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

Elimination of substances from the brain parenchyma: efflux via perivascular pathways and via the blood-brain barrier

This review considers efflux of substances from brain parenchyma quantified as values of clearances (CL, stated in µL g-1 min-1). Total clearance of a substance is the sum of clearance values for all available routes including perivascular pathways and the blood-brain barrier. Perivascular efflux contributes to the clearance of all water-soluble substances. Substances leaving via the perivascular routes may enter cerebrospinal fluid (CSF) or lymph. These routes are also involved in entry to the parenchyma from CSF. However, evidence demonstrating net fluid flow inwards along arteries and then outwards along veins (the glymphatic hypothesis) is still lacking. CLperivascular, that via perivascular routes, has been measured by following the fate of exogenously applied labelled tracer amounts of sucrose, inulin or serum albumin, which are not metabolized or eliminated across the blood-brain barrier. With these substances values of total CL ≅ 1 have been measured. Substances that are eliminated at least partly by other routes, i.e. across the blood-brain barrier, have higher total CL values. Substances crossing the blood-brain barrier may do so by passive, non-specific means with CLblood-brain barrier values ranging from < 0.01 for inulin to > 1000 for water and CO2. CLblood-brain barrier values for many small solutes are predictable from their oil/water partition and molecular weight. Transporters specific for glucose, lactate and many polar substrates facilitate efflux across the blood-brain barrier producing CLblood-brain barrier values > 50. The principal route for movement of Na+ and Cl- ions across the blood-brain barrier is probably paracellular through tight junctions between the brain endothelial cells producing CLblood-brain barrier values ~ 1. There are large fluxes of amino acids into and out of the brain across the blood-brain barrier but only small net fluxes have been observed suggesting substantial reuse of essential amino acids and α-ketoacids within the brain. Amyloid-β efflux, which is measurably faster than efflux of inulin, is primarily across the blood-brain barrier. Amyloid-β also leaves the brain parenchyma via perivascular efflux and this may be important as the route by which amyloid-β reaches arterial walls resulting in cerebral amyloid angiopathy.

Metabolic Flux and Compartmentation Analysis in the Brain In vivo

Through significant developments and progresses in the last two decades, in vivo localized nuclear magnetic resonance spectroscopy (MRS) became a method of choice to probe brain metabolic pathways in a non-invasive way. Beside the measurement of the total concentration of more than 20 metabolites, (1)H MRS can be used to quantify the dynamics of substrate transport across the blood-brain barrier by varying the plasma substrate level. On the other hand, (13)C MRS with the infusion of (13)C-enriched substrates enables the characterization of brain oxidative metabolism and neurotransmission by incorporation of (13)C in the different carbon positions of amino acid neurotransmitters. The quantitative determination of the biochemical reactions involved in these processes requires the use of appropriate metabolic models, whose level of details is strongly related to the amount of data accessible with in vivo MRS. In the present work, we present the different steps involved in the elaboration of a mathematical model of a given brain metabolic process and its application to the experimental data in order to extract quantitative brain metabolic rates. We review the recent advances in the localized measurement of brain glucose transport and compartmentalized brain energy metabolism, and how these reveal mechanistic details on glial support to glutamatergic and GABAergic neurons.

Steady-state brain glucose transport kinetics re-evaluated with a four-state conformational model

Glucose supply from blood to brain occurs through facilitative transporter proteins. A near linear relation between brain and plasma glucose has been experimentally determined and described by a reversible model of enzyme kinetics. A conformational four-state exchange model accounting for trans-acceleration and asymmetry of the carrier was included in a recently developed multi-compartmental model of glucose transport. Based on this model, we demonstrate that brain glucose (G(brain)) as function of plasma glucose (G(plasma)) can be described by a single analytical equation namely comprising three kinetic compartments: blood, endothelial cells and brain. Transport was described by four parameters: apparent half saturation constant K(t), apparent maximum rate constant T(max), glucose consumption rate CMR(glc), and the iso-inhibition constant K(ii) that suggests G(brain) as inhibitor of the isomerisation of the unloaded carrier. Previous published data, where G(brain) was quantified as a function of plasma glucose by either biochemical methods or NMR spectroscopy, were used to determine the aforementioned kinetic parameters. Glucose transport was characterized by K(t) ranging from 1.5 to 3.5 mM, T(max)/CMR(glc) from 4.6 to 5.6, and K(ii) from 51 to 149 mM. It was noteworthy that K(t) was on the order of a few mM, as previously determined from the reversible model. The conformational four-state exchange model of glucose transport into the brain includes both efflux and transport inhibition by G(brain), predicting that G(brain) eventually approaches a maximum concentration. However, since K(ii) largely exceeds G(plasma), iso-inhibition is unlikely to be of substantial importance for plasma glucose below 25 mM. As a consequence, the reversible model can account for most experimental observations under euglycaemia and moderate cases of hypo- and hyperglycaemia.

