Molecular dynamics study of the mechanical properties of drug loaded model systems: A comparison of a polymersome with a bilayer

In this work we implement a new methodology to study structural and mechanical properties of systems having spherical and planar symmetries throughout Molecular Dynamics simulations. This methodology is applied here to a drug delivery system based in polymersomes, as an example. The chosen model drug was the local anesthetic prilocaine due to previous parameterization within the used coarse grain scheme. In our approach, mass density profiles (MDPs) are used to obtain key structural parameters of the systems, and pressure profiles are used to estimate the curvature elastic parameters. The calculation of pressure profiles and radial MPDs required the development of specific methods, which were implemented in an in-house built version of the GROMACS 2018 code. The methodology presented in this work is applied to characterize poly(ethylene oxide)-poly(butadiene) polymersomes and bilayers loaded with the model drug prilocaine. Our results show that structural properties of the polymersome membrane could be obtained from bilayer simulations, with significantly lower computational cost compared to whole polymersome simulations, but the bilayer simulations are insufficient to get insights on their mechanical aspects, since the elastic parameters are canceled out for the complete bilayer (as consequence of the symmetry). The simulations of entire polymersomes, although more complex, offer a complementary approach to get insights on the mechanical behavior of the systems.

On the axial chirality of leucoindigo

The diagonal components and the trace of two tensors which account for chiroptical response of the leucoindigo molecule C 16 H 12 N 2 O 2 $$ {\mathrm{C}}_{16}{\mathrm{H}}_{12}{\mathrm{N}}_2{\mathrm{O}}_2 $$ that is, static anapole magnetizability, and dynamic electric dipole-magnetic dipole polarisability depending on the frequency of impinging light, are a function of the ϕ $$ \phi $$ dihedral angle of torsion about the central CC bond, assumed to lie in the y $$ y $$ direction of the coordinate system. They vanish for symmetry reasons at ϕ = 0 ∘ $$ \phi ={0}^{\circ } $$ and ϕ = 180 ∘ $$ \phi ={180}^{\circ } $$ , corresponding respectively to C 2 v $$ {C}_{2v} $$ and C 2 h $$ {C}_{2h} $$ point group symmetries, that is, cis and trans conformers characterized by the presence of molecular symmetry planes. Nonetheless, diagonal components and average value of static anapole polarizability and optical rotation tensors vanish at ϕ = 90 ∘ $$ \phi ={90}^{\circ } $$ , where leucondigo is unquestionably chiral from the geometrical viewpoint. Vanishing values of the average chiroptical properties have been observed also in the proximity of other ϕ $$ \phi $$ angles. Attempts have been made to explain the occurrence of accidental zeros of chiroptical properties in terms of transition frequencies and scalar products appearing in the numerator of their quantum mechanical definitions. Within the electric dipole approximation, the presence of anomalous vanishing values of tensor components of anapole magnetizability and electric-magnetic dipole polarizability is ascribed to physical achirality, arising from the lack of either toroidal or spiral electron flow along the x $$ x $$ , y $$ y $$ and z $$ z $$ directions.

Physical achirality in geometrically chiral rotamers of hydrazine and boranylborane molecules

The diagonal components and the trace of tensors which account for chiroptical response of the hydrazine molecule N₂ H₄ , that is, static anapole magnetizability and frequency-dependent electric dipole-magnetic dipole polarisability, are a function of the ϕ ≡ ∠ H─N─N─H dihedral angle. They vanish for symmetry reasons at ϕ = 0° and ϕ = 180°, corresponding respectively to C_2v and C_2h point group symmetries, that is, cis and trans conformers characterized by the presence of molecular symmetry planes. Nonetheless, vanishing diagonal components have been observed also in the proximity of ∠ H─N─N─H = 90°, in which the point group symmetry is C₂ and hydrazine is unquestionably chiral. In the boranylborane molecule B₂ H₄ , assuming the B─B bond in the y direction, the a_yy component of the anapole magnetizability tensor approximately vanishes for dihedral angles ∠ H─B─B─H corresponding to chiral rotamers which belong to D₂ symmetry. Such anomalous effects have been ascribed to physical achirality of these conformers, that is, to their inability to sustain electronic current densities inducing either anapole moments, or electric and magnetic dipole moments, about the chiral axis connecting heavier atoms, as well as perpendicular directions. In other terms, the structure of certain geometrically chiral rotamers may be such that neither toroidal nor helical flow, which determine chiroptical phenomenology, can take place in the presence of perturbing fields parallel or orthogonal to the chiral axis.

