Weak acid permeability through lipid bilayer membranes. Role of chemical reactions in the unstirred layer

The premeabilities of planar lipid bilayer (egg phosphatidylcholine- decane) membranes to butyric and formic acids were measured by tracer and pH electrode techniques. The purposes of the study were (a) to establish criteria for the applicability of each method and (b) to resolve a discrepancy between previously published permeabilities determined using the different techniques. Tracer fluxes of butyric acid were measured at several concentrations and pH's. Under symmetrical conditions the one-way flux of butyric acid(J) is described by 1/J = 1/Pul ([HA] + [A-]) + 1/Pm([HA]), where Pul and Pm are the unstirred layer and membrane permeability coefficients. Pm determined in this manner is 950 x 10(4) cm s-1. Published values for the butyric acid permeability for egg phosphatidylcholine-decane bilayers are 11.5 x 10(-4) (Wolosin and Ginsburg, 1975) and 640 x 10(-4) cm s-1 (Orbach and Finkelstein, 1980). Wolosin and Ginsburg measured net fluxes from a solution of pH = Pka into an unbuffered solution containing a pH electrode. Orbach and Finkelstein measured tracers fluxes under symmetrical conditions at pH 7.4. We reproduced the results of Wolosin and Ginsburg and showed that their apparently low Pm was caused by unstirred layer effects in their poorly buffered solutions. The permeability to formic acid (pKa = 3.75) measured by both tracer and pH electrode techniques was approximately 10(-2) cm s-1. However, if pm greater than Pul, the pH electrode technique cannot be used for measuring the permeabilities of weak acids with pKa's greater than approximately 4.     

Photosynthesis of Ulva fasciata. IV. pH, carbonic anhydrase and inorganic carbon conversions in the unstirred layer

Abstract. The common marine macroalga Ulva was found to have a surface pH of about 10 during photosynthesis. Under such a condition, the equilibrium CO₂ concentration within the unstirred layer would be below reported CO₂ compensation points, and dehydration of HCO₃ could not occur. Even at a compensation point approaching zero, uncatalysed rates of HCO₃ to CO₂ conversion within the unstirred layer volume could not support photosynthetic rates as measured under stirred conditions in the presence of a carbonic anhydrase inhibitor. Based on this, it is concluded that Ulva takes up HCO₃. It is likely that HCO₃ uptake leads to high internal CO₂ levels which, in turn, suppress photorespiration and thus cause this plant's efficient gas exchange features. Carbonic anhydrase activity was measurable only in plant extracts. However, inhibitor studies suggest the presence of a surface enzyme. The possible functions of extracellular carbonic anhydrase in Ulva are assessed in terms of CO₂ hydration during emergence and a possible HCO₃, transport system.     

Diffusion of inorganic carbon across an unstirred layer: a simplified quantitative approach

Abstract The quantitative approach used here is based on a model comprising a well-stirred medium, an unstirred layer, and a CO₂ absorbing leaf. The unstirred layer is divided up by planes into a number of sub-layers. Within each plane the concentration of each solute is everywhere the same as is the electric potential. These variables constitute the basic data. Thus the planes were characterized by their pH value. An equation is derived which enables the calculation of the basic data of a plane from the known data of another plane. In this way it is possible to calculate the basic data for all planes. From these data the rate of assimilation, the thickness of the unstirred layer and its sub-layers, the fluxes across the sub-layers and the conversions among the carbon components can be estimated. The CO₂ flux decreases, and the HCO^?₃ flux increases towards the leaf. There are negative fluxes of OH^& and CO^2–₃. H⁺ fluxes are of minor importance and can be ignored if the pH of the medium is higher than 8.0, provided no non-inorganic C buffers with appropriate pK_a are present. The significance of the carbon diffusion facilitating effect of an inorganic carbon system is expressed in various ways. The values obtained represent maxima, as the assumption is made that the equilibrium reactions are very fast. It is argued that even better effects are possible if the back-diffusion of CO^2–₃ could be prevented by lowering the pH of the unstirred layer.     

