Coupling of the overall molecular motion with the conformational transitions. II. The full rotational problem

The method proposed in the companion paper for analysing the coupling between overall and internal dynamics is applied to the study of the full rotational motion of a molecule with one internal degree of freedom. For systems characterized by a finite set of stable conformers determined by the minima of the intramolecular potential, a simplified time evolution operator of mixed type is derived, with the continuous diffusion equation and the generalized random walk operator representing the overall rotation and the internal dynamics, respectively. The dependence on the conformational state of the rotational diffusion tensor is one source of coupling between these two types of motion. Another source is represented by the recoil rotations acting on each subunit during a conformational transition. Both conformational-dependent rotational diffusion tensors and recoil rotations can be calculated from a model for the friction exerted by the solvent. Some applications of the theory are presented in relation to the butane molecule and the molecules having the structure of biphenyl, with particular emphasis on the calculation of the experimental observables in NMR and dielectric relaxation measurements.     

Reaction mechanism in crystalline solids: kinetics and conformational dynamics of the Norrish type II biradicals from α-adamantyl-p-methoxyacetophenone

In an effort to determine the details of the solid-state reaction mechanism and diastereoselectivity in the Norrish type II and Yang cyclization of crystalline α-adamantyl-p-methoxyacetophenone, we determined its solid-state quantum yields and transient kinetics using nanocrystalline suspensions. The transient spectroscopy measurements were complemented with solid-state NMR spectroscopy spin-lattice relaxation experiments using isotopically labeled samples and with the analysis of variable-temperature anisotropic displacement parameters from single-crystal X-ray diffraction to determine the rate of interconversion of biradical conformers by rotation of the globular adamantyl group. Our experimental findings include a solid-state quantum yield for reaction that is 3 times greater than that in solution, a Norrish type II hydrogen-transfer reaction that is about 8 times faster in crystals than in solution, and a biradical decay that occurs on the same time scale as conformational exchange, which helps to explain the diastereoselectivity observed in the solid state.     

Conformational flexibility of a microcrystalline globular protein: order parameters by solid-state NMR spectroscopy

The majority of protein structures are determined in the crystalline state, yet few methods exist for the characterization of dynamics for crystalline biomolecules. Solid-state NMR can be used to probe detailed dynamic information in crystalline biomolecules. Recent advances in high-resolution solid-state NMR have enabled the site-specific assignment of (13)C and (15)N nuclei in proteins. With the use of multidimensional separated-local-field experiments, we report the backbone and side chain conformational dynamics of ubiquitin, a globular microcrystalline protein. The measurements of molecular conformational order parameters are based on heteronuclear dipolar couplings, and they are correlated to assigned chemical shifts, to obtain a global perspective on the sub-microsecond dynamics in microcrystalline ubiquitin. A total of 38 Calpha, 35 Cbeta and multiple side chain unique order parameters are collected, and they reveal the high mobility of ubiquitin in the microcrystalline state. In general the side chains show elevated motion in comparison with the backbone sites. The data are compared to solution NMR order parameter measurements on ubiquitin. The SSNMR measurements are sensitive to motions on a broader time scale (low microsecond and faster) than solution NMR measurements (low nanosecond and faster), and the SSNMR order parameters are generally lower than the corresponding solution values. Unlike solution NMR relaxation-based order parameters, order parameters for (13)C(1)H(2) spin systems are readily measured from the powder line shape data. These results illustrate the potential for detailed, extensive, and site-specific dynamic studies of biopolymers by solid-state NMR.     

