Identification of partially disordered peptide intermediates through residue-specific NMR diffusion measurements

It is technically challenging to detect low-population partially disordered species that are in equilibrium with the folded and unfolded states. Residue-specific translational diffusion experiments measured by pulsed field gradient NMR have been used to detect the presence, and define the conformation, of such equilibrium intermediates. The experiment is demonstrated for equilibrium solutions of related triple helical peptides that model a small region of type I collagen with and without a mutation known to cause osteogenesis imperfecta. The data show that residue-specific diffusion coefficients of an interconverting trimer to monomer system can allow discrimination between a simple two-state model and more complex multistate models involving partially disordered intermediates.     

Molecular diffusion in liquid crystals and chiral discrimination. I. Theory

The possibility of using cholesteric phases for discriminating enantiomers of a chiral solute on the basis of their different transport properties, motivates the investigation of the translational diffusion by taking fully into account the roto-translational coupling. In this article a detailed theoretical analysis is presented for the transport properties evaluated according to the asymptotic limit of the mean-squared displacement. A general relation is derived for the transport coefficients, having as main ingredients the mean-field potential due to the mesophase, and the diffusion tensor with its purely translational and rotational components, and with the blocks describing the roto-translational coupling. The application of the theory to nematic phases shows that the roto-translational coupling generates a dynamical contribution reducing the transport coefficients evaluated by taking into account only the translational diffusion components in the center of diffusion. The theory is also specialized to a cholesteric phase with a given helical pitch for the director arrangement, in a form which is suitable for calculations of model systems of chiral solutes to be presented in a forthcoming paper.     

Interpretation of diffusion coefficients in nanostructured materials from random walk numerical simulation

We make use of the numerical simulation random walk (RWNS) method to compute the "jump" diffusion coefficient of electrons in nanostructured materials via mean-square displacement. First, a summary of analytical results is given that relates the diffusion coefficient obtained from RWNS to those in the multiple-trapping (MT) and hopping models. Simulations are performed in a three-dimensional lattice of trap sites with energies distributed according to an exponential distribution and with a step-function distribution centered at the Fermi level. It is observed that once the stationary state is reached, the ensemble of particles follow Fermi-Dirac statistics with a well-defined Fermi level. In this stationary situation the diffusion coefficient obeys the theoretical predictions so that RWNS effectively reproduces the MT model. Mobilities can be also computed when an electrical bias is applied and they are observed to comply with the Einstein relation when compared with steady-state diffusion coefficients. The evolution of the system towards the stationary situation is also studied. When the diffusion coefficients are monitored along simulation time a transition from anomalous to trap-limited transport is observed. The nature of this transition is discussed in terms of the evolution of electron distribution and the Fermi level. All these results will facilitate the use of RW simulation and related methods to interpret steady-state as well as transient experimental techniques.     

Influence of reptation on localized diffusion in crystallizing polymers

Crystalline texture in polymer spherulites appears to be determined in part by interplay during solidification between interface morphology and the diffusion of species segregated at crystal growth fronts; these species are molecules of lower molecular weight (fractionation) or molecules of stereoirregular structure. Early discussions of this behavior were based upon assumption of a single diffusion coefficient in each case. However, it is now known that, because of reptation, each molecule in a polymer melt diffuses with a diffusion coefficient dependent on its individual molecular weight. In this paper, the influence of reptation upon concentration profiles and diffusion ranges is examined. It is shown that such influence is slight when segregated species have relatively narrow distributions of molecular weight, such as are typical when segregation involves fractionation or is mostly confined to fractionated stereoirregular species blended with crystallizable host polymer. With broad distributions, however, concentration profiles are significantly altered and long segregated molecules dominate morphologically important behavior. Meaningful average diffusion ranges can often be derived and related to appropriately averaged molecular weights of participating molecules. Morphological implications of the various results are outlined.     

