Microscopic diffusion and hydrodynamic interactions of hemoglobin in red blood cells

The cytoplasm of red blood cells is congested with the oxygen storage protein hemoglobin occupying a quarter of the cell volume. The high protein concentration leads to a reduced mobility; the self-diffusion coefficient of hemoglobin in blood cells is six times lower than in dilute solution. This effect is generally assigned to excluded volume effects in crowded media. However, the collective or gradient diffusion coefficient of hemoglobin is only weakly dependent on concentration, suggesting the compensation of osmotic and friction forces. This would exclude hydrodynamic interactions, which are of dynamic origin and do not contribute to the osmotic pressure. Hydrodynamic coupling between protein molecules is dominant at short time- and length scales before direct interactions are fully established. Employing neutron spin-echo-spectroscopy, we study hemoglobin diffusion on a nanosecond timescale and protein displacements on the scale of a few nanometers. A time- and wave-vector dependent diffusion coefficient is found, suggesting the crossover of self- and collective diffusion. Moreover, a wave-vector dependent friction function is derived, which is a characteristic feature of hydrodynamic interactions. The wave-vector and concentration dependence of the long-time self-diffusion coefficient of hemoglobin agree qualitatively with theoretical results on hydrodynamics in hard spheres suspensions. Quantitative agreement requires us to adjust the volume fraction by including part of the hydration shell: Proteins exhibit a larger surface/volume ratio compared to standard colloids of much larger size. It is concluded that hydrodynamic and not direct interactions dominate long-range molecular transport at high concentration.     

Lateral diffusion in an archipelago. Distance dependence of the diffusion coefficient.

An understanding of the distance dependence of the lateral diffusion coefficient is useful in comparing the results of diffusion measurements made over different length scales, and in analyzing the kinetics of mobile redox carriers in organelles. A distance-dependent, concentration-dependent diffusion coefficient is defined, and it is evaluated by Monte Carlo calculations of a random walk by mobile point tracers in the presence of immobile obstacles on a triangular lattice, representing the diffusion of a lipid or a small protein in the presence of immobile membrane proteins. This work confirms and extends the milling crowd model of Eisinger, J., J. Flores, and W. P. Petersen (1986. Biophys J. 49:987-1001). Similar calculations for diffusion of mobile particles interacting by a hard-core repulsion yield the distance dependence of the self-diffusion coefficient. An expression for the range of short-range diffusion is obtained, and the distance scales for various diffusion measurements are summarized.     

Dynamics of Small Molecules in a Dense Polymer Matrix: Molecular Dynamics Studies

Abstract

The anomalous diffusion regime appearing in the self-diffusion of small molecules in bulk amorphous polymers has been extensively studied by molecular dynamics simulations. A rather long simulation of duration ～ 10 ^?8 s is performed on a polyethylene-like simple polymer model containing either oxygen molecules or helium atoms as a diffusant. Dynamic properties evaluated for these diffusants are the mean-square displacement, the van Hove self correlation function, and the self part of the density autocorrelation. It is first confirmed that the anomalous diffusion regime appears in a few hundred picoseconds for oxygen molecule, while the Einstein relation adopted beyond this regime results in the self-diffusion coefficient of the order of ～ 10^?5 cm²/s. This anomaly is still observed for helium that diffuses much faster than oxygen. In the anomalous diffusion regime, it is found that the correlation functions for the two diffusants show characteristic features and become essentially the same as time is scaled appropriately. These features allow the estimation of the two characteristic spatial scales which are probably dominated by the microstructure of the polymer matrix, namely, the cage size and the distance between adjacent cages. The time dependence of the mean-square displacements of the two diffusants can be well interpreted by these characteristic spatial scales as time is scaled with the self-diffusion coefficients. It is shown that the anomalous diffusion regime arises from the inhomogeneous microstructure of the polymer matrix.     

Comparison of the enhanced steady-state diffusion of calcium by calbindin-D9K and calmodulin: possible importance in intestinal calcium absorption

The diffusion of calcium was measured using the unidirectional flux of 45Ca across an aqueous layer. The aqueous layer was bounded by two dialysis membranes and convection was eliminated by gelling the aqueous layer with agarose. The apparent self-diffusion coefficient was determined by the dependence of the tracer flux on the diffusion distance. The apparent self-diffusion coefficient increased linearly with the concentration of calbindin-D9K and calmodulin, but the effect of calmodulin was markedly less than that of calbindin-D9K. This difference is attributed to the lower association constant for calmodulin. The ion-exchange resin Chelex-100 also increased the steady-state of 45Ca, but the effect of Chelex-100 was much less efficient than the effect of calbindin-D9K. The mechanism of enhanced diffusion was attributed to an enhanced gradient of total 45Ca. These results indicate that the steady-state unidirectional calcium flux is a superposition of free calcium diffusion and bound calcium diffusion, with only a small contribution due to a 'bucket brigade' mechanism. We suggest that this phenomenon may be important in calcium absorption across the intestine.     