Theory of molecular motions in flexible nematogens

Liquid crystal phases are typically formed by molecules having several degrees of internal freedom. These systems exhibit, therefore, complex dynamics, with internal motions superimposed on the rotational diffusion of the whole molecule. The problem of the internal transitions has been treated in terms of a master equation for jumps between configurational sites, derived by projecting the multidimensional diffusion equation for the torsional variables on a suitable set of site functions. The coupling with the overall diffusion has been taken into account explicitly, by considering the conformational dependence of both the mean field torque and the molecular diffusion tensor. A Marcelja-like potential acting on the various molecular moieties has been used, and the frictional effects have been calculated for the different chain conformations. In this way, the rates for the internal transitions are orientation dependent, and the solution of the diffusional problem requires a matrix representation in the full space of angular and site functions. The nematogen 4-n-pentyl-4'-cyanobiphenyl, for which a large amount of experimental data is available from detailed NMR relaxation measurements, is taken as a reference system. The spectral densities of the relevant correlation functions for the deuterons in the various positions of the molecule have been calculated, for different degrees of ordering and different choices of the energetic and hydrodynamic parameters.     

Rotational dynamics and conformational kinetics in liquid crystals

Two particular aspects of solute dynamics in ordered media are analysed on the basis of the solution of multivariate diffusion equations: the effects of the solvation dynamics on the rotational motions of dipolar probes in liquid crystal solvents, and the alteration of reaction pathways in isomerization kinetics caused by the solvent order. The introduction of a suitable solvent coordinate allows the interpretation of high frequency contributions in the rotational correlation functions observed by spectroscopic techniques, namely dielectric dispersion, IR and Raman spectroscopy, ESR lineshapes and optical Kerr effect. For molecular systems undergoing conformational changes, a method is offered to evaluate the modification of the torsional barriers resulting from the anisotropic torques modulated by the molecular shape changes along the reaction coordinate.     

Rotational dynamics and conformational kinetics in liquid crystals

Abstract

Two particular aspects of solute dynamics in ordered media are analysed on the basis of the solution of multivariate diffusion equations: the effects of the solvation dynamics on the rotational motions of dipolar probes in liquid crystal solvents, and the alteration of reaction pathways in isomerization kinetics caused by the solvent order. The introduction of a suitable solvent coordinate allows the interpretation of high frequency contributions in the rotational correlation functions observed by spectroscopic techniques, namely dielectric dispersion, IR and Raman spectroscopy, ESR lineshapes and optical Kerr effect. For molecular systems undergoing conformational changes, a method is offered to evaluate the modification of the torsional barriers resulting from the anisotropic torques modulated by the molecular shape changes along the reaction coordinate.     

Investigations of polypeptide rotational diffusion in aligned membranes by 2H and 15N solid-state NMR spectroscopy

Transmembrane and in-plane oriented peptides have been prepared by solid-phase peptide synthesis, labeled with 3,3,3-2H3-alanine and 15N-leucine at two selected sites, and reconstituted into oriented phophatidylcholine membranes. Thereafter, proton-decoupled 15N and 2H solid-state NMR spectroscopy at sample orientations of the membrane normal parallel to the magnetic field direction have been used to characterize the tilt and rotational pitch angle of these peptides in some detail. In a second step the samples have been tilted by 90 degrees . In this setup the spectral line shapes are sensitive indicators of the rate of rotational diffusion. Whereas monomeric transmembrane peptides exhibit spectral averaging and well-defined resonances, larger complexes are characterized by broad spectral line shapes. In particular the deuterium line shape is sensitive to association of a few transmembrane helices. In contrast, the formation of much larger complexes affects the 15N chemical shift spectrum. The spectra indicate that in liquid crystalline membranes an amphipathic peptide of 14 amino acids exhibits fast rotational diffusion on both the 2H and 15N time scales (>10(-5) s). Extending the sequences to 26 amino acids results in pronounced changes of the 2H solid-state NMR spectrum, whereas the signal intensities of 15N solid-state NMR spectra degrade. Below the phase transition temperature of the phospholipid bilayers, motional averaging on the time scale of the 2H solid-state NMR spectrum ceases for transmembrane and in-plane oriented peptides. Furthermore at temperatures close to the phase transition the total signal intensities of the deuterium solid-state NMR spectra strongly decrease.     

