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.     

Study of internal ring rotation and molecular reorientation in the liquid crystal 5O.7 by deuterium N.M.R. spectroscopy

The spectral densities of motion were determined by deuterium N.M.R. relaxation measurements in the nematic, smectic A and smectic C phases of 4-n-pentyloxybenzylidene-d₁-4'-heptylaniline and 4-n-pentyloxybenzylidene-4'-heptylaniline-2,3,5,6-d₄. By examining two atomic sites on a 5O.7 molecule, we were able to gain information on the reorientation motion and internal rotation of the aniline ring. It was also found that director fluctuations make some contribution to the spectral density J₁ (ω). We use the superimposed rotations model to account for the internal ring motion and the small step rotational diffusion model for the molecular reorientation. The derived rotational diffusion constants for the spinning and tumbling motions appear to give physically plausible activation energies in the mesophases of 5O.7.     

Internal dynamics features in the free jet rotational spectrum of the acetaldehyde-Kr molecular complex

The structure and the dynamics of internal motions in the complex formed between acetaldehyde and Kr are studied by free jet absorption microwave spectroscopy performed in the range 60-78 GHz. The fourfold structure of each rotational line is evidence of the vibration-rotation coupling between the overall rotation of the complex, a tunneling motion of the Kr atom between two equivalent positions and the internal rotation of the methyl group in the acetaldehyde moiety. The four sets of transitions could be fitted with a coupled Hamiltonian which allows for the Coriolis interaction obtaining the energy separation between the vibrational energy levels related to the tunneling motion, while the observed splittings due to the methyl group internal rotation were analyzed independently with an appropriate model. The potential energy barriers for the tunneling motion and the internal rotation of the methyl group have been calculated and the interaction of the rare gas atom with the acetaldehyde moiety is reflected in the change of the V(3) barrier to internal rotation in going from the molecule to the weakly bound complex.     

Study of internal ring rotation and molecular reorientation in the liquid crystal 5O.7 by deuterium N.M.R. spectroscopy

Abstract

The spectral densities of motion were determined by deuterium N.M.R. relaxation measurements in the nematic, smectic A and smectic C phases of 4-n-pentyloxybenzylidene-d ₁-4′-heptylaniline and 4-n-pentyloxybenzylidene-4′-heptylaniline-2,3,5,6-d ₄. By examining two atomic sites on a 5O.7 molecule, we were able to gain information on the reorientation motion and internal rotation of the aniline ring. It was also found that director fluctuations make some contribution to the spectral density J ₁ (ω). We use the superimposed rotations model to account for the internal ring motion and the small step rotational diffusion model for the molecular reorientation. The derived rotational diffusion constants for the spinning and tumbling motions appear to give physically plausible activation energies in the mesophases of 5O.7.     

Headgroup motion in a lyotropic lamellar phase by deuterium and nitrogen-14 relaxation studies

Deuterium (2H) and nitrogen-14 (14N) NMR spectroscopy were used to investigate the molecular dynamics of a lyotropic liquid crystal. Deuterium spectral densities of motion for the C1 deuterated site on the chain of the molecule decylammonium chloride (DACl) at the Larmor frequency 61.4 MHz and those for the (14)N at the headgroup (NH(3)(+)) at 28.9 MHz are analyzed quantitatively in the lamellar phase of the DACl-d(11)/water binary system to shed light on the headgroup dynamics. The motional model used is the small step rotational diffusion for reorientations plus internal rotations of the methylene group in the strong collision limit. The tumbling motion of the long axis of the DACl molecule in the aggregates seems to be as rigorous as the molecular spinning motion, likely due to the proposed motional model. The similarity of deuterium spectral densities from the C1 and C2/C3 sites may indicate a relatively rigid unit of C1-C2-C3 in the backbone.     

OCS in para-hydrogen clusters: rotational dynamics and superfluidity

We present a detailed analysis of the rotational excitations of the linear OCS molecule solvated by a variable number of para-hydrogen molecules (9 < or = N < or = 17). The effective rotational constant extracted from the fit of the rotational energy levels decreases up to N = 13, indicating near-rigid coupling between OCS rotations and para-hydrogen motion. Departure from rigidity is instead seen for larger clusters with 14 < or = N < or = 17. Path-integral Monte Carlo calculations show that the N dependence of the effective rotational constant can be explained in terms of a partial superfluid response of para-hydrogen to rotations about an axis perpendicular to the OCS axis. Complete para-hydrogen superfluid response to rotations about the OCS axis is found for N > or = 10.     

