Density Functional Theory Vibrational Frequencies of Amides and Amide Dimers

Refining protein amide I spectrum simulations with simple yet effective electrostatic models for local wavenumbers and dipole derivative magnitudes

Analysis of the amide I band of proteins is probably the most wide-spread application of bioanalytical infrared spectroscopy. Although highly desirable for a more detailed structural interpretation, a quantitative description of this absorption band is still difficult. This work optimized several electrostatic models with the aim to reproduce the effect of the protein environment on the intrinsic wavenumber of a local amide I oscillator. We considered the main secondary structures - α-helices, parallel and antiparallel β-sheets - with a maximum of 21 amide groups. The models were based on the electric potential and/or the electric field component along the CO bond at up to four atoms in an amide group. They were bench-marked by comparison to Hessian matrices reconstructed from density functional theory calculations at the BPW91, 6-31G** level. The performance of the electrostatic models depended on the charge set used to calculate the electric field and potential. Gromos and DSSP charge sets, used in common force fields, were not optimal for the better performing models. A good compromise between performance and the stability of model parameters was achieved by a model that considered the electric field at the positions of the oxygen, nitrogen, and hydrogen atoms of the considered amide group. The model describes also some aspects of the local conformation effect and performs similar on its own as in combination with an explicit implementation of the local conformation effect. It is better than a combination of a local hydrogen bonding model with the local conformation effect. Even though the short-range hydrogen bonding model performs worse, it captures important aspects of the local wavenumber sensitivity to the molecular surroundings. We improved also the description of the coupling between local amide I oscillators by developing an electrostatic model for the dependency of the dipole derivative magnitude on the protein environment.

Ionic Association in CH3-(CH2-CF2) n -CH3(PVDF)-Li+-(CF3SO2)2N- for n = 1, 4: A Computational Approach

The ionic conductivity of solid polymer electrolytes is governed by the ionic association caused by the polymer···Li⁺ and the anion···Li⁺ interactions. We performed the density functional calculation to analyze the molecular interactions in the CH₃-(CH₂-CF₂) _n -CH₃-Li⁺-(CF₃SO₂)₂N^- for n = 1,4 systems. The gauche conformation is predicted in the lowest energy conformer of pure polymer except for n = 1. The lithium coordination number with the polymer is changed from 3 to 2 in the presence of anion for n = 2, 4 systems. The consequences of the Li⁺ ion and Li⁺-(CF₃SO₂)₂N^- to the vibrational spectrum are studied to understand the ionic association at the molecular level.

A Self-Consistent Sonification Method to Translate Amino Acid Sequences into Musical Compositions and Application in Protein Design Using Artificial Intelligence

We report a self-consistent method to translate amino acid sequences into audible sound, use the representation in the musical space to train a neural network, and then apply it to generate protein designs using artificial intelligence (AI). The sonification method proposed here uses the normal mode vibrations of the amino acid building blocks of proteins to compute an audible representation of each of the 20 natural amino acids, which is fully defined by the overlay of its respective natural vibrations. The vibrational frequencies are transposed to the audible spectrum following the musical concept of transpositional equivalence, playing or writing music in a way that makes it sound higher or lower in pitch while retaining the relationships between tones or chords played. This transposition method ensures that the relative values of the vibrational frequencies within each amino acid and among different amino acids are retained. The characteristic frequency spectrum and sound associated with each of the amino acids represents a type of musical scale that consists of 20 tones, the "amino acid scale". To create a playable instrument, each tone associated with the amino acids is assigned to a specific key on a piano roll, which allows us to map the sequence of amino acids in proteins into a musical score. To reflect higher-order structural details of proteins, the volume and duration of the notes associated with each amino acid are defined by the secondary structure of proteins, computed using DSSP and thereby introducing musical rhythm. We then train a recurrent neural network based on a large set of musical scores generated by this sonification method and use AI to generate musical compositions, capturing the innate relationships between amino acid sequence and protein structure. We then translate the de novo musical data generated by AI into protein sequences, thereby obtaining de novo protein designs that feature specific design characteristics. We illustrate the approach in several examples that reflect the sonification of protein sequences, including multihour audible representations of natural proteins and protein-based musical compositions solely generated by AI. The approach proposed here may provide an avenue for understanding sequence patterns, variations, and mutations and offers an outreach mechanism to explain the significance of protein sequences. The method may also offer insight into protein folding and understanding the context of the amino acid sequence in defining the secondary and higher-order folded structure of proteins and could hence be used to detect the effects of mutations through sound.