Differential line broadening in MAS solid-state NMR due to dynamic interference

Many MAS (magic angle spinning) solid-state NMR investigations of biologically relevant protein samples are hampered by poor resolution, particularly in the 15N chemical shift dimension. We show that dynamics in the nanosecond-microsecond time scale in solid-state samples can induce significant line broadening of 15N resonances in solid-state NMR experiments. Averaging of 15NH(alpha/beta) multiplet components due to 1H decoupling induces effective relaxation of the 15N coherence in case the N-H spin pair undergoes significant motion. High resolution solid-state NMR spectra can then only be recorded by application of TROSY (Transverse Relaxation Optimized Spectroscopy) type techniques which select the narrow component of the multiplet pattern. We speculate that this effect has been the major obstacle to the NMR spectroscopic characterization of many membrane proteins and fibrillar aggregates so far. Only in very favorable cases, where dynamics are either absent or very fast (picosecond), high-resolution spectra were obtained. We expect that this approach which requires intense deuteration will have a significant impact on the quality and the rate at which solid-state NMR spectroscopic investigations will emerge in the future.     

Moving the frontiers in solution and solid-state bioNMR

A major research field in mechanistic systems biology is represented by the development of methods for investigating the structural and dynamic features of systems with multiple interacting components, in order to understand their function. A combination of NMR techniques can be used in such respect, among which the employment of paramagnetic metal ions, ¹³C direct detection, and solid-state NMR, possibly supported by other techniques like small angle X-ray scattering. Among the results, the information on the conformational heterogeneity experienced by multicomponent systems in solution can be mentioned. The structural and functional characterization of large biological systems, not affordable with standard solution NMR techniques, can be tackled through a synergistic use of solution and MAS solid-state NMR. ¹³C direct detection NMR spectroscopy is on the other hand advantageous for improving the quality and quantity of observed nuclear signals, for their intrinsically smaller linewidths and larger signal breadth. Details on these approaches are reviewed here.     

Solvation and crystal effects in bilirubin studied by NMR spectroscopy and density functional theory

The open-chain tetrapyrrole compound bilirubin was investigated in chloroform and dimethyl sulfoxide solutions by liquid-state NMR and as solid by (1)H, (13)C, and (15)N magic-angle spinning (MAS) solid-state NMR spectroscopy. Density functional theory (DFT) calculations were performed to interpret the data, using the B3LYP exchange-correlation functional to optimize geometries and to compute NMR chemical shieldings by the gauge-including atomic orbital method. The dependence of geometries and chemical shieldings on the size of the basis sets was investigated for the reference molecules tetramethylsilane, NH(3), and H(2)O, and for bilirubin as a monomer and in clusters consisting of up to six molecules. In order to assess the intrinsic errors of the B3LYP approximation in calculating NMR shieldings, complete basis set estimates were obtained for the nuclear shielding values of the reference molecules. The experimental liquid-state NMR data of bilirubin are well reproduced by a monomeric bilirubin molecule using the 6-311+G(2d,p) basis set for geometry optimization and for calculating chemical shieldings. To simulate the bilirubin crystal, a hexameric model was required. It was constructed from geometry-optimized monomers using information from the X-ray structure of bilirubin to fix the monomeric entities in space and refined by partial optimization. Combining experimental (1)H-(13)C and (1)H-(15)N NMR correlation spectroscopy and density functional theory, almost complete sets of (1)H, (13)C, and (15)N chemical shift assignments were obtained for both liquid and solid states. It is shown that monomeric bilirubin in chloroform solution is formed by 3-vinyl anti conformers, while bilirubin crystals are formed by 3-vinyl syn conformers. This conformational change leads to characteristic differences between the liquid- and solid-state NMR resonances.     

