Convective diffusion in parallel flow fields

Laminar motion of two viscous incompressible fluids through each other is treated for two cases: flow along the axis of a circular cylinder, and flow between parallel flat plates. Motion of either fluid entails that of the other. Regarding one fluid as a solvent, the other as a solute, and supposing the system to have ends impermeable to the former, it is found that the solvent streams with the solute down the center of the system, to return in the opposite direction out nearer the walls. Thus diffusion of a dissolved substance through a region in which the solvent is confined produces continual streaming in the latter.     

Untersuchungen zur Sauerstoffdiffusion in wäßrigen Xanthanlösungen

The determination of oxygen diffusion coefficients was carried out by a modified chronoamperometric method using a stationary platinum electrode. The determined diffusion coefficients are related to approximated η₀-values. It was shown a relation of D_i and η₀ according to the HAYDUK-CHENG-potential equation. That means a strong relative lowering of oxygen diffusion coefficients already by low viscosities, but a little influence at high viscosities. A simple laboratory thin film reactor is described, in which the oxygen supply is maintained by diffusion. This reactor is suitable very well for fermentations of viscous fluids.     

The stiffness of dsRNA: hydrodynamic studies on fluorescence-labelled RNA segments of bovine rotavirus.

The sedimentation coefficients of dsRNA segments of bovine rotavirus were determined in the analytical ultracentrifuge. The eleven segments were separated by preparative gel electrophoresis, and isolated by elution from gel pieces. The RNA was labelled by the intercalating fluorescent dye ethidium bromide at a ratio bound dye per base pair between 0.003 to 0.018. The analytical ultracentrifuge was equipped with a fluorescence recording optics. Sedimentation coefficients could be determined with amounts of RNA as little as 8 ng. All sedimentation coefficients were extrapolated to zero-concentration, zero-dye binding, and zero-impurities from the preparative gel electrophoresis. The hydrodynamic model of flexible cylinders was applied for the interpretation of the sedimentation coefficients. All dsRNA segments of rotavirus (663-3409 base pairs) and the dsRNA5 of cucumber mosaic virus (335 base pairs) fit the model of a "worm-like" or flexible cylinder with a persistence length of 1125 A and a hydrated diameter of 30 A. The results are compared with data from the literature on the persistence lengths of the B- and Z-forms of dsDNA and of viroids.     

Physicochemical studies on turnip-yellow-mosaic virus. Homogeneity, relative molecular masses, hydrodynamic radii and concentration-dependence of parameters in non-dissociating solvents.

Turnip-yellow-mosaic virus, with its stable, highly spherical and monodisperse character, was chosen as a suitable model substance with which to test hydrodynamic theories of transport. Sedimentation coefficients, diffusion coefficients (obtained through photon correlation spectroscopy) and viscosities were measured accurately as a function of concentration in well-defined and nearly neutral buffer systems. Ancillary information was also obtained from very-low-speed sedimentation-equilibrium experiments. The coefficients expressing the variation in sedimentation and diffusion coefficients with weight concentration were obtained, and by combination with other data it was possible to avoid assumptions concerning solvation and transform such regression coefficients into the form appropriate to volume fractions. Some measure of support for Batchelor's [(1972) J. Fluid Mech. 52, 245-268] calculations was thus obtained, but over most of the pH range the coefficients were significantly smaller than those calculated from his theory. It seems likely that electrostatic interactions are responsible for the discrepancies. Hydrodynamic radii (from diffusion coefficients) were in very fair agreement with those calculated from the thermodynamic excluded-volume term, but were higher than indicated by electron microscopy and X-ray diffraction, a discrepancy ascribable to solvation.     

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.     

Permeability of composite chondrocyte-culture-millipore membranes to solutes of varying size and shape.

A model connective-tissue system was developed that is amenable to the determination of permeability coefficients of diffusing solutes. The system involves the culture of 13-day chick-embryo chondrocytes on a Millipore filter (HA:0.45 micron pore size) to form what is, in effect, a confluent, extremely thin cartilage slice of uniform thickness. These cultured chondrocyte membranes were used to measure the steady-state flux of radioactively labelled low-molecular-weight solutes and micro-ions. Similarly, the permeability coefficients of either radioactively labelled or enzymically active proteins across the membranes were determined. The membrane was found to have no marked effects on the diffusional behaviour of low-molecular-weight non-electrolytes (water, proline, ribose, glucose, sorbitol, raffinose). For micro-ions (Na+, SO42-, Cl-, glutamate, glucuronate,), the diffusive behaviour was found to be markedly affected by the ionic strength of the solvent used in a manner which was consistent with a Donnan distribution resulting from the immobilized proteoglycans. Globular proteins permeated the membrane at rates which decreased as the molecular size of the diffusing solute increased. The apparent diffusion rates of fibrinogen and of collagen through the membranes were greater than would be expected on the basis of their diffusion coefficients in free solution. Reasons for this behaviour are discussed.     

