Scanning molecular sieve chromatography of interacting protein systems. II. Determination of large zone transport parameters by the difference profile method at low solute concentration.

The experimental determination of difference profiles for the study of large zone transport processes by scanning molecular sieve chromatography is described. Using the difference profile method, the progesterone-induced purple glycoprotein of the porcine uterus was found to exist as monomeric units in high ionic environment, with a partition coefficient of 0.269, partition cross-section of 0.488, partition radius of 25 A and a molecular weight of 33,500 g/mole. The technique was further applied in examining the association-dissociation properties of oxyhemoglobin. In a high tonic environment, the partition coefficient was found to be 0.365 for dimer and the partition cross-section, 0.419; for the tetramer in low ionic strength solution, the partition coefficient was 0.275 and the partition cross-section 0.377, with a dissociation constant of 1.03 x 10(-6) mole/l. This new technique should prove applicable in (1) readily locating the centroid positions of transport boundary profiles at the lowest practible protein concentration limits, (2) demonstrating the characteristic boundary shape and concentration-dependent centroid position for an interacting solute, (3) determining the axial dispersion coefficient characteristic of solute turbulence within the gel matrix, and (4) distinguishing the boundary between low and high ionic strength solvent phases in the gel column.     

Scanning molecular sieve chromatography of interacting protein systems. II. Determination of large zone transport parameters by the difference profile method at low solute concentration

The experimental determination of difference profiles for the study of large zone transport processes by scanning molecular sieve chromatography is described. Using the difference profile method, the progesterone-induced purple glycoprotein of the porcine uterus was found to exist as monomeric units in high ionic environment, with a partition coefficient of 0.269, partition cross-section of 0.488, partition radius of 25 A and a molecular weight of 33500 g mole . The technique was further applied in examining the association-dissociation properties of oxyhemoglobin. In a high tonic environment, the partition coefficient was found to be 0.365 for dimer and the partition cross-section, 0.419; for the tetramer in low ionic strength solution, the partition coefficient was 0.275 and the partition cross-section 0.377, with a dissociation constant of 1.03 x 10(-6) mole/1. This new technique should prove applicable in (1) readily locating the centroid positions of transport boundary profiles at the lowest practicable protein concentration limits, (2) demonstrating the characteristic boundary shape and concentration-dependent centroid position for an interacting solute, (3) determining the axial dispersion coefficient characteristic of solute turbulence within the gel matrix, and (4) distinguishing the boundary between low and high ionic strength solvent phases in the gel column.     

Equilibrium gel permeation: a single-photon counting spectrophotometer for studies of protein interaction.

When a small column or flow cell packed with gel particles is completely saturated with a solution containing molecular species of interest, the average cross-sectional area occupied by the solute (partition cross section) is conveniently and precisely determined by direct optical scanning. For a mixture of interacting solutes this equilibrium gel permeation measurement yields the weight average of the species partition cross sections and the variation of this quantity with solute concentration permits determination of the solute interaction parameters (stoichiometry, equilibrium constants). We have developed a computer-controlled single-photon counting spectrophotometer for these measurements. The instrument exhibits high precision over a wide range of optical density. With counting times in the range of 10-1000 s the standard deviations on optical densities of protein solutions measured at 220 nm are typically 0.0006 at 1 OD, 0.002 at 2 OD, 0.005 at 4 OD. Beer's law tests show that deviations from linearity are less than these precision limits. Partition cross-section measurements for proteins can be made with an accuracy of better than 0.001 and information can be obtained with protein solutions at least as low as 1 mug/ml.     

Effects of nonuniform column packing in analytical gel chromatography. I. Monodisperse solutes

The effect of nonuniform column packing on solute profile shapes in analytical gel chromatography has been investigated for monodisperse solutes. This investigation considers the influence of a family of nonuniform partition cross sections on the concentration profiles for small-zone experiments. The nonuniformity causes the dispersive and translational transport coefficients to be functions of position. It is shown that for presently encountered amounts of nonuniformity, the principal effect is in the deviation of peak position from linear dependence on time. There is very little effect on peak shape, when concentrations are expressed in terms of bulk solution values.     

