Protein effective rotational correlation times from translational self-diffusion coefficients measured by PFG-NMR

Molecular rotational correlation times are of interest for many studies carried out in solution, including characterization of biomolecular structure and interactions. Here we have evaluated the estimates of protein effective rotational correlation times from their translational self-diffusion coefficients measured by pulsed-field gradient NMR against correlation times determined from both collective and residue-specific (15)N relaxation analyses and those derived from 3D structure-based hydrodynamic calculations. The results show that, provided the protein diffusive behavior is coherent with the Debye-Stokes-Einstein model, translational diffusion coefficients provide rapid estimates with reasonable accuracy of their effective rotational correlation times. Effective rotational correlation times estimated from translational diffusion coefficients may be particularly beneficial in cases where i) isotopically labelled material is not available, ii) collective backbone (15)N relaxation rates are difficult to interpret because of the presence of flexible termini or loops, or iii) a full relaxation analysis is practically difficult because of limited sensitivity owing to low protein concentration, high molecular mass or low temperatures.     

Water transport and ion-water interaction in the gramicidin channel

The diffuse permeability and the diffusion coefficient of water (Dw) in the gramicidin channel is determined from the osmotic water permeability of the channel and "single file" pore theory. Dw is about 7% of the self-diffusion coefficient of bulk water. The diffusion coefficient of a single water molecule alone in the channel is also determined and is about equal to the value in bulk water. This provides an estimate of the mobility of water on the channel walls in the absence of water-water interaction. Since the gramicidin channel walls should be representative of uncharged polar protein surfaces, this result provides direct evidence that the presence of a cation in the channel reduces the hydraulic water permeability by a factor ranging from 60 for Tl+ to 5 for Na+. The diffusion coefficient of a cation (Dc) in the channel is estimated and compared with Dw. For Na+ it is found that Dc approximately equal to Dw, which implies that the movement of the row of water molecules through the channel determines the local mobility of Na+. Thus, it seems that short range ion-wall interactions are not important in determining the channel conductance for Na+. In contrast, for Li+, local ion-wall interactions probably do limit the conductance.     

Temperature dependence of macromolecular interactions in dilute and concentrated hemoglobin solutions

We studied the temperature-dependent effects of intramolecular interactions on the mutual diffusion coefficient of normal human oxygenated hemoglobin in salt solution. We used photon correlation spectroscopy to observe this temperature dependence of the mutual diffusion coefficient of two protein concentrations (1.25 and 17.0 g %) between 13 and 37°C. This coefficient was our probe for monitoring temperature-dependent structural changes of hydrated hemoglobin in solution. Comparison of our measured diffusion coefficient with that predicted by the Stokes-Einstein relationship in terms of solvent or solution viscosity showed a clear transition in the conformation of hemoglobin at approximately 22°C, independent of the hemoglobin concentration. We postulated that at this physiological temperature, a considerable quaternary rearrangement of the hemoglobin chains takes place. We believe this rearrangement changes the effective volume and the hydration sphere of the hemoglobin macromolecule.     

Brownian dynamics simulations of probe and self-diffusion in concentrated protein and DNA solutions.

We have developed a Brownian dynamics algorithm for simulating probe and self-diffusion in concentrated solutions of DNA and protein. In these simulations, proteins are represented as spheres with radii given by their hydrodynamic radii, while DNA is modeled as a wormlike chain of hydrodynamically equivalent spherical frictional elements. The molecular interaction potentials employed by the program allow for intramolecular stretching and bending motions of the DNA chains, short-range Lennard-Jones interactions, and long-range electrostatic interactions. To test the program, we have carried out simulations of bovine serum albumin (BSA) probe diffusion and DNA self-diffusion in solutions of short-chain DNA as a function of both DNA concentration and solution ionic strength. In addition, we report on simulations of BSA self-diffusion as a function of BSA concentration and ionic strength. Based on a comparison to available experimental data, we find that our simulations accurately predict these transport properties under conditions of physiological salt concentration and predict the stronger concentration dependence observed at lower salt concentrations. These results are discussed in light of the nature of the intermolecular interactions in such systems and the approximations and limitations of the simulation algorithm.     