The chemistry,physiology and pathology of pH in cancer

Cell survival is conditional on the maintenance of a favourable acid–base balance (pH). Owing to intensive respiratory CO₂ and lactic acid production, cancer cells are exposed continuously to large acid–base fluxes, which would disturb pH if uncorrected. The large cellular reservoir of H⁺-binding sites can buffer pH changes but, on its own, is inadequate to regulate intracellular pH. To stabilize intracellular pH at a favourable level, cells control trans-membrane traffic of H⁺-ions (or their chemical equivalents, e.g. ) using specialized transporter proteins sensitive to pH. In poorly perfused tumours, additional diffusion-reaction mechanisms, involving carbonic anhydrase (CA) enzymes, fine-tune control extracellular pH. The ability of H⁺-ions to change the ionization state of proteins underlies the exquisite pH sensitivity of cellular behaviour, including key processes in cancer formation and metastasis (proliferation, cell cycle, transformation, migration). Elevated metabolism, weakened cell-to-capillary diffusive coupling, and adaptations involving H⁺/H⁺-equivalent transporters and extracellular-facing CAs give cancer cells the means to manipulate micro-environmental acidity, a cancer hallmark. Through genetic instability, the cellular apparatus for regulating and sensing pH is able to adapt to extracellular acidity, driving disease progression. The therapeutic potential of disturbing this sequence by targeting H⁺/H⁺-equivalent transporters, buffering or CAs is being investigated, using monoclonal antibodies and small-molecule inhibitors.     

Generation of potential in lipid bilayer membranes as a result of proton-transfer reactions in the unstirred layers

The addition of an uncoupler in the presence of a concentration gradient of weak acids or bases (sodium acetate and ammonium chloride) leads to the generation of a potential on lipid bilayer membranes (LBM) which is positive in sign on the side of the membrane with a high concentration of sodium acetate and negative on the side with a high concentration of ammonium chloride. It is shown that the potential was caused by the pH gradient in the unstirred layers. These effects can be understood in terms of the previously described [Science,182, 1258 (1973)] model for the transfer of weak acids and bases through LBM. This system described may be useful for quantitation of permeabilities for weak acids and bases through bilayer membranes.     

Diffusion of carbon dioxide through lipid bilayer membranes. Effects of carbonic anhydrase, bicarbonate, and unstirred layers

Diffusion of (14)C-labeled CO(2) was measured through lipid bilayer membranes composed of egg lecithin and cholesterol (1:1 mol ratio) dissolved in n-decane. The results indicate that CO(2), but not HCO(3-), crosses the membrane and that different steps in the transport process are rate limiting under different conditions. In one series of experiments we studied one-way fluxes between identical solutions at constant pCO(2) but differing [HCO(3-)] and pH. In the absence of carbonic anhydrase (CA) the diffusion of CO(2) through the aqueous unstirred layers is rate limiting because the uncatalyzed hydration-dehydration of CO(2) is too slow to permit the high [HCO(3-)] to facilitate tracer diffusion through the unstirred layers. Addition of CA (ca. 1 mg/ml) to both bathing solutions causes a 10-100-fold stimulation of the CO(2) flux, which is proportional to [HCO(3-)] over the pH range 7-8. In the presence of CA the hydration- dehydration reaction is so fast that CO(2) transport across the entire system is rate limited by diffusion of HCO(3-) through unstirred layers. However, in the presence of CA when the ratio [HCO(3-) + CO(3=)]:[CO(2)] more than 1,000 (pH 9-10) the CO(2) flux reaches a maximum value. Under these conditions the diffusion of CO(2) through the membrane becomes rate limiting, which allows us to estimate a permeability coefficient of the membrane to CO(2) of 0.35 cm s(-1). In a second series of experiments we studied the effects of CA and buffer concentration on the net flux of CO(2). CA stimulates the net CO(2) flux in well buffered, but no in unbuffered, solutions. The buffer provides a proton source on the upstream side of the membrane and proton sink on the downstream side, thus allowing HCO(3-) to facilitate the net transport of CO(2) through the unstirred layers.     

Role of bicarbonate in the regulation of intracellular pH in the mammalian ventricular myocyte.