A Density Functional Theory Study of Optical Rotation in Some Aziridine and Oxirane Derivatives

We present time-dependent density functional theory (TDDFT) calculations of the electronic optical rotation (ORP) for seven oxirane and two aziridine derivatives in the gas phase and in solution and compare the results with the available experimental values. For seven of the studied molecules it is the first time that their optical rotation was studied theoretically and we have therefore investigated the influence of several settings in the TDDFT calculations on the results. This includes the choice of the one-electron basis set, the exchange-correlation functional or the particular polarizable continuum model (PCM). We can confirm that polarized quadruple zeta basis sets augmented with diffuse functions are necessary for converged results and find that the aug-pc-3 basis set is a viable alternative to the frequently employed aug-cc-pVQZ basis set. Based on our study, we cannot recommend the generalized gradient functional KT3 for calculations of the ORP in these compounds, whereas the hybrid functional PBE0 gives results quite similar to the long-range correct CAM-B3LYP functional. Finally, we observe large differences in the solvent effects predicted by the integral equation formalism of PCM and the SMD variant of PCM. For the majority of solute/solvent combinations in this study, we find that the SMD model in combination with the PBE0 functional and the aug-pc-3 basis set gives the best agreement with the experimental values.

Magnesium interactions with a CX26 connexon in lipid bilayers

Following our previous work, where we described the interaction of calcium with the Cx26 hemichannel, we further explore the same system by atomistic molecular dynamics simulations considering a different di-cation, magnesium. Specifically, the interaction of magnesium di-cation with the previously reported calcium binding sites (ASP2, ASP117, ASP159, GLU114, GLU119, GLU120, and VAL226) was investigated to identify similarities and differences between them. In order to do so, four extensive simulations were carried out. Two of them considered a Cx26 hemichannel embedded on a POPC bilayer with one of the di-cations and a sodium-chlorine solution. For the remaining two, no di-cations were included and a sodium-chlorine or potassium-chlorine solution was considered. Potassium has a similar atomic mass to calcium, and sodium to magnesium, but they both differ in charge (1e and 2e respectively). Magnesium and calcium, even having the same charge, showed different affinity for the explored protein. From the calcium binding sites referred above, we found that the magnesium di-cations only binds strongly to the GLU114 site of one connexin. For the sodium and potassium simulations, no specific interactions with the protein were found. Altogether, these results suggest that mass and steric effects play an important role in determining cation binding to Cx26 hemichannels.

Calcium interactions with Cx26 hemmichannel: Spatial association between MD simulations biding sites and variant pathogenicity

Connexinophaties are a collective of diseases related to connexin channels and hemichannels. In particular many Cx26 alterations are strongly associated to human deafness. Calcium plays an important role on this structures regulation. Here, using calcium as a probe, extensive atomistic Molecular Dynamics simulations were performed on the Cx26 hemichannel embedded in a lipid bilayer. Exploring different initial conditions and calcium concentration, simulation reached ∼4 μs. Several analysis were carried out in order to reveal the calcium distribution and localization, such as electron density profiles, density maps and distance time evolution, which is directly associated to the interaction energy. Specific amino acid interactions with calcium and their stability were capture within this context. Few of these sites such as, GLU42, GLU47, GLY45 and ASP50, were already suggested in the literature. Besides, we identified novel calcium biding sites: ASP2, ASP117, ASP159, GLU114, GLU119, GLU120 and VAL226. To the best of our knowledge, this is the first time that these sites are reported within this context. Furthermore, since various pathologies involving the Cx26 hemichannel are associated with pathogenic variants in the corresponding CJB2 gene, using ClinVar, we were able to spatially associate the 3D positions of the identified calcium binding sites within the framework of this work with reported pathogenic variants in the CJB2 gene. This study presents a first step on finding associations between molecular features and pathological variants of the Cx26 hemichannel.

