Kinetic model for membrane transport. 1. Effects of membrane volume and partitioning kinetics

Equations for the transport of solutes through a membrane are derived, taking into account both the membrane volume and the partitioning kinetics, and have been found to involve two rate constants for solute transport, namely, those corresponding to solute transport from the solution to the membrane (k1) and from the membrane to the solution (k2). The time course followed before partitioning equilibrium has been attained, which is usually ignored, is shown to depend strongly on the relative magnitudes of k1 and k2.     

Membrane transport equations with a time delay. A model for overshoot and oscillatory permeation

Membrane transport equations with a time delay are proposed and their analytic solution is derived. This solution is found to exhibit under certain conditions overshoot and oscillatory permeation.     

Kinetic analysis of active membrane transport systems: equations for net velocity and isotope exchange.

Equations for the initial net velocity and for isotope exchange velocities in active membrane transport systems are presented. The equations are expressed entirely in terms of kinetic constants which are experimentally determinable from appropriate reciprocal plots, and replots of slope and intercept (for net velocity) or 1/Δslope and 1/Δintercept (for isotope exchange). The equations and plots are equally applicable to a soluble iso uni uni enzyme system.The effect of pH on sulfate transport by an ATP-sulfurylase negative mutant of Penicillium notatum was analyzed assuming that ³⁵SO₄²⁻ and H⁺ are cosubstrates of the transport system. The kinetics are consistent with an ordered addition to the carrier of one H⁺ ion followed by ³⁵SO₄²⁻, with H⁺ in equilibrium with the carrier and the carrier-H⁺ complex.     

Glucose transport in lysosomal membrane vesicles. Kinetic demonstration of a carrier for neutral hexoses

Lysosomal membrane vesicles isolated from rat liver were exploited to analyze the mechanism of glucose transport across the lysosomal membrane. Uptake kinetics of [14C]D-glucose showed a concentration-dependent saturable process, typical of carrier-mediated facilitated transport, with a Kt of about 75 mM. Uptake was unaffected by Na+ and K+ ions, membrane potentials, and proton gradients but showed an acidic pH optimum. Lowering the pH from 7.4 to 5.5 had no effect on the affinity of the carrier for the substrate but increased the maximum rate of transport about 3-fold. As inferred from the linearity of Scatchard plots, a single transport mechanism could account for the uptake of glucose under all conditions tested. As indicated by the transstimulation properties of the carrier, other neutral monohexoses, including D-galactose, D-mannose, D- and L-fucose were transported by this carrier. The transport rates and affinities of these sugars, measured by the use of their radiolabeled counterparts, were in the same range as those for D-glucose. Pentoses, sialic acid, and other acidic monosaccharides including their lactones, aminosugars, N-acetyl-hexosamines, and most L-stereoisomers, particularly those not present in mammalian tissues, were not transported by this carrier. Glucose uptake and transstimulation were inhibited by cytochalasin B and phloretin. The biochemical properties of this transporter differentiate it from other well-characterized lysosomal sugar carriers, including those for sialic acid and N-acetylhexosamines. The acidic pH optimum of this glucose transporter is a unique feature not shared with any other known glucose carrier and is consistent with its lysosomal origin.     

Equations for membrane transport. Experimental and theoretical tests of the frictional model.

Frictional models for membrane transport are tested experimentally and theoretically for the simple case of a solution consisting of a mixture of two perfect gases and a membrane consisting of a porous graphite septum. Serious disagreement is found, which is traced to a missing viscous term. Kinetic theory is then used as a guide in formulating a corrected set of transport equations, and in giving a physical interpretation to the frictional coefficients. Sieving effects are found to be attributable to entrance effects rather than to true frictional effects within the body of the membrane. The results are shown to be compatible with nonequilibrium thermodynamics. Some correlations and predictions are made of the behavior of various transport coefficients for general solutions.     

A physical model for the simultaneous membrane transport and metabolism of drugs.

A simple model for the simultaneous passive membrane transport and bioconversion of a drug, which may be a weak electrolyte or a neutral molecule, is mathematically described. It includes an aqueous diffusion layer and an operational aqueous pore pathway. The applicability of the model is shown for the in situ rat intestinal transport of prostaglandin F_2a.     

Energy-barrier models for membrane transport.