Molecular probe techniques for studying diffusion and relaxation in thin and ultrathin polymer films

Two optically based, molecular probe techniques are employed to study relaxation and small-molecule translational diffusion in thin and ultrathin (thicknesses < ∼200 nm) polymer films. Second harmonic generation (SHG) is used to study the reorientational dynamics of a nonlinear optical chromophore, Disperse Red 1 (DR1) (previously shown to be an effective probe of α-relaxation dynamics) either covalently attached or freely doped in polymer films. Our studies on films ranging in thickness from 7 nm to 1 μm show little change in T_g with film thickness; however, a substantial broadening of the relaxation distribution is observed as film thickness decreases below approximately 150 nm. Experimental guidelines are given for using fluorescence nonradiative energy transfer (NRET) to study translational diffusion in ultrathin polymer films. Appropriate choice of a fluorescence donor species is important along with ensuring that diffusion is slow enough to be measured appropriately. Initial results on the diffusion of a small-molecule probe, lophine, in poly(isobutyl methacrylate) indicates that there is little change in probe diffusion coefficients in films as thin as 90 nm as compared to bulk films. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2795–2802, 1997     

Translational diffusion of intermediate species in solutions

In this article, applications of the TG method to measurements of the translational diffusion of photochemically created intermediate species are reviewed. The intermediate species include unstable isomers, photochromic charged molecules, transient radicals created by photochemical reactions, and the electronically photoexcited species. Diffusional behaviors of these intermediates are different from those of stable molecules, which have been investigated extensively so far. The investigations of the diffusion of these species will provide opportunity to reveal the unique intermolecular interaction between the intermediates and matrix. Furthermore, by using products of photochemical reactions as probe molecules, the molecular dynamics of the system can be studied. This information will be valuable for understanding photochemistry in solution.     

Translational diffusion of macromolecules and nanoparticles modeled as non-overlapping bead arrays in an effective medium

There are three objectives to the present work. First, starting from a boundary element (BE) formulation of low Reynolds number hydrodynamics, model the translational diffusion of macromolecules modeled as an array of non-overlapping beads, and show how this approach is equivalent to previous formulations of "bead hydrodynamics" and under what conditions. Second, show how this approach can be improved upon by accounting for the variation in forces over the surfaces of individual beads and also extending the approach to a gel modeled as an effective medium, EM. Third, develop a "combined obstruction and hydrodynamic effect" model of the translational diffusion of irregularly shaped macromolecules in a gel. In one of the cases studied, the BE approach is shown to be equivalent to previous "bead model" formulations in which intersubunit hydrodynamic interaction is modeled using the Rotne-Prager tensor. A bead model that accounts for the variation in hydrodynamic stress forces over the individual bead surfaces is shown to be in best agreement with exact results for simple bead arrays made up of 2-4 subunits. The translational diffusion of rods, modeled as strings of from 2 to 100 touching beads in dilute gels is examined. Interpolation formulas valid over a range of gel concentrations and rod lengths are derived for the parallel and perpendicular components of the diffusion tensor as well as the orientationally averaged diffusion tensor. The EM model accounts for the long-range hydrodynamic interaction exerted by the gel support matrix on the diffusing particle of interest but does not account for the reduction in diffusion caused by the direct obstruction of the gel, or steric effect. Both effects are accounted for by writing the translational diffusion in a gel as the product of two terms representing long-range hydrodynamic interaction and steric effects. Finally, the diffusion of a 564 base pair DNA in a 2% agarose gel is examined and model results are compared to experiment (Pluen, A.; Netti, P. A.; Jain, R. K.; Berk, D. A. Biophys. J. 1999, 77, 542-552). For reasonable choices of model parameters, fair agreement between theory and experiment is achieved.     