Bicarbonate is important for pHi control in cardiac cells. It is a major part of the intracellular buffer apparatus, it is a substrate for sarcolemmal acid-equivalent transporters that regulate intracellular pH, and it contributes to the pHo sensitivity of steady-state pHi, a phenomenon that may form part of a whole-body response to acid/base disturbances. Both bicarbonate and H+/OH- transporters participate in the sarcolemmal regulation of pHi, namely Na(+)-HCO3-cotransport (NBC), Cl(-)-HCO3- exchange (i.e., anion exchange, AE), Na(+)-H+ exchange (NHE), and Cl(-)-OH- exchange (CHE). These transporters are coupled functionally through changes of pHi, while pHi is linked to [Ca2+]i through secondary changes in [Na+] mediated by NBC and NHE. Via such coupling, decreases of pHo and pHi can ultimately lead to an elevation of [Ca2+]i, thereby influencing cardiac contractility and electrical rhythm. Bicarbonate is also an essential component of an intracellular carbonic buffer shuttle that diffusively couples cytoplasmic pH to the sarcolemma and minimises the formation of intracellular pH microdomains. The importance of bicarbonate is closely linked to the activity of the enzyme carbonic anhydrase (CA). Without CA activity, intracellular bicarbonate-dependent buffering, membrane bicarbonate transport, and the carbonic shuttle are severely compromised. There is a functional partnership between CA and HCO3- transport. Based on our observations on intracellular acid mobility, we propose that one physiological role for CA is to act as a pH-coupling protein, linking bulk pH to the allosteric H+ control sites on sarcolemmal acid/base transporters.     

Weak acid transport across bilayer lipid membrane in the presence of buffers. Theoretical and experimental pH profiles in the unstirred layers.

This paper presents a simple model to describe experimental data on weak acid transport across planar bilayer lipid membrane separating two buffered solutions. The model takes into account multiple proton-transfer reactions occurring in the unstirred layers (ULs) adjacent to the membrane. Differential equations of the model are shown to be reduced to a set of nonlinear algebraic equations. Since the latter equations depend monotonically on unknown variables, they can be easily solved numerically, using bisection method. For the particular system studied experimentally (with acetate as the weak acid and TRIS+MES as the buffer mixture) pH profiles in the ULs are calculated from the model. These results are compared with experimental data obtained using pH microelectrode. The agreement between theoretical and experimental pH profiles is found to be satisfactory. The most pronounced deviations are observed at the UL/bulk solution boundary. To obtain a better correlation between the theoretical and experimental results, two other, less idealized models are considered. They take into account, respectively, (a) the electric field arising in the ULs from ion diffusion and (b) finiteness of the rates of proton-transfer reactions. However, both acetate membrane fluxes and pH profiles in the ULs computed from these models are found to be close to those of the simple model. One can thus conclude that the difference between experimental and theoretical pH profiles is due to the inconsistency of the generally accepted model of the "unstirred layer", assuming the existence of a strict boundary between the regions of "pure diffusion" and "ideal stirring".     

pH gradients and a mirco-pore filter at the luminal surface affect fluxes of propionic acid across guinea pig large intestine

A neutral pH microclimate had been shown at the luminal surface of the large intestine. The aim was to estimate to what extent fluxes of propionic acid/propionate are affected by changes of the luminal pH when this microclimate is present, largely reduced or absent. Fluxes of propionic acid/propionate (J ^Pr) across epithelia from the caecum, the proximal and the distal colon of guinea pigs were measured in Ussing chambers with and without a filter at the luminal surface. With bicarbonate and with a neutral or an acid pH of mucosal solutions (pH 7.4 or 6.4), mucosal-to-serosal fluxes (J _ms^Pr) were 1.5 to 1.9-fold higher at the lower pH, in bicarbonate-free solutions and carbonic anhydrase (CA) inhibition 2.1 to 2.6-fold. With a filter at the mucosal surface and with bicarbonate containing solutions, J _ms^Pr was not or only little elevated at the lower pH. Without bicarbonate J _ms^Pr was clearly higher. We conclude that the higher J _ms^Pr after luminal acidification is due to vigorous mixing in Ussing chambers resulting in a markedly reduced unstirred layer. Therefore, an effective pH microclimate at the epithelial surface is missing. J _ms^Pr is not or is little affected by lowering of pH because in the presence of bicarbonate the filter maintains the pH microclimate. However, in bicarbonate-free solutions J _ms^Pr was higher at pH 6.4 because a pH microclimate does not develop. Findings confirm that 30–60% of J _ms^Pr results from non-ionic diffusion.     

