Intestinal absorption by carrier-mediated transports: two-dimensional laminar flow model

The two-dimensional laminar flow model was adapted to the intestinal absorption of drug and biological substances by carrier-mediated transports in the single perfusion experiments and we investigated the effects of the unstirred water layer on the Michaelis constant and the maximum transport velocity. According to the calculated values, the half saturation concentration at the inlet was larger than the true Michaelis constant at the intestinal wall. The apparent values of the Michaelis constant and the maximum transport velocity obtained by the Lineweaver-Burk plots were larger than the true ones, and the relations were not linear. These deviations increased as the ratio of the maximum transport velocity to the Michaelis constant increased and as the perfusion rate decreased. In the concurrent presence of a passive transport, underestimation of the carrier-mediated transport component of the absorption rate (at steady state) was predicted. It is considered to cause the underestimation of the maximum transport velocity. When water was absorbed (or secreted), the absorption rate increased (or decreased) and did not saturate. This two-dimensional laminar flow model would enable us to analyze the experimental data to determine the true values of the Michaelis constant and the maximum transport velocity.     

The determination of the kinetic parameters of a carrier mediated transport process in the presence of an unstirred water layer

A procedure is described, based on the Eadie-Hofstee plot, from which it is possible to determine the Michaelis constant and the maximum velocity of a membrane bound transport process that is separated from the substrate in the bulk solution by an unstirred layer. This can be done without knowing the magnitude of the latter provided that its effective thickness can be varied by altering the rate of stirring. Further, if the affinity of the carrier for the substrate is sufficiently large, then, it is possible to determine the rate constant and the effective concentration of the membrane bound carrier.     

Derivation of the equations that describe the effects of unstirred water layers on the kinetic parameters of active transport processes in the intestine

Unidirectional flux of solutes into the intestinal mucosal cells is determined by the rate of movement of these molecules across both an unstirred water layer and the microvillus membrane of the epithelial cell. Therefore, an equation is derived in this paper that describes the velocity of active transport as a function of the characteristics of both the transport carrier in the membrane and the resistance of the overlying unstirred water layer. Using this equation a series of curves are presented that depict the effect on the kinetics of active transport of varying the thickness (d) or surface area (S_w) of the unstirred water layer, the free diffusion coefficient (D) of the solute, the distribution of active transport sites along the villus ($\text{?}{}_{\mathrm{<mtext>n</mtext>}}$), the maximal transport velocity (J^m_d) and the true Michaelis constant (K_m). These theoretical curves illustrate the serious limitations inherent in interpretation of previously published data dealing with active transport processes in the intestine.     

Limitations of the Eadie-Hofstee plot to estimate kinetic parameters of intestinal transport in the presence of an unstirred water layer

Summary In the presence of an intestinal unstirred water layer, the relationship between substrate concentration (C ₁) and unidirectional flux (J _d) is not described by the equation for a rectangular hyperbole. Accordingly, transformations of the Michaelis-Menten equation may not necessarily be linear and may lead to serious errors in the estimation of the affinity constant (K _m) and maximal transport rate (J _d ^m ) of carrier-mediated processes. An equation has previously been derived which describedJ _d under conditions of varying effective thickness or surface area of the unstirred water layer, the free diffusion coefficient of the probe molecule, and the distribution of transport sites along the villus. These theoretical curves have been analyzed by using the Eadie-Hofstee transformation (J _d vs. J_d/C₁) of the Michaelis-Menten equation. Use of this plot leads to serious discrepancies between the true and apparent affinity constants and between true and apparent maximal transport rates. These differences are further magnified by failure to correct for the contribution of passive permeation. The Eadie-Hofstee plot is of use, however, to infer certain qualitative characteristics of active transport processes, such as the variation in affinity constants and overlying resistance of the unstirred water layer at different sites along the villus and to predict the adequacy of the correction for the contribution of passive permeation.Abbreviations Used in the Text C ₁ Concentration of the probe molecule in the bulk phase - C ₂ Concentration of the probe molecule at the aqueous-membrane interface - d Effective thickness of UWL - D Free diffusion coefficient - d ⁿ d atn th segment of the villus - f _n Proportion of total carrier transport sites present on each segment of villus - J Unidirectional flux of probe molecule, uncorrected for surface area - J _d Unidirectional flux of probe molecule determined experimentally, corrected for surface area - J _d ^m Maximal transport rate, corrected for surface area - J _d ^m* Apparent maximal transport rate - J ^m Maximal transport rate, uncorrected for surface area - K _m Michaelis constant (true affinity constant) - K _m ^* Apparent affinity constant - K _m ⁿ K _m atnth segment of the villus - n The perpendicular height of the villus was divided into ten equal segments numberedn ₁ ton ₁₀ - p Passive permeability coefficient - S _m Functional surface area of the membrane - S _w Effective surface of UWL - S _w ⁿ S _w atnth segment of the villus - UWL Intestinal unstirred water layer     

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.     