Determination of diffusion and permeability coefficients in muscle

A theory is presented for the study of diffusion in heterogeneous tissue-like structures. It is applicable to a common type of measurement in which the change of the amount of substance remaining in the tissue is determined as the substance diffuses from the tissue into an adjacent medium, for instance, Ringer's solution. The main objective of this paper is to obtain a method for the calculation of the diffusion coefficient in the intercellular space and of the permeability coefficients between this space and the cells, based on the type of measurement mentioned above. Although the fundamental ideas upon which the theory is based are applicable to any type of tissue, the formulae derived are limited to the case in which the cells form a flat bundle of parallel fibers. The theory is applied to the experimental results of E. J. Harris and G. P. Burn on diffusion of sodium in the sartorius muscle of the frog. We find that if we know the ratio of the cellular and intercellular volumes of the muscle the ratio of the equilibrium concentrations of sodium outside and inside the cells can be determined. A very simple mathematical analysis of the experimental relation between the amount of substance diffusing out of the muscle and the time of diffusion gives us this ratio. The ratio of the equilibrium sodium concentrations in the case of the sartorius frog muscle is between about 10 and 30, depending on the muscle used. The same mathematical analysis makes it possible to obtain the permeability coefficients of muscle fibers through simple calculations, if their sizes are known. The permeability coefficients for the experimental work mentioned above using sodium are 1.25 to 11.5×10⁻⁸ cm/sec for the flow into the fibers and 3.2 to 16×10⁻⁷ cm/sec for the flow in the opposite direction. The determination of the diffusion coefficient in the intercellular space is more laborious and yields only an order of magnitude: 10⁻⁶ cm²/sec.     

Diffusion of phosphate to plant roots in soil

Summary Improved resolution in autoradiography, achieved by the use of the low energy isotope, P³³, as tracer for soil phosphorus, enables the exchangeable phosphorus in a soil block to be measured quantitatively. A technique is described for the autoradiography of the P-depletion zone around the roots growing in soil, from which the P gradients are measured by microdensitometry.The amounts of P taken up by rape (Brassica napus) on a P-treated Begbroke Sandy Loam compared well with that removed from the soil as measured from the autoradiograph of the depletion zone. The P gradient around the roots suggests intense root hair activity; but the zone of depletion extended well beyound the tips of root hairs. The experimentally observed gradient is much closer to the one predicted from diffusion theory considering uniform depletion from within the equivalent root hair cylinder, than to the one obtained assuming the root hairs are inactive.A rapid depletion of up to about 60 per cent of the exchangeable P was observed within the root hair cylinder during the initial 3 days of absorption. The corresponding concentration of P in solution within the cylinder determined from a desorption isotherm, is hence brought down to a low level very rapidly, and is held at or near this level at later periods. The amounts transferred into the root hair cylinder from outside as calculated from a diffusion model were lower than the experimental values. It is suggested that the discrepancy may lie in the calculation of the effective diffusion coefficients for P in the soil from a P-desorption isotherm, owing to difficulties involved in simulating the root environment in the desorption isotherm experimentSoil Science Laboratory, Department of Agricultural Science, University of Oxford     

Diffucison of OXYGEN, Nitrogen and water in hyluronate solutions.

A method is reported for the measurement of the diffusion coefficients in water of some sparingly soluble gases. The results obtained for the diffusion coefficients of oxygen and nitrogen gas through water at 25 degrees C are 2.12. 10-5 and 2.61 . 10-5 cm-2 . s-1, respectively. A check on the accuracy of the teachnique using tritiated water as the diffusing substance gave a value of 2.15 . 10-5 cm-2 . s-1 which agrees within 3% with recent values from the literature. The method was applied to the measurement of oxygen, nitrogen, and tritiated water diffusion coefficients through agarose gels and through agarose gels containing hyluronate. The results indicate that the hyaluronate had only a small effect as a barrier to the diffusion of such low molecular weight substance.     

On simultaneous determinations of the permeability of a membrane and of the diffusion coefficient in an adjacent medium

This paper deals with diffusion into a medium of finite thickness through a flat structure which can be considered either as a slice of tissue or as a membrane. Formulae are given to determine the diffusion coefficients in both the flat structure and the adjacent medium from the knowledge of the amount of substance penetrating the medium. The meaning of the formula: (permeability coefficient) = (diffusion coefficient)/(membrane thickness) and the experimentally observed variability of the permeability coefficient in the non-steady state are interpreted on the basis of the mathematical theory of diffusion.     