Diblock copolymer bilayers as model for polymersomes: A coarse grain approach

This paper presents a new model for polymersomes developed using a poly(ethylene oxide)-poly(butadiene) diblock copolymer bilayer. The model is based on a coarse-grained approach using the MARTINI force field. Since no MARTINI parameters exist for poly(butadiene), we have refined these parameters using quantum mechanical calculations and molecular dynamics simulations. The model has been validated using extensive molecular dynamics simulations in systems with several hundred polymer units and reaching up to 6 μs. These simulations show that the copolymer coarse grain model self-assemble into bilayers and that NPT and NP_NγT ensemble runs reproduce key structural and mechanical experimental properties for different copolymer length chains with a similar hydrophilic weight fraction.

Mechanical properties of drug loaded diblock copolymer bilayers: A molecular dynamics study

In this work, we present results of coarse-grained simulations to study the encapsulation of prilocaine (PLC), both neutral and protonated, on copolymer bilayers through molecular dynamics simulations. Using a previously validated membrane model, we have simulated loaded bilayers at different drug concentrations and at low (protonated PLC) and high (neutral PLC) pH levels. We have characterized key structural parameters of the loaded bilayers in order to understand the effects of encapsulation of PLC on the bilayer structure and mechanical properties. Neutral PLC was encapsulated in the hydrophobic region leading to a thickness increase, while the protonated species partitioned between the water phase and the poly(ethylene oxide)-poly(butadiene) (PBD) interface, relaxing the PBD region and leading to a decrease in the thickness. The tangential pressures of the studied systems were calculated, and their components were decomposed in order to gain insights on their compensation. In all cases, it is observed that the loading of the membrane does not significantly decrease the stability of the bilayer, indicating that the system could be used for drug delivery.

Electric Dipole-Magnetic Dipole Polarizability and Anapole Magnetizability of Hydrogen Peroxide as Functions of the HOOH Dihedral Angle

The trace of tensors that account for chiroptical response of the H₂O₂ molecule is a function of the HO-OH dihedral angle. It vanishes at 0° and 180°, due to the presence of molecular symmetry planes, but also for values in the range 90-100° of this angle, in which the molecule is unquestionably chiral. Such an atypical effect is caused by counterbalancing contributions of diagonal tensor components with nearly maximal magnitude but opposite sign, determined by electron flow in open or closed helical paths, and associated with induced electric and magnetic dipole moments and anapole moments. For values of dihedral angle external to the 90-100° interval, the helical paths become smaller in size, thus reducing the amount of cancellation among diagonal components. Shrinking of helical paths determines the appearance of extremum values of tensor traces approximately at 50° and 140° dihedral angles.

Report on the sixth blind test of organic crystal structure prediction methods

The sixth blind test of organic crystal structure prediction (CSP) methods has been held, with five target systems: a small nearly rigid molecule, a polymorphic former drug candidate, a chloride salt hydrate, a co-crystal and a bulky flexible molecule. This blind test has seen substantial growth in the number of participants, with the broad range of prediction methods giving a unique insight into the state of the art in the field. Significant progress has been seen in treating flexible molecules, usage of hierarchical approaches to ranking structures, the application of density-functional approximations, and the establishment of new workflows and `best practices' for performing CSP calculations. All of the targets, apart from a single potentially disordered Z' = 2 polymorph of the drug candidate, were predicted by at least one submission. Despite many remaining challenges, it is clear that CSP methods are becoming more applicable to a wider range of real systems, including salts, hydrates and larger flexible molecules. The results also highlight the potential for CSP calculations to complement and augment experimental studies of organic solid forms.