Effect of blood flow on near-the-wall mass transport of drugs and other bioactive agents: a simple formula to estimate boundary layer concentrations

Transport of bioactive agents through the blood is essential for cardiovascular regulatory processes and drug delivery. Bioactive agents and other solutes infused into the blood through the wall of a blood vessel or released into the blood from an area in the vessel wall spread downstream of the infusion/release region and form a thin boundary layer in which solute concentration is higher than in the rest of the blood. Bioactive agents distributed along the vessel wall affect endothelial cells and regulate biological processes, such as thrombus formation, atherogenesis, and vascular remodeling. To calculate the concentration of solutes in the boundary layer, researchers have generally used numerical simulations. However, to investigate the effect of blood flow, infusion rate, and vessel geometry on the concentration of different solutes, many simulations are needed, leading to a time-consuming effort. In this paper, a relatively simple formula to quantify concentrations in a tube downstream of an infusion/release region is presented. Given known blood-flow rates, tube radius, solute diffusivity, and the length of the infusion region, this formula can be used to quickly estimate solute concentrations when infusion rates are known or to estimate infusion rates when solute concentrations at a point downstream of the infusion region are known. The developed formula is based on boundary layer theory and physical principles. The formula is an approximate solution of the advection-diffusion equations in the boundary layer region when solute concentration is small (dilute solution), infusion rate is modeled as a mass flux, and there is no transport of solute through the wall or chemical reactions downstream of the infusion region. Wall concentrations calculated using the formula developed in this paper were compared to the results from finite element models. Agreement between the results was within 10%. The developed formula could be used in experimental procedures to evaluate drug efficacy, in the design of drug-eluting stents, and to calculate rates of release of bioactive substances at active surfaces using downstream concentration measurements. In addition to being simple and fast to use, the formula gives accurate quantifications of concentrations and infusion rates under steady-state and oscillatory flow conditions, and therefore can be used to estimate boundary layer concentrations under physiological conditions.     

Active enzyme gel chromatography. I. Experimental aspects.

Transport properties of active enzyme species can be studied effectively by layering a small band of enzyme-containing sample on a gel chromatographic column previously saturated with substrate. The column is optically scanned at successive time intervals to yield profiles representing the appearance of chromophoric product or disappearnce of chromophoric substrate. These profiles permit determination of the specific activity and rate of transport of the active species. Initial studies on mechanic of the technique establish the feasibility of accurately determining transport properties of active enzyme species chromatographed on gel columns. Illustrative results are presented for L-glutamate dehydrogenase and for homoserine dehydrogenase studied in both forward and reverse reactions. It is shown that the partititon cross sections derived from the rates of motion of catalytic activity are the same as those determined by equilibrium saturation experiments which directly measure the degree of partitioning by the protein. These results establish the validity of the technique for a variety of future studies. Active enzyme gel chromatography appears comparable in precision to the active enzyme sedimentation technique at current stages of development.     

The osmotic migration of cells in a solute gradient.

The effect of a nonuniform solute concentration on the osmotic transport of water through the boundaries of a simple model cell is investigated. A system of two ordinary differential equations is derived for the motion of a single cell in the limit of a fast solute diffusion, and an analytic solution is obtained for one special case. A two-dimensional finite element model has been developed to simulate the more general case (finite diffusion rates, solute gradient induced by a solidification front). It is shown that the cell moves to regions of lower solute concentration due to the uneven flux of water through the cell boundaries. This mechanism has apparently not been discussed previously. The magnitude of this effect is small for red blood cells, the case in which all of the relevant parameters are known. We show, however, that it increases with cell size and membrane permeability, so this effect could be important for larger cells. The finite element model presented should also have other applications in the study of the response of cells to an osmotic stress and for the interaction of cells and solidification fronts. Such investigations are of major relevance for the optimization of cryopreservation processes.     

Effects of ionic strength on lysozyme uptake rates in cation exchangers. I: Uptake in SP Sepharose FF

Fluorescence scanning confocal microscopy was used in parallel with batch uptake and breakthrough measurements of transport rates to study the effect of ionic strength on the uptake of lysozyme into SP Sepharose FF. In all cases the adsorption isotherms were near-rectangular. As described previously, the intraparticle profiles changed from slow-moving self-sharpening fronts at low salt concentration, to fast-moving diffuse profiles at high salt concentration, and batch uptake rates correspondingly increased with increasing salt concentration. Shrinking core and homogeneous diffusion frameworks were used successfully to obtain effective diffusivities for the low salt and high salt conditions, respectively. The prediction of column breakthrough was generally good using these frameworks, except for low-salt uptake results. In those cases, the compressibility of the stationary phase coupled with the shrinking core behavior appears to reduce the mass transfer rates at particle-particle contacts, leading to shallower breakthrough curves. In contrast, the fast uptake rates at high ionic strength appear to reduce the importance of mass transfer limitations at the particle contacts, but the confocal results do show a flow rate dependence on the uptake profiles, suggesting that external mass transfer becomes more limiting at high ionic strength. These results show that the complexity of behavior observable at the microscopic scale is directly manifested at the column scale and provides a phenomenological basis to interpret and predict column breakthrough. In addition, the results provide heuristics for the optimization of chromatographic conditions.     

