Rotational Diffusion Constants Research Articles

Predicting Transmembrane Dimerization and the Interfaces in Thyroid-Stimulating Hormone Receptor (TSHR) Using Brownian Dynamics Stimulation

The TSHR receptor, a member of the GPCR protein family, has not been fully modeled. Only the crystal structure of the ecto-domain has been reported. Experimental data with truncated TSHRs indicate that the trans-membrane region has a major role in dimerization/ multimirization of this receptor. Biophysical (FRET) and biochemical (co-immunoprecipitation) studies from our laboratory have established that the TSH receptor, similar to other GPCRs, has the propensity to form dimers and multimers both in native and non-native cells. Recent experimental studies also from this laboratory have further reported that dimerization interfaces can reside in the extracellular domain. In addition, the TSHR, bereft of the ectodomain, shows similar characteristics, indicating that the transmembrane domains of TSHR are also involved in dimerization, receptor stability and trafficking.As server-based predictions for possible dimerization interfaces, have large uncertainties and wide variances precluding any definitive conclusions, we have resorted to the more robust and refined algorithm of Brownian dynamics in predicting transmembrane dimerization, a standard and established technique in such biological phenomena. A recently developed variant of Brownian dynamics has become an important computational tool to predict dimerization/multimerization of transmembrane proteins.The method is implemented in a program called Macrodox and involves complementing the Poisson-Boltzmann equation based calculation of the electrostatic interactions with the calculation of Van der Waals interactions. Furthermore, in this method the sampling efficiency is enhanced by restricting the protein movements within the membrane plane. Both translational (0.101x10−01 A 2/ps) and rotational diffusion constants (0.165x10−04 A 2/ps) and several other physical parameters (radius of gyration=18.17 A) have been computed for each TSHR monomer. We will present the results for contact residues from the trajectory of simulations and abrogation of dimerization following mutation of critical contact residues.

Effects of Energy Dissipation on Motional Dynamics in Unilamellar Vesicles

We have investigated the molecular reorientation dynamics of perylene incorporated into the nonpolar acyl chain region of 100 nm diameter phosphocholine unilamellar vesicles. When perylene is excited to the S(1) electronic manifold, it exhibits a different fluorescence anisotropy decay than when it is excited to its S(2) electronic manifold. In addition to differences in the polarization of the two transitions, there is a difference in the amount of excitation energy dissipated nonradiatively, because for both excitation conditions radiative emission is from the S(1) state. The data reveal a faster rotational diffusion constant for excitation to the S(2) manifold, and we interpret this finding in the context of local heating of the chromophore immediate environment by the nonradiative dissipation of energy associated with rapid relaxation from the S(2) to S(1) manifolds. Our results are consistent with transient heating on the order of 4 K, with the actual temperature increase depending subtly on whether the phospholipid acyl chains are in the gel phase or the fluid phase.

The director and molecular dynamics of the field-induced alignment of a Gay–Berne nematic phase: An isothermal-isobaric nonequilibrium molecular dynamics simulation study

Isothermal-isobaric molecular dynamics simulations have been performed for the generic Gay–Berne (GB) mesogen, GB(4.4, 20.0, 1, 1), to investigate director and molecular rotational motion during the field-induced alignment of a nematic. The alignment process for the director is discussed within the context of a hydrodynamic analysis based on the Ericksen–Leslie theory and this is found to predict the simulated behavior well. The dependence of the relaxation time for the alignment on the field strength is also in good accord with the theory. The rotational viscosity coefficient estimated from the simulation is smaller than that typically observed for real nematics and the possible reasons for this are discussed. However, the simulation results are found to follow not only the theory but also the experiments, at least qualitatively. No significant variation in the local and long-range structure of the nematic phase is found during the field-induced alignment process. In addition, we have explored the molecular dynamics in the nematic phase in the presence of the field using the first- and second-rank time autocorrelation functions. More importantly we are able to show that the director relaxation time is longer than that for molecular rotation. It is also possible to use the two orientational correlation times to explore the relationship between the rotational viscosity coefficient and the rotational diffusion constant. The diffusion constants determined from the orientational correlation times, based on the short-time expansion of the autocorrelation functions, are found to be significantly different. In consequence it is not possible to test, unambiguously, the relationship between the rotational viscosity coefficient and the rotational diffusion constant. However, it would seem that the second-rank rotational correlation time provides the most reliable route to the rotational viscosity coefficient.