On the equivalence of conformational and enantiomeric changes of atomic configuration for vibrational circular dichroism signs

We study systematically the vibrational circular dichroism (VCD) spectra of the conformers of a simple chiral molecule, with one chiral carbon and an "achiral" alkyl substituent of varying length. The vibrational modes can be divided into a group involving the chiral center and its direct neighbors and the modes of the achiral substituent. Conformational changes that consist of rotations around the bond from the next-nearest neighbor to the following carbon, and bond rotations further in the chain, do not affect the modes around the chiral center. However, conformational changes within the chiral fragment have dramatic effects, often reversing the sign of the rotational strength. The equivalence of the effect of enantiomeric change of the atomic configuration and conformational change on the VCD sign (rotational strength) is studied. It is explained as an effect of atomic characteristics, such as the nuclear amplitudes in some vibrational modes as well as the atomic polar and axial tensors, being to a high degree determined by the local topology of the atomic configuration. They reflect the local physics of the electron motions that generate the chemical bonds rather than the overall shape of the molecule.     

Effects of the bead-bead potential on the restricted rotational diffusion of nonrigid macromolecules

The influence of the bead-bead interaction on the rotational dynamics of macromolecules which are immersed into a solution has been investigated by starting from the microscopic theory of the macromolecular motion, i.e., from a Fokker-Planck equation for the phase-space distribution function. From this equation, we then derived an explicit expression for the configuration-space distribution function of a nonrigid molecule which is immobilized on a surface. This function contains all the information about the interaction among the beads as well as the effects from the surrounding solvent particles and from the surface. For the restricted rotational motion, the dynamics of the macromolecules can now be characterized in terms of a rotational diffusion coefficient as well as a radial distribution functions. Detailed computations for the rotational diffusion coefficient and the distribution functions have been carried out for HOOKEAN, finitely extensible nonlinear elastic, and a DNA type bead-bead interaction.     

Methylsalicylate: a rotational spectroscopy study

We report the free-jet rotational spectra of methylsalicylate, a molecule with a possible tautomeric and conformational equilibrium. In the ground electronic state, the molecule adopts a form stabilized by an intramolecular hydrogen bond between the phenolic hydrogen and the carbonylic oxygen, and this structure is characterized as the lowest-energy form by quantum chemical calculations. All rotational transitions are split because of the internal rotation of the methyl group, and the value of the barrier for this motion was determined to be V(3) = 5.38 kJ mol(-1).     

Comparison of aqueous molecular dynamics with NMR relaxation and residual dipolar couplings favors internal motion in a mannose oligosaccharide.

An investigation has been performed to assess how aqueous dynamical simulations of flexible molecules can be compared against NMR data. The methodology compares state-of-the-art NMR data (residual dipolar coupling, NOESY, and (13)C relaxation) to molecular dynamics simulations in water over several nanoseconds. In contrast to many previous applications of residual dipolar coupling in structure investigations of biomolecules, the approach described here uses molecular dynamics simulations to provide a dynamic representation of the molecule. A mannose pentasaccharide, alpha-D-Manp-(1-->3)-alpha-D-Manp-(1-->3)-alpha-D-Manp-(1-->3)-alpha-D-Manp-(1-->2)-D-Manp, was chosen as the model compound for this study. The presence of alpha-linked mannan is common to many glycopeptides, and therefore an understanding of the structure and the dynamics of this molecule is of both chemical and biological importance. This paper sets out to address the following questions. (1) Are the single structures which have been used to interpret residual dipolar couplings a useful representation of this molecule? (2) If dynamic flexibility is included in a representation of the molecule, can relaxation and residual dipolar coupling data then be simultaneously satisfied? (3) Do aqueous molecular dynamics simulations provide a reasonable representation of the dynamics present in the molecule and its interaction with water? In summary, two aqueous molecular dynamics simulations, each of 20 ns, were computed. They were started from two distant conformations and both converged to one flexible ensemble. The measured residual dipolar couplings were in agreement with predictions made by averaging the whole ensemble and from a specific single structure selected from the ensemble. However, the inclusion of internal motion was necessary to rationalize the relaxation data. Therefore, it is proposed that although residual dipolar couplings can be interpreted as a single-structure, this may not be a correct interpretation of molecular conformation in light of other experimental data. Second, the methodology described here shows that the ensembles from aqueous molecular dynamics can be effectively tested against experimental data sets. In the simulation, significant conformational motion was observed at each of the linkages, and no evidence for intramolecular hydrogen bonds at either alpha(1-->2) or alpha(1-->3) linkages was found. This is in contrast to simulations of other linkages, such as beta(1-->4), which are often predicted to maintain intramolecular hydrogen bonds and are coincidentally predicted to have less conformational freedom in solution.     