Determination of intrinsic membrane transport parameters from perfused intestine experiments: a boundary layer approach to estimating the aqueous and unbiased membrane permeabilities

A boundary layer approach is developed for estimating the aqueous resistance in a perfused rat intestine experiment. Knowing the aqueous resistance allows the membrane surface concentration to be calculated as a function of the perfusate inlet concentration and perfusional flow rate. Determination of membrane uptake as a function of the membrane surface concentration rather than the perfusate concentration gives the intrinsic, unbiased membrane parameters for the uptake mechanism of Michaelis-Menten-type kinetics in parallel with passive diffusion. The aqueous resistance derived in the analysis is verified by comparison with flux data for 1-leucine and progesterone measured at various flow rates and intestinal lengths. The approach allows for a direct estimate to be made of the unbiased membrane permeability parameters.     

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.     

Experimental demonstration of the effect of the unstirred water layer on the kinetic constants of the membrane transport ofd-glucose in rabbit jejunum

Summary The rate of active transport of a probe molecule into the intestinal mucosal cells is determined by the rate of movement of the solute molecule across two barriers, the unstirred water layer and the microvillus membrane of the epithelial cell. Previously a theoretical equation has been derived which describedJ _d, the velocity of unidirectional flux, as a function of the characteristics of the transport carrier in the membrane and of the resistance of the overlying unstirred water layer (UWL). The predictions of these equations have been tested experimentally by studying the effect of the rate of stirring of the bulk phase on thein vitro uptake ofd-glucose by rabbit jejunum. These studies demonstrated that, first, alterations in the UWL have a profound effect on the magnitude of the apparent affinity constant, xK _m ^* , of the active transport process. Second, at bulk phase concentrations in excess of theK _m the passive component of the experimentally determined flux rate becomes of such magnitude as to introduce significant error into the estimate of both the maximal transport rate,J _d ^m , and the trueK _m. Third, as a result of the UWL, the use of double-reciprocal plots to determineJ _d ^m andK _m leads to the overestimation of these constants. Finally, failure to account for the UWL leads to important quantitative errors describing a number of the characteristics of the transport process: these include an underestimation of the Q₁₀ and the effect of sodium ion on the active transport of glucose in the jejunum. The results confirm that the kinetic characteristics of the uptake of an actively transported molecule are a complex function of the resistance of both the UWL and the mucosal cell membrane, and this transport process can be adequately described by a newly-derived equation. It is apparent that there are serious limitations in the interpretation of much of the previously published data dealing with active transport processes in the intestine, since these studies failed to account for the effect of the UWL.     

Determination of the membrane permeability coefficient and the reflection coefficient by the two-dimensional laminar flow model for intestinal perfusion experiments

We performed single perfusion experiments in the small intestine of rats in order to prove that the two-dimensional laminar flow model is suitable to determine the membrane permeability coefficient and the reflection coefficient. We used progesterone as an aqueous-diffusion-limited drug, urea as a membrane transport-limited drug and the tritiated water as an intermediate substance. The membrane permeability coefficient for progesterone was calculated to be 3.6 X 10(-4) cm/s. This value did not change when the thickness of the aqueous diffusion layer was altered by increasing the perfusion rate 10-fold. It was directly demonstrated that the two-dimensional laminar flow model was suitable to analyze the data of intestinal perfusion experiments. Membrane permeability coefficients for urea and tritiated water were determined to be 3.4 X 10(-5) cm/s and 8.9 X 10(-5) cm/s, respectively. In the presence of water absorption with the hypotonic perfusion solution, the reflection coefficient for urea was 0.84. This value is thought to be theoretically reasonable, suggesting the usefullness of the two-dimensional laminar flow model to obtain the reflection coefficient in the intestinal membrane.     