Crystal Structure Prediction from First Principles: The Crystal Structures of Glycine

Here we present the results of our unbiased searches of glycine polymorphs obtained using the Genetic Algorithms search implemented in Modified Genetic Algorithm for Crystals coupled with the local optimization and energy evaluation provided by Quantum Espresso. We demonstrate that it is possible to predict the crystal structures of a biomedical molecule using solely first principles calculations. We were able to find all the ambient pressure stable glycine polymorphs, which are found in the same energetic ordering as observed experimentally and the agreement between the experimental and predicted structures is of such accuracy that the two are visually almost indistinguishable.

The structures of two aldazines: [1,1'-(1E,1'E)-hydrazine-1,2-diylidenebis(methan-1-yl-1-ylidene)dinaphthalen-2-ol] (Lumogen) and 2,2'-(1E,1'E)-hydrazine-1,2-diylidenebis(methan-1-yl-1-ylidene)diphenol (salicylaldazine) in the solid state and in solution

A combination of NMR spectroscopy and theoretical methods Density functional theory including dispersion corrections (DFT-D) was used to study the structures of Lumogen and salicylaldazine. In the solid state, Lumogen exists as the dihydroxy tautomer 1a (an azine, C=N-N=C) as was already known from an X-ray determination. In a deuterated dimethyl sulfoxide solution, another tautomer is observed besides 1a; its structure corresponds to the hydroxy-oxo tautomer 1b (a hydrazone, C=N-NH-Csp(2)). In what concerns salicylaldazine, we have observed only the dihydroxy tautomer 2a.

Electric field effects on nuclear magnetic shielding of the 1:1 and 2:1 (homo and heterochiral) complexes of XOOX' (X, X' = H, CH3) with lithium cation and their chiral discrimination

The set of 1:1 and 2:1 complexes of XOOX' (X, X' = H, CH(3)) with lithium cation has been studied to determine if they are suitable candidates for chiral discrimination in an isotropic medium via nuclear magnetic resonance spectroscopy. Conventional nuclear magnetic resonance is unable to distinguish between enantiomers in the absence of a chiral solvent. The criterion for experimental detection is valuated by the isotropic part of nuclear shielding polarisability tensors, related to a pseudoscalar of opposite sign for two enantiomers. The study includes calculations at coupled Hartree-Fock and density functional theory schemes for (17)O nucleus in each compound. Additional calculations for (1)H are also included for some compounds. A huge static homogeneous electric field, perpendicular to the magnetic field of the spectromer, as big as ≈1.7 × 10(8) V m(-1) should be applied to observe a shift of ≈1 ppm for (17)O magnetic shielding in the proposed set of complexes.

Towards crystal structure prediction of complex organic compounds--a report on the fifth blind test

Following on from the success of the previous crystal structure prediction blind tests (CSP1999, CSP2001, CSP2004 and CSP2007), a fifth such collaborative project (CSP2010) was organized at the Cambridge Crystallographic Data Centre. A range of methodologies was used by the participating groups in order to evaluate the ability of the current computational methods to predict the crystal structures of the six organic molecules chosen as targets for this blind test. The first four targets, two rigid molecules, one semi-flexible molecule and a 1:1 salt, matched the criteria for the targets from CSP2007, while the last two targets belonged to two new challenging categories - a larger, much more flexible molecule and a hydrate with more than one polymorph. Each group submitted three predictions for each target it attempted. There was at least one successful prediction for each target, and two groups were able to successfully predict the structure of the large flexible molecule as their first place submission. The results show that while not as many groups successfully predicted the structures of the three smallest molecules as in CSP2007, there is now evidence that methodologies such as dispersion-corrected density functional theory (DFT-D) are able to reliably do so. The results also highlight the many challenges posed by more complex systems and show that there are still issues to be overcome.

Transition from exo- to endo- Cu absorption in CuSi(n) clusters: A Genetic Algorithms Density Functional Theory (DFT) Study

The characterization and prediction of the structures of metal silicon clusters is important for nanotechnology research because these clusters can be used as building blocks for nano devices, integrated circuits and solar cells. Several authors have postulated that there is a transition between exo to endo absorption of Cu in Si(n) clusters and showed that for n larger than 9 it is possible to find endohedral clusters. Unfortunately, no global searchers have confirmed this observation, which is based on local optimizations of plausible structures. Here we use parallel Genetic Algorithms (GA), as implemented in our MGAC software, directly coupled with DFT energy calculations to show that the global search of CuSi(n) cluster structures does not find endohedral clusters for n < 8 but finds them for n ≥ 10.