Measuring the translational diffusion coefficients of small DNA molecules by capillary electrophoresis

The apparent translational diffusion coefficients of four 20 base pair (bp) DNA oligonucleotides with different sequences have been measured by capillary electrophoresis, using the stopped migration method. The diffusion coefficients of the four oligomers were equal within experimental error, and averaged (120 +/- 10) x 10(-8) cm(2) s(-1) in 40 mM Tris-acetate-EDTA buffer at 25 degrees C. Since this value is nearly identical to the translational diffusion coefficient determined for a different 20-bp oligomer using other methods, the stopped migration method can accurately measure the diffusion coefficients of small DNA oligomers. The apparent diffusion coefficient of a 118-bp DNA restriction fragment was also measured by the stopped migration method. However, the observed value was approximately 25% larger than expected from other measurements, possibly because the diffusion coefficients of larger DNA molecules are somewhat dependent on the ionic strength of the solution.     

A Model of Isotope Separation in Plants

A model representing isotope separation during water evaporation in plants was constructed. The model accounts for substance diffusion, convective transfer and evaporation from the surface of the leaves. The dependence of the system’s separation and enrichment coefficients on various parameters (liquid velocity, diffusion coefficient, and potential barriers for molecules and their thermal velocities) was determined. A comparison was made between the enrichment coefficients calculated from experimental data from different plants and those based on the model. Qualitative agreement between the experimental and theoretical values was obtained for the case of \(\frac{uh}{D} {\gg} 1\), where u is the average velocity of water in the plant, h is the height of the plant, and D is the diffusion coefficient of the substance.     

Diffusion in Pseudomonas aeruginosa biofilms: a pulsed field gradient NMR study

A Pseudomonas aeruginosa biofilm is studied with pulsed field gradient echo nuclear magnetic resonance. Although not all spectral components are assigned yet, the experimental results show that a biofilm consists of components with very different diffusion coefficients. The various biofilm components that give motionally narrowed 1H NMR signals, can be grouped into five classes with diffusion coefficients, ranging from 2 x 10(-9) to 1 x 10(-13) m2 s-1. Investigation of the diffusion behavior of water in the biofilm shows three fractions with different diffusion coefficients. Besides the highly mobile bulk water at least two other fractions with much lower diffusion coefficients are detected. It is shown that one of the fractions with the low diffusion coefficient probably arises from intracellular water. Also for another component of the biofilm, glycerol, three fractions with diffusion coefficients that differ more than a factor ten are detected. Also a group of signals exists which result from practically immobile components.     

Permeation of ammonia across bilayer lipid membranes studied by ammonium ion selective microelectrodes.

Ammonium ion and proton concentration profiles near the surface of a planar bilayer lipid membrane (BLM) generated by an ammonium ion gradient across the BLM are studied by means of microelectrodes. If the concentration of the weak base is small compared with the buffer capacity of the medium, the experimental results are well described by the standard physiological model in which the transmembrane transport is assumed to be limited by diffusion across unstirred layers (USLs) adjacent to the membrane at basic pH values (pH > pKa) and by the permeation across the membrane itself at acidic pH values. In a poorly buffered medium, however, these predictions are not fulfilled. A pH gradient that develops within the USL must be taken into account under these conditions. From the concentration distribution of ammonium ions recorded at both sides of the BLM, the membrane permeability for ammonia is determined for BLMs of different lipid composition (48 x 10(-3) cm/s in the case of diphytanoyl phosphatidylcholine). A theoretical model of weak electrolyte transport that is based on the knowledge of reaction and diffusion rates is found to describe well the experimental profiles under any conditions. The microelectrode technique can be applied for the study of the membrane permeability of other weak acids or bases, even if no microsensor for the substance under study is available, because with the help of the theoretical model the membrane permeability values can be estimated from pH profiles alone. The accuracy of such measurements is limited, however, because small changes in the equilibrium constants, diffusion coefficients, or concentrations used for computations create a systematic error.     

Gelation conditions and transport properties of hollow calcium alginate capsules

The diameter, membrane thickness, and compression intensity of hollow Ca-alginate capsules were measured at different gelation conditions, such as the reactant concentration, dropping velocity, and gelation time. The optimum operation conditions for preparing capsules were determined at 100 g/L CaCl(2), 10 g/L sodium alginate (Na-alginate), a dropping velocity of 150 droplets/min, and a gelation time of 10 min. Diffusion of some saccharide and amino acid from bulk solution into capsules was investigated, and the diffusion coefficients were calculated by the developed mathematical model. All the tested substances can diffuse easily into the capsules. The combined diffusion coefficients of the capsule D(m) are 92-99% as large as their diffusion coefficients in pure water, while the diffusion coefficients in the capsule membrane D(1) are 60-95% as large as those. By employing polyethylene glycol (PEG) and bovine serum albumin (fraction V) (BSA(V)), the molecular weight cut-off of the capsule was determined. For linear macromolecules, hollow Ca-alginate capsules have a molecular weight cut-off of 4000. No diffusion of BSA(V) into the capsules was observed.     