Effects of pressure on the structure and lattice dynamics of α-glycine: a combined experimental and theoretical study

This concomitant experimental and theoretical study provides a definitive EOS for α-glycine up to the record pressure of 50 GPa.

Strategy for Modeling the Electrostatic Responses of the Spectroscopic Properties of Proteins

For better understanding and more efficient use of the spectroscopic probes (vibrational and NMR) of the local electrostatic situations inside proteins, appropriate modeling of the properties of those probes is essential. The present study is devoted to examining the strategy for constructing such models. A more well-founded derivation than the ones in previous studies is given in constructing the models. Theoretical analyses are conducted on two representative example cases related to proteins, i.e., the peptide group of the main chains and the CO and NO ligands to the Fe²⁺ ion of heme, with careful treatment of the behavior of electrons in the electrostatic responses and with verification of consistency with observable quantities. It is shown that, for the stretching frequencies and NMR chemical shifts, it is possible to construct reasonable electrostatic interaction models that encompass the situations of hydration and uniform electric field environment and thus are applicable also to the cases of nonuniform electrostatic situations, which are highly expected for inside of proteins.

The interaction strengths and spectroscopy parameters of the C2H2∙∙∙HX and HCN∙∙∙HX complexes (X = F, Cl, CN, and CCH) and related ternary systems valued by fluxes of charge densities: QTAIM, CCFO, and NBO calculations

This theoretical work exhibits a new systematic study of structural parameters, electronic properties, infrared vibration modes, and molecular topography of hydrogen complexes, namely linear-type HCN⋯HX and T-type C₂H₂⋯HX (X = F, Cl, CN, and CCH). Ideally, the knowledge of the ternary systems of C₂H₂⋯HCN⋯HF and HCN⋯HCN⋯HF whose subparts integrate the linear and T-shaped complexes were used to give support in this current research. By means of computational calculations carried out in both levels B3LYP and MP2, the variations of the HX bond lengths are clearly overestimated in the HCN⋯HX linear complexes. In agreement with the analyses of the electrostatic potentials, the higher intermolecular energies of these complexes agree with the larger red-shifts in the stretch frequencies in HX. Also, the QTAIM descriptors and NBO calculations were used to inspect the interaction strength as well as to confirm the π cloud as a proton accepting center. By taking into account the absorption intensity ratio as a standard parameter to predict the interaction strength and intermolecular characterization, the formalism of the charge-charge flux-overlap modified (CCFO) was applied.

Correcting the record: the dimers and trimers of trans-N-methylacetamide

Raman jet spectroscopy reveals three N-methylacetamide molecules organizing into a ring structure, previously overlooked in computations.

An innovative synergistic grid approach to the computational study of protein aggregation mechanisms

Thanks to the advances in grid technologies, we are able to propose here an evolution of our molecular simulator that, when moving to larger systems, instead of reducing the granularity of the dynamical treatment (as is often done in molecular dynamics studies of such systems) exploits the extra power of the grid approach to the end of preserving the detailed nature of theatomistic formulation of the interaction. Key steps of such evolution are: (1) the assemblage of the interaction based on a composition of the ab initio intramolecular data and a portable parameterization of the intermolecular potential linking ab initio evaluation of intramolecular potentials and the partitioning of molecular polarizability; (2) the exploitation of an efficient coordinated porting and running of molecular dynamics codes on the European grid distributed computing infrastructure. As a prototype case study, the N-methylacetamide dimer in vacuo has been considered and the formation of possible conformers is analyzed.