Thiamine transport in thiamine-deficient rats. Role of the unstirred water layer.

As part of a systematic study of alcoholism and thiamine absorption, the effect of diet-induced thiamine deficiency and the role of the unstirred water layer on the thiamine transport were investigated. Using 3H-labeled dextran as a marker of adherent mucosal volume, jejunal uptake of 14C-labeled thiamine hydrochloride was measured, in vitro, in thiamine-deficient rats and pair-fed controls. Uptake of low thiamine concentrations (0.2 and 0.5 muM) was greater in the thiamine-deficient rats than in the controls. In contrast, uptake rates for high thiamine concentrations (20 and 50 muM) were similar in both groups. While Jmax was unaltered, Km was decreased in thiamine deficiency, suggesting a decrease in unstirred water layer thickness. Accordingly, the thickness of the water layer was measured in both groups of animals and correlated with Jmax and Km under unstirred and stirred conditions. Without stirring, there was no difference in Jmax between the two groups. In contrast, both Km and the water layer were reduced in the thiamine-deficient rats. With stirring, Jmax was not affected, but both Km and the water layer thickness were reduced to similar values in both groups. Reversal of thiamine deficiency resulted in the return of thiamine uptake and the unstirred water layer thickness to control values. These data support the concept of a dual system of thiamine transport and emphasize the role of the unstirred water layer as an important determinant of transport kinetics not only under physiologic situations but also in diet-induced rat thiamine deficiency, a model for a clinical patholigical state. The decrease in the unstirred water layer thickness in thiamine deficiency may be also viewed as a possible adaptive mechanism to facilitate absorption of meager supplies of thiamine.     

The effect of auxiliary conditions on intestinal unstirred layer diffusion modelled by numerical simulation.

Estimation of intestinal unstirred layer thickness usually involves inducing transmural potential difference changes by altering the content of the solution used to perfuse the small intestine. Osmotically active solutes, such as mannitol, when added to the luminal solution diffuse across the unstirred water layer (UWL) and induce osmotically dependent changes in potential difference. As an alternative procedure, the sodium ion in the luminal fluid can be replaced by another ion. As the sodium ion diffuses out of the UWL, the change in concentration next to the intestinal membrane alters the transmural potential difference. In both cases, UWL thickness is calculated from the time course of the potential difference changes, using a solution to the diffusion equation. The diffusion equation solution which allows the calculation of intestinal unstirred layer thickness was examined by simulation, using the method of numerical solutions. This process readily allows examination of the time course of diffusion under various imposed circumstances. The existing model for diffusion across the unstirred layer is based on auxiliary conditions which are unlikely to be fulfilled in the same intestine. The present simulation additionally incorporated the effects of membrane permeability, fluid absorption and less than instantaneous bulk phase concentration change. Simulation indicated that changes within the physiologically relevant range in the chosen auxiliary conditions (with the real unstirred layer length kept constant) can alter estimates of the apparent half-time. Consequently, changes in parameters unassociated with the unstirred layer would be misconstrued as alterations in unstirred layer thickness.     

A weak base-generating system suitable for selective manipulation of lysosomal pH

pH varies widely among the different intracellular compartments. The establishment and maintenance of a particular pH appears to be critical for proper organellar function. This has been deduced from experiments where intraorganellar pH was altered by means of weak acids or bases, ionophores or inhibitors of the vacuolar H(+)-ATPase (V-ATPase). These manipulations, however, are not specific and simultaneously alter the pH of multiple compartments. As a result, it is difficult to assign their effect to a defined organelle. To circumvent this limitation, we designed and implemented a procedure to selectively manipulate the pH of a compartment of choice, using lysosomes as a model organelle. The approach is based on the targeted and continuous enzymatic generation of weak electrolyte, which enabled us to overcome the high buffering capacity of the lysosomal lumen, without altering the pH of other compartments. We targeted jack-bean urease to lysosomes and induced the localized generation of ammonia by providing the membrane-permeant substrate, urea. This resulted in a marked, rapid and fully reversible alkalinization that was restricted to the lysosomal lumen, without measurably affecting the pH of endosomes or of the cytosol. The acute alkalinization induced by urease-urea impaired the activity of pH-dependent lysosomal enzymes, including cathepsins C and L, without altering endosomal function. This approach, which can be extended to other organelles, enables the analysis of the role of pH in selected compartments, without the confounding effects of global disturbances in pH or vesicular traffic.     