The concentration dependence of the hemoglobin mutual diffusion coefficient

Laser correlation Spectroscopy was used to measure the mutual diffusion coefficient, D, of human cyanomethemoglobin (Fe⁺⁺⁺:CN) at varying protein concentrations. These measurements were male at 20°C in a 0.1 M phosphate buffer solution at pH 7.0. For low protein concentrations we find D = (6.43 ± 0.26) × 10^?7 cm²/S and that there is a near linear decrease from this value at higher concentrations. The linear relation between the diffusion coefficient and protein concentration allows us to deduce the value of the linear frictional volume fraction coefficient, K_f= 7.75. and to extrapolate to hemoglobin concentrations equivalent to that in the red blood cell where we estimate D = 4.25 × 10^?7 cm²/s Various theoretical predictions of the dependence of the mutual diffusion coefficient on concentration are tested; we find that the generalized Stokes-Einstein relation can be made to fit our high concentration data if we assume a hard-sphere model and if we include a term involving a hydrodynamic interaction integral.     

Concentration dependence of protein diffusion.

The concentration dependence of protein self-diffusion constants is described by a free volume diffusion theory which accounts for the effects of local protein concentration fluctuations.     

A simulation study of the anomalous osmotic behavior of red cells

The factors responsible for movements of water across cell membranes were described mathematically and incorporated into a model which simulates water balance in the cell. Included in the model are a variable charge and osmotic coefficient of hemoglobin, a Na/K pump whose rate varies with ionic concentrations, and the standard electroneutrality and osmotic equilibrium assumptions. The model was used to investigate the phenomena whereby human red cells placed in media of varying tonicities exhibit steady state volume changes less than those predicted by van't Hoff's Law. The model results showed that this anomalous osmotic behavior was primarily due to changes in the osmotic coefficient of hemoglobin as its concentration in the cell varied. A second factor accounting for a part of this behavior was the alteration in the rate of the Na/K pump due to intracellular ionic concentration changes as cell volume varied. The effect of variable electrical charge on the hemoglobin molecule was found to be in the wrong direction to account for the observed osmotic behavior. Also, this effect was seen to produce relatively large changes in cell membrane potential, a result inconsistent with experimental data. It was concluded from the model results that the anomalous osmotic behavior of human red cells is primarily due to the variation in the osmotic coefficient of hemoglobin as the cell volume changes, and that the variable charge effect on the hemoglobin molecule, if it exists, does not play a role in this response.     

Diffusion coefficients of segmentally flexible macromolecules with two spherical subunits

The translational and rotational diffusion coefficients have been calculated for a simple, segmentally flexible model: the hinged dumbbell (HD). In the HD, two spherical subunits are attached to an universal joint by means of frictionless connectors. In addition to the case in which hydrodynamic interactions are neglected (NI), we have also considered two more cases, including hydrodynamic interaction by means of the Kirkwood-Riseman approximate treatment (KR) and using accurate procedure based in the series expansions for the two-sphere diffusion tensor (SE). Expressions for the friction coefficients of the HD are given for the three cases, and the diffusion coefficients are evaluted inverting the 9 × 9 resistance matrix, for two HDs with different dimensions. The KR treatment, which includes a contribution from the finite volume of the subunits, is shown to be an excellent approximation to the more rigorous procedure. In the NI case for rotation, the various coefficients present different deviations with respect to the SE results. A rough estimate of the errors of the NI relaxation times indicates that they may be smaller than 15% for a HD with identical beads. However, the influence of hydrodynamic interaction should be more important for the rotational diffusivity of a small sphere attached to a larger one. The error of the NI result for the translational diffusion coefficient is of about 25% for the two HDs.     

Hydrodynamics of concentrated proteoglycan solutions

The dynamics of water transport in proteoglycan compartments has been studied in relation to osmotic flow (proteoglycan diffusion) and hydraulic permeability (proteoglycan sedimentation) in concentrated solutions of proteoglycan subunit and native proteoglycan aggregate isolated from Swarm rat chondrosarcoma. A central parameter that describes the kinetics of both types of water movement is the hydrodynamic frictional coefficient of water with proteoglycan. The frictional coefficient is markedly concentration dependent, increasing with increasing concentration, and highlights important structural features and types of organization of the proteoglycans in concentrated solutions. These include the requirements that proteoglycans in the extracellular matrix not to be immobilized but to have translational diffusive mobility and concentration gradients to be osmotically active, that chondroitin sulfate segmental mobility describing translational motion largely determines osmotic flow and hydraulic permeability of the proteoglycans, and that the proteoglycans exhibit an enhanced ability to resist flow as compared to other macromolecules. Additional dynamic studies suggest the formation of transient super-aggregate structures may occur at high concentrations which endows the proteoglycan subunit hydrodynamic properties similar to proteoglycan aggregate.     

The molecular basis of the solution properties of hyaluronan investigated by confocal fluorescence recovery after photobleaching.

