The determination of membrane transport parameters with the cell pressure probe: theory suggests that unstirred layers have significant impact

A simulation model was written to compute the time-kinetics of turgor pressure, P, change in Chara corallina during cell pressure probe experiments. The model allowed for the contribution of a membrane plus zero, one, or two unstirred layers of any desired thickness. The hypothesis that a cell with an unstirred layer is a composite membrane that will follow the same kind of kinetics with or without unstirred layers was tested. Typical ‘osmotic pulse’ experiments yield biphasic curves with minimum or maximum pressures, P_min(max), at time t_min(max) and a solute exponential decay with halftime . These observed data were then used to compute composite membrane properties, namely the parameters L_p = the hydraulic conductance, σ = reflection coefficient and P_s = solute permeability using theoretical equations. Using the simulation model, it was possible to fit an experimental data set to the same values of P_min(max), t_min(max) and incorporating different, likely values of unstirred layer thickness, where each thickness requires a unique set of plasmalemma membrane values of L_p, σ and P_s. We conclude that it is not possible to compute plasmalemma membrane properties from cell pressure probe experiments without independent knowledge of the unstirred layer thickness.     

Recycling ofd-glucose in collagenous cuticle: A means of nutrient conservation?

Summary Transport by an epithelium, possessing an accumulating, saturable transport system in the apical membrane as well as a finite Fick permeability to the transported solute, was considered in the steady state in the case of zerocis concentration, and in the presence of a peripheral diffusion resistance in a layer apposing thecis face of the tissue (unstirred solution or structural coating). Under suitable conditions, the combination of peripheral diffusion resistance and accumulating epithelial transport may lead to recycling of solute at thecis face of the epithelium. This causes a decrease of the effective permeability to diffusionaltrans-cis flow across the tissue. The phenomenon is discussed in terms of epidermald-glucose transport by the integument of aquatic animals with a collagenous cuticle, such as the seawater-acclimated polychaete wormNereis diversicolor. The recycling phenomenon may be of significance to other epithelia with the function of maintaining large concentration gradients of permeating substances.List of Symbols and Fixed Parameter Values C _m Bulk medium solute concentration,cis face of epidermisC _m=0 mol cm^–3 - C _i Concentration of solute at interface between cuticle and unstirred medium (mol cm^–3) - C _s Concentration of solute atcis face of apical epidermal membrane (mol cm^–3) - C _e Concentration of solute in extracellular fluid,trans-side of epidermisC _e=1.0×10^–6 mol cm^–3 - D _m Diffusion coefficient of solute in outside mediumD _m=6.7×10^–6 cm² sec^–1 - D _c Diffusion coefficient of solute in cuticleD _c=7.4×10^–9 cm² sec^–1 - _m Operative thickness of unstirred medium layer - _c Thickness of cuticle - J Steady-state net flux of solute through cuticle or unstirred layer (flux is positive indirectioncis-trans) (mol cm^–2 sec^–1) - J _i ^max Maximal influx through saturable transport system in apical membraneJ _i ^max =2.0×10^–12 mol cm^–2 sec^–1 - K _t Transport constant, saturable systemK _t=1.0×10^–7 mol cm^–3 - P Epithelial permeability (cm sec^–1)     

Osmosis in Cortical Collecting Tubules : A Theoretical and Experimental Analysis of the Osmotic Transient Phenomenon