Relationship between Recrystallization Rate of Ice Crystals in Sugar Solutions and Water Mobility in Freeze-Concentrated Matrix

To better understand the relation between recrystallization rate and water mobility in freeze-concentrated matrix, isothermal ice recrystallization rates in several sugar aqueous solutions and self-diffusion coefficients of water component in corresponding freeze-concentrated matrix were measured. The sugars used were fructose, glucose, maltose, and sucrose. The sugar concentrations and temperature were varied so that ice contents for all samples were almost equal. Neither recrystallization rates nor diffusion coefficients depended uniformly on temperature. The recrystallization rates increased with increasing the diffusion coefficients, and a direct relationship was found between recrystallization rate and diffusion coefficient. This indicated that self-diffusion coefficient of water component in freeze-concentrated matrix is a useful parameter for predicting and controlling recrystallization rate in sugar solutions relevant to frozen desserts.     

On the relative contribution of viscous flow vs. diffusional (frictional) flow to the stationary state flow of water through a "tight" membrane

The practice of calculating the diffusion contribution to the total pressure-driven flow of water through a tight membrane by using the self-diffusion coefficient for tritiated water is examined by a theoretical analysis. Equations of motion for water and membrane in pressure-driven water flow and water, membrane, and tritiated water in self-diffusion of tritiated water are adapted from Bearman and Kirkwood (1958). These equations of motion are used to develop an equation for the pressure-driven flow of water. Because of the lack of specific information about the detailed structure of most membranes, as well as considerations of the need to eliminate some of the mathematical difficulties, an "equivalent capillary" model is used to find a solution to the equation of motion. The use of the equivalent capillary model and possible ambiguities in distinctions between diffusion and hydrodynamic flow are discussed     

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.     

Lateral diffusion of cholesterol and dimyristoylphosphatidylcholine in a lipid bilayer measured by pulsed field gradient NMR spectroscopy

The pulsed field gradient NMR method for measuring self-diffusion has been used for a direct determination of the lateral diffusion coefficient of cholesterol, fluorine labeled at the 6-position, for an oriented lamellar liquid-crystalline phase of dimyristoylphosphatidylcholine (DMPC)/cholesterol/water. It is found that the diffusion coefficients of DMPC and cholesterol are equal over a large temperature interval. The apparent energy of activation for the diffusion process (58 kJ/mol) is about the same as for a lamellar phase of DMPC/water, whereas the phospholipid lateral diffusion coefficient is approximately four times smaller in the presence of cholesterol.     

Parametrization of direct and soft steric-undulatory forces between DNA double helical polyelectrolytes in solutions of several different anions and cations.

Directly measured forces between DNA helices in ordered arrays have been reduced to simple force coefficients and mathematical expressions for the interactions between pairs of molecules. The tabulated force parameters and mathematical expressions can be applied to parallel molecules or, by transformation, to skewed molecules of variable separation and mutual angle. This "toolbox" of intermolecular forces is intended for use in modelling molecular interactions, assembly, and conformation. The coefficients characterizing both the exponential hydration and the electrostatic interactions depend strongly on the univalent counterion species in solution, but are only weakly sensitive to anion type and temperature (from 5 to 50 degrees C). Interaction coefficients for the exponentially varying hydration force seen at spacings less than 10 to 15 A between surfaces are extracted directly from pressure versus interaxial distance curves. Electrostatic interactions are only observed at larger spacings and are always coupled with configurational fluctuation forces that result in observed exponential decay lengths that are twice the expected Debye-Huckel length. The extraction of electrostatic force parameters relies on a theoretical expression describing steric forces of molecules "colliding" through soft exponentially varying direct interactions.     

A model for the diffusion of fluorescent probes in the septate giant axon of earthworm. Axoplasmic diffusion and junctional membrane permeability.