Calculating excited state properties using Kohn-Sham density functional theory

The accuracy of excited states calculated with Kohn-Sham density functional theory using the maximum overlap method has been assessed for the calculation of adiabatic excitation energies, excited state structures, and excited state harmonic and anharmonic vibrational frequencies for open-shell singlet excited states. The computed Kohn-Sham adiabatic excitation energies are improved significantly by post self-consistent field spin-purification, but remain too low compared with experiment with a larger error than time-dependent density functional theory. Excited state structures and vibrational frequencies are also improved by spin-purification. The structures show a comparable accuracy to time-dependent density functional theory, while the harmonic vibrational frequencies are found to be more accurate for the majority of vibrational modes. The computed harmonic vibrational frequencies are also further improved by perturbative anharmonic corrections, suggesting a good description of the potential energy surface. Overall, excited state Kohn-Sham density functional theory is shown to provide an efficient method for the calculation of excited state structures and vibrational frequencies in open-shell singlet systems and provides a promising technique that can be applied to study large systems.

Modeling the infrared and circular dichroism spectroscopy of a bridged cyclic diamide

Density functional theory based molecular dynamics simulations are used to study the structure, infrared (IR) spectroscopy, circular dichroism (CD) spectroscopy, and coupling between the amide I vibrations of a bridged cyclic diamide in the gas phase and in aqueous solution. IR spectra computed via the dipole moment time correlation function show a large red-shift of 30 cm(-1) in the amide I vibration in solution compared to the gas phase, and are in good agreement with experiment. Conformationally averaged CD spectra computed using the CIS(D) method are highly sensitive to the structures used, and structures sampled in the aqueous phase simulation are required to obtain qualitatively correct CD spectra. Analysis of the coupling between the amide I modes shows that in the aqueous phase there is an increased localization of the vibrations on the individual peptide groups and a reduction in the mode coupling parameter compared to the gas phase. Overall, the results illustrate the significance of incorporating molecular dynamics in the simulation of IR and CD spectra.

Infrared characterization of the guanine radical cation: finger printing DNA damage

Oxidation of DNA represents a major pathway of genetic mutation. We have applied infrared spectroscopy in 77 K glass with supporting density functional theory (DFT) calculations (EDF1/6-31+G*) to provide an IR signature of the guanine radical cation G(+*), formed as a result of 193 nm photoionization of DNA. Deprotonation of this species to produce the neutral radical G(-H)(*) does not occur in 77 K glass. DFT calculations indicate that the formation of G(+*) within the double helix does not significantly perturb the geometry of the G/C pair, even though there is a significant movement of the N(1) proton away from G toward C. However, this is in stark contrast to drastic changes that are expected if full deprotonation of G/C occurs, producing the G(-H)(*)/C pair. These results are discussed in light of solution-phase time-resolved IR spectroscopic studies and demonstrate the power of IR to follow dynamics of DNA damage in natural environments.

Theoretical spectroscopy of floppy peptides at room temperature. A DFTMD perspective: gas and aqueous phase

Theoretical spectroscopy is mandatory for a precise understanding and assignment of experimental spectra recorded at finite temperature. We review here room temperature DFT-based molecular dynamics simulations for the purpose of interpreting finite temperature infrared spectra of peptides of increasing size and complexity, in terms of temperature-dependent conformational dynamics and flexibility, and vibrational anharmonicities (potential energy surface anharmonicities, vibrational mode couplings and dipole anharmonicities). We take examples from our research projects in order to illustrate the main key-points and strengths of dynamical spectra modeling in that context. The calculations are presented in relation to room temperature gas phase IR-MPD experiments and room temperature liquid phase IR absorption experiments. These illustrations of floppy polypeptides have been chosen in order to convey the following ideas: temperature-dependent spectra modeling is pivotal for a precise understanding of gas phase spectra recorded at room temperature, including conformational dynamics and vibrational anharmonicities; harmonic spectroscopy (as commonly performed in the literature) can be misleading and even erroneous for a proper interpretation of spectra recorded at finite temperature; taking into account vibrational anharmonicities is pivotal for a proper interplay between theory and experiments; amide I-III bands are not necessarily the most relevant fingerprints for unraveling the local structures of peptides and more complex systems; liquid phase simulations have unraveled relationships between the zwitterionic properties of the peptide bonds and infrared signatures. The review presents a state-of-the-art account of the domain and offers perspectives and new developments for future still more challenging applications.