Evaluating rotational diffusion from protein MD simulations

It is now feasible to carry out molecular dynamics simulations of proteins in water that are long compared to the overall tumbling of the molecule. Here, we examine rotational diffusion in four small, globular proteins (ubiquitin, binase, lysozyme, and fragment B3 of protein G) with the TIP3P, TIP4P/EW, and SPC/E water models, in simulations that are 6 to 60 times as long as the mean rotational tumbling time. We describe a method for extracting diffusion tensors from such simulations and compare the results to experimental values extracted from NMR relaxation measurements. The simulation results accurately follow a diffusion equation, even for spherical harmonic correlation functions with l as large as 8. However, the best-fit tensors are significantly different from experiment, especially for the commonly used TIP3P water model. Simulations that are 20 to 100 times longer than the rotational tumbling times are needed for good statistics. A number of residues exhibit internal motions on the nanosecond time scale, but in all cases examined here, a product of internal and overall time-correlation functions matches the total time-correlation function well.     

Theoretical modeling of energy redistribution and stereodynamics in CF scattering from Si(100) under grazing incidence

We have simulated CF scattering from Si(100) using the molecular dynamics method. Translational energy loss spectra are presented. The shape of the energy loss distribution as a result of internal energy release is analyzed. At the classical turning point, the internal energy of the molecule is mainly in the form of rotational energy. The strong rotational excitation results in additional molecule-surfaces interactions during the latter half of the collision. These additional collisions permit some molecules that initially gain internal energy exceeding the bond strength to ultimately survive the collision process via rotational de-excitation. The rotational motion exhibited by surviving molecules is determined by the combination of the molecular axis orientation and the local surface structure during the collision process. The rotation planes of the surviving molecules are preferentially aligned with the surface normal (cartwheel-like and propeller-like motions). In this study, propeller-like motion of the surviving molecules is predicted. The majority of surviving molecules exhibit a cartwheel-like motion. However, molecules that gain a propeller-like rotation exhibit a much better alignment of their planes-of-rotation compared with molecules exhibiting cartwheel-like motion.     

Molecular dynamics assignment of NMR correlation times to specific motions in a "basket-handle porphyrin" heme

Iron (II) basket-handle porphyrins (BHP) are a series of encumbered heme models designed several years ago to mimic the ligand binding site of hemoproteins. Contrary to expectations, kinetic investigations have revealed that the k(on) rates for CO and/or O2 binding were only marginally affected by the assumed central steric hindrance of the iron atom. Thus, it was hypothesized that the internal dynamics of the molecule might be at the origin of the poor steric protection. To address this issue, measurements of nuclear magnetic resonance relaxation rates, fluorescence anisotropy experiments, and molecular dynamics simulations were undertaken. The size of BHP is small enough to allow the simulation in explicit chloroform with an almost complete sampling of the conformational space. The order parameters calculated from the MD trajectory compare well with the NMR experimental data and the predicted rotational correlation time corresponding to the Brownian motion of the molecule is in good agreement with the fluorescence measurements. Moreover, combining the results obtained using the three techniques allows the attribution of each internal NMR correlation time to a particular internal motion, revealing that even such medium-sized molecules are able to display quite complex internal dynamics. In particular, the handle phenyls that were assumed to sandwich the porphyrin have in fact a vanishing probability to be found in the proximity of the iron atom. They are therefore unable to reduce ligand accessibility significantly, which may explain the behavior of the k(on) rates.     