A study of the relation between translational and rotational diffusion through measurement of molecular recollision

Translational and rotational diffusion rates of perdeuterated tempone (PDT) in ethanol are determined using electron paramagnetic resonance spectroscopy. The translational motion is measured on two scales: the macroscopic, as represented by the Heisenberg spin-exchange rate, and the microscopic, which entails recollisions between the same spin-exchange particle pair. The spin-exchange and recollision rates are used together to calculate the overall translational diffusion coefficient without recourse to assumptions concerning the value of the Stokes radius or collision distance. When observed as a function of solvent isothermal compressibility, the recollision time in ethanol is displaced from the common alkane curve at low temperatures but joins that curve at higher temperatures. Rotational correlation times in ethanol are obtained and show a decreasing rotation-translation coupling with increasing temperature, revealing a pattern that is qualitatively identical with respect to both collision and recollision. In comparison, an examination of PDT diffusion in toluene reveals an increasing rotation-translation coupling with increasing temperature. The contrasting behavior of the coupling in the two solvents is attributable to the degree of anisotropy in PDT rotation.     

NMR diffusion studies of translational properties of oil inside core-shell latex particles

The diffusion behavior of core-shell latex particles with a liquid core of hexadecane and a solid polystyrene shell in water solution has been studied using the pulsed field gradient spin-echo (PFG-SE) NMR technique. The apparent diffusion coefficient and the root mean square displacement of oil were strongly dependent on the diffusion time Delta. With increasing diffusion time, the obstructing effect from the particle wall caused a decrease in the apparent oil diffusion coefficient. The root mean square displacement of oil inside the particle core was constant for all diffusion times and was used for the calculation of the particle radius. The volume fraction dependence of the apparent diffusion coefficient was found to be roughly consistent with the hard-sphere model. The diffraction pattern in the echo decay predicted from the q-space formalism for molecules diffusing inside a spherical cavity was almost completely smeared out due to polydispersity and wall relaxation effects. It was observed that 10-20% (w/w) of the particle shell consisted of hexadecane. This fact imparted a slow component to the echo decay, since the exchange time between oil in the shell and oil in the cavity was slow, which further contributed to the smearing out of the diffraction pattern. It was concluded that by using the core-shell concept very good signal-to-noise is obtained in the PFG-SE experiment, thus making possible studies of translational properties of colloidal particles in different environments to an extent that previously has been very difficult to perform.     

Enhanced translational diffusion of rubrene in sucrose benzoate

The translational diffusion of rubrene in the fragile molecular glass former, sucrose benzoate (SB) (fragility index m approximately 94), has been studied from T(g)+6 K to T(g)+71 K(T(g)=337 K) by using the technique of holographic fluorescence recovery after photobleaching. In the temperature range of the measurements, the translational relaxation functions were observed to decay exponentially, indicating that Fick's law of diffusion governs the translational motion of rubrene in sucrose benzoate. The value of the translational diffusion coefficient D(T) obtained from the 1e time of the translational relaxation function varied from 5.3 x 10(-15) cm2 s(-1) at 343 K to 5.0x10(-9) cm2 s(-1) at 408 K. The temperature dependence of D(T) for diffusion of rubrene in SB is compared with that of the viscosity and the dielectric relaxation time tau(D) of SB. The temperature dependence of D(T) is weaker than that of Teta for T<1.2T(g) but tracks the reciprocal of the dielectric relaxation time 1tau(D) for 1.05T(g)相似文献   

Anomalous diffusion and cage effects in the isotropic phase of a liquid crystal

The translational motion of 4-n-hexyl-4'-cyanobiphenyl (6CB) in its isotropic phase has been studied by atomistic molecular dynamics simulation from 280 to 330 K. The mean square displacement shows evidence of a subdiffusive dynamics, with a plateau that becomes very apparent at the lowest temperatures. A three-time self-intermediate scattering function reveals that this plateau is connected with a homogeneous dynamics that, at longer times, becomes heterogeneous and finally exponential. These features are shared by, for example, a high-density system of hard spheres, which supports the universal character of the translational dynamics of liquids in their supercooled condition. As predicted by the idealized version of the mode-coupling theory (MCT), the diffusion coefficient dependence upon temperature is well described by a power law, with a critical temperature very close to that obtained by experimental measurements on orientational relaxation. This agreement might indicate a complete freezing of both rotational and translational intradomain dynamics. The time-temperature superposition principle also holds. The shape of the cage that surrounds a 6CB molecule has been reconstructed, and this analysis suggests a preferential side-by-side arrangement of molecules, which locally tend to align their long axes even in the isotropic phase.     