Transport of iron and manganese in relation to the shapes of their concentration-depth profiles

A model is presented which describes the transport of iron and manganese in the vicinity of a redox boundary. It is based on input of a particulate component, to form a point source, from which soluble species diffuse along a concentration gradient. The shapes of concentration-depth profiles in marine and freshwater sediments and water columns are reviewed and discussed in terms of the model. Transport, either entirely within a water column or within the sediment, may be simply treated because the rate of vertical transport can be regarded as constant. The discontinuity in the rate of vertical transport which occurs at the sediment-water interface can provide a complicated example of the model, especially when it coincides with the redox boundary. Authigenic mineral formation processes can modify the model, sometimes to such an extent that it becomes invalid. This is particularly true for soluble iron profiles in organically rich marine sediments. Sampling interval is critical to the resultant profile shape and must be relevant to the particular environment, e.g. metres in water columns and millimetres in sediments. The differences in the rates of reduction and oxidation of iron and manganese tend to modify both the position of the profile with respect to the redox-cline and its stage of development in a seasonally anoxic system. It is these factors which determine why most of the iron which reaches a sediment is permanently incorporated whereas manganese is re-released. This mechanism determines the average ratio of iron to manganese in sedimentary rocks. The development of peaked profile shapes in water columns implies that under certain conditions dissolved iron and manganese may be transported from the water column to the pore waters of the sediment.     

Effects of nonuniform column packing in analytical gel chromatography. II. Associating solutes

Effects of nonuniform column packing on boundary profiles for selfassociating systems have been investigated by computer simulation. Migration rate of each of the interconverting solute species changes along the column as a result of nonuniform packing, and the difference in velocity of monomer and n-mer is not constant as the sample moves down the column. A greater amount of overall axial dispersion results, as compared to the constant-column case. Procedures developed in this study can be applied to any experimentally measured column nonuniformity.     

On the use of size exclusion chromatography for the resolution of mixed amyloid aggregate distributions: I. equilibrium partition models

In this study, we investigated the theoretical potential of size exclusion chromatography (SEC) for resolving mixtures of protein aggregates (of various sizes and shapes) produced in the generation of amyloid fibrils. We present our findings in the form of an equilibrium partition model. We first review the general characteristics of SEC and discuss the physicochemical features affecting solute transport and partition. We then develop new methods for estimating the transport and partition coefficients of protein aggregates on the basis of their molecular dimensions and the SEC column properties. We detail how these calculated properties can be used to estimate the likely resolving power of an SEC column. Model predictions were found to be in general agreement with experimental data gained from the measurement of the elution profile of sheared amyloid fibrils prepared from bovine insulin and passed through a Superose 6 precision SEC column. Our formalism should provide a basic appreciation of the competing factors at work and allow an informed choice to be made for optimal selection of SEC column medium to separate a desired size range of aggregate.     

Transient solute diffusion in articular cartilage

The one-dimensional transient diffusion of glucose, inulin and dextran into adult bovine knee articular cartilage was determined for transport times of 1, 5, 15 and 60 min, and 4, 12, 24 and 48 h. The apparent diffusion coefficient and apparent interface partition coefficient were calculated from the concentration-depth profiles within the tissue using a theoretical model for non-steady state solute diffusion. The diffusion coefficient was found to decrease with both solute size and transport time. The partition coefficient also decreased with solute size but increased with transport time. Neither coefficient was dependent on normal tissue fluid or proteoglycan content variations.     