This paper reports a theoretical analysis of osmotic transients and an experimental evaluation both of rapid time resolution of lumen to bath osmosis and of bidirectional steady-state osmosis in isolated rabbit cortical collecting tubules exposed to antidiuretic hormone (ADH). For the case of a membrane in series with unstirred layers, there may be considerable differences between initial and steady-state osmotic flows (i.e., the osmotic transient phenomenon), because the solute concentrations at the interfaces between membrane and unstirred layers may vary with time. A numerical solution of the equation of continuity provided a means for computing these time-dependent values, and, accordingly, the variation of osmotic flow with time for a given set of parameters including: P_f (cm s^–1), the osmotic water permeability coefficient, the bulk phase solute concentrations, the unstirred layer thickness on either side of the membrane, and the fractional areas available for volume flow in the unstirred layers. The analyses provide a quantitative frame of reference for evaluating osmotic transients observed in epithelia in series with asymmetrical unstirred layers and indicate that, for such epithelia, P_f determinations from steady-state osmotic flows may result in gross underestimates of osmotic water permeability. In earlier studies, we suggested that the discrepancy between the ADH-dependent values of P_f and P_DDw (cm s^–1, diffusional water permeability coefficient) was the consequence of cellular constraints to diffusion. In the present experiments, no transients were detectable 20–30 s after initiating ADH-dependent lumen to bath osmosis; and steady-state ADH-dependent osmotic flows from bath to lumen and lumen to bath were linear and symmetrical. An evaluation of these data in terms of the analytical model indicates: First, cellular constraints to diffusion in cortical collecting tubules could be rationalized in terms of a 25-fold reduction in the area of the cell layer available for water transport, possibly due in part to transcellular shunting of osmotic flow; and second, such cellular constraints resulted in relatively small, approximately 15%, underestimates of P_f.     

Hypotonically induced changes in the plasma membrane of cultured mammalian cells

Summary Cells from three cell lines were electrorotated in media of osmotic strengths from 330 mOsm to 60 mOsm. From the field-frequency dependence of the rotation speed, the passive electrical properties of the surfaces were deduced. In all cases, the area-specific membrane capacitance (C _m) decreased with osmolality. At 280 mOsm (iso-osmotic), SP2 (mouse myeloma) and G8 (hybridoma) cells had C _mvalues of 1.01 ± 0.04 F/cm² and 1.09 ± 0.03 F/cm², respectively, whereas dispase-treated L-cells (sarcoma fibroblasts) exhibited C _m=2.18±0.10/F/cm². As the osmolality was reduced, the C _mreached a well-defined minimum at 150 mOsm (SP2) or 180 mOsm (G8). Further reduction in osmolality gave a 7% increase in C _m, after which a plateau close to 0.80F/cm2²was reached. However, the whole-cell capacities increased about twofold from 200 mOsm to 60 mOsm. L-cells showed very little change in C _mbetween 280 mOsm and 150 mOsm, but below 150 mOsm the C _mdecreased rapidly. The changes in C _mcorrelate well with the swelling of the cells assessed by means of van't Hoff plots. The apparent membrane conductance (including the effect of surface conductance) decreased with C _m, but then increased again instead of exhibiting a plateau. The rotation speed of the cells increased as the osmolality was lowered, and eventually attained almost the theoretical value. All measurements indicate that hypo-osmotically stressed cells obtain the necessary membrane area by using material from microvilli. However, below about 200 mOsm the whole-cell capacities indicate the progressive incorporation of extra membrane into the cell surface.We thank Mr. B.G. Klarmann for his help with the measurements. This work was supported by grants of the DFG (SFB 176 B5 to U.Z. and W.M.A.) and of the BMFT (DARA 50 WB 9212 to U.Z.). We also thank the Umweltbundesamt, Berlin, for support enabling the construction of some of the rotation generators used in this work.     

The equivalent circuit of single crab muscle fibers as determined by impedance measurements with intracellular electrodes

The input impedance of muscle fibers of the crab was determined with microelectrodes over the frequency range 1 cps to 10 kc/sec. Care was taken to analyze, reduce, and correct for capacitive artifact. One dimensional cable theory was used to determine the properties of the equivalent circuit of the membrane admittance, and the errors introduced by the neglect of the three dimensional spread of current are discussed. In seven fibers the equivalent circuit of an element of the membrane admittance must contain a DC path and two capacitances, each in series with a resistance. In two fibers, the element of membrane admittance could be described by one capacitance in parallel with a resistance. In several fibers there was evidence for a third very large capacitance. The values of the elements of the equivalent circuit depend on which of several equivalent circuits is chosen. The circuit (with a minimum number of elements) that was considered most reasonably consistent with the anatomy of the fiber has two branches in parallel: one branch having a resistance R_e in series with a capacitance C_e; the other branch having a resistance R_b in series with a parallel combination of a resistance R_m and a capacitance C_m. The average circuit values (seven fibers) for this model, treating the fiber as a cylinder of sarcolemma without infoldings or tubular invaginations, are R_e = 21 ohm cm²; C_e = 47 µf/cm²; R_b = 10.2 ohm cm²; R_m = 173 ohm cm²; C_m = 9.0 µf/cm². The relation of this equivalent circuit and another with a nonminimum number of circuit elements to the fine structure of crab muscle is discussed. In the above equivalent circuit R_m and C_m are attributed to the sarcolemma; R_e and C_e, to the sarcotubular system; and R_b, to the amorphous material found around crab fibers. Estimates of actual surface area of the sarcolemma and sarcotubular system permit the average circuit values to be expressed in terms of unit membrane area. The values so expressed are consistent with the dielectric properties of predominantly lipid membranes.     