Orientational and Translational Dynamics of Polyether/Water Solutions

Optical heterodyne-detected optical Kerr effect (OHD-OKE) experiments and pulsed field-gradient spin-echo NMR (PFGSE-NMR) experiments were performed to measure the rotational and translational diffusion constants of a polyether, tetraethylene glycol dimethyl ether (TEGDE), in binary mixtures with water over concentrations ranging from pure TEGDE to approaching infinite dilution. In addition, hydrodynamic calculations of the rotational and translational diffusion constants for several rigid TEGDE conformations in the neat liquid and in the infinitely dilute solution were performed to supplement the experimental data. The rotational relaxation data follow the Debye-Stokes-Einstein (DSE) equation within experimental error over the entire water concentration range. The agreement with the DSE equation indicates that there is no significant structural change of the polyether as the water content is changed. In contrast to the rotational dynamics, the translational diffusion data show a distinct deviation from Stokes-Einstein (SE) behavior. As the water content of the mixture is reduced, the translational diffusion rate decreases less rapidly than the increase in viscosity alone predicts until the water/TEGDE mole ratio of 7:1 is reached. Upon further reduction of water content, the translational diffusion tracks the viscosity. Comparison of the translational data with the rotational data and the hydrodynamic computations shows that the translational dynamics cannot be explained by a molecular shape change and that the low water fraction solutions are the ones that deviate from hydrodynamic behavior. A conjecture is presented as a possible explanation for the different behaviors of the rotational and translational dynamics.

Solid-State NMR Investigation of Membrane-Associated Peptides and Proteins

Solid-state NMR spectroscopy has a proven record during the investigation of the structure and dynamics of membrane-associated polypeptides. In particular from oriented samples considerable details on the structure and topology of the protein is obtained. A solid-state NMR approach which allows for the accurate determination of the tilt and rotational pitch angles of peptides reconstituted into uniaxially oriented membranes will be presented. Proton-decoupled 15N and 2H solid-state NMR spectroscopy have been used to characterize the tilt and rotational pitch angle of several peptides in considerable detail. Furthermore, valuable information on the rotational diffusion constants in membranes and thereby the size of peptide complexes is obtained.Here we present solid-state NMR results that have been obtained from the heterodimeric antimicrobial peptide distinctin as well as from the two chains independently. The data indicate that upon membrane insertion the protein unfolds, that the amphipathic helix of chain 2 orients parallel to the membrane surface and stably anchors the polypeptide into the membrane. In contrast chain 1 remains more loosely associated and changes its alignment by about 5 degrees when in contact with chain 2. Figure from PNAS, 106, 16639 (2009)View Large Image | View Hi-Res Image | Download PowerPoint Slide

Electron spin relaxation at low field

The low field ESR lineshape and the electron spin-lattice relaxation correlation function are calculated using the stochastic Liouville theory for an effective electron spin quantum number S = 1. When an axially symmetric permanent zero field splitting provides the dominant relaxation mechanism, and when it is much larger than the rotational diffusion constant, it is shown that both electron spin correlation functions S(0)S(t) (n = 0,1) are characterized by the same relaxation time tau(S) = (4D(R))(-1). This confirms the conjectures made by Schaefle and Sharp, J. Chem. Phys., 2004, 121, 5287 and by Fries and Belorizky, J. Chem. Phys., 2005, 123, 124510, based on numerical results using a different formalism. The stochastic Liouville approach also gives the paramagnetically enhanced nuclear spin relaxation time constants, T(1) and T(2), and the ESR lineshape function I(omega). In particular, the L-band (B(0) = 0.035 T) ESR spectrum of a low symmetry Ni(ii)-complex with a cylindrical ZFS tensor is shown to be detectable at sufficiently slowly reorientation of the complex. The analysis shows that the L-band spectrum becomes similar to the zero-field spectrum with a electron spin relaxation time tau(S) = (4D(R))(-1).

Coupling and Decoupling between Translational and Rotational Dynamics in a Supercooled Molecular Liquid

We use molecular dynamics simulations to investigate the coupling and decoupling between translational and rotational dynamics in a glass-forming liquid of dumbbells. We find that the coupling between the translational (tau_{q;{*}};{C}) and rotational (tau_{2}) relaxation times increases with decreasing temperature T, whereas the coupling decreases between the translational (D_{t}) and rotational (D_{r}) diffusivities. In addition, the T dependence of D_{t} decouples from that of 1/tau_{2}. We show that the decreasing coupling between D_{t} and D_{r} is only apparent due to the inadequacy of the concept of the rotational diffusion constant for describing the reorientational dynamics in the supercooled state. We also argue that the coupling between tau_{q;{*}};{C} and tau_{2} and the decoupling between D_{t} and 1/tau_{2} can be consistently understood in terms of the growing dynamic length scale.