Thermodynamic driving force for diffusion: comparison between theory and simulation

In previous work, lattice density functional theory equations have been recast into differential form to determine a property whose gradient is universally proportional to the diffusive flux. For color counter diffusion, this property appears as the impingement rate onto vacancies and molecules of a species whose density gradient can be influenced by diffusion. Therefore, the impingement rate of a diffusing molecule depends on the mobility of its surroundings. In order to determine the validity of this finding, molecular dynamics simulations of color counter diffusion were performed in which the mobility of the solvent was varied to determine if the flux of the diffusing species responded to the change when all other factors, such as density gradient, available volume, and temperature are held constant.     

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.     

Rotational diffusion tensors for non-spherical molecules

The rotational diffusion tensors of several rigid molecules are determined from the rotational friction tensor. The molecular friction tensor is modeled as a sum over the translational Stokes law friction coefficients of the constituent atoms of the molecule. Agreement of the theory with experimental rotational diffusion constants and onentational correlation times is surprisingly good.     

Guanidinium chloride molecular diffusion in aqueous and mixed water-ethanol solutions

Solutions containing guanidinium chloride (GdmCl), or equivalently guanidine hydrochloride (GdnHCl), are commonly used to denature macromolecules such as proteins and DNA in, for example, microfluidics studies of protein unfolding. To design and study such applications, it is necessary to know the diffusion coefficients for GdmCl in the solution. To this end, we use molecular dynamics simulations to calculate the diffusion coefficients of GdmCl in water and in water-ethanol solutions, for which no direct experimental measurements exist. The fully atomistic simulations show that the guandinium cation Gdm (+) diffusion decreases as the concentration of both Gdm (+) and ethanol in the solution increases. The simulations are validated against available literature data, both transformed measured viscosity values and computed diffusion coefficients, and we show that a prudent choice of water model, namely TIP4P-Ew, gives calculated diffusion coefficients in good agreement with the transformed measured viscosity values. The calculated Gdm (+) diffusion behavior is explained as a dynamic mixture of free cation, stacked cation, and ion-paired species in solution, with weighted contributions to Gdm (+) diffusion from the stacked and paired states helping explain measured viscosity data in terms of atom-scale dynamics.     

Mapping concentration profiles within the diffusion layer of an electrode: Part III. Steady-state and time-dependent profiles via amperometric measurements with an ultramicroelectrode probe

A platinum-disk ultramicroelectrode is used to monitor amperometrically the concentrations of the electroactive substrate and of its electrogenerated product(s) inside the diffusion layer created by a larger working electrode. This allows a direct monitoring of the target species concentration profiles without any assumption even when diffusion coefficients differ significantly. The validity of the method is established experimentally through the study of the one-electron reversible oxidation of the Fe(CN)₆³⁻/Fe(CN)₆⁴⁻ couple in aqueous KCl, under steady-state or under transient diffusion conditions. Under steady-state conditions, the results compare excellently with those we obtained by means of the potentiometric method reported in Part II of this series. Under transient diffusion conditions, the measured concentration profiles match perfectly those predicted for planar diffusion, which demonstrates the interest of the method for the analysis of dynamic diffusion-kinetic problems. The validity of the method in a complex diffusional situation is established as previously (Part II) by the investigation of the effect of a conproportionation reaction taking place during the second reduction of tetracyanoquinodimethane (TCNQ) in DMF.     