Tumor-associated carbonic anhydrase 9 spatially coordinates intracellular pH in three-dimensional multicellular growths

CA9 is a membrane-tethered, carbonic anhydrase (CA) enzyme, expressed mainly at the external surface of cells, that catalyzes reversible CO(2) hydration. Expression is greatly enhanced in many tumors, particularly in aggressive carcinomas. The functional role of CA9 in tumors is not well established. Here we show that CA9, when expressed heterologously in cultured spheroids (0.5-mm diameter, ~25,000 cells) of RT112 cells (derived from bladder carcinoma), induces a near-uniform intracellular pH (pH(i)) throughout the structure. Dynamic pH(i) changes during displacements of superfusate CO(2) concentration are also spatially coincident (within 2 s). In contrast, spheroids of wild-type RT112 cells lacking CA9 exhibit an acidic core (~0.25 pH(i) reduction) and significant time delays (~9 s) for pH(i) changes in core versus peripheral regions. pH(i) non-uniformity also occurs in CA9-expressing spheroids after selective pharmacological inhibition of the enzyme. In isolated RT112 cells, pH(i) regulation is unaffected by CA9 expression. The influence of CA9 on pH(i) is thus only evident in multicellular tissue. Diffusion-reaction modeling indicates that CA9 coordinates pH(i) spatially by facilitating CO(2) diffusion in the unstirred extracellular space of the spheroid. We suggest that pH(i) coordination may favor survival and growth of a tumor. By disrupting spatial pH(i) control, inhibition of CA9 activity may offer a novel strategy for the clinical treatment of CA9-associated tumors.     

Intestinal transport of weak electrolytes. Evidence in favor of a three-compartment system

A study has been made of the transmural fluxes of benzoic, phenylacetic, and pentanoic acids, benzylamine, hexylamine, and D-amphetamine across rat jejunum incubated in vitro. The M to S fluxes of the weak acids were greater than their corresponding S to M fluxes, and the S to M fluxes of the weak bases were larger than their M to S fluxes. These patterns of asymmetric movements were observed when the transmural electrical potential difference was clamped at 0 mV, and when the pH values of the mucosal and serosal fluids were identical. The effects of a weak acid on the fluxes of other weak electrolytes were qualitatively similar when the effector weak acid was added to the mucosal fluid, and when it was added to the serosal fluid. But the effects of a weak base on the fluxes of other weak electrolytes were dependent upon its location, and the interactions observed when the effector weak base was added to the mucosal fluid were qualitatively different than those seen when it was added to the serosal fluid. The interactions between weak electrolytes could readily be explained in terms of the function of a system of three compartments in series, in which the pH of the intermediate compartment is greater than that of the bulk phases. But these observations could not be explained in terms of an analogous system involving an intermediate compartment of low pH, or in terms of a carrier mediated system. The transport function of the three-compartment system can be described in the form of an equation, and it is found that a pH difference of less than 0.5 unit may explain our observations on weak electrolyte transport.     

