The Relation between Salt and Ionic Transport Coefficients

The reflection coefficient was originally introduced by Staverman to describe the movement of nonelectrolytes through membranes. When this coefficient is extended to salts, one has a choice of defining this term for the whole salt moving as a single electrically neutral component or for the individual ions of the salt. The latter definition is meaningful only in the absence of an electric field across the permeability barrier. This condition may be achieved with the voltage clamp or short-circuit technique and is especially useful in dealing with biological systems in which one rarely has only a single salt or even equal concentrations of the major anion and cation. The relations between the transport coefficients for the salt and its individual ions are derived. The special conditions which may result in negative osmosis through a charged membrane in the presence of a salt are discussed.     

Reflection coefficients of permeant molecules in human red cell suspensions

The Staverman reflection coefficient, sigma for several permeant molecules was determined in human red cell suspensions with a Durrum stopped-flow spectrophotometer. This procedure was first used with dog, cat, and beef red cells and with human red cells. The stopped-flow technique used was similar to the rapid-flow method used by those who originally reported sigma measurements in human red cells for molecules which rapidly penetrate the red cell membrane. The sigma values we obtained agreed with those previously reported for most of the slow penetrants, except malonamide, but disagreed with all the sigma values previously reported for the rapid penetrants. We were unable to calculate an "equivalent pore radius" with our sigma data. The advantages of our equipment and our experimental procedure are discussed. Our sigma data suggest that sigma is indirectly proportional to the log of the nonelectrolyte permeability coefficient, omega. Since a similar trend has been previously shown for log omega and molar volume of the permeant molecules, a correlatioo was shown between sigma and molar volume suggesting the membrane acts as a sieve.     

Coupling satellite data with in situ measurements and numerical modeling to study fine suspended-sediment transport: a study for the lagoon of New Caledonia

This paper investigates the potential of remotely sensed data to map turbidity in a coral reef lagoon and to calibrate a numerical model of fine suspended-sediment transport. Simultaneous measurements of turbidity depth-profile and above-water spectral reflectance integrated according Landsat 7 ETM+ band 2 spectral sensitivity provide a linear regression relationship for the southwest lagoon of New Caledonia (r²=0.95, n=40). This relationship is applied to an empirically atmospherically corrected Landsat ETM+ image of the lagoon acquired on October 23, 2002. A comparison between Landsat estimates of turbidity and concurrent measurements at 14 stations indicates that the mean standard error in the satellite-estimated turbidity is 17.5%. The numerical model introduced in Douillet et al. (2001) is used to simulate the transport of fine suspended sediments in the lagoon in October 2002. A calibration of the erosion rate coefficient required by the model is proposed using in situ turbidity profiles and the remotely sensed turbidity field. In situ data are used to tune locally the erosion rate coefficient, while satellite data are used to determine its spatial zonation. We discuss necessary improvements in coupled studies of fine-sediment transport in coastal zones, namely relationships between turbidity and sediment concentration, integration of wave influence in the model, and correction of bottom reflection in satellite data processing.     

Solute concentration effect on osmotic reflection coefficient

A theory for the effect of concentration on osmotic reflection coefficient, correct to first order, was developed at the molecular level by considering the effect of solute-solute interactions on solute concentration and the fluid stress tensor within a solvent-filled pore. The solvent was modeled as a continuous fluid and potential energies between solute molecules and the pore wall were assumed to be pairwise additive. Although the theory is more general, calculations are presented only for excluded volume effects (hard-sphere for solute, hard-wall for pore). The relationship between the first-order concentration effect and the infinite dilution value of reflection coefficient appears to be geometry independent. The theory is discussed in light of experimental studies of osmotic flow that have recently appeared in the literature.     

A novel haemoprotein induced by isosafrole pretreatment in the rat

The relationship between the initial rates of respiration dependent calcium transport by isolated rabbit cardiac mitochondria and the free calcium concentration of the reaction media has been examined at 10°C and 25°C. Initial rates of calcium transport were determined using an adaption of the EGTA/ruthenium red quench technique described by Reed and Bygrave (5). At 10°C the initial rate of calcium transport was found to be a sigmoidal function of free calcium concentration, with a Hill coefficient of approximately 1.9. Elevation of the temperature to 25°C produced a less sigmoidal relationship, the Hill coefficient being lowered to approximately 1.3.     

Photosystem II Electron Transport Rates and Oxygen Production in Natural Waterblooms of Freshwater Cyanobacteria During a Diel Cycle

The relationship between electron transport rate through PSIIand photosynthetic oxygen evolution in cyanobacterial surfacewaterblooms was followed over a diel cycle. Chlorophyll fluorescenceand photosynthetic oxygen evolution (PSOE) measurements wereperformed in a small-volume incubatin chamber on samples takenfrom a fish pond. Measurement of light-response curves showeda close to linear relationship between electron transport rates(ETR) and PSOE up to irradiancies of 800 quanta^–2 s^–1,except during mid-morning conditions. At higher irradiances,the relationship was non-linear. The regression coefficient     

Transport across homoporous and heteroporous membranes in nonideal, nondilute solutions. I. Inequality of reflection coefficients for volume flow and solute flow.