Conformational dependence of anharmonic vibrations in peptides: amide-I modes in model dipeptide

The conformational dependence of a set of anharmonic vibrational parameters for the amide-I modes in peptides has been examined at the level of Hartree-Fock theory. By using glycine dipeptide as a model molecule, the phi-psi maps of diagonal and off-diagonal anharmonicities, local mode mixing angle, zero-order local mode frequencies, as well as intermode coupling, were calculated, and all were found to exhibit certain conformational sensitivities. The characteristics of the phi-psi maps of the diagonal and off-diagonal anharmonicities were found to be complementary to each other, and the latter was found to correlate well with that of the mixing angle, reflecting the fact that these anharmonic parameters are interconnected and all determined by the same set of underlying anharmonic force field. The mean values of the diagonal and off-diagonal anharmonicities were found to be 15.7 cm(-1) and 9.9 cm(-1) respectively. The mean value for the two local mode frequency differences was estimated to be 9.7 cm(-1), showing a nondegenerate local mode picture. For significant peptide conformations, the calculated anharmonic parameters were found to be in reasonable agreement with values obtained at the level of density functional theory as well as values obtained with recent two-dimensional infrared experiments.

Determination of conformational preferences of dipeptides using vibrational spectroscopy

The NMR coupling constants ((3)J(H(N), H(alpha))) of dipeptides indicate that the backbone conformational preferences vary strikingly among dipeptides. These preferences are similar to those of residues in small peptides, denatured proteins, and the coil regions of native proteins. Detailed characterization of the conformational preferences of dipeptides is therefore of fundamental importance for understanding protein structure and folding. Here, we studied the conformational preferences of 13 dipeptides using infrared and Raman spectroscopy. The main advantage of vibrational spectroscopy over NMR spectroscopy is in its much shorter time scale, which enables the determination of the conformational preferences of short-lived states. Accuracy of structure determination using vibrational spectroscopy depends critically on identification of the vibrational parameters that are sensitive to changes in conformation. We show that the frequencies of the amide I band and the A12 ratio of the amide I components of dipeptides correlate with the (3)J(H(N), H(alpha)). These two infrared vibrational parameters are thus analogous to (3)J(H(N), H(alpha)), indicators for the preference for the dihedral angle phi. We also show that the intensities of the components of the amide III bands in infrared spectra and the intensities of the skeletal vibrations in Raman spectra are indicators of populations of the P(II), beta, and alpha(R) conformations. The results show that alanine dipeptide adopts predominantly a PII conformation. The population of the beta conformation increases in valine dipeptides. The populations of the alpha(R) conformation are generally small. These data are in accord with the electrostatic screening model of conformational preferences.

Anharmonicity of amide modes

The principal contributions to the anharmonic coupling of amide vibrations are explored with the objective of comparing recent experiments with density functional theory and evaluating simple models of mode coupling. Experimental information obtained by means of two-dimensional infrared spectroscopy (2D IR) is reasonably well predicted by the computed one- and two-quantum anharmonic modes of amide-A, -I, and -II types in mono-, di- and tripeptides. The expansion of the vibrational energy up to the cubic and quartic coupling of harmonic modes suggested criteria to assess how localized are the forces determining the anharmonicity. The off-diagonal anharmonicity between an amide-A and one other amide mode was shown to be mainly determined by forces involving only these two modes, whereas the off-diagonal anharmonicity of two amide-I modes in peptides depended significantly on forces due to motions other than those of the amide-I type. Both the diagonal and off-diagonal anharmonicities exhibit sensitivity to peptide structures. These results should prove useful in linking 2D IR experimental results to secondary structure. Further, the results are used to evaluate the vibrational exciton model for the mixed-mode anharmonicities of the amide-I transitions.