Generalized finite element solution to one-dimensional flux problems

A finite element numerical solution to the general one-dimensional flow equation is derived in a form that provides a convenient and general means to simulate a wide variety of one-dimensional flow techniques of interest to biological scientists, e.g., ultracentrifugation, electrophoresis, chromatography, etc. Diverse physical models defined in terms of column geometry, solute interactions, and the dependence of transport parameters on column position, time, or concentrations of one or more solutes, can be accommodated. A particularly useful aspect of the formulation is that a wide variety of boundary conditions can be simply applied to the end result, without rederivation of the solution for each new case. The numerical solution is expressed as matrix equations that are sufficiently general so that incorporation of particular models can be effected by substitution of appropriate quantities into the final result.     

Protein crystal growth. Growth kinetics for tetragonal lysozyme crystals

A method for immobilizing protein crystals has been devised for determining face growth rates, and used to investigate the growth kinetics of hen egg white lysozyme crystals. Growth rates were determined at 22 degrees C in 0.1 M sodium acetate, 5% NaCl, pH 4.0, on the visually identified (110) face of tetragonal lysozyme crystals. Protein concentrations ranged from 13 to 57 mg/ml (saturation concentration = 1.7 mg/ml). Growth rate data were fit to the equation R = kappa sigma ri, where R = rate in cm/s; kappa = constant; sigma i = solute growth interface supersaturation; and r = rate dependence upon super-saturation, with the result that kappa = 0.146 X 10(-8) cm/s and r = 2.0. A model of the growth process was developed and the experimental data were used to determine the relative roles of transport and interfacial kinetics in the growth of this crystal. Values for the width of the boundary layer delta, the interfacial concentration Ci, and growth rate R were determined. The model may be used to extrapolate to other growth conditions. The relative role of transport and interfacial kinetics can be expressed by the coefficient gamma = (CB - Ci)/(CB - Cs), when CB is the bulk concentration and Cs the saturation. Values for gamma were found to range from much less than 0.1 for submicron-size crystals to approximately 0.15 for cm sizes. The results indicate that attachment or surface effects are rate-limiting in lysozyme crystal growth in Earth's gravity because solutal convection always provides more transport of solute than can be accommodated by the interface. In order to grow such crystals under transport limiting conditions, it would be necessary to suppress this solutal convection.     

Asymptotic method for peristaltic transport

The purpose of this paper is to justify an asymptotic method developed for the study of peristaltic transport in a tube of arbitrary cross section. Within the framework of long wave approximation, the three-dimensional nonlinear Navier-Stokes equations are reduced to a sequence of two-dimensional linear boundary value problems of Laplace and biharmonic operators. It is shown that, if a Reynolds number is less than some constant, the solution of the approximate equations is indeed an asymptotic approximation to the exact solution of the problem as the ratio of the maximum radius of the tube to the wave length of the peristaltic motion of the wall tends to zero, and the error estimates are expressed inL ₂ norms. Furthermore, under the same condition the exact solution is shown to be unique and stable under arbitrary perturbation of spatially periodic disturbance. Application of the stability condition to peristaltic transport in a tube of circular cross section is given.     

Transport,anoxia and end-product accumulation control carbon dioxide and methane production and release in peat soils

Anaerobic respiration and methanogenesis have been found to slow-down in water saturated peat soils with accumulation of metabolic end-products, i.e. dissolved inorganic carbon (DIC) and methane (CH₄), due to a lack of solute and gas transport. So far it is not well understood how solute and gas transport may control this effect. We conducted a column experiment with homogenized ombrotrophic peat over a period of 300 days at 20 °C. We specifically evaluated the effects of diffusive flux as control, downward advective water flux, intensified ebullition by conduit gas transport and diffusive oxygen supply on controlling anaerobic decomposition rates and carbon (C) turnover. To simulate advective flux, water and solutes were recirculated downward through the column after stripping of dissolved gases. We analyzed DIC and CH₄ concentrations, production rates and fluxes, gas filled porosity, oxygen profiles (O₂) and microbial C biomass over time. DIC residence time thereby served as proxy to characterize transport. A slowdown of anaerobic respiration and methanogenesis evolved with the accumulation of the end-products DIC and CH₄ and set in after 150 days. This slow-down was accompanied by a decrease in the distribution of microbial biomass C with depths. Anaerobic DIC and CH₄ production rates were fastest close to the water table and sharply slowed with depth. Accumulation of DIC and CH₄ in the homogeneous peat material throughout the column decreased decomposition constants from about 10^?5 near the surface to 10^?9 year^?1 deeper in the profile. Advective water transport extended the zone of active methanogenesis compared to a diffusive system; experimental enhancement of ebullition had little or no effect as well as strictly anoxic conditions. DIC residence time was negatively correlated to anaerobic respiration suggesting this parameter to be a predictor of anaerobic peat decomposition in peatlands. Overall, this study suggests that burial of peat and accumulation of metabolic end-products effectively slows decomposition and that this effect needs to be considered to explain peat accumulation and the response of peat mineralization rates to changes in environmental conditions.     