Hyaluronan (HA) is a highly hydrated polyanion, which is a network-forming and space-filling component in the extracellular matrix of animal tissues. Confocal fluorescence recovery after photobleaching (confocal-FRAP) was used to investigate intramolecular hydrogen bonding and electrostatic interactions in hyaluronan solutions. Self and tracer lateral diffusion coefficients within hyaluronan solutions were measured over a wide range of concentrations (c), with varying electrolyte and at neutral and alkaline pH. The free diffusion coefficient of fluoresceinamine-labeled HA of 500 kDa in PBS was 7.9 x 10(-8) cm(2) s(-1) and of 830 kDa HA was 5.6 x 10(-8) cm(2) s(-1). Reductions in self- and tracer-diffusion with c followed a stretched exponential model. Electrolyte-induced polyanion coil contraction and destiffening resulted in a 2.8-fold increase in self-diffusion between 0 and 100 mM NaCl. Disruption of hydrogen bonds by strong alkali (0.5 M NaOH) resulted in further larger increases in self- and tracer-diffusion coefficients, consistent with a more dynamic and permeable network. Concentrated hyaluronan solution properties were attributed to hydrodynamic and entanglement interactions between domains. There was no evidence of chain-chain associations. At physiological electrolyte concentration and pH, the greatest contribution to the intrinsic stiffness of hyaluronan appeared to be due to hydrogen bonds between adjacent saccharides.     

Brownian dynamics simulation of probe diffusion in DNA: effects of probe size, charge and DNA concentration

We have used Brownian dynamics simulation to study probe diffusion in solutions of short chain DNA using our previously developed simulation algorithm. We have examined the effect of probe size, charge, and DNA concentration on the probe diffusion coefficient, with the aim of gaining insight into the diffusion of proteins in a concentrated DNA environment. In these simulations, DNA was modeled as a worm-like chain of hydrodynamically equivalent spherical frictional elements while probe particles were modeled as spheres of given charge and hydrodynamic radius. The simulations allowed for both short range Lennard-Jones interactions and long ranged electrostatic interactions between charged particles. For uncharged systems, we find that the effects of probe size and DNA concentration on the probe diffusion coefficient are consistent with excluded volume models and we interpret our results in terms of both empirical scaling laws and the predictions of scaled particle theory. For charged systems, we observe that the effects of probe size and charge are most pronounced for the smallest probes and interpret the results in terms of the probe charge density. For an ionic strength of 0.1 M we find that, below a critical probe surface charge density, the probe diffusion coefficient is largely independent of probe charge and only weakly dependent on the DNA charge. These effects are discussed in terms of the interactions between the probe and the DNA matrix and are interpreted in terms of both the underlying physics of transport in concentrated solutions and the assumptions of the simulation model.     

Adair was right in his time

The subunit molar mass of hemoglobin was established in the 19th century by chemical analysis, the tetramer structure by osmotic pressure determination in 1924 and by the newly developed analytical ultracentrifuge in 1926, which became a powerful tool for biological macromolecule molar mass determinations. The Svedberg equation was derived by eliminating the translational friction coefficient relating to sedimentation and diffusion in the ultracentrifuge in a strictly solute/solvent vanishing concentration two-component system analysis. A differential equation describing the radial equilibrium concentration distribution in the ultracentrifuge was also derived, both yielding the buoyant molar mass (1-nu2rho)M2 term. Many years later it was realized that solutions of biological macromolecules are multicomponent systems and the two-component analysis leads to minor or major erroneous results. Thermodynamic derivation of an equation for multicomponent systems redefines the buoyant molar mass terms by (deltarho/deltac2)muM2, leading to correct molar mass (g/mol) values following determination of the density increment at constant chemical potentials of diffusible solutes, and powerfully connects the analytical sedimentation equation to the osmotic pressure concentration derivative and, in a broad complementary sense, to light, X-ray and neutron scattering experiments. Macromolecular interactions can be studied with high precision and solute-solvent interactions yield powerful information relating to "thermodynamic" hydration, closely related to hydration derived from X-ray diffraction, as well as solute-cosolute interactions. A series of examples is given to demonstrate the correctness and usefulness of the thermodynamic multicomponent system approach. It is a strange fact that in current analytical ultracentrifugation analysis the elegant and powerful multicomponent solution technology is almost totally disregarded and the classical limited validity Svedberg approach is used uniquely.     