Crystal structure prediction of flexible molecules using parallel genetic algorithms with a standard force field

This article describes the application of our distributed computing framework for crystal structure prediction (CSP) the modified genetic algorithms for crystal and cluster prediction (MGAC), to predict the crystal structure of flexible molecules using the general Amber force field (GAFF) and the CHARMM program. The MGAC distributed computing framework includes a series of tightly integrated computer programs for generating the molecule's force field, sampling crystal structures using a distributed parallel genetic algorithm and local energy minimization of the structures followed by the classifying, sorting, and archiving of the most relevant structures. Our results indicate that the method can consistently find the experimentally known crystal structures of flexible molecules, but the number of missing structures and poor ranking observed in some crystals show the need for further improvement of the potential.

Significant progress in predicting the crystal structures of small organic molecules--a report on the fourth blind test

We report on the organization and outcome of the fourth blind test of crystal structure prediction, an international collaborative project organized to evaluate the present state in computational methods of predicting the crystal structures of small organic molecules. There were 14 research groups which took part, using a variety of methods to generate and rank the most likely crystal structures for four target systems: three single-component crystal structures and a 1:1 cocrystal. Participants were challenged to predict the crystal structures of the four systems, given only their molecular diagrams, while the recently determined but as-yet unpublished crystal structures were withheld by an independent referee. Three predictions were allowed for each system. The results demonstrate a dramatic improvement in rates of success over previous blind tests; in total, there were 13 successful predictions and, for each of the four targets, at least two groups correctly predicted the observed crystal structure. The successes include one participating group who correctly predicted all four crystal structures as their first ranked choice, albeit at a considerable computational expense. The results reflect important improvements in modelling methods and suggest that, at least for the small and fairly rigid types of molecules included in this blind test, such calculations can be constructively applied to help understand crystallization and polymorphism of organic molecules.

Electric quadrupole polarizabilities of nuclear magnetic shielding in some small molecules

Computational procedures, based on (i) the Ramsey common origin approach and (ii) the continuous transformation of the origin of the quantum mechanical current density-diamagnetic zero (CTOCD-DZ), were applied at the Hartree-Fock level to determine electric quadrupole polarizabilities of nuclear magnetic shielding for molecules in the presence of a nonuniform electric field with a uniform gradient. The quadrupole polarizabilities depend on the origin of the coordinate system, but values of the magnetic field induced at a reference nucleus, determined via the CTOCD-DZ approach, are origin independent for any calculations relying on the algebraic approximation, irrespective of size and quality of the (gaugeless) basis set employed. On the other hand, theoretical estimates of the induced magnetic field obtained by single-origin methods are translationally invariant only in the limit of complete basis sets. Calculations of electric quadrupole polarizabilities of nuclear magnetic shielding are reported for H(2), HF, H(2)O, NH(3), and CH(4) molecules.

Calculation of the electric hypershielding at the nuclei of molecules in a strong magnetic field

The third-rank electric hypershielding at the nuclei of 14 small molecules has been evaluated at the Hartree-Fock level of accuracy, by a pointwise procedure for the geometrical derivatives of magnetic susceptibilities and by a straightforward use of its definition within the Rayleigh-Schrodinger perturbation theory. The connection between these two quantities is provided by the Hellmann-Feynman theorem. The magnetically induced hypershielding at the nuclei accounts for distortion of molecular geometry caused by strong magnetic fields and for related changes of magnetic susceptibility. In homonuclear diatomics H(2), N(2), and F(2), a field along the bond direction squeezes the electron cloud toward the center, determining shorter but stronger bond. It is shown that constraints for rotational and translational invariances and hypervirial theorems provide a natural criterion for Hartree-Fock quality of computed nuclear electric hypershielding.