Langevin Network Model of Myosin

Langevin mode theory and the coarse-grained elastic network model (ENM) for proteins are combined to yield the Langevin network model (LNM). Hydrodynamic radii of 6 A were assigned to each alpha-carbon on the basis of matching experimental translational and rotational diffusion constants of lysozyme, myoglobin, and hemoglobin with those calculated using a rigid body bead model with hydrodynamic interactions described by the Rotne-Prager tensor. LNM analysis of myosin II indicates that all ENM-like modes are overdamped at water viscosities. The low-frequency LNM modes in the pre-power stroke structure (PDB code: 1VOM) are substantially less mixed than the corresponding modes of the post-power stroke structure (1Q5G). Results from a four-bead model of the myosin "lever arm" indicate that coupling between modes increases as the array departs from linearity and are consistent with the results for 1VOM and 1Q5G. The decay times for all overdamped Langevin modes are shorter than the calculated rotational tumbling times found for lysozyme and myosin.

Evaluating the Role of Chromophore Side Group Identity in Mediating Solution-Phase Rotational Motion

We report on the rotational diffusion dynamics of the chromophore 7-nitrobenz-2-oxa-1,3-diazole (NBD) in a series of protic and polar aprotic solvents, as a function of the identity of the side group appended to the chromophore amine functionality. The central issue we address is whether or not the side groups play a role in mediating the anisotropic reorientation dynamics of the chromophore. To understand the motional properties of the chromophores in detail, we use both one-photon and two-photon excited fluorescence anisotropy decay measurements, and from these complementary excitation methods, we extract two of the Cartesian components of the rotational diffusion constant, D. The experimental data indicate that, regardless of the functionality of the pendant side group, the reorienting moieties exhibit ratios of Dz/Dx in the range 1.8-2.0. There is a small but discernible difference between the substituted chromophores. For all of the substituted NBD chromophores, dielectric friction plays a discernible role in determining their reorientation dynamics.

Size-Dependent Diffusion of Membrane Inclusions

Experimentally determined diffusion constants are often used to elucidate the size and oligomeric state of membrane proteins and domains. This approach critically relies on the knowledge of the size-dependence of diffusion. We have used mesoscopic simulations to thoroughly quantify the size-dependent diffusion properties of membrane inclusions. For small radii R, we find that the lateral diffusion coefficient D is well described by the Saffman-Delbrück relation, which predicts a logarithmic decrease of D with R. However, beyond a critical radius R c ≈ hη m/(2 η c) ( h, bilayer thickness; η m/c, viscosity of the membrane/surrounding solvent) we observe significant deviations and the emergence of an asymptotic scaling D ∼ 1/ R 2. The latter originates from the asymptotic hydrodynamics and the inclusion’s internal degrees of freedom that become particularly relevant on short timescales. In contrast to the lateral diffusion, the size dependence of the rotational diffusion constant D r follows the predicted hydrodynamic scaling D r ∼ 1/ R 2 over the entire range of sizes studied here.

Dynamics of bolaamphiphilic fluorescent polyenes in lipid bilayers from polarization emission spectroscopy

The rotational motions of the biamphiphilic polyenes (bolapolyenes) dimethyl all-( E)-octacosa-10,12,14,16,18-pentaenedioate (DE28:5) and dimethyl all-( E)-tetratriaconta-13,15,17,19,21-pentaenedioate (DE34:5), with head-to-head distances of 34 and 42 Å, respectively, have been examined by fluorescence anisotropy methods. The membrane-spanning bolapolyenes, which contain a central emitting pentaene group tethered to two methoxycarbonyl opposite polar heads by symmetric C 8 (DE28:5) and C 11 (DE34:5) polymethylene chains, were dispersed in lipid bilayers of DPPC or DMPC, and the stationary and picosecond-resolved emission was recorded as a function of temperature. In fluid-phase DMPC bilayers, three relaxation times could be determined, assigned to fast (0.2 and 2 ns) single-bond isomerization processes localized on the alkyl chains, and to whole-molecule oscillations (∼11 ns), respectively. The anisotropy decay parameters were further analyzed in terms of a diffusive model for wobbling in a Gaussian ordering potential, to assess the anchoring effect of the symmetric polar heads. In this way, the average rotational diffusion constant of the bolapolyenes, D ⊥, could be estimated as 0.022–0.026 rad 2 ns − 1 (DMPC bilayers, 35 °C), a value that is only 1 / 3 of that corresponding to the related pentaene fatty acid spanning a single membrane monolayer. In contrast, the amplitude of the equilibrium orientational distribution ( θ half-cone∼50°) is very similar for both the transmembrane and the single-headed polyenes. The reorientational oscillations of the central emitting group in the bolapolyenes necessarily would produce large-amplitude (2–5 Å) and very fast (ns) translational motions of the polar heads.

