General continuum analysis of transport through pores. II. Nonuniform pores.

A general continuum derivation of the nonelectrolyte (Js) and volume (Jv) flux through a pore whose cross section is a function of axial position (nonuniform) is given. In general, the flux equations cannot be reduced to the same form as for a uniform pore and it is not possible to characterize the pore kinetics by three constants as in the uniform pore case. However, it is shown that under certain conditions, the nonuniform pore equations can be approximated by the uniform pore form and can be characterized by three constants (omega, sigma, Lp). The only condition needed to reduce the Jv equation to the uniform form is that the solution be dilute. The deviation of the Js equation from the uniform form is characterized by an asymmetrical function of Jv whose maximum value is estimated. It is shown that the maximum posible fractional deviation of the Js equation from the uniform form is given by the parameter: 0:5sigmaJv/omegaRT. Since this parameter is less then 0.15 for most membrane studies, the nonuniform Js equation can usually be approximated by the uniform pore form. The general results are illustrated by explicit calculations on several models of nonuniform pores. It is shown, for example, that the "equivalent pore radius" defined in the usual way is a function of the experimental parameter that is measured and is not unique.     

Osmotic flow equations for leaky porous membranes

A basic set of equations describing the flows of volume (Jv) and solute (Js) across a leaky porous membrane, coupled to the differences of osmotic and hydrostatic pressures d pi and dP has been derived by using general frictional theory. Denoting the mean pore concentration of solute by c*s and the hydraulic and diffusive conductances by Lp and Ps/RT the equations take the form Jv = LpdP + sigma sLp d pi Js = c*s(1 - sigma f)Jv + Ps d pi/RT sigma s = theta (1 - DsVs/DwVw - Ds/Dos) sigma f = 1 - theta DsVs/DwVw - Ds/Dos in which Dw and Ds are the diffusion coefficients for water and solute in the pore and Dos that for free solution. The relation between the reflection coefficients sigma s and sigma f for osmosis and ultrafiltration is then given by sigma s = sigma f - (1- theta)(1 - Ds/Dos), where theta is the diffusive-driven:pressure-driven flow ratio. These equations follow from the fact that in leaky pores osmosis occurs by diffusion alone and that there cannot be any Onsager symmetry leading to sigma s = sigma f. Symmetry holds in the limits where either the pore is small, when sigma s = sigma f = 1, or where the pore is large when sigma s = sigma f = 0.     

Permeability-surface area product and reflection coefficient of the parietal pleura in dogs.

The parameters describing the permeability of the parietal pleura to liquid and total plasma proteins were measured in five anesthetized adult dogs. Small areas of parietal pleura (approximately 1 cm2) and the underlying endothoracic fascia were exposed through resection of the skin and the intercostal muscles. The portion of the thorax containing the pleural windows was removed from the chest and fixed over a bath of whole autologous plasma, the inner parietal pleural surface facing the bath. Small hemispheric Perspex capsules (surface area 0.28 cm2) connected to a pressure manometer were glued to the pleural windows; a subatmospheric pressure was set into the capsule chamber to create step hydraulic transpleural pressure gradients (delta P) ranging from 5 to 60 cmH2O. Transpleural liquid flows (Jv) and protein concentration of the capsular filtrate (Cfilt) and of the plasma bath were measured at each delta P. The transpleural protein flux (Js) at each delta P was calculated by multiplying Jv by the corresponding Cfilt. The hydraulic conductivity (Lp) of the parietal pleura was obtained from the slope of the Jv vs. delta P linear regression. The average Lp from 14 capsules was 9.06 +/- 4.06 (SD) microliters.h-1.cmH2O-1.cm-2. The mathematical treatment of the Js vs. Jv relationship allowed calculation of the unique Peclet number at the maximal diffusional protein flux and a corresponding osmotic permeability coefficient for plasma protein of 1 x 10(-5) +/- 0.97 x 10(-5) cm/s. The reflection coefficient calculated from the slope of the linear phase of the Js vs. Jv relationship was 0.11 +/- 0.05.(ABSTRACT TRUNCATED AT 250 WORDS)     

Generalization of the Spiegler-Kedem-Katchalsky frictional model equations of the transmembrane transport for multicomponent non-electrolyte solutions.