Theoretical study of the adsorption of H on Sin clusters, (n=3–10)

A recently proposed local Fukui function is used to predict the binding site of atomic hydrogen on silicon clusters. To validate the predictions, an extensive search for the more stable SinH (n=3-10) clusters has been done using a modified genetic algorithm. In all cases, the isomer predicted by the Fukui function is found by the search, but it is not always the most stable one. It is discussed that in the cases where the geometrical structure of the bare silicon cluster suffers a considerable change due to the addition of one hydrogen atom, the situation is more complicated and the relaxation effects should be considered.

A third blind test of crystal structure prediction

Following the interest generated by two previous blind tests of crystal structure prediction (CSP1999 and CSP2001), a third such collaborative project (CSP2004) was hosted by the Cambridge Crystallographic Data Centre. A range of methodologies used in searching for and ranking the likelihood of predicted crystal structures is represented amongst the 18 participating research groups, although most are based on the global minimization of the lattice energy. Initially the participants were given molecular diagrams of three molecules and asked to submit three predictions for the most likely crystal structure of each. Unlike earlier blind tests, no restriction was placed on the possible space group of the target crystal structures. Furthermore, Z′ = 2 structures were allowed. Part-way through the test, a partial structure report was discovered for one of the molecules, which could no longer be considered a blind test. Hence, a second molecule from the same category (small, rigid with common atom types) was offered to the participants as a replacement. Success rates within the three submitted predictions were lower than in the previous tests – there was only one successful prediction for any of the three `blind' molecules. For the `simplest' rigid molecule, this lack of success is partly due to the observed structure crystallizing with two molecules in the asymmetric unit. As in the 2001 blind test, there was no success in predicting the structure of the flexible molecule. The results highlight the necessity for better energy models, capable of simultaneously describing conformational and packing energies with high accuracy. There is also a need for improvements in search procedures for crystals with more than one independent molecule, as well as for molecules with conformational flexibility. These are necessary requirements for the prediction of possible thermodynamically favoured polymorphs. Which of these are actually realised is also influenced by as yet insufficiently understood processes of nucleation and crystal growth.

Why Downfield Proton Chemical Shifts Are Not Reliable Aromaticity Indicators

Traces of magnetizability, traces of magnetic shielding at the hydrogen nuclei, and nucleus-independent chemical shift are not reliable aromaticity quantifiers for planar conjugated hydrocarbons. A measure of aromaticity is provided by the out-of-plane tensor components, whose magnitude is influenced by the pi-ring currents. The failure of nucleus-independent chemical shift in this regard was proved for the molecule shown in the abstract graphic, sustaining a diatropic pi-current. The validity of the ring-current model is reaffirmed. [structure: see text]

Ring current effects on nuclear magnetic shielding of carbon in the benzene molecule

The differential Biot-Savart law of classical electrodynamics was applied to develop a ring current model for the magnetic shielding of the carbon nucleus in benzene. It is shown that the local effect of the pi currents, induced by a magnetic field normal to the molecular plane, on the sigmaC out-of-plane shielding tensor component vanishes. However, approximately 10% of sigmaC is due to the shielding contributions from pi current density in the region of the other carbon atoms. Magnetic shielding density maps obtained via quantum mechanical procedures confirm the predictions of the classical model.

Nonlinear response of the benzene molecule to strong magnetic fields

The fourth-rank hypermagnetizability tensor of the benzene molecule has been evaluated at the coupled Hartree-Fock level of accuracy within the conventional common-origin approach, adopting gaugeless basis sets of increasing size and flexibility. The degree of convergence of theoretical tensor components has been estimated allowing for two different coordinate systems. It is shown that a strong magnetic field perpendicular to the plane of the molecule causes a distortion of the electron charge density, which tends to concentrate in the region of the C-C bonds. This charge contraction has a dynamical origin, and can be interpreted as a feedback effect in terms of the classical Lorentz force acting on the electron current density.