Quantitating the Dynamics of NBD Hexanoic Acid in Homogeneous Solution and in Solutions Containing Unilamellar Vesicles

We report here on the motional and fluorescence lifetime dynamics of the chromophore NBDHA (6-(N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino)hexanoic acid) in neat solvents and in aqueous solutions containing unilamellar vesicles of varying composition. We measure the transient response of this chromophore by time-correlated single-photon counting, using one- and two-photon excitation to resolve the Cartesian components of the rotational diffusion constant, D. Our experimental data for NBDHA in selected solvents of varying viscosity demonstrate that one- and two-photon excitation probe different components of the rotational diffusion constant and that this chromophore reorients as a prolate rotor with an aspect ratio of approximately 2. For NBDHA in aqueous solutions containing unilamellar vesicles of varying composition, we recover the same reorientation behavior regardless of vesicle composition. Fluorescence lifetime and steady-state fluorescence data show the chromophore to reside in a polar environment that is different from neat water. We understand these data in the context of the chromophore residing in close proximity to the unilamellar vesicle polar headgroups in all cases.

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.

Molecular Dynamics Study of Translational and Rotational Diffusion in Liquid Ortho-terphenyl

NVT molecular dynamics simulations were performed on liquid o-terphenyl as a function of temperature in the range 320-480 K. Computed translational diffusion coefficients displayed the non-Arrhenius behavior expected of a fragile glass-forming liquid and were in good, semiquantitative agreement with experimental results. Rotational correlation functions calculated for various vectors within the molecule exhibited a very short time (0-1 ps) initial decay, followed by a reversal, which corresponds to free reorientation within the "solvent" cage prior to collision with a wall. Rotational correlation times of three orthogonal vectors fixed on the central benzene were close to equal at all temperatures, indicating nearly isotropic overall molecular reorientation. The average correlation times exhibited a non-Arrhenius temperature dependence and were in very good agreement with experimental values derived from 2D and 1H NMR relaxation times. Correlation times of vectors located on the lateral phenyl rings were used to calculate the "spinning" internal rotation diffusion coefficients, which were approximately twice as great as the overall rotational diffusion constants, indicating rapid internal rotation of the phenyl side groups over wide ranges of angle in the liquid.

Identifiability analysis of models for reversible intermolecular two-state excited-state processes coupled with species-dependent rotational diffusion monitored by time-resolved fluorescence depolarization.

A deterministic identifiability analysis of the kinetic model for a reversible intermolecular two-state excited-state process with species-dependent rotational diffusion described by Brownian reorientation is presented. The cases of both spherically and cylindrically symmetric rotors, with no change in the principal axes of rotation on interconversion in the latter case, are specifically considered. The identifiability analysis is carried out in terms of compartmental modeling based on the S(t) identical with I( parallel)(t)+2I( perpendicular)(t) and D(t) identical with I( parallel)(t)-I( perpendicular)(t) functions, where I( parallel)(t) and I( perpendicular)(t) are the delta-response functions for fluorescence, polarized, respectively, parallel and perpendicular to the electric vector of linearly polarized excitation. It is shown that, from polarized time-resolved fluorescence data collected at two concentrations of coreactant and three appropriately chosen emission wavelengths, (a) a unique set of rate constants for the overall excited-state process is always obtained by making use of polarized measurements and (b) the rotational diffusion constants and geometrical factors associated with the different anisotropy decay components can be uniquely determined and assigned to each species. The geometrical factors are determined by the absorption and emission transitions in the two rotating species. For spherical rotors, these factors depend directly on the relative orientations of the transition moments, while for cylindrically symmetric rotors they depend on the orientations with respect to each other and to the symmetry axis.