The Spiegler-Kedem-Katchalsky frictional model equations of the transmembrane transport for systems containing n-component, non-ionic solutions is presented. The frictional interpretation of the phenomenological coefficients of membrane and the expressions connecting the practical coefficients (Lp, sigma i, omega ij) with frictional coefficients (fij) are presented.     

Effect of lymphatic cannula outflow height on lung microvascular permeability estimations

Estimates of the pulmonary microvascular membrane reflection coefficient (sigma) and permeability-surface area product (PS) are frequently made with the assumption that a percent change in transmicrovascular fluid flux (Jv) will be represented by an equal percent change in the lymph flow rate (QL) from a single cannulated lung lymph vessel. To test this, we measured QL in seven anesthetized dogs with the outflow end of the lymph cannula set at several heights (H) above and below the lung hilus. The left atrial pressure was then elevated to increase Jv, and QL was again measured at several H's. The percent increase in QL at elevated left atrial pressure depended on H. We used the QL data and lymph and plasma protein concentrations to estimate sigma and PS with a modified form of the Kedem and Katchalsky equations. The calculated values varied considerably with H. Our results indicate that changes in Jv are not represented by equal changes in QL. Therefore, techniques for estimating permeability that depend upon QL as an estimate of Jv may lead to erroneous estimates of sigma and PS.     

Osmosis: a bimodal theory with implications for symmetry

A theory is advanced that volume transfer across a membrane pore during osmosis takes place in two modes: if solute is sterically excluded from the pore a pressure gradient is set up and viscous flow of solvent results; if solute can enter the pore then osmotic flow is a diffusive phenomenon, and there is no pressure gradient in any part of the pore to which solute has access, even at low concentration due to a repulsive wall field. As a consequence the reflexion coefficients sigma s and sigma f for osmosis and ultrafiltration are not equal, although equality is usually assumed to result from an underlying thermodynamic reciprocity; instead, the two coefficients represent essentially different processes. These results follow from three basic thermodynamic considerations which have usually been overlooked: (i) there is a qualitative difference between a permeable pore and an impermeable one, the latter having a discontinuity of solute activity at the mouth, which the former does not; (ii) the osmotic pressure within the pore is determined by the activity of solute not the concentration; (iii) the effective resistance to flow through a channel depends upon the nature of the régime, being different for diffusive and viscous flow. An expression for sigma s is derived and shown to be compatible with experimental data on polymer membranes and homoporous bilayers.     

A simple model for DNA elution from filters

DNA chain scission, induced both in vitro and in vivo by various agents, is an event of great biological relevance. The damage is currently evaluated by empirical membrane separation techniques; the results are quite reproducible and the sensitivity higher than 1 single strand break per 10(9) Daltons. We outline a simple theory of the filtration of coiled macrosolutes, having a random size distribution, through porous membranes, considered as being in quasi-steady flow. The basic transport equation Jj = cj (1 - sigma)Jv is solved by considering that the value of sigma j, the reflection coefficient of component j, (1 less than or equal to j less than or equal to N), is given by (1 - KjRj), where Kj is the partition constant between pore and solution, a function of the conformational entropy loss of the coil, and Rj accounts for the frictional force experienced by a particle moving along the pore. The problem of evaluating the volume Vs filled up with solute has been approached according to a simplified theory of the excluded volume for flexible polymers; the result is Vs = sigma nj4/3 pi(rGj)3 where rGj is the jth radius of gyration. The solution of the resulting set of N differential equations gives nj, the number of molecules of component j remaining on the filter, as a function of the elution volume V. The theory demonstrates that the process is governed by the average dimensions of the coil, so affording a universal calibration of filter elution methods, in excellent agreement with the experiments.     

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.     

Cooperative ligand-lattice binding. Approximate Gaussian binding distribution

Nearest-neighbor cooperative binding of a ligand covering n sites and binding with equilibrium constant K and cooperativity factor omega to a large molecule with m binding sites (m much greater than n omega, n/omega) can be approximately described by a Gaussian distribution P(q-qmax), where q is the number of ligands bound and qmax the most probable value of q. The variance of the Gaussian is equal to the derivative dqmax/d ln(L), where L is the free ligand concentration. This variance, sigma 2, is a complicated function of qmax. However, in the limits of very large cooperativity, omega much greater than 1, very large anticooperativity, omega much less than 1, or noncooperativity, omega = 1, simpler expressions for sigma 2 can be given. For qmax = m/(n + 1), where the most probable number of bound ligands equals the number of free binding sites, sigma 2 has a particularly simple form: sigma 2 = 2m omega 1/2/(n + 1)3. The Gaussian and the infinite lattice approximations for the average number of ligands bound are good approximations only if sigma is much smaller than the number of binding sites. The variance may therefore provide an easy check on the validity of the infinite lattice approximation, which is commonly used to analyze experimental binding data.     