椭球形粒子扩散动力学的研究进展

椭球形粒子作为一类重要的各向异性粒子,在生物、化工以及材料等领域有着广泛的应用。对椭球形粒子的扩散动力学进行深入地研究,不仅可以增进人们对各向异性粒子扩散动力学中基本科学问题的理解,而且可以为含各向异性粒子材料的设计与加工提供理论依据。因此,椭球形粒子的扩散问题一直是粒子扩散研究的焦点。虽然椭球形粒子扩散动力学的研究已经有一百多年的历史,其相关理论、实验和模拟研究工作很多,并取得了较大的进展,但是,系统的综述性文章相对较少。本文系统地总结了椭球形粒子扩散动力学的相关工作,包括:不同流体力学边界条件下椭球形粒子的扩散动力学和平动与转动扩散的耦合行为等。此外,本文还分析了椭球形粒子扩散动力学领域存在的关键科学问题,并对该领域研究方向进行了展望。     

Water hydrogen bond analysis on hydrophilic and hydrophobic biomolecule sites

Elastic and quasielastic neutron scattering experiments have been used to investigate the hydrogen bonding network dynamics of hydration water on hydrophilic and hydrophobic sites. To this end the evolution of hydration water dynamics of a prototypical hydrophobic amino acid with polar backbone, N-acetyl-leucine-methylamide (NALMA), and hydrophilic amino acid, N-acetyl-glycine-methylamide (NAGMA), has been investigated as a function of the molecular ratio water : peptide. The results suggest that the dynamical contribution of the intrinsic and low hydration molecules of water is characteristic of pure librational/rotational movement. The water molecule remains attached to the hydrophilic site with only the possibility of hindered rotations that eventually break the bond with the peptide and reform it immediately after. A gradual evolution from librational motions to hindered rotations is observed as a function of temperature. When the hydration increases, we observe (together with the hindered rotations of hydrogen bonds) a slow diffusion of water molecules on the surface of the peptides.     

正丙醇水溶液准弹性中子散射光谱的分子动力学模拟

准弹性中子散射(QENS)光谱是获取溶液分子动力学性质的重要方法,但光谱解析模型的有效性和去耦合近似的合理性仍存在争议.本文利用分子动力学模拟方法获取纯水和正丙醇水溶液中羟基氢原子的自相关中间散射函数FS(Q,t)和去耦合近似函数FP(Q,t),以及相关性质来评价它们的合理性.结果表明,在低动量转移范围内平-转去耦合近似相对合理,水分子的平-转耦合贡献较小,混合溶液中水分子的平-转耦合项和转动项随动量转移Q值增大而增大,二者显现相互抵消趋势.对于混合溶液中的正丙醇羟基氢原子,由于FS(Q,t)和质心自相关中间散射函数FCM(Q,t)偏差较大,利用实验光谱直接拟合分子平动扩散系数是不合适的.三种平动模型获取的纯水和正丙醇水溶液分子平动扩散系数与实验结果一致,略高于Einstein均方位移方法所得结果.水分子在纯水和混合溶液中表现为跳跃转动,而不是连续转动.正丙醇分子存在转动各向异性,羟基氢原子沿羟基向量为跳跃转动,沿相对质心向量可近似为连续转动.模拟结果显示,高动量转移范围平-转耦合项贡献较大,直接拟合实验光谱获取分子转动扩散系数或弛豫时间是不合适的.鉴于低动量转移范围内转动和平转耦合贡献较小,以及二者的抵消作用,在此范围内获取水分子平动信息是现实可行的.     

Characterization of the transition state of functional enzyme dynamics

Through characterization of the solvent isotope effect on protein dynamics, we have examined determinants of the rate limitation to enzyme catalysis. A global conformational change in Ribonuclease A limits the overall rate of catalytic turnover. Here we show that this motion is sensitive to solvent deuterium content; the isotope effect is 2.2, a value equivalent to the isotope effect on the catalytic rate constant. We further demonstrate that the protein motion possesses a linear proton inventory plot, indicating that a single proton is transferred in the transition state. These results provide compelling evidence for close coupling between enzyme dynamics and function and demonstrate that characterization of the transition state for protein motion in atomic detail is experimentally accessible.     

Effect of intramolecular dynamics on state-to-state photochemistry: Fragmentation of the à state of trans-DONO

The effect of intramolecular dynamics on state-selected photolysis of trans-DONO is probed through measurements on the OD fragment ejected by the à state with one and two quanta of energy in the -NO stretching vibration ν₂. The fragment in the latter case is rotationally hotter, more polarized at high rotational energies, and is associated with a higher population non-equilibrium in the Λ-doublet fine-structure states. These effects are traced back to coupling between the ν₂ vibration and the in-plane DON angle-bending motion ν₃ in the parent molecule.