Nuclear spin relaxation study of the solution reorientation of 3,5‐dichlorophenyl‐ and phenylethynyl‐mercury cyanide molecules and shielding tensors of nuclei forming the –HgCN and –CCHgCN groups: estimation of the heavy atom effect of mercury

Abstract3,5‐Dichlorophenylmercury cyanide (1) and phenylethynylmercury cyanide (2) dissolved in DMSO‐d6 have been investigated using 13C, 15N and 199Hg NMR and density functional theory (DFT) calculations. The longitudinal relaxation times of 13C and 199Hg nuclei of compounds 1 and 2 and of the 15N nucleus of 1 have been measured at two magnetic fields. On the basis of these data the rotational diffusion constants describing the reorientation rates of the investigated molecules in solution and the shielding anisotropy parameters for nuclei of atoms forming the –HgCN group have been determined. The available NMR characteristics of several other cyanomercury compounds and those containing the ethynylmercury fragment have also been collected. The experimental values of carbon and nitrogen shielding parameters for the cyanomercury and ethynylmercury groups have been compared with those calculated theoretically using the DFT GIAO method. This comparison has allowed an estimation of the size of the deshielding heavy atom effect experienced by the sp‐hybridized mercury‐bonded carbons atoms. Copyright © 2003 John Wiley & Sons, Ltd.

Mobility of side chains in a discotic liquid crystal studied by deuteron spin relaxation

A hexaether-substituted rufigallol mesogen is studied by measuring deuteron spin–lattice relaxation times T 1Z and T 1Q in the hexagonal D ho phase. Small-step rotations of discotic molecules within each column are described by the so-called ‘anisotropic viscosity’ model, giving rotational diffusion constants D α and D β for rotations of the disc normal around and perpendicular to the director. A libration model is used to describe the wagging motions in different side chains as seen by the first CD bonds, which diffuse in a circular arc within a defined apex angle. The chain libration rates and corresponding apex angles are also derived.

Rotation of propane molecules in supercages of Na–Y zeolite

Rotational dynamics of propane in Na–Y zeolite at room temperature is studied by molecular dynamics (MD) simulations and quasi-elastic neutron scattering (QENS) measurements. It is found that propane undergoes very fast rotational motion in the cages of Na–Y zeolite as first observed in the MD study and later confirmed by the QENS measurements. The dynamics of propane is described by isotropic rotational diffusion on a sphere of radius 1.88 (±0.05) Å, which is also the average distance of the hydrogen atoms from the center of mass of the propane molecule. The rotational diffusion constant as obtained from the QENS and MD simulation is in close agreement. This is the first ever study of the rotational dynamics of propane in a zeolite.

Rotational dynamics of propane in Na-Y zeolite: a molecular dynamics and quasielastic neutron-scattering study.

We report results from molecular dynamics (MD) simulations and quasielastic neutron-scattering (QENS) measurements on the rotational dynamics of propane in Na-Y zeolite at room temperature with a loading of four molecules per alpha cage. Rotational part of the intermediate scattering function F(Q,t) obtained from the MD simulation suggests that rotational motion is faster relative to the translational motion. Various rotational models fitted to the MD data suggest that rotation is isotropic. It is found that the hydrogen atoms lie, on the average, on a sphere of radius 1.88+/-0.05 A, which is also the average distance of the hydrogen atoms from the center of mass of the propane molecule. Results from QENS measurements are in excellent agreement with those obtained from MD, suggesting that the intermolecular potential employed in the MD simulation provides a realistic description of propane motion within faujasite. The rotational diffusion constant D(R) is 1.05+/-0.09 x 10(12) sec(-1) from the QENS data, which may be compared with that obtained from the MD data (0.82+/-0.05 x 10(12) sec(-1)).

Derivation of the analytical form for holographic contrast growth in photorefractive polymers

The derivation of the analytical form for index-contrast growth during hologram formation in a photorefractive-polymer composite is presented. The transfer function for chromophore rotation in an amorphous medium is found initially, and this is then convolved with an exponentially growing space-charge field to determine the index-contrast transient. This analysis reveals that index-contrast growth is fully characterized by just two parameters: the rise time of the space-charge field and the rotational diffusion constant. Good agreement between theory and measurement is found for a range of materials and experimental conditions.