Energy-barrier models are analyzed to find hidden assumptions and establish ranges of validity. The analysis proceeds by comparison with integrated results for model continuum membranes. The main conclusions are that a simple energy-barrier model has a wide range of validity, is remarkably accurate even when its conditions of validity are not strictly met, and is almost always superior to the analogous equations of irreversible thermodynamics. Its major limitations are a possible nonphysical divergence at high electric fields or volume flows caused by breakdown of the transition-state approximation, and the inability to treat multicomponent mixtures except in a pseudobinary (Nernst-Planck) approximation.     

A model for membrane transport through alpha-helical protein pores

In this communication we explore possible mechanisms by which hydrogen-bonded, knobs-into-holes packed side chains from adjoining α-helical segments could function in proton transport through membranes and mechanisms by which proton transport could be coupled to active transport of other substances.     

Kinetic transport model for cellular regulation of pH and solute concentration in the renal proximal tubule.

An open circuit kinetic model was developed to calculate the time course of proximal tubule cell pH, solute concentrations, and volume in response to induced perturbations in luminal or peritubular fluid composition. Solute fluxes were calculated from electrokinetic equations containing terms for known carrier saturabilities, allosteric dependences, and ion coupling ratios. Apical and basolateral membrane potentials were determined iteratively from the requirements of cell electroneutrality and equal opposing transcellular and paracellular currents. The model converged to membrane potentials accurate to 0.05% in one to four iterations. Model variables included cell concentrations of Na, K, HCO3, glucose, pH (uniform CO2), volume, and apical and basolateral membrane potentials. The basic model contained passive apical membrane transport of Na/H, Na/glucose, H and K, basolateral transport of Na/3HCO3, K, H, and glucose, and paracellular transport of Na, K, Cl, and HCO3; apical H and basolateral 3Na/2K-ATPases were present. Apical Na/H and basolateral K transport were regulated allosterically by pH. Apical Na/H transport, basolateral Na/3HCO3 transport, and the 3Na/2K-ATPase were saturable. Model parameters were chosen from data in the rat proximal tubule. Model predictions for the magnitude and time course of cell pH, Na, and membrane potential in response to rapid changes in apical and peritubular Na and HCO3 were in excellent agreement with experiment. In addition, the model requires that there exist an apical H-ATPase, basolateral Na/3HCO3 transport saturable with HCO3, and electroneutral basolateral K transport.     

Kinetic model for nitrogen-limited wine fermentations.

A physical and mathematical model for wine fermentation kinetics has been developed to predict sugar utilization curves based on experimental data from wine fermentations with various initial nitrogen and sugar concentrations in the juice. The model is based on: (1) yeast cell growth limited by nitrogen; (2) sugar utilization rates and ethanol production rates proportional solely to the number of viable cells; and (3) a death rate for cells proportional to alcohol content. All but one parameter in the model can be estimated from existing data. However, experiments to find this final parameter, a constant describing cell death, indicate that cell death may not be the critical factor in determining fermentation kinetics as cell viability remains significant until sugar utilization has ceased. The model, nevertheless, predicts a transition from normal to sluggish to stuck fermentations as initial nitrogen levels decrease. It also predicts that fermentations with high initial Brix levels may go to completion when supplemented with nitrogen in the form of ammonia. Therefore, we hypothesize that the model is valid but that ethanol causes the yeast cells to become inactive while remaining viable. Experimental verification of the model has been performed using flask-scale experiments. The model has also been used to evaluate the possibility of using nitrogen or viable cell additions to avoid or correct problem (i.e., sluggish or stuck) fermentations.     

Plant membrane transport.

Recent developments in plant membrane transport, particularly concerning the vacuolar and plasma membranes, have increased our understanding of molecular aspects of primary pumps, carrier systems and ion channels.     

Kinetic properties of membrane dopamine-beta-hydroxylase.

We studied membrane bound dopamine-beta-hydroxylase (DBH) from chromaffin granules, in order to determine whether a biological form of immobilization of the enzyme altered its kinetic properties. The results obtained suggested that DBH either in soluble or solubilized form showed a ping-pong mechanism whereas the membrane bound DBH did not. Affinity for the substrate and the pH stability were lower in soluble or solubilized form than in membrane bound DBH.     