An analysis of unstirred layers in series with "tight" and "porous" lipid bilayer membranes

The present experiments were designed to evaluate the effective thickness of the unstirred layers in series with native and porous (i.e., in the presence of amphotericin B) lipid bilayer membranes and, concomitantly, the respective contributions of membranes and unstirred layers to the observed resistances to the diffusion of water and nonelectrolytes between aqueous phases. The method depended on measuring the tracer permeability coefficients for the diffusion of water and nonelectrolytes (P_DDi, cm sec^-1) when the aqueous phase viscosity (η) was increased with solutes having a unity reflection coefficient, such as sucrose or dextran. The effective thickness of the unstirred layers (α^t, cm) and the true, or membrane, permeability coefficients for diffusion of water and nonelectrolytes (P_mmi, cm sec^-1) were computed from, respectively, the slope and intercept of the linear regression of 1/P_DDi on η. In both the native and porous membranes, α^t was approximately 110 x 10^-4 cm. The ratio of P_f, the osmotic water permeability coefficient (cm sec^-1) to P_mmH2O was 1.22 in the native membranes and 3.75 in the porous membranes. For the latter, the effective pore radius, computed from Poiseuille's law, was approximately 5.6 A. A comparison of P_mmi and P_DDi, indicated that the porous membranes accounted for 16, 25, and 66% of the total resistance to the diffusion of, respectively, H₂O, urea, and glycerol, while the remainder was referable to the unstirred layers.     

Challenge from the simple: some caveats in linearization of the Boyle-van't Hoff and Arrhenius plots

Some aspects of proper linearization of the Boyle-van’t Hoff (BVH) relationship for calculation of the osmotically inactive volume v_b, and Arrhenius plot (AP) for the activation energy E_a are discussed. It is shown that the commonly used determination of the slope and the intercept (v_b), which are presumed to be independent from each other, is invalid if the initial intracellular molality m₀ is known. Instead, the linear regression with only one independent parameter (v_b) or the Least Square Method (LSM) with v_b as the only fitting LSM parameter must be applied. The slope can then be calculated from the BVH relationship as the function of v_b. In case of unknown m₀ (for example, if cells are preloaded with trehalose, or electroporation caused ion leakage, etc.), it is considered as the second independent statistical parameter to be found. In this (and only) scenario, all three methods give the same results for v_b and m₀. AP can be linearized only for water hydraulic conductivity (L_p) and solute mobility (ω_s) while water and solute permeabilities P_w ≡ L_pRT and P_s ≡ ω_sRT cannot be linearized because they have pre-exponential factor (RT) that depends on the temperature T.     

Effect of Cavβ Subunits on Structural Organization of Cav1.2 Calcium Channels

Background

Voltage-gated Ca_v1.2 calcium channels play a crucial role in Ca²⁺ signaling. The pore-forming α_1C subunit is regulated by accessory Ca_vβ subunits, cytoplasmic proteins of various size encoded by four different genes (Ca_vβ₁ - β₄) and expressed in a tissue-specific manner.

Methods and Results

Here we investigated the effect of three major Ca_vβ types, β_1b, β_2d and β₃, on the structure of Ca_v1.2 in the plasma membrane of live cells. Total internal reflection fluorescence microscopy showed that the tendency of Ca_v1.2 to form clusters depends on the type of the Ca_vβ subunit present. The highest density of Ca_v1.2 clusters in the plasma membrane and the smallest cluster size were observed with neuronal/cardiac β_1b present. Ca_v1.2 channels containing β₃, the predominant Ca_vβ subunit of vascular smooth muscle cells, were organized in a significantly smaller number of larger clusters. The inter- and intramolecular distances between α_1C and Ca_vβ in the plasma membrane of live cells were measured by three-color FRET microscopy. The results confirm that the proximity of Ca_v1.2 channels in the plasma membrane depends on the Ca_vβ type. The presence of different Ca_vβ subunits does not result in significant differences in the intramolecular distance between the termini of α_1C, but significantly affects the distance between the termini of neighbor α_1C subunits, which varies from 67 Å with β_1b to 79 Å with β₃.