Intestinal transport of weak electrolytes: Determinants of influx at the luminal surface

The determinants of weak electrolyte influx into everted segments of rat small intestine have been studied. Preliminary experiments showed that the observed influxes could be described as unidirectional, diffusional fluxes of the nonionized compound uncomplicated by a parallel ionic component. It is shown that the determinants of weak electrolyte influx in this situation may be described in terms of the resistance of the unstirred layer to movement from the bulk phase to the cell surface, the degree of ionization of the weak electrolyte at the cell surface, and the cellular permeability to the nonionized weak electrolyte. Quantitative considerations indicated that the unstirred layer was totally rate-limiting in the cases of some poorly ionized, or highly permeant compounds, but the unstirred layer was not totally rate limiting for most of the compounds studied. Calculation of cellular permeabilities for the nonionized forms of weak electrolytes required assumptions to be made concerning the pH value in the surface fluid layer. A uniform set of permeability data including both weak acids and weak bases was obtained only when it was assumed that the pH in the surface fluid layer was equal to that in the bulk phase, and it was concluded that these studies do not support the concept of a microclimate of distinctive pH at the epithelial surface as a determinant of weak electrolyte transport.     

Comparative assessment of the resistance of the unstirred water layer to solute transport between two different intestinal perfusion systems

The resistance of the unstirred water layer to solute transport was estimated in two different intestinal single-pass perfusion systems for a comparative study, using D-glucose as a model compound. One is a well established perfusion system in anesthetized rats as a standard (system A). The other is the one in unanesthetized rats for comparison (system B). It was demonstrated that in system B as well as in system A the resistance of the unstirred water layer to D-glucose transport should be taken into account and this resistance, accordingly, the effective thickness of the unstirred water layer (delta) which is assumed to be in proportion to its resistance, could be described as a function of the perfusion rate by using a film model. The delta decreased with increasing perfusion rate and was larger in system A than in system B at each perfusion rate; 785 microns in system A versus 319 microns in system B at the perfusion rate of 0.16 ml/min and 337 microns versus 184 micron at that of 2.95 ml/min. Thus in system B the effective thickness, accordingly, the resistance, of the unstirred water layer was reduced to about 50% of that in system A, but the resistance of the unstirred water layer could still account for 85% of the total resistance at the maximum as far as D-glucose absorption was concerned, while 93% in system A. These results suggest that, compared with perfusion experiments in anesthetized rats (system A), the resistance of the unstirred water layer is reduced but cannot be left out of consideration even if perfusion experiments are performed in unanesthetized rats (system B). And the lower resistance of the unstirred water layer in system B was attributed to a turbulent flow in contrary to a laminar flow in system A.     

The influence of a transmembrane pH gradient on protonation probabilities of bacteriorhodopsin: the structural basis of the back-pressure effect

Bacteriorhodopsin pumps protons across a membrane using the energy of light. The proton pumping is inhibited when the transmembrane proton gradient that the protein generates becomes larger than four pH units. This phenomenon is known as the back-pressure effect. Here, we investigate the structural basis of this effect by predicting the influence of a transmembrane pH gradient on the titration behavior of bacteriorhodopsin. For this purpose we introduce a method that accounts for a pH gradient in protonation probability calculations. The method considers that in a transmembrane protein, which is exposed to two different aqueous phases, each titratable residue is accessible for protons from one side of the membrane depending on its hydrogen-bond pattern. This method is applied to several ground-state structures of bacteriorhodopsin, which residues already present complicated titration behaviors in the absence of a proton gradient. Our calculations show that a pH gradient across the membrane influences in a non-trivial manner the protonation probabilities of six titratable residues which are known to participate in the proton transfer: D85, D96, D115, E194, E204, and the Schiff base. The residues connected to one side of the membrane are influenced by the pH on the other side because of their long-range electrostatic interactions within the protein. In particular, D115 senses the pH at the cytoplasmic side of the membrane and transmits this information to D85 and the Schiff base. We propose that the strong electrostatic interactions found between D85, D115, and the Schiff base as well as the interplay of their respective protonation states under the influence of a transmembrane pH gradient are responsible for the back-pressure effect on bacteriorhodopsin.     