Cation-Modulated Electron-Transfer Channel: H-Atom Transfer vs Proton-Coupled Electron Transfer with a Variable Electron-Transfer Channel in Acylamide Units

The mechanism of proton transfer (PT)/electron transfer (ET) in acylamide units was explored theoretically using density functional theory in a representative model (a cyclic coupling mode between formamide and the N-dehydrogenated formamidic radical, FF). In FF, PT/ET normally occurs via a seven-center cyclic proton-coupled electron transfer (PCET) mechanism with a N-->N PT and an O-->O ET. However, when different hydrated metal ions are bound to the two oxygen sites of FF, the PT/ET mechanism may significantly change. In addition to their inhibition of PT/ET rate, the hydrated metal ions can effectively regulate the FF PT/ET cooperative mechanism to produce a single pathway hydrogen atom transfer (HAT) or a flexible proton coupled electron transfer (PCET) mechanism by changing the ET channel. The regulation essentially originates from the change in the O...O bond strength in the transition state, subject to the binding ability of the hydrated metal ions. In general, the high valent metal ions and those with large binding energies can promote HAT, and the low valent metal ions and those with small binding energies favor PCET. Hydration may reduce the Lewis acidity of cations, and thus favor PCET. Good correlations among the binding energies, barrier heights, spin density distributions, O...O contacts, and hydrated metal ion properties have been found, which can be used to interpret the transition in the PT/ET mechanism. These findings regarding the modulation of the PT/ET pathway via hydrated metal ions may provide useful information for a greater understanding of PT/ET cooperative mechanisms, and a possible method for switching conductance in nanoelectronic devices.

Computation of the amide I band of polypeptides and proteins using a partial Hessian approach

A partial Hessian approximation for the computation of the amide I band of polypeptides and proteins is introduced. This approximation exploits the nature of the amide I band, which is largely localized on the carbonyl groups of the backbone amide residues. For a set of model peptides, harmonic frequencies computed from the Hessian comprising only derivatives of the energy with respect to the displacement of the carbon, oxygen, and nitrogen atoms of the backbone amide groups introduce mean absolute errors of 15 and 10 cm(-1) from the full Hessian values at the Hartree-Fock/STO-3G and density functional theory EDF16-31G(*) levels of theory, respectively. Limiting the partial Hessian to include only derivatives with respect to the displacement of the backbone carbon and oxygen atoms yields corresponding errors of 24 and 22 cm(-1). Both approximations reproduce the full Hessian band profiles well with only a small shift to lower wave number. Computationally, the partial Hessian approximation is used in the solution of the coupled perturbed Hartree-Fock/Kohn-Sham equations and the evaluation of the second derivatives of the electron repulsion integrals. The resulting computational savings are substantial and grow with the size of the polypeptide. At the HF/STO-3G level, the partial Hessian calculation for a polypeptide comprising five tryptophan residues takes approximately 10%-15% of the time for the full Hessian calculation. Using the partial Hessian method, the amide I bands of the constituent secondary structure elements of the protein agitoxin 2 (PDB code 1AGT) are calculated, and the amide I band of the full protein estimated.

Vibrational anharmonic calculations in solution: Performance of various DFT approaches

We report anharmonic spectra calculated for formaldehyde in acetonitrile solution using the quartic force field obtained for various DFT/solvent coupled models. A statistical study has been carried out for each mode by using several classes of DFT functionals and comparing them to the reference ab-initio CCSD(T)/cc-pVQZ calculations. Results lead to the recommended use of hybrid functionals associated with the 6-31+G** basis set and the Polarized Continuum model (PCM) to predict the expected shifts relative to the gas phase.