Conclusions

Thus, our results show that the structural organization of Ca_v1.2 channels in the plasma membrane depends on the type of Ca_vβ subunits present.     

Water permeability of thin lipid membranes

The osmotic permeability coefficient, P_f, and the tagged water permeability coefficient, P_d, were determined for thin (<100 A) lipid membranes formed from ox brain lipids plus DL-α-tocopherol; their value of approximately 1 x 10^-3 cm/sec is within the range reported for plasma membranes. It was established that P_f = P_d. Other reports that P_f > P_d can be attributed to the presence of unstirred layers in the experimental determination of P_d. Thus, there is no evidence for the existence of aqueous pores in these thin phospholipid membranes. The adsorption onto the membrane of a protein that lowers its electrical resistance by a factor of 10³ was found not to affect its water permeability; however, glucose and sucrose were found to interact with the membrane to modify P_f. Possible mechanisms of water transport across these films are discussed, together with the implications of data obtained on these structures for plasma membranes.     

Exploring sequence requirements for C₃/C₄ carboxylate recognition in the Pseudomonas aeruginosa cephalosporinase: Insights into plasticity of the AmpC β-lactamase

In Pseudomonas aeruginosa, the chromosomally encoded class C cephalosporinase (AmpC β-lactamase) is often responsible for high-level resistance to β-lactam antibiotics. Despite years of study of these important β-lactamases, knowledge regarding how amino acid sequence dictates function of the AmpC Pseudomonas-derived cephalosporinase (PDC) remains scarce. Insights into structure-function relationships are crucial to the design of both β-lactams and high-affinity inhibitors. In order to understand how PDC recognizes the C₃/C₄ carboxylate of β-lactams, we first examined a molecular model of a P. aeruginosa AmpC β-lactamase, PDC-3, in complex with a boronate inhibitor that possesses a side chain that mimics the thiazolidine/dihydrothiazine ring and the C₃/C₄ carboxylate characteristic of β-lactam substrates. We next tested the hypothesis generated by our model, i.e. that more than one amino acid residue is involved in recognition of the C₃/C₄ β-lactam carboxylate, and engineered alanine variants at three putative carboxylate binding amino acids. Antimicrobial susceptibility testing showed that the PDC-3 β-lactamase maintains a high level of activity despite the substitution of C₃/C₄ β-lactam carboxylate recognition residues. Enzyme kinetics were determined for a panel of nine penicillin and cephalosporin analog boronates synthesized as active site probes of the PDC-3 enzyme and the Arg349Ala variant. Our examination of the PDC-3 active site revealed that more than one residue could serve to interact with the C₃/C₄ carboxylate of the β-lactam. This functional versatility has implications for novel drug design, protein evolution, and resistance profile of this enzyme.     

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     

The influence of external potassium on the inactivation of sodium currents in the giant axon of the squid, Loligo pealei

Isolated giant axons were voltage-clamped in seawater solutions having constant sodium concentrations of 230 mM and variable potassium concentrations of from zero to 210 mM. The inactivation of the initial transient membrane current normally carried by Na⁺ was studied by measuring the Hodgkin-Huxley h parameter as a function of time. It was found that h reaches a steady-state value within 30 msec in all solutions. The values of h _∞, τ_h, α_h,and β_h as functions of membrane potential were determined for various [K _o]. The steady-state values of the h parameter were found to be inversely related, while the time constant, τ_h, was directly related to external K⁺ concentration. While the absolute magnitude as well as the slopes of the h _∞ vs. membrane potential curves were altered by varying external K⁺, only the magnitude and not the shape of the corresponding τ_h curves was altered. Values of the two rate constants, α_h and β_h, were calculated from h_∞ and τ_h values. α_h is inversely related to [K_o] while β_h is directly related to [K_o] for hyperpolarizing membrane potentials and is independent of [K_o] for depolarizing membrane potentials. Hodgkin-Huxley equations relating α_h and β_h to E_m were rewritten so as to account for the observed effects of [K_o]. It is concluded that external potassium ions have an inactivating effect on the initial transient membrane conductance which cannot be explained solely on the basis of potassium membrane depolarization.     