Translational diffusion of fluorescent proteins by molecular fourier imaging correlation spectroscopy

The ability to noninvasively observe translational diffusion of proteins and protein complexes is important to many biophysical problems. We report high signal/noise (>or=250) measurements of the translational diffusion in viscous solution of the fluorescent protein, DsRed. This is carried out using a new technique: molecular Fourier imaging correlation spectroscopy (M-FICS). M-FICS is an interferometric method that detects a collective Fourier component of the fluctuating density of a small population of fluorescent molecules, and provides information about the distribution of molecular diffusivities. A theoretical analysis is presented that expresses the detected signal fluctuations in terms of the relevant time-correlation functions for molecular translational diffusion. Furthermore, the role played by optical orientational degrees of freedom is established. We report Fickian self-diffusion of the DsRed tetramer at short timescales. The long-time deviation of our data from Fickian behavior is used to determine the variance of the distribution of the protein self-diffusion coefficient. We compare our results to the expected outcomes for 1), a bi-disperse distribution of protein species, and 2), dynamic disorder of the host solvent.     

NMR investigations of the 4-ethyl guaicol self-diffusion in iota (ι)-carrageenan gels

Self-diffusion coefficient of an aroma molecule (4-ethyl guaicol) was measured using the pulsed field gradient spin echo NMR (PGSE-NMR) method in order to investigate the influence of a macromolecular matrix on its diffusion and release processes. Iota (ι)-carrageenan was used for its ability to form thermoreversible gels in aqueous salt solutions. Variations of the ι-carrageenan and the salt concentrations permitted various gels with different thermal and rheological properties to be obtained. These latter were modified by an isotope effect obtained by preparing gels in D₂O. The NMR self-diffusion measurements realised for water and the aroma molecules indicated neither chemical interactions with ι-carrageenan, nor obstruction effects from the polysaccharide chains. In ι-carrageenan gels, the diffusional phenomenon was highly dependent on the heterogeneous gel structure and controlled by hydrodynamic interactions due to frictional drag between each molecule of the system and water microviscosity changes.     

PFG-NMR measurements of the self-diffusion coefficients of water in equilibrium poly(HEMA-co-THFMA) hydrogels

The self-diffusion coefficients for water in a series of copolymers of 2-hydroxyethyl methacrylate, HEMA, and tetrahydrofurfuryl methacrylate, THFMA, swollen with water to their equilibrium states have been studied at 310 K using PFG-NMR. The self-diffusion coefficients calculated from the Stejskal-Tanner equation, D(obs), for all of the hydrated polymers were found to be dependent on the NMR storage time, as a result of spin exchange between the proton reservoirs of the water and the polymers, reaching an equilibrium plateau value at long storage times. The true values of the diffusion coefficients were calculated from the values of D(obs) in the plateau regions by applying a correction for the fraction of water protons present, obtained from the equilibrium water contents of the gels. The true self-diffusion coefficient for water in polyHEMA obtained at 310 K by this method was 5.5 x 10(-10) m(2)s-1. For the copolymers containing 20% HEMA or more a single value of the self-diffusion coefficient was found, which was somewhat larger than the corresponding values obtained for the macroscopic diffusion coefficient from sorption measurements. For polyTHFMA and copolymers containing less than 20% HEMA, the PFG-NMR stimulated echo attenuation decay curves and the log-attenuation plots were characteristic of the presence of two diffusing water species. The self-diffusion coefficients of water in the equilibrium-hydrated copolymers were found to be dependent on the copolymer composition, decreasing with increasing THFMA content.     

Translational and rotational motions of proteins in a protein crowded environment

Fluorescence correlation spectroscopy (FCS) was used to measure the translational diffusion of labeled apomyoglobin (tracer) in concentrated solutions of ribonuclease A and human serum albumin (crowders), as a quantitative model system of protein diffusive motions in crowded physiological environments. The ratio of the diffusion coefficient of the tracer protein in the protein crowded solutions and its diffusion coefficient in aqueous solution has been interpreted in terms of local apparent viscosities, a molecular parameter characteristic for each tracer-crowder system. In all protein solutions studied in this work, local translational viscosity values were larger than the solution bulk viscosity, and larger than rotational viscosities estimated for apomyoglobin in the same crowding solutions. Here we propose a method to estimate local apparent viscosities for the tracer translational and rotational diffusion directly from the bulk viscosity of the concentrated protein solutions. As a result of this study, the identification of protein species and the study of hydrodynamic changes and interactions in model crowded protein solutions by means of FCS and time-resolved fluorescence depolarization techniques may be expected to be greatly simplified.     

A model to explain the osmotic pressure behavior of hemoglobin and serum albumin

Previously published osmotic pressure data on hemoglobin and bovine serum albumin were used to determine the osmotically unresponsive solvent volume per unit dry mass of protein. A model is presented that accounts for the osmotic pressure of globular proteins based on a surface-associated osmotically unresponsive solvent volume. The model also accounts for changes in the osmotically unresponsive solvent volume owing to changes in pH, cosolute salt concentration, protein conformation, and protein aggregation.