Rotational and translational diffusion of peptide-coated CdSe/CdS/ZnS nanorods studied by fluorescence correlation spectroscopy

CdSe/CdS/ZnS nanorods (NRs) of three aspect ratios were coated with phytochelatin-related peptides and studied using fluorescence correlation spectroscopy (FCS). Theoretical predictions of the NRs' rotational diffusion contribution to the correlation curves were experimentally confirmed. We monitored rotational and translational diffusion of NRs and extracted hydrodynamic radii from the extracted diffusion constants. Translational and rotational diffusion constants (D(trans) and D(rot)) for NRs were in good agreement with Tirado and Garcia de la Torre's as well as with Broersma's theories when accounting for the ligand dimensions. NRs fall in the size range where rotational diffusion can be monitored with higher sensitivity than translational diffusion due to a steeper length dependence, D(rot) approximately L(-)(3) versus D(trans) approximately L(-)(1). By titrating peptide-coated NRs with bovine serum albumin, we monitored (nonspecific) binding through rotational diffusion and showed that D(rot) is an advantageous observable for monitoring binding. Monitoring rotational diffusion of bioconjugated NRs using FCS might prove to be useful for observing binding and conformational dynamics in biological systems.     

Extremely slow Li ion dynamics in monoclinic Li(2)TiO(3)-probing macroscopic jump diffusion via(7)Li NMR stimulated echoes

A thorough understanding of ion dynamics in solids, which is a vital topic in modern materials and energy research, requires the investigation of diffusion properties on a preferably large dynamic range by complementary techniques. Here, a polycrystalline sample of Li(2)TiO(3) was used as a model substance to study Li motion by both (7)Li spin-alignment echo (SAE) nuclear magnetic resonance (NMR) and ac-conductivity measurements. Although the two methods do probe Li dynamics in quite different ways, good agreement was found so that the Li diffusion parameters, such as jump rates and the activation energy, could be precisely determined over a dynamic range of approximately eleven decades. For example, Li solid-state diffusion coefficients D(σ) deduced from impedance spectroscopy range from 10(-23) m(2) s(-1) to 10(-12) m(2) s(-1) (240-835 K). These values are in perfect agreement with the coefficients D(SAE) deduced from SAE NMR spectroscopy. As an example, D(SAE) = 2 × 10(-17) m(2) s(-1) at 433 K and the corresponding activation energy determined by NMR amounts to 0.77(2) eV (400-600 K). At room temperature D(σ) takes a value of 3 × 10(-21) m(2) s(-1).     

Site-Resolved Measurement of Microsecond-to-Millisecond Conformational-Exchange Processes in Proteins by Solid-State NMR Spectroscopy

We demonstrate that conformational exchange processes in proteins on microsecond-to-millisecond time scales can be detected and quantified by solid-state NMR spectroscopy. We show two independent approaches that measure the effect of conformational exchange on transverse relaxation parameters, namely Carr-Purcell-Meiboom-Gill relaxation-dispersion experiments and measurement of differential multiple-quantum coherence decay. Long coherence lifetimes, as required for these experiments, are achieved by the use of highly deuterated samples and fast magic-angle spinning. The usefulness of the approaches is demonstrated by application to microcrystalline ubiquitin. We detect a conformational exchange process in a region of the protein for which dynamics have also been observed in solution. Interestingly, quantitative analysis of the data reveals that the exchange process is more than 1 order of magnitude slower than in solution, and this points to the impact of the crystalline environment on free energy barriers.     

Conformational analysis of N-Boc-N,O-isopropylidene-α-serinals. A combined DFT and NMR study

This work describes an extensive conformational analysis of Garner's aldehyde and its α-methylated homologue—two important chiral building blocks that are widely used in organic synthesis. A combination of density-functional theory and NMR spectroscopy confirmed the existence of a dynamic equilibrium between two possible conformers of the carbamate group in these compounds. The calculated properties such as conformer populations and rotational barriers around the (CO)-N bond are in good agreement with the experimental values. Finally, the dipole moments of the molecules appear to be a decisive factor in the stabilization of the conformers in solution.     