Revisiting the Münch pressure-flow hypothesis for long-distance transport of carbohydrates: modelling the dynamics of solute transport inside a semipermeable tube

A mathematical model of the Münch pressure-flow hypothesis for long-distance transport of carbohydrates via sieve tubes is constructed using the Navier-Stokes equation for the motion of a viscous fluid and the van't Hoff equation for osmotic pressure. Assuming spatial dimensions that are appropriate for a sieve tube and ensuring suitable initial profiles of the solute concentration and solution velocity lets the model become mathematically tractable and concise. In the steady-state case, it is shown via an analytical expression that the solute flux is diffusion-like with the apparent diffusivity coefficient being proportional to the local solute concentration and around seven orders of magnitude greater than a diffusivity coefficient for sucrose in water. It is also shown that, in the steady-state case, the hydraulic conductivity over one metre can be calculated explicitly from the tube radius and physical constants and so can be compared with experimentally determined values. In the time-dependent case, it is shown via numerical simulations that the solute (or water) can simultaneously travel in opposite directions at different locations along the tube and, similarly, change direction of travel over time at a particular location along the tube.     

Effects of small scale fluid motion on bacterial growth and respiration

1. Laboratory experiments were conducted to investigate the effect of small‐scale turbulent motion on the growth and respiration of bacteria in an oscillating grid apparatus. The experiments were performed under a range of energy dissipation levels similar to those occurring in freshwater systems. 2. The results showed that small‐scale turbulent motion does have an effect on bacterial growth and respiration. A higher gradient in the dissolved oxygen time series, higher 5‐day biochemical oxygen demand values, increased bacterial abundance, increased bacterial specific respiration, higher bacterial growth rate and increased nutrient uptake were all observed when the energy dissipation rate in the water column was increased. 3. This has implications for traditional laboratory procedures that are used to characterise bacterial metabolic rates under stagnant fluid‐flow conditions, such as biochemical oxygen demand (BOD), which would be influenced by the effects of the small‐scale fluid motion inherent in aquatic environments. According to our results, BOD values in natural systems experiencing fluid motion would be higher than traditional bottle‐derived rates.     

Contribution of solvent drag through intercellular junctions to absorption of nutrients by the small intestine of the rat

The lumen of the small intestine in anesthetized rats was recirculated with 50 ml perfusion fluid containing normal salts, 25 mM glucose and low concentrations of hydrophilic solutes ranging in size from creatinine (mol wt 113) to Inulin (mol wt 5500). Ferrocyanide, a nontoxic, quadrupally charged anion was not absorbed; it could therefore be used as an osmotically active solute with reflection coefficient of 1.0 to adjust rates of fluid absorption, Jv, and to measure the coefficient of osmotic flow, Lp. The clearances from the perfusion fluid of all other test solutes were approximately proportional to Jv. From Lp and rates of clearances as a function of Jv and molecular size we estimate (a) the fraction of fluid absorption which passes paracellularly (approx. 50%), (b) coefficients of solvent drag of various solutes within intercellular junctions, (c) the equivalent pore radius of intercellular junctions (50 A) and their cross sectional area per unit path length (4.3 cm per cm length of intestine). Glucose absorption also varied as a function of Jv. From this relationship and the clearances of inert markers we calculate the rate of active transport of glucose, the amount of glucose carried paracellularly by solvent drag or back-diffusion at any given Jv and luminal glucose concentration and the concentration of glucose in the absorbate. The results indicate that solvent drag through paracellular channels is the principal route for intestinal transport of glucose or amino acids at physiological rates of fluid absorption and concentration. In the absence of luminal glucose the rate of fluid absorption and the clearances of all inert hydrophilic solutes were greatly reduced. It is proposed that Na-coupled transport of organic solutes from lumen to intercellular spaces provides the principal osmotic force for fluid absorption and triggers widening of intercellular junctions, thus promoting bulk absorption of nutrients by solvent drag. Further evidence for regulation of channel width is provided in accompanying papers on changes in electrical impedance and ultrastructure of junctions during Na-coupled solute transport.