Diffusion of 133Xe through frog skins, toad bladders, and water boundary layers.

We have measured the total permeability coefficients P as a function of stirring frequency omega for 133Xe through frog skins and toad bladders. The permeability coefficients for the frog skins and toad bladders proper are, respectively, Pm = (3.9 +/- 0.8) X 10(-4) cm/s and (7.4 +/- 4.2) X 10(-4) cm/s. "Unstirred" water layer thickness delta is determined concurrently, from the frequency dependence of P(omega); the result for frog skin is delta = (0.060 +/- 0.016) square root of omega(rad/s) cm. The stirring frequency range is from omega = 7.5 rad/s (72 rpm) to 55 rad/s (530 rpm). The results support the conclusions that the principal barrier to Xe diffusion in these epithelia is inter- and intracellular water, and that the diffusion is passive and rapid. The experimental method may be straightforwardly adapted to the measurement of diffusion or counterdiffusion of any gamma-radioactive soluble or partly soluble solute through any flat membrane or through a solvent. We estimate the amount of total body-absorbed radioactivity due to environmental 133Xe to be 50 fCi for an ambient concentration of 2.6 pCi/m3 of air.     

Interchangeability of delta subunits of RNA polymerase from different species of the genus Bacillus.

RNA polymerase was purified from five species of Bacillus, including Bacillus subtilis. Each polymerase had a subunit composition analogous to that reported for B. subtilis, i.e., beta beta '2 alpha sigma delta omega 1 omega 2. The delta subunits from the B. subtilis and Bacillus thuringiensis polymerases were interchangeable, as judged from their effects on promoter selection in the polymerase binding assay.     

Boundary analysis in sedimentation transport experiments: a procedure for obtaining sedimentation coefficient distributions using the time derivative of the concentration profile.

A procedure is described for computing sedimentation coefficient distributions from the time derivative of the sedimentation velocity concentration profile. Use of the time derivative, (delta c/delta t)r, instead of the radial derivative, (delta c/delta r)t, is desirable because it is independent of time-invariant contributions to the optical baseline. Slowly varying baseline changes also are significantly reduced. An apparent sedimentation coefficient distribution (i.e., uncorrected for the effects of diffusion), g*(s), can be calculated from (delta c/delta t)r as [formula: see text] where s is the sedimentation coefficient, omega is the angular velocity of the rotor, c0 is the initial concentration, r is the radius, rm is the radius of the meniscus, and t is time. An iterative procedure is presented for computing g*(s)t by taking into account the contribution to (delta c/delta t)r from the plateau region to give (delta c/delta t)corr. Values of g*(s)t obtained this way are identical to those of g*(s) calculated from the radial derivative to within the roundoff error of the computations. Use of (delta c/delta t)r, instead of (delta c/delta r)t, results in a significant increase (greater than 10-fold) in the signal-to-noise ratio of data obtained from both the uv photoelectric scanner and Rayleigh optical systems of the analytical ultracentrifuge. The use of (delta c/delta t)r to compute apparent sedimentation coefficient distributions for purposes of boundary analysis is exemplified with an antigen-antibody system.     

Segmental barrier properties of the pulmonary microvascular bed.

We determined liquid flux across single pulmonary microvessels of dog, ferret, and rat by our split-drop technique (J. Appl. Physiol. 64: 2562-2567, 1988). Data are reported from 58 lungs excised under halothane or pentobarbital sodium anesthesia and then blood perfused. We stopped blood flow at known vascular pressures and then micropunctured microvessels to inject oil, which we split with albumin solution. From measurements of vessel diameter and split oil drop length, we calculated Jv, the liquid transport rate per unit surface area [x 10(-6) ml/(cm2.s)]. At constant vascular pressure, Jv was not significantly different after different periods of oil-endothelium contact and at different sites within a single vessel. From measurements of Jv at different vascular pressures, we determined Lp, the hydraulic conductivity [x 10(-7) ml/(cm2.s.cmH2O)], and Pzf, the zero filtration pressure. From determinations of Pzf at different albumin concentrations, we quantified sigma alb, the albumin reflection coefficient. Lp and Pzf did not differ among venules of the same lung. However, in venules, Lp was 40% higher and sigma alb 25% lower than in arterioles (P less than 0.01). We conclude that 1) micropuncture procedures incidental to our split-drop technique do not progressively deteriorate the experimental microvessel and 2) in lung, permeability is higher in venules than in arterioles.     