Ca2+ transport across the platelet plasma membrane. A role for membrane glycoproteins IIB and IIIA

Human platelets maintain a low cytosolic free Ca2+ concentration in part by controlling plasma membrane Ca2+ transport. The present studies examine the role in this process of two well-characterized membrane proteins: glycoproteins IIb and IIIa. These glycoproteins form a Ca2+-dependent complex which serves as both the platelet fibrinogen receptor and the principle site for high affinity Ca2+ binding on the platelet surface. The kinetics of plasma membrane Ca2+ exchange were compared in normal platelets and in thrombasthenic platelets, which lack the IIb X IIIa complex. Under steady-state conditions, the maximum rate of plasma membrane Ca2+ exchange in the thrombasthenic platelets was half the rate observed in normal platelets. The size of the cytosolic exchangeable Ca2+ pool and the cytosolic free Ca2+ concentration, however, were normal. A quantitatively similar decrease in plasma membrane Ca2+ exchange was seen in normal platelets after incubation with ethylene glycol bis(beta-aminoethyl ether)-N,N,N',N'-tetraacetic acid (EGTA) at 37 degrees C, conditions that dissociate the IIb X IIIa complex. This decrease in the Ca2+ exchange rate in normal platelets could be prevented by preincubating platelets with a complex-specific anti-IIb X IIIa monoclonal antibody, but not by preincubating platelets with an anti-IIIa monoclonal antibody. In order to determine whether loss of the IIb X IIIa complex primarily affects Ca2+ influx or Ca2+ efflux, both processes were also examined under nonsteady-state conditions. An immediate decrease in the 45Ca2+ influx rate was seen when Ca2+ was added back to platelets preincubated with EGTA at 37 degrees C. The 45Ca2+ efflux rate, on the other hand, was not immediately affected. These data suggest, therefore, that an intact IIb X IIIa complex is necessary for normal Ca2+ homeostasis in platelets.     

Anion transport and membrane morphology.

Freeze-fracture electronmicroscopy has been used to examine the membrane ultrastructure of human red blood cells in the presence of inhibitors of chloride exchange. The extent of inhibition was correlated with a decrease of intramembrane particle density on the B-fracture face. Dimethylsulfoxide (DMSO) and glycerol, which markedly and reversibly reduced the intramembrane particle density, were shown to drastically and reversibly inhibit chloride self-exchange. DMSO was shown to be a noncompetitive inhibitor of chloride flux.     

Kinetic analysis of L-glutamine transport into porcine jejunal enterocyte brush-border membrane vesicles

L-Glutamine transport into porcine jejunal enterocyte brush border membrane vesicles was studied. Uptake was mediated by a Na(+)-dependent and a Na(+)-independent pathway as well as by diffusion. The initial rates of glutamine uptake over a range of concentrations is both Na(+)-gradient and Na(+)-free conditions were analyzed and kinetic parameters were obtained. Na(+)-dependent glutamine transport had a K(m) of 0.77 +/- 0.16 mM and a Jmax of 70.7 +/- 5.8 pmol mg protein-1 s-1; Na(+)-independent glutamine transport had a K(m) of 3.55 +/- 0.78 mM and a Jmax of 55.1 +/- 6.6 pmol mg protein-1 s-1. The non-saturable component measured with HgCl2-poisoned brush border membrane vesicles in the Na(+)-free condition contained passive diffusion and non-specific membrane binding and was defined to be apparent glutamine diffusion and the glutamine permeability coefficient (Kdiff) was estimated to be Kdiff = 3.78 +/- 0.06 pmol 1 mg protein-1 mmol-1 s-1. Results of inhibition experiments showed that Na(+)-dependent glutamine uptake occurred primarily through the brush border system-B degree transporters, whereas Na(+)-independent glutamine uptake occurred via the system-L transporters. Furthermore, the kinetics of L-leucine and L-cysteine inhibition of L-glutamine uptake demonstrated that neutral amino acids sharing the same brush border transporters can effectively inhibit each other in their transport.     

Time lag in a model of a biochemical reaction sequence with end product inhibition

The model studied is that of Goodwin, in which all but one of the reactions obey linear kinetics, while the end-product inhibits the first reaction in a term of Michaelis-Menten form, with Hill coefficient ?:

$\text{z=}\text{∫}\text{?∞}\text{t}\text{x}{}_{\mathrm{n}}\text{(T)G(t?T)dt}$

The results obtained relate to time lag in the off diagonal terms in these equations. The time lag is taken in distributed form, for example replacing x_n in the first equation by

$\text{dx}{}_{\mathrm{t}}\text{dt}\text{=k}{}_1\text{x}{}_{\mathrm{t??}}\text{1?b}{}_1\text{x}{}_{\mathrm{t}}\text{, i=2, …n.}$

For any non-negative G, time lag in these terms can not destabilize the equilibrium point in the case ? = 1. For a particular class of functions G one can obtain some insight into the consequences of time lag by relating the model to that with a longer loop of reactions. Then known results can be used for general ? and n.