Short-term pH regulation in plants

Cellular pH regulation consists of two features: (i) Long-term pH homeostasis, which ensures that all H⁺ or OH⁻ produced in excess is ultimately removed from the cell and which requires metabolic energy; (ii) short-term reactions of the cell(s) to sudden shifts in intracellular pH, in order to prevent acute disturbances of metabolism. Recent progress in measuring and understanding of mainly short-term cellular regulation is summarized, including cellular responses to pH loads that arise from different sources such as external pH, weak acids/bases, protonophores, metabolic inhibitors, H⁺/cotransport, light and phytohormones. Whereas the plasma membrane H⁺ pump and metabolic adjustments may serve both long- and short-term pH control, physico-chemical buffering and the translocation of H⁺ from and to cellular compartments render only time-limited capacity for the neutralization of pH loads and seem exhausted within minutes. In spite of the widespread opinion that, because of tight regulation, intracellular pH does not vary with time, there is good evidence for long-lasting pH changes in plant cells, i.e. after hormonal stimulation, light/dark changes or carboxylation during crassulacean acid metabolism (CAM). This emphasizes that cytoplasmic pH, besides being well regulated, is essential not only for the regulation of membrane transport but also as a cellular messenger.     

Thiamine transport in thiamine-deficient rats role of the unstirred water layer

As part or a systematic study of alcoholism and thiamine absorption, the effect of diet-induced thiamine deficiency and the role of the unstirred water layer on thiamine transport were investigated. Using ³H-labeled dextran as a marker of adherent mucosal volume, jejunal uptake of ¹⁴C-labeled thiamine hydrochloride was measured, in vitro, in thiamine-deficient rats and pair-fed controls. Uptake of low thiamine concentrations (0.2 and 0.5 μM) was greater in the thiamine-deficient rats thatn in the controls. In contrast, uptake rates for high thiamine concentrations (20 and 50 μM) were similar in both groups. While $\text{1J}{}_{\max }$ was unaltered, $\text{1K}{}_{\mathrm{m}}$ was decreased in thiamine deficiency, suggesting a decrease in unstirred water layer thickness. Accordingly, the thickness of the water layer was measured in both groups of animals and correlated with $\text{1J}{}_{\max }$ and $\text{1K}{}_{\mathrm{m}}$ under unstirred and st irred conditions. Without stirring, there was no difference in $\text{1J}{}_{\max }$ between the two groups. In contrast, both $\text{1K}{}_{\mathrm{m}}$ and the water layer were reduced in the thiamine-deficient rats. With stirring, $\text{1J}{}_{\max }$ was not affected, but both $\text{1K}{}_{\mathrm{m}}$ and the water layer thickness were reduced to similar values in both groups. Reversal of thiamine deficiency resulted in the return of thiamine uptake and the unstirred water layer thickness to control values. These data support the concept of a dual system of thiamine transport and emphasize the role of the unstirred water layer as an important determinant of transport kinetics not only under physiologic situations but also in diet-induced rat thiamine deficiency, a model for a clinical pathological state. The decrease in the unstirred water layer thickness in thiamine deficiency may be also viewed as a possible adaptive mechanism to facilitate absorption of meager supplies of thiamine.     

The development of osmotic flow through an unstirred layer

We investigate the errors involved in estimating the osmotic permeability of a semi-permeable membrane, from the measured osmotic flow and the difference in concentration of osmotically active solute across it, without taking account of the unstirred layer in the solution next to the membrane. In the problem solved, this layer is represented as a region of thickness δ at the far side of which a solute concentration C_b is imposed for time . The initial diffusion of solute towards the membrane causes the concentration at the membrane C_m to rise, generating an osmotic flow of water, J, whose convective effect opposes the diffusion. The problem is made non-linear by the dependence of J on C_m. Ultimately a steady state is set up, in which C_m is less than C_b. The solution is shown to depend on a single parameter β, equal to (L_pRT) δ C_b/D, where L_pRT is the osmotic permeability of the membrane and D is the diffusivity of solute. Solution of the steady state leads to a prediction of C_m/C_b as a function of β, and analysis of the decay of transient terms leads to a prediction of the decay time π, also as a function of β. Numerical data for membranes with a wide range of osmotic permeabilites, and for a reasonable range of solute, i.e. sucrose, concentrations, suggest that values of β can range from 0.001 or below to 7.5 or above. The former value implies negligible error in neglecting the unstirred layer, while the latter implies a 79%. error. For β = 0.1 and for δ = 2 × 10⁻⁴ m, π is predicted to be around 74 s. This decreases as β increases (for fixed δ); for values of β above about 27, the decay of transients is no longer monotonic but takes the form of damped oscillations.