Temperature sensitivity of the low-moisture-content limit to negative seed longevity--moisture content relationships in hermetic storage

• Background and Aims The negative logarithmic relationship between orthodox seed longevity and moisture content in hermetic storage is subject to a low-moisture-content limit (m_c), but is m_c affected by temperature?• Methods Red clover (Trifolium pratense) and alfalfa (Medicago sativa) seeds were stored hermetically at 12 moisture contents (2–15 %) and five temperatures (–20, 30, 40, 50 and 65 °C) for up to 14·5 years, and loss in viability was estimated.• Key Results Viability did not change during 14·5 years hermetic storage at −20 °C with moisture contents from 2·2 to 14·9 % for red clover, or 2·0 to 12·0 % for alfalfa. Negative logarithmic relationships between longevity and moisture contents >m_c were detected at 30–65 °C, with discontinuities at low moisture contents; m_c varied between 4·0 and 5·4 % (red clover) or 4·2 and 5·5 % (alfalfa), depending upon storage temperature. Within the ranges investigated, a reduction in moisture content below m_c at any one temperature had no effect on longevity. Estimates of m_c were greater the cooler the temperature, the relationship (P < 0·01) being curvilinear. Above m_c, the estimates of C_H and C_Q (i.e. the temperature term of the seed viability equation) did not differ (P > 0·10) between species, whereas those of K_E and C_W did (P < 0·001).• Conclusions The low-moisture-content limit to negative logarithmic relationships between seed longevity and moisture content in hermetic storage increased the cooler the storage temperature, by approx. 1·5 % over 35 °C (4·0–4·2 % at 65 °C to 5·4–5·5 % at 30–40 °C) in these species. Further reduction in moisture content was not damaging. The variation in m_c implies greater sensitivity of longevity to temperature above, compared with below, m_c. This was confirmed (P < 0·005).     

Study of the Solute Flows of Multicomponent and Heterogeneous Non-Ionic Solutions in Double-Membrane System

The solute flows were studied in a double-membrane osmotic-diffusive cell, in which two membranes mounted in horizontal planes separate three compartments (l,m,r) containing the non-homogeneous, non-electrolytic binary and ternary solutions. The volume of inter-membrane compartment (m), which is the infinitesimally layer of solution, and volume of external compartments (l and r) fulfill the conditions V _m 0 and V _l =V _r , respectively. In an initial moment, the solution concentrations satisfy the condition (C ^o _s ) _l < (C ^o _s ) _m >(C ^o _s ) _r. The double-membrane osmotic-diffusive cell is composed of two complexes: boundary layer/membrane/boundary layer, mounted in horizontal planes. In the cell, solute flux was measured as a function of concentration and gravitational configuration. The linear dependencies of the solute flux on concentration difference in binary solutions and nonlinear – in ternary solutions were obtained. It was shown that the double-membrane osmotic-diffusive cell has rectifying and amplifying properties of solute flows.     

Osmotic water permeability of plasma and vacuolar membranes in protoplasts I. High osmotic water permeability in radish ( Raphanus sativus ) root cells as measured by a new method

Intra- and transcellular water movements in plants are regulated by the water permeability of the plasma membrane (PM) and vacuolar membrane (VM) in plant cells. In the present study, we investigated the osmotic water permeability of both PM (P _f1) and VM (P _f2), as well as the bulk osmotic water permeability of a protoplast (P _f(bulk)) isolated from radish (Raphanus sativus) roots. The values of P _f(bulk) and P _f2 were determined from the swelling/shrinking rate of protoplasts and isolated vacuoles under hypo- or hypertonic conditions. In order to minimize the effect of unstirred layer, we monitored dropping or rising protoplasts (vacuoles) in sorbitol solutions as they swelled or shrunk. P _f1 was calculated from P _f(bulk) and P _f2 by using the ‘three-compartment model’, which describes the theoretical relationship between P _f1, P _f2 and P _f(bulk) (Kuwagata and Murai-Hatano in J Plant Res, 2007). The time-dependent changes in the volume of protoplasts and isolated vacuoles fitted well to the theoretical curves, and solute permeation of PM and VM was able to be neglected for measuring the osmotic water permeability. High osmotic water permeability of more than 500 μm s⁻¹, indicating high activity of aquaporins (water channels), was observed in both PM and VM in radish root cells. This method has the advantage that P _f1 and P _f2 can be measured accurately in individual higher plant cells. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users. It includes four appendices, four tables and two figures. Mari Murai-Hatano and Tsuneo Kuwagata contributed equally to the paper. An erratum to this article is available at .     