Determination of the kinetic constants of fructose transport and phosphorylation in the perfused rat liver

The kinetics of fructose uptake was determined in perfused rat liver during steady-state fructose elimination. On the basis of the corresponding values of fructose concentration in the affluent and in the effluent medium, and the fructose and ATP concentration in biopsies, the kinetics of membrane transport and intracellular phosphorylation in the intact organ was calculated according to a model system. Carrier-mediated fructose transport has a high $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ (67 mM) and $\text{V}$ (30 μmoles · min^?1 ·g^?1). The calculated kinetic constants of the intracellular phosphorylation were compared with values obtained with an acid-treated rat liver high speed supernatant (values given in parentheses). $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ with fructose 1.0 mM (0.7 mM), $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ with ATP 0.54 mM (0.37 mM), $\text{V}$ 10.3 μmoles · min^?1 · g^?1 (10.1 μmoles · min^?1 · g^?1, calculated on the basis of the highest measured rate of fructose uptake correcting the ATP concentration to saturating values). The kinetics of fructose uptake reveals that at Physiological fructose concentrations the membrane transport limits the rate of fructose uptake, thus protecting the liver from severe depletion of adenine nucleotides.     

The determination of kinetic parameters for carrier-mediated transport of non-labelled substrate analogues: a general method applied to the study of divalent anion transport in placental membrane vesicles

A method is described that allows the determination of kinetic parameters for carrier-mediated transport of unlabelled compounds. The ability of these compounds to relieve the inhibition of labelled substrate efflux produced by addition of an external competitive inhibitor is studied. The method is of general applicability and does not depend upon any intrinsic asymmetry in the ratio of the rates of translocation of the loaded and unloaded carrier. In this paper it is used in a study of the human placental sulphate transporter. Experiments on brush-border membrane vesicles show the method to predict quantitatively kinetic parameters for unlabelled sulphate entry. Further analysis shows this carrier to have a broad specificity for other oxyanions (selenate, tung-state, molybdate and chromate) with the following selectivity sequence: for rate of translocation, SO4, SeO4 greater than WO4 greater than MoO4 much greater than CrO4; for binding affinity, CrO4 greater than MoO4, WO4 greater than SO4, SeO4.     

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.     

Measurement of sodium ion concentration in the unstirred layer of rat small intestine by polymer Na+-sensitive electrodes

[14C]Formate is incorporated into the C-2 of the pyrimidine moiety of thiamin by Escherichia coli and Salmonella typhimurium. In Saccharomyces cerevisiae, it is incorporated into C-4. Radioactive carbons of [1-14C]glycine and [2-14C]glycine are incorporated by S. typhimurium into the C-4 and C-6 of the pyrimidine, respectively, but not by S. cerevisiae. These facts suggest that procaryotes and eucaryotes have different biosynthetic pathways for pyrimidine. In this study, the procaryotes tested incorporated [14C]formate into the C-2 and the eucaryotes incorporated it into the C-4 of the pyrimidine.     

Peristaltic transport in a channel with a porous peripheral layer: model of a flow in gastrointestinal tract

Peristaltic transport in a two dimensional channel, filled with a porous medium in the peripheral region and a Newtonian fluid in the core region, is studied under the assumptions of long wavelength and low Reynolds number. The fluid flow is investigated in the waveframe of reference moving with the velocity of the peristaltic wave. Brinkman extended Darcy equation is utilized to model the flow in the porous layer. The interface is determined as a part of the solution using the conservation of mass in both the porous and fluid regions independently. A shear-stress jump boundary condition is used at the interface. The physical quantities of importance in peristaltic transport like pumping, trapping, reflux and axial velocity are discussed for various parameters of interest governing the flow like Darcy number, porosity, permeability, effective viscosity etc. It is observed that the peristalsis works as a pump against greater pressure in two-layered model with a porous medium compared with a viscous fluid in the peripheral layer. Increasing Darcy number Da decreases the pumping and increasing shear stress jump constant beta results in increasing the pumping. The limits on the time averaged flux Q for trapping in the core layer are obtained. The discussion on pumping, trapping and reflux may be helpful in understanding some of the fluid dynamic aspects of the transport of chyme in gastrointestinal tract.     