Phenotypes of Bacillus subtilis mutants altered in the precursor-specific region of sigma E.

sigma E is a sporulation-specific sigma factor of Bacillus subtilis that is synthesized from an inactive precursor protein (P31). The structural gene (sigE) for P31 was reengineered by oligonucleotide-directed mutagenesis to encode sigma E directly. The sequence specifying the first amino acid of sigma E (GGC) was placed immediately downstream of the initiating codon (ATG) of P31. The resulting sigE allele (sigE delta 84) encodes a sigma E-like protein which differs from the "processed product" by a single Met residue at its amino terminus. B. subtilis strains which carried this allele were Spo- and contained no detectable sigma E. The sigE delta 84 allele generated a product in Escherichia coli which, by quantitative Western immunoblot analysis, was present at 10 to 20% of the level of product (P31) obtained from a wild-type allele. A sigma E-like product was also not detected in two B. subtilis strains with missense mutations in the sequence encoding the processed region of P31. These results suggest that sigma E is a highly labile protein that is stabilized during its synthesis by an element of the precursor sequence. A mutant allele (sigE delta 48) which made an active sigma E-like protein in B. subtilis was isolated. This gene specified a product in which five amino acids, not derived from the P31 processed region, were joined to P31 at a position eight amino acids upstream of the processing site. The sigE delta 48 product was not processed, but it activated the sigma E -dependent spoIID promoter in vivo. The sigE delta 48 product therefore lost both an essential target for processing and a region which inhibited sigma sigma E activity. Cells which carried sig E delta 48 were Spo-. The basis of the sigE delta 48-dependent defect in sporulation is unknown, but the sigma E delta 48 activity appeared to persist beyond the time in development (4 h after onset sporulation) when wild-type sigma E activity declines. Thus, it may interfere with the proper regulation of late sporulation genes.     

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.     

Theory of fluorescence recovery after photobleaching measurements on cylindrical surfaces.

The theory of fluorescence recovery after photobleaching measurements of isotropic diffusion on a cylindrical surface is developed for Gaussian beam illumination centered perpendicular to an infinitely-long cylinder. A general analytical solution is obtained which is a function of the ratio of the cylindrical radius (r) to the beam exp [-2] radius omega. Numerical analysis of this solution demonstrates that significant deviations from one dimensional recovery are observed for omega less than 3r and from two-dimensional recovery for omega greater than or equal to 0.5r. Numerical data and an algorithm for analysis of recovery data where 0.5r less than or equal to omega less than or equal to 3r is presented.     

Transepithelial transport in cell culture. A theoretical and experimental analysis of the biophysical properties of domes.

Dissociated cells of transporting epithelia, when cultured on an impermeant substratum, form polarized monolayers frequently characterized by the presence of domes. If the assumption is made that the monolayer exhibits a uniform stretch modulus of elasticity and tension of cell-dish adhesion, Ta, then biophysical properties of the epithelium can be predicted. We have shown that for such epithelia, domes should (a) have circular bases, (b) be sections of spheres with a constant height to radius, h/r, ratio, (c) have a dome-wall tension, Tw, that is constant, and (d) have a dome volume that is a function of radius alone. Additionally, a Laplace equation derived for this geometry predicted the hydrostatic pressure from within to outside domes as a decreasing function of radius alone. By microscopy, domes had predominantly circular bases and were found to be sections of spheres with a constant height, h, to radius, r, ratio of 0.684. Using the Laplace equation derived for this geometry and measurements of delta P and r, the tension of cell-dish adhesion, Ta, and dome-wall tension, Tw, were found to be constants of 6.60 and 7.08 torr, respectively. Combining the constants for Ta and h/r ratio, and the fact that domes are sections of spheres, delta P and dome volume were shown to be known functions of radius alone. In addition, the modulus of elasticity of the epithelium was calculated to be 4.82 X 10(3) dyn/cm2.