Picosecond time-resolved infrared study of 2-aminopurine ionisation in solution

Two photon ionisation of 2-aminopurine (2AP) has been monitored following 267 nm irradiation in neutral and acidic aqueous solutions using picosecond time-resolved infrared spectroscopy (ps-TRIR). The transient infrared spectra obtained in neutral and acidic conditions show significant differences that are consistent with the formation of different species, namely the 2AP radical cation, 2AP+*, in acidic conditions and the uncharged radical, 2AP*(-H+), in neutral conditions. The ps-TRIR data indicate that deprotonation of 2AP+* in neutral solution takes place within <2 ps following photoionisation. DFT calculations (EDF1/6-31+G*) were used to support the assignment of the intermediates observed in these spectroscopic experiments.

New Theoretical and Experimental Infrared Results on Formaldehyde in Solution

An extension of our combined procedure to determine a complete quartic force field and to resolve a vibrational problem thanks to a variational treatment is proposed for quantitative calculations of vibrational spectra in solution. Energies and gradients are obtained through a polarizable continuum model (PCM), the so-called self-consistent isodensity (SCI)-PCM. We present in this paper new experimental results dealing with formaldehyde in solution in cyclohexane, chloroform, THF, acetonitrile, DMSO and water; the obtained vibrational spectra are then compared with CCSD(T)/cc-pVQZ calculations. In addition, density functional theory (DFT) calculations have been carried out with the aim of both anticipating and positioning these approaches for larger sized molecules.

All-cis Cyclic Peptides

Amide bonds -NH-CO- preferentially exist in trans conformations, the cis conformation being thermodynamically unfavored with respect to the trans by about 2 kcal/mol. Yet, the main reason most proteins or peptides cannot be made from cis-peptide plaques only lies in that connecting them into open chains appears to be sterically impracticable. It is possible, however, to build all-cis cyclic peptides in which all cis-plaques are efficiently locked. The present work examines, through quantum calculations, the structural and energetic issues associated with these peculiar arrangements. Systematic exploration at DFT-B3LYP level of the potential-energy surfaces for all-cis cyclopolyglycines cG(n)(c) (n = 2-10,15), and to a lesser extent, for all-cis cyclopolyalanines and all-cis cyclopolyphenylalanines confirms that all these structures are true minima. Optimal ring size occurs around eight peptide units, resulting in planar cG7(c), cG8(c), and cG9(c). In smaller systems, the ring strain is relieved through nonplanar cup-like distortions, particularly in cG6(c). From 10 peptide units and beyond, the ring framework distorts into a saddle-edge shape. These molecules disclose some molecular flexibility, as combinatorial tilting of the plaques may give sets of minima close in energy. Indexes based on isodesmic reactions are used to estimate the energy for joining all-cis or all-trans plaques into cyclic peptides. One of them, the mean plaque-junction energy (MPJE) suggests that within sensible sizes from six peptide units and beyond, all-cis plaque association is almost equally favorable as all-trans one. The frame of radiating cis-amide bonds can be considered as defining a new kind of peptidic material, endowed with specific self-assembling properties.

How to Model Solvation of Peptides? Insights from a Quantum-mechanical and Molecular Dynamics Study ofN-Methylacetamide. 1. Geometries, Infrared, and Ultraviolet Spectra in Water

This paper represents the first part of a study of solvation in peptides using quantum-mechanical and classical approaches. In this study, the peptide is modeled as its simplest analogue, namely, N-methyl-acetamide, and the effects of the solvent (here water, and in the second part of the study, water and acetone) are introduced at three different levels, e.g., through a continuum description, using solute-solvent clusters, and using the same clusters embedded in an external continuum. In turn, the solute-solvent clusters have been obtained in two alternative ways, either by using QM optimization procedures or extracting a proper set of structures from MD simulations. In this part of the study, geometries, IR, and UV spectra are calculated in terms of the different solvation models, and the results are analyzed and compared to get insights about different aspects of solvation involving dynamic and static effects on one hand and bulk or specific interactions on the other hand.