The Kirkwood formulation of the Stefan-Maxwell equations is used to develop the transport equations for a membrane bounded by nonideal, nondilute solutions. The reflection coefficients for volume flow and solute flow are not equal but are related by a simple expression that depends on the concentration of the bounding solutions. The ratio of the two coefficients is independent of heteroporous membrane structure and the thickness of adjacent boundary layers. Experimental measurements of these reflection coefficients for sucrose transport across Cuprophan verify this relationship; this indicates that the Onsager reciprocal relation, which is assumed by the theory, holds for nonideal, nondilute solutions. The two reflection coefficients may be made operationally identical by a simple redefination of the osmotic driving force.     

The relation between local and global transport parameters in an epithelial membrane having an asymmetric transport mechanism

The relationship between local and global transport parameters is derived for an epithelial membrane having series-parallel topology and an asymmetric transport mechanism at its apical and/or basolateral cell membranes. The result shows that the difference in the local forward and backward solute permeability coefficients is manifest in the global volume flow equation as distinct forward and backward reflection coefficients. The analytical result is applicable to the first order (low concentration) domain of Michaelis-Menten kinetics and a procedure is given for simulating the remainder of the domain on SPICE2.     

A Physical Interpretation of the Phenomenological Coefficients of Membrane Permeability

A "translation" of the phenomenological permeability coefficients into friction and distribution coefficients amenable to physical interpretation is presented. Expressions are obtained for the solute permeability coefficient ω and the reflection coefficient σ for both non-electrolytic and electrolytic permeants. An analysis of the coefficients is given for loose membranes as well as for dense natural membranes where transport may go through capillaries or by solution in the lipoid parts of the membrane. Water diffusion and filtration and the relation between these and capillary pore radius of the membrane are discussed. For the permeation of ions through the charged membranes equations are developed for the case of zero electrical current in the membrane. The correlation of σ with ω and L_p for electrolytes resembles that for non-electrolytes. In this case ω and σ depend markedly on ion concentration and on the charge density of the membrane. The reflection coefficient may assume negative values indicating anomalous osmosis. An analysis of the phenomena of anomalous osmosis was carried out for the model of Teorell and Meyer and Sievers and the results agree with the experimental data of Loeb and of Grim and Sollner. A set of equations and reference curves are presented for the evaluation of ω and σ in the transport of polyvalent ions through charged membranes.     

Integration of Raman microscopy, differential interference contrast microscopy, and attenuated total reflection Fourier transform infrared spectroscopy to investigate chlorhexidine spatial and temporal distribution in Candida albicans biofilms.

Two spectroscopic techniques, attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR) and Raman microscopy (RM), were used to characterize transport of chlorhexidine digluconate (CHG) in Candida albicans (CA) biofilms. Different (volumetric) regions of the biofilm are sampled by these two vibrational spectroscopies making them complementary techniques. Simple mathematical models were developed to analyze ATR-FTIR and RM data to obtain an effective diffusion coefficient describing transport through CA biofilms. CA biofilms were composed primarily of yeast and hyphal forms, with some pseudohyphae. Upper regions of biofilms that had become confluent, (i.e., biofilms that completely covered the germanium (Ge) substratum) were composed primarily of a tangled mass of hyphae with openings between germtubes about 10 to 50 microm across. Quantitative analysis of ATR-FTIR kinetic data curves indicated that the effective diffusion coefficient for transport of CHG through confluent biofilms about 200-microm thick was reduced 0.1 to 0.3 times compared to the diffusion coefficient for CHG in water. Effective diffusion coefficients obtained from analysis of RM data were consistently higher than those indicated by ATR-FTIR data suggesting that transport is more hindered in regions near the base of the biofilm than in the outer layers. Analysis of both ATR-FTIR and RM data obtained from thicker films indicated that adsorption of CHG to biofilm components was responsible for a substantial portion of the transport limitation imposed by the biofilm. Comparison of ATR-FTIR and RM data for both types of biofilms indicated that sites of CHG adsorption were more concentrated in the interfacial region than in the bulk biofilm. Comparison of results for ATR-FTIR and RM measurements suggests that these relatively thick CA biofilms can be modeled, for purposes of predicting transport, approximately as a homogeneous thin planar sheet. Thus, these biofilms offer a relatively tractable model system for initial investigations of the relation between antimicrobial transport and kinetics of antimicrobial action.     

A New Approach to Molecular Configuration Applied to Aqueous Pore Transport

A cylindrical treatment of the configuration of small molecules in solution has been proposed. Cylindrical dimensions were obtained from Fisher-Hirschfelder molecular models, and these dimensions were used in an analysis of three sets of reflection coefficient values from the literature. The correlation between solute dimensions and the reflection coefficient was subjected to both statistical analyses and graphical examination, with particular emphasis given to parameter interdependence. The results consistently indicated a significant relation between the reflection coefficient and solute diameter. The dependence on diameter suggests a lengthwise orientation of solute within the membrane. Furthermore it is shown that this orientation is occurring within the aqueous region of the membrane, and thus this region has a structural characteristic which is responsible for the lengthwise orientation of solute.     