Modeling solid-state effects on NMR chemical shifts using electrostatic models

This paper presents a comparison of the embedded ion method (EIM) and the surface charge representation of the electrostatic embedding potential (SCREEP) method, two methods which can be used to calculate solid-state effects on NMR chemical shifts. The results in a selected group of compounds with known single-crystal solid-state NMR data and neutron diffraction structures, confirm that these effects are important in both (13)C and (15)N chemical shifts. The solid-state effects calculated by both methods are similar and of equal statistical quality when compared with the experimental data.

Calculation of the fourth-rank molecular hypermagnetizability of some small molecules

A computational scheme has been developed within the framework of Rayleigh-Schrödinger perturbation theory to evaluate nonlinear interaction energy contributions for a molecule in the presence of an external spatially uniform, time-independent magnetic field. Terms connected with the fourth power of the perturbing field, representing the fourth-rank hypermagnetizabilities of five small molecules, have been evaluated at the coupled Hartree-Fock level of accuracy within the conventional common-origin approach. Gaugeless basis sets of increasing size and flexibility have been employed in a numerical test, adopting two different coordinate systems to estimate the degree of convergence of theoretical tensor components.

Calculation of dipole-shielding polarizabilities (sigma(alphabetagamma)I): the influence of uniform electric field effects on the shielding of backbone nuclei in proteins

A significant contribution to the chemical shielding of a nucleus can arise from uniform electric fields that act to distort the electronic charge distribution surrounding a nucleus and, hence, affect the nuclear shielding. It has been shown by Buckingham (Buckingham, A. D. Can. J. Chem. 1960, 38, 300) that the nuclear magnetic shielding tensor sigmaalphabetaI of a nucleus in the presence of an external weak static uniform electric field E may be expanded using sigmaalphabetaI(E) = sigmaalphabetaI + sigmaalphabetagammaIEgamma + 1/2sigmaalphabetagammadeltaIEgammaEdelta + sigmaalphabeta,gammadeltaIEgammadelta ... The third rank tensor sigmaalphabetagammaI is referred to as the dipole-shielding polarizability and describes the nonlinear response of the electron cloud to first order in E, muI, and B0. We report calculations of sigmaalphabetagammaI for the N, HN, and C' nuclei in N-methyl acetamide (NMA) and show that these tensors can be used to provide considerable insight into the behavior of uniform electric fields upon the shielding of backbone nuclei in proteins. The sigmaalphabetagammaI values for the N, HN, and C' of NMA were calculated using the continuous transformation of the origin of the current density (CTOCD) scheme with the diamagnetic contribution set to zero (CTOCD-DZ). Values are given for the individual tensor components of sigmaalphabetagammaI for each nucleus. To test that the calculations have provided a reasonable estimate for the sigmaalphabetagammaI of N, HN, and C' nuclei in proteins, a pH titration was performed using Hen Lysozyme (HEWL). The pH-induced isotropic shielding changes for the C', N, and HN nuclei in some peptide bonds close to E35 ( approximately <8 A) were extracted from sets of fitted titration curves. Assuming the experimental shielding changes arise solely from uniform electric field effects caused by the deprotonation of E35, without any other pH-induced structural alterations which might lead to a shielding change, the experimental shielding differences were compared to those calculated via the product Agamma(I).Egamma where Agamma(I) = (1/3)sigmaalphaalphagammaIota. The agreement with the experimental data is in many cases reasonable and suggests that, within the Buckingham formalism, the complete sigmaalphabetagammaI tensors reported here will be helpful to resolve the importance of uniform electric fields upon isotropic and anisotropic shielding in proteins and their complexes.

Modeling NMR chemical shifts: a comparison of charge models for solid state effects on 15N chemical shift tensors

This paper presents results from applying different point charge models to take into account intermolecular interactions to model the solid state effects on the 15N NMR chemical shifts tensors. The DFT approach with the BLYP gradient corrected exchange correlation functional has been used because it can include electron correlation effects at a reasonable cost and is able to reproduce 15N NMR chemical shifts with reasonable accuracy. The results obtained with the point charge models are compared with the experimental data and with results obtained using the cluster model, which includes explicitly neighboring molecular fragments. The results show that the point charge models can take into account solid state effects at a cost much lower than the cluster methods.