Model-Free or Not?

Relaxation in nuclear magnetic resonance is a powerful method for obtaining spatially resolved, timescale-specific dynamics information about molecular systems. However, dynamics in biomolecular systems are generally too complex to be fully characterized based on NMR data alone. This is a familiar problem, addressed by the Lipari-Szabo model-free analysis, a method that captures the full information content of NMR relaxation data in case all internal motion of a molecule in solution is sufficiently fast. We investigate model-free analysis, as well as several other approaches, and find that model-free, spectral density mapping, LeMaster’s approach, and our detector analysis form a class of analysis methods, for which behavior of the fitted parameters has a well-defined relationship to the distribution of correlation times of motion, independent of the specific form of that distribution. In a sense, they are all “model-free.” Of these methods, only detectors are generally applicable to solid-state NMR relaxation data. We further discuss how detectors may be used for comparison of experimental data to data extracted from molecular dynamics simulation, and how simulation may be used to extract details of the dynamics that are not accessible via NMR, where detector analysis can be used to connect those details to experiments. We expect that combined methodology can eventually provide enough insight into complex dynamics to provide highly accurate models of motion, thus lending deeper insight into the nature of biomolecular dynamics

Temperature dependence of protein dynamics simulated with three different water models

The effect of variation of the water model on the temperature dependence of protein and hydration water dynamics is examined by performing molecular dynamics simulations of myoglobin with the TIP3P, TIP4P, and TIP5P water models and the CHARMM protein force field at temperatures between 20 and 300 K. The atomic mean-square displacements, solvent reorientational relaxation times, pair angular correlations between surface water molecules, and time-averaged structures of the protein are all found to be similar, and the protein dynamical transition is described almost indistinguishably for the three water potentials. The results provide evidence that for some purposes changing the water model in protein simulations without a loss of accuracy may be possible

NMR Relaxometry Accessing the Relaxation Spectrum in Molecular Glass Formers

It is a longstanding question whether universality or specificity characterize the molecular dynamics underlying the glass transition of liquids. In particular, there is an ongoing debate to what degree the shape of dynamical susceptibilities is common to various molecular glass formers. Traditionally, results from dielectric spectroscopy and light scattering have dominated the discussion. Here, we show that nuclear magnetic resonance (NMR), primarily field-cycling relaxometry, has evolved into a valuable method, which provides access to both translational and rotational motions, depending on the probe nucleus. A comparison of ¹H NMR results indicates that translation is more retarded with respect to rotation for liquids with fully established hydrogen-bond networks; however, the effect is not related to the slow Debye process of, for example, monohydroxy alcohols. As for the reorientation dynamics, the NMR susceptibilities of the structural (α) relaxation usually resemble those of light scattering, while the dielectric spectra of especially polar liquids have a different broadening, likely due to contributions from cross correlations between different molecules. Moreover, NMR relaxometry confirms that the excess wing on the high-frequency flank of the α-process is a generic relaxation feature of liquids approaching the glass transition. However, the relevance of this feature generally differs between various methods, possibly because of their different sensitivities to small-amplitude motions. As a major advantage, NMR is isotope specific; hence, it enables selective studies on a particular molecular entity or a particular component of a liquid mixture. Exploiting these possibilities, we show that the characteristic Cole–Davidson shape of the α-relaxation is retained in various ionic liquids and salt solutions, but the width parameter may differ for the components. In contrast, the low-frequency flank of the α-relaxation can be notably broadened for liquids in nanoscopic confinements. This effect also occurs in liquid mixtures with a prominent dynamical disparity in their components

NMR and MD studies of the temperature-dependent dynamics of RNA YNMG-tetraloops

In a combined NMR/MD study, the temperature-dependent changes in the conformation of two members of the RNA YNMG-tetraloop motif (cUUCGg and uCACGg) have been investigated at temperatures of 298, 317 and 325 K. The two members have considerable different thermal stability and biological functions. In order to address these differences, the combined NMR/MD study was performed. The large temperature range represents a challenge for both, NMR relaxation analysis (consistent choice of effective bond length and CSA parameter) and all-atom MD simulation with explicit solvent (necessity to rescale the temperature). A convincing agreement of experiment and theory is found. Employing a principle component analysis of the MD trajectories, the conformational distribution of both hairpins at various temperatures is investigated. The ground state conformation and dynamics of the two tetraloops are indeed found to be very similar. Furthermore, both systems are initially destabilized by a loss of the stacking interactions between the first and the third nucleobase in the loop region. While the global fold is still preserved, this initiation of unfolding is already observed at 317 K for the uCACGg hairpin but at a significantly higher temperature for the cUUCGg hairpin