PFG-NMR investigations of the binding of cationic neuropeptides to anionic and zwitterionic micelles

The mechanism by which peptides bind to micelles is believed to be a two-phase process, involving (i). initial electrostatic interactions between the peptide and micelle surface, followed by (ii). hydrophobic interactions between peptide side chains and the micelle core. To better characterize the electrostatic portion of this process, a series of pulse field gradient nuclear magnetic resonance (PFG-NMR) spectroscopic experiments were conducted on a group of neuropeptides with varying net cationic charges (+1 to +3) and charge location to determine both their diffusion coefficients and partition coefficients when in the presence of detergent micelles. Two types of micelles were chosen for the study, namely anionic sodium dodecylsulfate (SDS) and zwitterionic dodecylphosphocholine (DPC) micelles. Results obtained from this investigation indicate that in the case of the anionic SDS micelles, peptides with a larger net positive charge bind to a greater extent than those with a lesser net positive charge (bradykinin > substance P > neurokinin A > Met-enkephalin). In contrast, when in the presence of zwitterionic DPC micelles, the degree of mixed-charge nature of the peptide affects binding (neurokinin A > substance P > Met-enkephalin > bradykinin). Partition coefficients between the peptides and the micelles follow similar trends for both micelle types. Diffusion coefficients for the peptides in SDS micelles, when ranked from largest to smallest, follow a trend where increasing net positive charge results in the smallest diffusion coefficient: Met-enkephalin > neurokinin A > bradykinin > substance P. Diffusion coefficients when in the presence of DPC micelles, when ranked from largest to smallest, follow a trend where the presence of negatively-charged side chains results in the smallest diffusion coefficient: bradykinin > Met-enkephalin > substance P > neurokinin A.     

A modelling approach towards epidermal homoeostasis control

In order to grasp the features arising from cellular discreteness and individuality, in large parts of cell tissue modelling agent-based models are favoured. The subclass of off-lattice models allows for a physical motivation of the intercellular interaction rules. We apply an improved version of a previously introduced off-lattice agent-based model to the steady-state flow equilibrium of skin. The dynamics of cells is determined by conservative and drag forces, supplemented with delta-correlated random forces. Cellular adjacency is detected by a weighted Delaunay triangulation. The cell cycle time of keratinocytes is controlled by a diffusible substance provided by the dermis. Its concentration is calculated from a diffusion equation with time-dependent boundary conditions and varying diffusion coefficients. The dynamics of a nutrient is also taken into account by a reaction-diffusion equation. It turns out that the analysed control mechanism suffices to explain several characteristics of epidermal homoeostasis formation. In addition, we examine the question of how in silico melanoma with decreased basal adhesion manage to persist within the steady-state flow equilibrium of the skin. Interestingly, even for melanocyte cell cycle times being substantially shorter than for keratinocytes, tiny stochastic effects can lead to completely different outcomes. The results demonstrate that the understanding of initial states of tumour growth can profit significantly from the application of off-lattice agent-based models in computer simulations.     

Determination of diffusion and permeability coefficients in nerve trunks

A mathematical theory is developed which permits the determination of certain parameters of an inhomogenous tissue, such as a nerve trunk without its epineurium. The parameters are the permeability coefficients for entrance into an exit of a substance from the nerve fibers, and the diffusion coefficient of the interstitial material. The experimental data required are the dimensions of the cross-section, the average diameter of the fibers, and the ratio of the cross-sectional are of the fibers to the total cross-section, as well as the time course of the decrease of the fraction of the substance left in the nerve trunk, when the trunk is immersed in a bathing solution containing none of it.     

Dielectric behavior of polyelectrolytes II. The cylinder

The dipolar correlation function for a system of coupterions diffusing on the surface of a polyelectrolyte cylinder is computed. The influence of screened coulombic repulsions on the dielectric increment is determined. Dissociation and reassociation of the counterions to the cylinder is treated microscopically and the coupled bulk diffusion is solved in the presence of the Poisson-Boltzmann potential. It is found that the correlation function contains a small, fast decaying, molecular weight independent part arising from diffusion around the cylinder and a large, slowly decaying, molecular weight dependent part arising from diffusion along the cylinder axis. The dissociation-reassociation kinetics can play a large, possible dominant, role in determining the relaxation rates.