The diffusion of the three fluorescent probes dichlorofluorescein, carboxyfluorescein, and Lucifer Yellow within the septate median giant axon of the earthworm was monitored using fluorometric methods. A diffusion model was derived that allowed computation of the apparent axoplasmic diffusion coefficient, junctional membrane permeability (septal membranes), and plasma membrane permeability for each probe. Dichlorofluorescein and carboxyfluorescein have similar apparent axoplasmic diffusion coefficients, which were reduced by a factor of eight relative to that predicted from the Einstein-Stokes equation. Nonspecific reversible binding appears to be the major cause of the retarded diffusion coefficients. Junctional membrane permeability for dichlorofluorescein was 4.7 to 73-fold greater than that for carboxyfluorescein. This difference could not be explained on the basis of molecular size but can be explained by the difference in charge between the two molecules. Diffusion coefficients and junctional membrane permeabilities remained constant with time for both dyes. The diffusion of Lucifer Yellow within the axoplasm and permeability through the junctional membranes did not remain constant with time but declined. From this it was inferred that Lucifer Yellow experienced a slow, irreversible binding to axoplasmic elements. All three probes had finite plasma membrane permeabilities.     

Microscopic versus macroscopic diffusion in model membranes by electron spin resonance spectral-spatial imaging.

The macroscopic and the microscopic diffusion coefficients of a phospholipid spin label (16-PC) in the model membrane 1-palmitoyl-2-oleoyl-sn-glycero-phosphatidylcholine have been measured simultaneously in the same sample utilizing the new technique of spectral-spatial electron spin resonance imaging. The macroscopic diffusion coefficient Dmacro for self-diffusion of 16-PC spin label is obtained from imaging the concentration profiles as a function of time, and it is (2.3 +/- 0.4) x 10(-8) cm2/s at 22 degrees C. The microscopic diffusion coefficient Dmicro for relative diffusion of the spin probes is obtained from the variation of the spectral line broadening with spin label concentration, which is due to spin-spin interactions. Dmicro is found to be substantially greater than Dmacro for the same sample at the same conditions, and is estimated to be at least (1.0 +/- 0.4) x 10(-7) cm2/s. Possible sources for their difference are briefly discussed in terms of the models used for Dmicro.     

The self-diffusion of water in Artemia cysts

The self-diffusion coefficient of water molecules has been measured by nuclear magnetic resonance in cysts of Artemia over a wide range of hydration. Compared to the value for bulk water, the diffusion coefficient is reduced by a factor of 7 at the highest hydration and by approximately 100 at the lowest hydration. The results are used to evaluate various models that have been proposed to account for the reduction of water self-diffusion coefficients in complex systems.     

Diffusion of Ions in Myelinated Nerve Fibers

The diffusion of ions towards or away from the inner side of the nodal membrane in preparations, the cut ends of which are placed in various media, was investigated. The ion concentration changes were calculated by numerical solution of the unidimensional electrodiffusion equation under a variety of media compositions, axoplasmic diffusion coefficients, and internal anionic compositions. The potassium and cesium ion diffusion along the axon towards the node was determined experimentally by two different electrophysiological methods. On the basis of comparison between the experimental data and the computational predictions the axoplasmic potassium ion diffusion coefficient was determined to be almost equal to that in free aqueous solution, while that of cesium ion was close to one half of that in aqueous solution. Utilizing the values of diffusion parameters thus determined, we solved the electrodiffusion equation for a number of common experimental procedures. We found that in short fibers, cut 0.1-0.2 cm at each side of the node, the concentration approached values close to the new steady-state values within 5-30 min. In long fibers (over 1 cm long) steady-state concentrations were obtained only after a few hours. Under some conditions the internal concentrations transiently overshot the steady-state values. The diffusion potentials generated in the system were also evaluated. The ion concentration changes and generation of diffusion potential cannot be prevented by using side pools with cation content identical to that of the axoplasm.     

Kinetic Theory Model for Ion Movement through Biological Membranes: III. Steady-State Electrical Properties with Solution Asymmetry

An electrodiffusion model for plasma membrane ion transport, which takes into account the influence of high electric field strengths and ion-membrane molecule interactions, is presented and analyzed. A generalized Nernst-Planck equation for steady-state situations is derived which has electric field-dependent mobility and diffusion coefficients. Under the assumption of a constant electric field within the membrane, this equation is integrated to give a more general form of the Goldman equation. Based on this equation numerical computations of ionic chord conductance as a function of applied electric field strength were carried out for several permeant ion concentration ratios. The model is capable of yielding significantly larger rectification ratios than is the Goldman equation. Further, high field asymptotes to the current vs. electric field strength curve do not generally intersect at the origin.     