Kinetic constants for intestinal transport of four monosaccharides determined under conditions of variable effective resistance of the unstirred water layer

Summary Theoretical considerations have suggested that variations in the resistance of the unstirred water layer (UWL) have a profound effect on the kinetic constants of intestinal transport. In this study, a previously validatedin vitro technique was employed to determine the unidirectional flux rate of glucose, galactose, 3-O-methyl glucose and fructose into the rabbit jejunum under carefully-defined conditions of stirring of the bulk phase known to yield different values for the effective resistance of the UWL. For each monosaccharide, uptake is much greater when the resistance of the UWL is low than when high. The maximal transport rate,J _d ^m , of glucose was half as large as theJ _d ^m of galactose and 3-O-methyl glucose (3-O-MG), and was twice as great as theJ _d ^m of fructose. The apparent affinity constant,K _m ^* ,of glucose is less than that of fructose, which was lower than theK _m ^* of galactose and 3-O-MG. The use of the Lineweaver-Burk double reciprocal plot is associated with an overestimation of bothJ _d ^m andK _m ^* .This discrepancy between the true and apparent values of the kinetic constants is much greater for lower than for higher values ofJ _d ^m andK _m ^* ;variations in the resistance of the unstirred layer influences the magnitude and direction of the discrepancy. The apparent passive permeability coefficient is similar for each sugar, but because of the different values ofJ _d ^m , passive permeation contributes relatively more to the uptake of glucose and fructose than of galactose or 3-O-MG. Under conditions of high unstirred layer resistance, differences in uptake rates of the sugars are due to differences in theirJ _d ^m rather than theirK _m ^* .Kinetic analysis is compatible with the suggestion that the glucose carriers are predominantly near the tip of the villus, whereas those for galactose and 3-O-MG are located along the entire villus and theK _m ^* of their carriers at the tip is lower than theirK _m ^* towards the base of the villus. It is proposed that there are multiple or heterogeneous intestinal carriers for glucose, galactose and 3-O-methyl glucose in the jejunum of the rabbit.Abbreviations Used in this Paper C ₁ Concentration of the probe molecule in the bulk phase - C ₂ Concentration of the probe molecule at the aqueous-membrane interface - d Effective thickness of the intestinal unstirred water layer - D Free diffusion coefficient of the probe molecule     

Alcoholysis catalyzed by Candida antarctica lipase B in a gas/solid system: effects of water on kinetic parameters

The influence of water on the kinetics of alcoholysis of methyl propionate and n-propanol catalyzed by immobilized lipase B from Candida antarctica was studied in a continuous solid/gas reactor. In this reactor, the solid phase is composed of a packed enzymatic sample which is percolated by gaseous nitrogen, simultaneously carrying gaseous substrates to the enzyme while removing reaction products. In this system, interactions between the enzyme and nonreacting molecules are avoided, since no solvent is present, and it is thus more easy to assess the role of water. To this end, alcohol inhibition constant, substrates dissociation constants as well as acylation rate constant and ratio of acylation to deacylation rate constants have been determined as a function of water activity (a(w)). Data obtained highlight that n-propanol inhibition constant and dissociation constant of methyl propionate are a lot affected by a(w) variations whereas water has no significant effect on the catalytic acylation step nor on the ratio of acylation to deacylation rate constants. These results suggest the water-independent character of the transition step.     

Regulation of ion and water transport across the eel intestine: effects of acetylcholine and serotonin

Summary Both acetylcholine (ACh) and serotonin (5-HT) lowered the serosa-negative transepithelial potential difference (PD) and the short-circuit current (I_sc), accompanied by a decrease in NaCl and water absorption across the eel intestine. These inhibitory effects of ACh and 5-HT were blocked by atropine, a muscarinic receptor antagonist, and ICS-205930, a 5-HT₃ receptor antagonist, respectively. Even after blocking the ACh receptor with atropine, 5-HT inhibited the PD and I_sc, and ACh lowered them after blocking the 5-HT receptor with ICS-205930, indicating that ACh and 5-HT act independently. Similar inhibition in the PD and the I_sc was observed after electrical field stimulation (EFS) which is expected to release endogenous regulators. These effects of EFS were reduced by 70% after simultaneous addition of atropine and ICS-205930. Since atropine and ICS-205930 block ACh and 5-HT receptors, respectively, these results suggest that endogenous ACh and 5-HT are released by EFS.Abbreviations ACh acetylcholine - EFS electrical field stimulation - 5-HT serotonin - I _sc short-circuit current - PD transepithelial potential difference - R _t tissue resistance - TTX tetrodotoxin