Natural-abundance solid-state 2H NMR spectroscopy at high magnetic field

High-resolution solid-state (2)H NMR spectroscopy provides a method for measuring (1)H NMR chemical shifts in solids and is advantageous over the direct measurement of high-resolution solid-state (1)H NMR spectra, as it requires only the application of routine magic angle sample spinning (MAS) and routine (1)H decoupling methods, in contrast to the requirement for complex pulse sequences for homonuclear (1)H decoupling and ultrafast MAS in the case of high-resolution solid-state (1)H NMR. However, a significant obstacle to the routine application of high-resolution solid-state (2)H NMR is the very low natural abundance of (2)H, with the consequent problem of inherently low sensitivity. Here, we explore the feasibility of measuring (2)H MAS NMR spectra of various solids with natural isotopic abundances at high magnetic field (850 MHz), focusing on samples of amino acids, peptides, collagen, and various organic solids. The results show that high-resolution solid-state (2)H NMR can be used successfully to measure isotropic (1)H chemical shifts in favorable cases, particularly for mobile functional groups, such as methyl and -N(+)H(3) groups, and in some cases phenyl groups. Furthermore, we demonstrate that routine (2)H MAS NMR measurements can be exploited for assessing the relative dynamics of different functional groups in a molecule and for assessing whole-molecule motions in the solid state. The magnitude and field-dependence of second-order shifts due to the (2)H quadrupole interaction are also investigated, on the basis of analysis of simulated and experimental (1)H and (2)H MAS NMR spectra of fully deuterated and selectively deuterated samples of the α polymorph of glycine at two different magnetic field strengths.     

Stochastic modeling of CW-ESR spectroscopy of [60]fulleropyrrolidine bisadducts with nitroxide probes

In this work, we address the interpretation of continuous wave electron spin resonance (CW-ESR) spectra of fulleropyrrolidine bisadducts with nitroxide addends. Our approach is based on a definition of the spin Hamiltonian which includes exchange and dipolar interactions and on a complete numerical solution of the resulting stochastic Liouville equation, with inclusion of diffusive rotational dynamics. CW-ESR spectra are simulated for a series of C60 bisadducts made up of four trans isomers and the equatorial isomer. A nonlinear least-squares fitting procedure allows extraction directly from the available experimental spectra of a wide range of parameters, namely interprobe relative distances, diffusion tensors, and values of the exchange parameter J. Results are in good agreement with previous, more phenomenological estimates, proving that the combination of sensitive ESR spectroscopy based on multiple spin labeling with nitroxide radicals and sophisticated modeling can be highly helpful in providing structural and dynamic information on molecular systems.     

Influences of local polymer-solvent π-π-interaction on dynamics of phenyl ring rotation and its role on photophysics of conjugated polymer

In this report, the role of local polymer-solvent π-π-interaction on rotational dynamics of phenyl rings of poly[2-methoxy-5-(2′-ethyl-hexyloxy)-1,4-phenylenevinylene] (MEH-PPV) is examined by utilizing nuclear magnetic resonance (NMR) spectroscopy. We have found that an aromatic solvent can couple strongly with the phenyl rings via favorable local π-π-interaction, causing a restriction of the ring rotation. The dynamic process takes place at much faster rate in a non-aromatic solvent. NMR line shape analysis indicates the existence of two side chain configurations with relatively long life-time in toluene and pyridine while a single time-averaged configuration is detected in chloroform and tetrahydrofuran. Addition of chloroform or cyclohexane to a solution of MEH-PPV in toluene is accompanied by an increase of the rotational dynamics. This indicates that the expansion or collapse of main chain upon varying solvent quality play a minor role on the rotational dynamics. The relationship between the dynamics of ring rotation and photophysics of MEH-PPV in solution is discussed.