Dipolar Relaxation of Water Protons in the Vicinity of a Collagen-like Peptide

Quantitative magnetic resonance imaging is one of the few available methods for noninvasive diagnosis of degenerative changes in articular cartilage. The clinical use of the imaging data is limited by the lack of a clear association between structural changes at the molecular level and the measured magnetic relaxation times. In anisotropic, collagen-containing tissues, such as articular cartilage, the orientation dependency of nuclear magnetic relaxation can obscure the content of the images. Conversely, if the molecular origin of the phenomenon would be better understood, it would provide opportunities for diagnostics as well as treatment planning of degenerative changes in these tissues. We study the magnitude and orientation dependence of the nuclear magnetic relaxation due to dipole–dipole coupling of water protons in anisotropic, collagenous structures. The water–collagen interactions are modeled with molecular dynamics simulations of a small collagen-like peptide dissolved in water. We find that in the vicinity of the collagen-like peptide, the dipolar relaxation of water hydrogen nuclei is anisotropic, which can result in orientation-dependent relaxation times if the water remains close to the peptide. However, the orientation-dependency of the relaxation is different from the commonly observed magic-angle phenomenon in articular cartilage MRI.

Quadrupolar 14N NMR Relaxation from Force-Field and Ab Initio Molecular Dynamics in Different Solvents

Quadrupolar NMR spin relaxation rates and corresponding line widths were computed for the quadrupolar nucleus ¹⁴N for neat acetonitrile as well as for 1-methyl-1,3-imidazole and 1-methyl-1,3,4-triazole in different solvents. Molecular dynamics (MD) was performed with forces from the Kohn-Sham (KS) theory (ab initio MD) and force-field molecular mechanics (classical MD), followed by KS electric field gradient (EFG) calculations. For acetonitrile the agreement of the ¹⁴N line width with experiment is very good. Relative line widths for the azole nitrogens are improved over simpler approximations used previously in conjunction with single-point calculations at the multiconfigurational self-consistent field level. Overall, the NMR line widths are computed within a factor of 2 of the experimental values, giving access to reasonable estimates both of the dynamic EFG variance in the solvated systems as well as the associated correlation times that determine the relaxation rates.

Quadrupolar NMR Relaxation from ab Initio Molecular Dynamics: Improved Sampling and Cluster Models versus Periodic Calculations

Quadrupolar NMR relaxation rates are computed for ¹⁷O and ²H nuclei of liquid water, and of ²³Na⁺, and ³⁵Cl^- in aqueous solution via Kohn-Sham (KS) density functional theory ab initio molecular dynamics (aiMD) and subsequent KS electric field gradient (EFG) calculations along the trajectories. The calculated relaxation rates are within about a factor of 2 of experimental results and improved over previous aiMD simulations. The relaxation rates are assessed with regard to the lengths of the simulations as well as configurational sampling. The latter is found to be the more limiting factor in obtaining good statistical sampling and is improved by averaging over many equivalent nuclei of a system or over several independent trajectories. Further, full periodic plane-wave basis calculations of the EFGs are compared with molecular-cluster atomic-orbital basis calculations. The two methods deliver comparable results with nonhybrid functionals. With the molecular-cluster approach, a larger variety of electronic structure methods is available. For chloride, the EFG computations benefit from using a hybrid KS functional.

Prediction of low-field nuclear singlet lifetimes with molecular dynamics and quantum-chemical property surface

Molecular dynamics and quantum chemistry methods are implemented to quantify nuclear spin-1/2 pair singlet-state relaxation rates. Illustrated is the relevant spin-internal-motion mechanism (SIM).

Xenon NMR of liquid crystals confined to cylindrical nanocavities: a simulation study

Coarse-grained simulations show that the ¹²⁹Xe NMR shielding reflects the smooth changes of orientational order in liquid crystals confined to nanocavities.

Curie-type paramagnetic NMR relaxation in the aqueous solution of Ni(ii)

The magnetic field of the Curie spin manifests itself as both the pNMR shielding tensor and Curie relaxation, in analogy with CSA relaxation theory.

