on the calculation of protein infrared amide bands directly with quantum chemical methods.

Characterizing the Cooperativity in H-Bonded Amino Structures

Density functional theory calculations were used to examine the effect of H-bond cooperativity on the magnitude of the NMR chemical shifts and spin-spin coupling constants in a C4h-symmetric G-quartet and in structures consisting of six cyanamide monomers. These included two ring structures (a planar C6h-symmetric structure and a nonplanar S6-symmetric structure) and two linear chain structures (a fully optimized planar Cs-symmetric chain and a planar chain structure where all intra- and intermolecular parameters were constrained to be identical). The NMR parameters were computed for the G-quartet and cyanamide structures, as well as for shorter fragments derived from these assemblies without reoptimization. In the ring structures and the chain with identical monomers, the intra- and intermolecular geometries of the cyanamides were identical, thereby allowing the study of cooperative effects in the absence of geometry changes. The magnitude of the |1JNH| coupling, 1H and 15N chemical shifts of the H-bonding amino N-H group, and the |h2JNN| H-bond coupling increased, whereas the size of the |1JNH| coupling of the non-H-bonded amino N-H bonds of the first amino group in the chain, which are roughly perpendicular to the H-bonding network, decreased in magnitude when H-bonding monomers were progressively added to extending ring or chain structures. These effects are attributed to electron redistribution induced by the presence of the nearby H-bonding guanine or cyanamide molecules.

Cooperative Hydrogen Bonding Effects Are Key Determinants of Backbone Amide Proton Chemical Shifts in Proteins

A computational methodology for backbone amide proton chemical shift (delta(H)) predictions based on ab initio quantum mechanical treatment of part of the protein is presented. The method is used to predict and interpret 13 delta(H) values in protein G and ubiquitin. The predicted amide-amide delta(H) values are within 0.6 ppm of experiment, with a root-mean-square deviation (RMSD) of 0.3 ppm. We show that while the hydrogen bond geometry is the most important delta(H)-determinant, longer-range cooperative effects of extended hydrogen networks make significant contributions to delta(H). We present a simple model that accurately relates the protein structure to delta(H).

Electron Density Redistribution Accounts for Half the Cooperativity of α Helix Formation

The energy of alpha helix formation is well known to be highly cooperative, but the origin and relative importance of the contributions to helical cooperativity have been unclear. Here we separate the energy of helix formation into short range and long range components by using two series of helical dimers of variable length. In one dimer series two monomeric helices interact by forming hydrogen bonds, while in the other they are coupled only through long range, primarily electrostatic interactions. Using Density Functional Theory, we find that approximately half of the cooperativity of helix formation is due to electrostatic interactions between residues, while the other half is due to nonadditive many-body effects brought about by redistribution of electron density with helix length.

Two-Dimensional Infrared Spectra of the 13C18O Isotopomers of Alanine Residues in an α-Helix

The parameters needed to describe the two-dimensional infrared (2D IR) spectra of the isotopically labeled alpha-helix are presented. The 2D IR spectra in the amide-I' spectral region of a series of singly 13C=18O-labeled 25-residue alpha-helices were measured by three-pulse heterodyned spectral interferometry. The dependence of the spectra on the population time was measured. Individual isotopomer levels (residues 11-14) were clearly identified in 2D IR, downshifted by approximately 61 cm(-1) from the main helical band. By analyzing the line shapes of the 13C=18O diagonal peaks that appeared at approximately 1571.3 +/- 0.8 cm(-1) for all four labeled samples, we observed wider structural distributions for residues 14 and 11 than those for 12 and 13. A small fast component in the correlation function was used to estimate the dynamics of these distributions. In all cases, the v = 1 --> 2 transition showed a more Lorentzian-like line shape and also decayed faster than the v = 0 --> 1 transition, indicating that the population relaxation time of the v = 2 state was significantly faster than the v = 1 state. The amide transitions with naturally abundant 13C=16O appeared at approximately 1594 cm(-1), forming very weak and blurred cross-peaks with 13C=18O isotopomer modes. The effects of spectral interferences on the coherence time dependence of the detection frequency spectrum were also investigated. The methods of first moments and Wigner analysis were developed to circumvent the interference effects on the weak isotopomer transitions. The structural origin of the distributions for individual isotopomers was proposed to be an effect of nearby lysine residues on the intrahelical hydrogen-bond network.

A new scheme for determining the intramolecular seven-membered ring N–H⋯OC hydrogen-bonding energies of glycine and alanine peptides

In this paper a new scheme was proposed to calculate the intramolecular hydrogen-bonding energies in peptides and was applied to calculate the intramolecular seven-membered ring N-H...O=C hydrogen-bonding energies of the glycine and alanine peptides. The density-functional theory B3LYP6-31G(d) and B3LYP6-311G(d,p) methods and the second-order Moller-Plesset perturbation theory MP26-31G(d) method were used to calculate the optimal geometries and frequencies of glycine and alanine peptides and related structures. MP26-311++G(d,p), MP26-311++G(3df,2p), and MP2/aug-cc-pVTZ methods were then used to evaluate the single-point energies. It was found that the B3LYP6-31G(d), MP26-31G(d), and B3LYP6-311G(d,p) methods yield almost similar structural parameters for the conformers of the glycine and alanine dipeptides. MP2/aug-cc-pVTZ predicts that the intramolecular seven-membered ring N-H...O=C hydrogen-bonding strength has a value of 5.54 kcal/mol in glycine dipeptide and 5.73 and 5.19 kcal/mol in alanine dipeptides, while the steric repulsive interactions of the seven-membered ring conformers are 4.13 kcal/mol in glycine dipeptide and 6.62 and 3.71 kcal/mol in alanine dipeptides. It was also found that MP26-311++G(3df,2p) gives as accurate intramolecular N-H...O=C hydrogen-bonding energies and steric repulsive interactions as the much more costly MP2/aug-cc-pVTZ does.

Hydrogen-bonded acetic acid dimers: Anharmonic coupling and linear infrared spectra studied with density-functional theory

Anharmonic vibrational force field calculations provide a quantitative understanding of the width and substructure of the linear IR-absorption spectrum of the O-H stretching mode in acetic acid dimers (CH3-COOH)2 and (CD3-COOH)2. Anharmonic coupling of the high-frequency upsilon(OH) mode to fingerprint and low-frequency modes is included resulting in 11- and 9-dimensional vibrational Hamiltonians. A sixth-order force field covering up to three-body interactions is used. Force constants are calculated by fitting one-dimensional potential-energy surfaces and a finite difference procedure applying density-functional theory [Becke 3 Lee-Yang-Parr 6-311+G(d,p)]. It is demonstrated that both anharmonic coupling to low-frequency modes as well as Fermi resonance coupling with fingerprint modes are important mechanisms explaining the line shape of the O-H stretching IR-absorption band in acetic acid dimers.