C60 solvate with (1,1,2)-trichloroethane: dynamic statistical disorder and mixed conformation

We present a full characterization of the orientationally disordered cocrystal of C-60 with (1,1,2)-triChloroethane (C2H3Cl3), by means of X-ray diffraction, Raman spectroscopy, and broadband dielectric spectroscopy. Our results include the determination of molecular con formations, lattice structure, positional disorder, and, molecular reorientational dynamics down to the microsecond time scale. We find that, while in the disordered solid phase of pure C2H3Cl3 the molecules exist only in the gauche conformation, both gauche and transoid conformers are present in the solvate, where they occupy the largest interstitial cavities between the fullerene species. The two C2H3Cl3 conformers exhibit separate, independent relaxations, exhibiting simply activated behavior in the measured temperature range. The relaxation, of the transoid conformer, which has twice the dipole moment of the gmiehe isomer, is significantly slower than that of the latter, due to the high polarizability of C-60 resulting in an electrostatic drag against the reorientations of the dipolar C2H3O3 species. The observation of two distinct, simply activated relaxations freezing at distinct temperatures indicates:that they are not truly many-body relaxations, which may be rationalized considering:that the C2H3Cl3 molecules are separated by the relatively bulky C-60 spacers.Peer ReviewedPostprint (published version

Investigation of Slow Dynamics in Proteins: NMR Pulse Sequence Development and Application in Triosephosphate Isomerase

The dynamics of proteins on the millisecond time scale are on the same time scale as typical catalytic turnover rates, and can sometimes be closely related to enzymes' functions. Solid state NMR, equipped with magic angle spinning, is a very good technique to detect such millisecond dynamics, because it is suitable for many protein systems such as membrane proteins, and the anisotropic interactions recoupled in the solid state NMR can supply valuable geometric information regarding the dynamics. In this thesis, I mainly focus on the developing new dynamics detection pulse sequences based on previous Centerband-Only Detection of Exchange (CODEX) experiment and applying CODEX experiments to an enzyme system, triosephosphate isomerase (TIM), for studying the function of the millisecond dynamics in catalysis. Two newly developed pulse sequences, Dipolar CODEX and R-CODEX use the 13C-15N (Dipolar CODEX) and 1H-13C or 1H-15N (R-CODEX) dipolar couplings to detect dynamics. Compared with the chemical shift anisotropy used in the CODEX experiment, the dipolar coupling has a more direct relationship with the molecular geometry and could be better for extracting geometric information regarding reorientations. A special characteristic of the R-CODEX sequence is that the use of an R-type dipolar recoupling sequence can suppress the effect of 1H-1H homonuclear couplings. This approach paves the way to detect both the correlation time and reorientational angle of the dynamics in fully protonated samples. These two pulse sequences are tested by detecting the π flip motion of urea and methylsulfone imidazole. The R-CODEX experiment is compared with two other millisecond dynamics detection methods: 2D-exchange experiments and line-shape analysis, using the example of in crystalline L-phenylalanine hydrochloride. The millisecond ring flip motion of the aromatic ring in L-phenylalanine hydrochloride is characterized in detail for the first time. The comparison between these three methods shows that the R-CODEX experiment does not require a chemical shift change in the process of the motion and that it can detect the dynamics even if there is the peak overlap in the spectra. Triosephosphate isomerase (TIM) is a well-known highly efficient enzyme. Its loop motion (loop 6) has been extensively studied and been proven to be correlated with product release and be a rate-limiting step for the catalysis. Another highly conserved loop near the active site, loop 7 also has large changes in dihedral angles during ligand binding. Its motion is suspected to be correlated with loop 6 based on mutant experiments and solution NMR studies. However, the core sequence of loop 7, YGGS, is missing in the solution NMR spectrum. We assigned the GG pair in loop 7 (G209-G210) using 1-13C, 15N glycine labeling and solid state NMR experiments, and detected the loop 7's motion using 1-13C glycine labeling and CODEX experiments. We found that loop 7's motional rate (300+/-100 s-1) at -10oC agrees well with previously detected motional rates of loop 6 extrapolated from higher temperatures using an Arrhenius plot. This suggeststhat the motion of loop 6 probably correlates with loop 7. At the same time, the line-shape analysis for another GG pair (G232-G233), which forms hydrogen bonds with the ligand, indicates a ligand release rate (400+/-100 s-1) similar to loop 7's rate, supporting the hypothesis that the ligand release is also probably correlated with the motion of loop 7 and loop 6