Quadrupolar NMR Spin Relaxation Calculated Using Ab Initio Molecular Dynamics: Group 1 and Group 17 Ions in Aqueous Solution

Electric field gradient (EFG) fluctuations for the monoatomic ions (7)Li(+), (23)Na(+), (35)Cl(-), (81)Br(-), and (127)I(-) in aqueous solution are studied using Car-Parrinello ab initio molecular dynamics (aiMD) simulations based on density functional theory. EFG calculations are typically performed with 1024 ion-solvent configurations from the aiMD simulation, using the Zeroth Order Regular Approximation (ZORA) relativistic Hamiltonian. Autocorrelation functions for the spherical EFG tensor elements are computed, transformed into the corresponding spectral densities (under the extreme narrowing condition), and subsequently converted into NMR quadrupolar relaxation rates for the ions. The relaxation rates are compared with experimental data. The order of magnitude is correctly predicted by the simulations. The computational protocol is tested in detail for (81)Br(-).

An extrapolation method for the efficient calculation of molecular response properties within Born-Oppenheimer molecular dynamics

The calculation of molecular response properties in dynamic molecular systems is a major challenge that requires sampling over many steps of, e.g., Born-Oppenheimer molecular dynamics (BO-MD) simulations. We present an extrapolation scheme to accelerate such calculations for multiple steps within BO-MD trajectories or equivalently within other sampling methods of conformational space. The extrapolation scheme is related to the one introduced by Pulay and Fogarasi [Chem. Phys. Lett., 2004, 386, 272] for self-consistent field (SCF) energy calculations. We extend the extrapolation to the quantities within our density matrix-based Laplace-transformed coupled perturbed SCF (DL-CPSCF) method that allows for linear-scaling calculations of response properties for large molecular systems. Here, we focus on the example of calculating NMR chemical shifts for which the number of required DL-CPSCF iterations reduces by roughly 40-70%.

Utilizing a water-soluble cryptophane with fast xenon exchange rates for picomolar sensitivity NMR measurements

Hyperpolarized (129)Xe chemical exchange saturation transfer ((129)Xe Hyper-CEST) NMR is a powerful technique for the ultrasensitive, indirect detection of Xe host molecules (e.g., cryptophane-A). Irradiation at the appropriate Xe-cryptophane resonant radio frequency results in relaxation of the bound hyperpolarized (129)Xe and rapid accumulation of depolarized (129)Xe in bulk solution. The cryptophane effectively "catalyzes" this process by providing a unique molecular environment for spin depolarization to occur, while allowing xenon exchange with the bulk solution during the hyperpolarized lifetime (T(1) ≈ 1 min). Following this scheme, a triacetic acid cryptophane-A derivative (TAAC) was indirectly detected at 1.4 picomolar concentration at 320 K in aqueous solution, which is the record for a single-unit xenon host. To investigate this sensitivity enhancement, the xenon binding kinetics of TAAC in water was studied by NMR exchange lifetime measurement. At 297 K, k(on) ≈ 1.5 × 10(6) M(-1) s(-1) and k(off) = 45 s(-1), which represent the fastest Xe association and dissociation rates measured for a high-affinity, water-soluble xenon host molecule near rt. NMR line width measurements provided similar exchange rates at rt, which we assign to solvent-Xe exchange in TAAC. At 320 K, k(off) was estimated to be 1.1 × 10(3) s(-1). In Hyper-CEST NMR experiments, the rate of (129)Xe depolarization achieved by 14 pM TAAC in the presence of radio frequency (RF) pulses was calculated to be 0.17 μM·s(-1). On a per cryptophane basis, this equates to 1.2 × 10(4)(129)Xe atoms s(-1) (or 4.6 × 10(4) Xe atoms s(-1), all Xe isotopes), which is more than an order of magnitude faster than k(off), the directly measurable Xe-TAAC exchange rate. This compels us to consider multiple Xe exchange processes for cryptophane-mediated bulk (129)Xe depolarization, which provide at least 10(7)-fold sensitivity enhancements over directly detected hyperpolarized (129)Xe NMR signals.