Application of underwater light measurements in nutrient and production studies in shallow rivers

Due to fluctuations in water turbidity, river depth and total reflection from one river section to another, plant production is poorly correlated to solar radiation incident on the water surface. A relationship was observed between daily relative photosynthesis and photosynthetically available radiation (PAR) at the plant depth for Cladophora, with a correlation coefficient (r) of 0·73. Therefore, the effect of low light levels can be compensated for when evaluating nutrient-growth relationships for Cladophora in the field.     

Determination of reflection coefficients for various ions and neutral molecules in sarcoplasmic reticulum vesicles through osmotic volume change studied by stopped flow technique

Osmotic volume change of sarcoplasmic reticulum vesicles was studied by following the change in light-scattering intensity using a stopped flow apparatus. From the analysis of the initial rate of scattering change, reflection coefficients for various ions and neutral molecules were determined. The following are typical results: K+, 0.72; Tris+, 0.98; choline 1; NO3-, 0.32; Cl-, 0.46; methanesulfonate, 0.62; gluconate, 0.96; glycerol, 0.86; and glucose, 1. When the K+ permeability was increased in the presence of 10(-6) g valinomycin/ml, the reflection coefficient for K+ changed from 0.72 to 0.31. It was found that there was a close relationship between the reflection coefficients and the permeabilities of the solutes. Hydraulic conductivity was also determined from the initial rate of light scattering change and was not different for the different solutes. The water permeability was estimated to be 2.1 x 10(-3) cm/sec at 23 degrees C.     

Abscisic Acid transport coefficients of phaseolus root systems

Diffusive and convective transport coefficients of Phaseolus vulgaris L. cv. Ouray root systems for abscisic acid for (ABA) were measured. The convective coefficient (reflection coefficient or osmotic efficiency factor) σ was determined to be 0.96 for ABA while the diffusive coefficient, ω, was found to be 1.44 × 10⁻¹¹ mole per square centimeter per second per bar. Steady-state concentrations of ABA in the root system exudates were not achieved until at least three hours after the applications suggesting either a slow saturation of binding sites or equilibration with tissues surrounding the xylem.     

A model for radial water transport across plant roots

Summary A model based on the canal theory (Katou andFurumoto 1986 a, b) is proposed for the absorption of solute and water at the root periphery. The present canal model in the periphery and the model which was previously proposed for the exudation in the stele (Katou et al. 1987), are organized into a model for radial transport across excised plant roots, in the light of anatomical and physiological knowledge of maize roots. The canal equations for both canals are numerically solved to give quite a good explanation for the observed exudation of maize roots. It is found that the regulation of solute transport has a primary importance in the regulation of water transport across excised roots. The internal cell pressure of the symplast adjusts the water absorption at the root periphery to the water secretion into the vessels. There seems no need for this explanation of the radial water transport across roots to assume cell membranes with low reflection coefficient or variable water permeability. It would seem that the apoplast wall layers play a crucial role in metabolic control of water transport in roots as well as in hypocotyls.Abbreviations J _s ^ex* the theoretically estimated rate of solute exudation per unit surface area of model maize roots - J that of volume exudation per unit surface area of model maize roots - the reflection coefficient of the cell membrane against solutes     

Mechanistic approach to membrane mass transport processes (mini review)

Since the physical interpretation of practical Kedem-Katchalsky equations is not clear, we consider an alternative, mechanistic approach to membrane transport generated by osmotic and hydraulic pressure. We study a porous membrane with randomly distributed pore sizes (radii). We postulate that the reflection coefficient (sigma(p)) of a single pore may equal 1 or 0 only. From this postulate we derive new (mechanistic) transport equations. Their advantage is in clear physical interpretation.     

Phenomenological description of active transport of salt and water

The phenomenological definition of active transport by Kedem and the methods of Kedem and Katchalsky have been used to obtain practical equations describing active transport in the single salt and bi-ionic systems. Procedures were devised to evaluate the required set of 10 coefficients for the single salt case and 15 for the bi-ionic. Three of these coefficients are unusual. They express the effects of active transport, i.e. of entrainment between metabolism and the conventional transport flows: active salt transport coefficient, a volume pump coefficient, and an electrogenicity coefficient. In the bi-ionic case a new passive coefficient, lambda, was used to express the linkage between the fluxes of the two salts. However, if primary active transport involves only one ion, for example in the bi-ionic case, 12 coefficients suffice and certain relations can be predicted between the practical coefficients. Particular types of primary active transport could be identified by this means. The relation of active transport to membrane electrogenesis was also examined and the flux ratio equation was rederived in terms of the practical coefficients. Applications to specific parallel and series membrane systems have been analyzed.     

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.