Permeability of lysozyme tetragonal crystals to water

Diffusion of water within cross-linked tetragonal crystals of hen egg-white lysozyme has been measured and simulated on a computer using the X-ray structure of water-filled channels within the crystal lattice. Relative to the self-diffusion coefficient of bulk water molecules, the experimental diffusion coefficient of water within the crystal was found to be 13 times reduced in the (001) crystallographic plane and 5 times reduced in the [001] direction. Comparison of the experimental and computer simulated diffusion coefficients shows that steric limitations for water diffusion are mostly responsible for this reduction of the water diffusion in the crystal, with the self-diffusion coefficient of intracrystalline water reduced by no more than 30–40% as compared to that of bulk water.     

Macromolecular diffusion of biological polymers measured by confocal fluorescence recovery after photobleaching.

Fluorescence recovery after photobleaching with an unmodified confocal laser scanning microscope (confocal FRAP) was used to determine the diffusion properties of network forming biological macromolecules such as aggrecan. The technique was validated using fluorescein isothiocyanate (FITC)-labeled dextrans and proteins (molecular mass 4-2000 kDa) at 25 degrees C and with fluorescent microspheres (207 nm diameter) over a temperature range of 5-50 degrees C. Lateral diffusion coefficients (D) were independent of the focus position, and the degree and extent of bleach. The free diffusion coefficient (Do) of FITC-aggrecan determined by confocal FRAP was 4.25 +/- 0.6 x 10(-8) cm2 s-1, which is compatible with dynamic laser light scattering measurements. It appeared to be independent of concentration below 2.0 mg/ml, but at higher concentrations (2-20 mg/ml) the self-diffusion coefficient followed the function D = Do(e)(-Bc). The concentration at which the self-diffusion coefficient began to fall corresponded to the concentration predicted for domain overlap. Multimolecular aggregates of aggrecan ( approximately 30 monomers) had a much lower free diffusion coefficient (Do = 6.6 +/- 1.0 x 10(-9) cm2 s-1) but showed a decrease in mobility with concentration of a form similar to that of the monomer. The method provides a technique for investigating the macromolecular organization in glycan-rich networks at concentrations close to those found physiologically.     

Intracellular diffusion of water

Self-diffusion of cell water has been measured at diffusion times ranging from 0.3 ms to 1.0 s for human red cells, yeast, and brine shrimp using various pulsed gradient NMR methods. Intracellular diffusion coefficients and membrane permeabilities are calculated from these data with the aid of previous theoretical results for regularly spaced permeable planar barriers. The intracellular diffusion coefficients of water range from 1.2 X 10(-6) to 6 X 10(-6) cm2/s for the various samples. Outer-membrane permeabilities to water range from 0.0001 to 0.01 cm/s. The self-diffusion coefficient of lipid in a sample of human breast adipose tissue was found to be 1.5 X 10(-7) cm2/s.     

An NMR study of the temperature dependence of the coefficient of water self-diffusion through lipid bilayer membranes

The temperature dependence of the coefficient of water self-diffusion through plane-parallel lipid multilayers of the phospholipid dioleoylphosphatidylcholine oriented on a glass support has been studied in the temperature range of 20-60 degrees C by the method of NMR with magnetic field pulse gradient. The values of the coefficients of transbilayer water diffusion are by four orders of magnitude less than for bulky water and ten times less than the coefficients of lateral diffusion of the lipid under the same conditions. The temperature dependence of the coefficient of water diffusion is described by the Arrhenius law with an apparent activation energy of about 41 kJ/mol, which far exceeds the activation energy for the diffusion of bulky water (18 kJ/mol). The experimental data were analyzed using a "dissolving-diffusion" model, by simulating the passage of water through membrane channels, and by analyzing the exchange of water molecules in states with different modes of translation mobility, including pore channels and bilayer "defects". Each of the approaches used made it possible to take the significance of bilayer permeability for the apparent energy of activation of water diffusion into account and estimate the energies of activation of water diffusion in the hydrophobic moiety of the bilayer, which were found to be close to the values for bulky water. The coefficients of water diffusion in the system under examination and the coefficients of permeation of water through the bilayer were estimated, and the effect of bilayer "defects" on the coefficients of water diffusion along and across bilayers was studied.