Effects of translational and rotational diffusion on the association in kinetic model of nucleation

Kinetics of an association and dissociation of single elements with the effects of translational and rotational diffusion and angular limitations is discussed. Separated clusters embedded in a solution of orientable single elements are considered.Steady-state positional and angular distribution of single elements is calculated from the equation of translational-rotational diffusion and the boundary conditions proposed for orientation-limited association. Although spherical orientable elements are assumed, the model can be used for non-spherical particles with aspect ratios close to unity.Diffusion-limited rate constants of association and dissociation are proposed which depend on translational and rotational diffusion constants of single elements, the tolerance angle of the association, and the cluster size.Effective concentration of single elements and effective rate constants are expressed by the equilibrium and diffusion-limited rate constants. Effects of finite diffusion rates and finite tolerance angle are discussed.The equations of the kinetic model of nucleation are modified due to the diffusion-limited rate of the association.     

Transient diffusion in a tube with dead ends

A particle diffusing in a tube with dead ends, from time to time enters a dead end, spends some time in the dead end, and then comes back to the tube. As a result, the particle spends in the tube only a part of the entire observation time that leads to slowdown of its diffusion along the tube. We study the transient diffusion in a tube with periodic identical dead ends formed by cavities of volume V(cav) connected to the tube by cylindrical channels of length L and radius a, which is assumed to be much smaller than the tube radius R and the distance l between neighboring dead ends. Assuming that the particle initial position is uniformly distributed over the tube, we analyze the monotonic decrease of the particle diffusion coefficient D(t) from its initial value D(0)=D, which characterizes diffusion in the tube without dead ends, to its asymptotic long-time value D(infinity)=D(eff)相似文献   

Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking

Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is connected with non-ergodic behaviour. In such cases the time averages remain random variables and hence irreproducible. Here we present a detailed analysis of the time averaged mean squared displacement for systems governed by anomalous diffusion, considering both unconfined and restricted (corralled) motion. We discuss the behaviour of the time averaged mean squared displacement for two prominent stochastic processes, namely, continuous time random walks and fractional Brownian motion. We also study the distribution of the time averaged mean squared displacement around its ensemble mean, and show that this distribution preserves typical process characteristics even for short time series. Recently, velocity correlation functions were suggested to distinguish between these processes. We here present analytical expressions for the velocity correlation functions. The knowledge of the results presented here is expected to be relevant for the correct interpretation of single particle trajectory data in complex systems.     

Residue-specific real-time NMR diffusion experiments define the association states of proteins during folding

Characterizing the association states of proteins during folding is critical for understanding the nature of protein-folding intermediates and protein-folding pathways, protein aggregation, and disease-related aggregation. To study the association states of unfolded, folded, and intermediate species during protein folding, we have introduced a novel residue-specific real-time NMR diffusion experiment. This experiment, a combination of NMR real-time folding experiments and 3D heteronuclear pulsed field gradient NMR diffusion experiments (LED-HSQC), measures hydrodynamic properties, or molecular sizes, of kinetic species directly during the folding process. Application of the residue-specific real-time NMR diffusion experiments to characterize the folding of the collagen triple helix motif shows that this experiment can be used to determine the association states of unfolded, folded, and kinetic intermediates with transient lifetimes simultaneously. The ratio of the apparent translational diffusion coefficients of the unfolded to the folded form of the triple helix is 0.59, which correlates very well with a theoretical ratio for monomer to linear trimer. The apparent diffusion coefficients of the kinetic intermediates formed during triple helix folding indicate the formation of trimer-like associates which is consistent with previously published kinetic and relaxation data. The residue-specific time dependence of apparent diffusion coefficients of monomer and trimer peaks also illustrates the ability to use diffusion data to probe the directionality of triple helix formation. NMR diffusion experiments provide a new strategy for the investigation of protein-folding mechanisms, both to understand the role of kinetic intermediates and to determine the time-dependent aggregation processes in human diseases.