Inorganic mercury (Hg2+) transport through lipid bilayer membranes

Summary Diffusion of inorganic mercury (Hg²⁺) through planar lipid bilayer membranes was studied as a function of chloride concentration and pH. Membranes were made from egg lecithin plus cholesterol in tetradecane. Tracer (²⁰³Hg) flux and conductance measurements were used to estimate the permeabilities to ionic and nonionic forms of Hg. At pH 7.0 and [Cl^–] ranging from 10–1000mm, only the dichloride complex of mercury (HgCl₂) crosses the membrane at a significant rate. However, several other Hg complexes (HgOHCl, HgCl ₃ ^– and HgCl ₄ ^2– ) contribute to diffusion through the aqueous unstirred layer adjacent to the membrane. The relation between the total mercury flux (J _Hg), Hg concentrations, and permeabilities is: 1/J _Hg=1/P ^ul[Hg ^t ]+1/P ^m [HgCl₂], where [Hg ^t ] is the total concentration of all forms of Hg,P ^ul is the unstirred layer permeability, andP ^m is the membrane permeability to HgCl₂. By fitting this equation to the data we find thatP ^m =1.3×10^–2 cm sec^–1. At Cl^– concentrations ranging from 1–100mm, diffusion of Hg ^t through the unstirred layer is rate limiting. At Cl^– concentrations ranging from 500–1000mm, the membrane permeability to HgCl₂ becomes rate limiting because HgCl₂ comprises only about 1% of the total Hg. Under all conditions, chemical reactions among Hg²⁺, Cl^– and/or OH^– near the membrane surface play an important role in the transport process. Other important metals, e.g., Zn²⁺, Cd²⁺, Ag⁺ and CH₃Hg⁺, form neutral chloride complexes under physiological conditions. Thus, it is likely that chloride can facilitate the diffusion of a variety of metals through lipid bilayer and biological membranes.     

The permeability of thin lipid membranes to bromide and bromine

Thin lipid (optically black) membranes were made from sheep red cell lipids dissolved in n-decane. The flux of Br across these membranes was measured by the use of tracer ⁸²Br. The unidirectional flux of Br (in 50–100 mM NaBr) was 1–3 x 10^-12 mole/cm²sec. This flux is more than 1000 times the flux predicted from the membrane electrical resistance (>10⁸ ohm-cm²) and the transference number for Br^- (0.2–0.3), which was estimated from measurements of the zero current potential difference. The Br flux was not affected by changes in the potential difference imposed across the membrane (±60 mv) or by the ionic strength of the bathing solutions. However, the addition of a reducing agent, sodium thiosulfate (10^-3 M), to the NaBr solution bathing the membrane caused a 90% reduction in the Br flux. The inhibiting effect of S₂O₃ ⁼ suggests that the Br flux is due chiefly to traces of Br₂ in NaBr solutions. As expected, the addition of Br₂ to the NaBr solutions greatly stimulated the Br flux. However, at constant Br₂ concentration, the Br flux was also stimulated by increasing the Br^- concentration, in spite of the fact that the membrane was virtually impermeable to Br^-. Finally, the Br flux appeared to saturate at high Br₂ concentrations, and the saturation value was roughly proportional to the Br^- concentration. These results can be explained by a model which assumes that Br crosses the membrane only as Br₂ but that rapid equilibration of Br between Br₂ and Br^- occurs in the unstirred layers of aqueous solution bathing the two sides of the membrane. A consequence of the model is that Br^- "facilitates" the diffusion of Br across the unstirred layers.     

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     

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.