Effects of yeast suspension density on the accumulation ratio of transported solutes

The previously described effect of cell suspension density on metabolic and transport phenomena in yeast, apparently caused by inhibition by dissolved carbon dioxide, is also observed with the accumulation ratio of both sugars and amino acids where not only a kinetic but also a energetic factor comes into play. Unlike all previously measured metabolic and transport parameters, the dependence of the accumulation ratio on suspension density is not monotonic but shows a pronounced maximum in the range of 4-8 mg dry wt/ml, depending on yeast species and on cultivation conditions. In Rhodotorula gracilis and in Lodderomyces elongisporus it is not due to CO2 but is semiquantitatively related to the proton-motive force across the plasma membrane as well as to the intracellular ATP content. It is observed both in oxygen and in argon, over a wide range of pH values and of temperatures, but it is suppressed by metabolic inhibitors. It is expressed only in a range of transported solute concentrations between about 0.1 and 10 mM.

Kinetics of sodium D-glucose cotransport in bovine intestinal brush border vesicles

Brush border membrane vesicles ( BBMV ) purified from steer jejunum were used to study the kinetics of sodium D-glucose cotransport under voltage clamped, zero-trans conditions. When the initial rate of glucose transport ( Jgluc ) was measured over a wide range of glucose concentrations ([S] = 0.01-20 mM), curvature of the Woolf - Augustinsson -Hofstee plots was seen, compatible with a diffusional and one major, high capacity (maximal transport rate Jmax = 5.8-8.8 nmol/mg X min) saturable system. Further studies indicated that changes in cis [Na] altered the Kt, but not the Jmax, suggesting the presence of a rapid-equilibrium, ordered bireactant system with sodium adding first. Trans sodium inhibited Jgluc hyperbolically, KCl-valinomycin diffusion potentials, inner membrane face positive, lowered Jgluc , while potentials of the opposite polarity raise Jgluc . At low glucose concentrations ([S] less than 0.05 mM), a second, minor, high affinity transport system was indicated. Further evidence for this second saturable system was provided by sodium activation curves, which were hyperbolic when [S] = 0.5 mM, but were sigmoidal when [S] = 0.01 mM. Simultaneous fluxes of 22Na and [3H]glucose at 1 mM glucose and 30 mM NaCl yielded a cotransport-dependent flux ratio of 2:1 sodium/glucose, suggestive of 1:1 (Na/glucose) high capacity, low affinity system and a approximately 3:1 (Na/glucose) high affinity, low capacity system. Kinetic experiments with rabbit jejunal brush borders revealed two major Na-dependent saturable systems. Extravesicular (cis) Na changed the Kt, but not the Jmax of the major system.

Generalized kinetic analysis of ion-driven cotransport systems: a unified interpretation of selective ionic effects on Michaelis parameters

A major obstacle to the understanding of gradient-driven transport systems has been their apparently wide kinetic diversity, which has seemed to require a variety of ad hoc mechanisms. Ordinary kinetic analysis, however, has been hampered by one mathematically powerful but physically dubious assumption: that rate limitation occurs in transmembrane transit, so that ligand-binding reactions are at equilibrium. Simple models lacking that assumption turn out to be highly flexible and are able to describe most of the observed kinetic diversity in co- and counter-transport systems. Our "minimal" model of cotransport consists of a single transport loop linking six discrete states of a carrier-type molecule. The state transitions include one transmembrane charge-transport step, and one step each for binding of substrate and cosubstrate (driver ion) at each side of the membrane. The properties of this model are developed by sequential use of realistic experimental simplifications and generalized numerical computations, focussed to create known effects of substrate, driver ion, and membrane potential upon the apparent Michaelis parameters (Jmax, Km) of isotopic substrate influx. Specific behavior of the minimal model depends upon the arrangement of magnitudes of individual reaction constants among the whole set (12) in the loop. Well defined arrangements have been found which permit either increasing membrane potential or increasing external driver-ion selectively to reduce the substrate Km, elevate Jmax, jointly raise both Km and Jmax, or lower Km while raising Jmax. Other arrangements allow rising internal driver ion to act like either a competitive or a noncompetitive inhibitor of entry, or allow internal substrate to shut down ("transinhibit") influx despite large inward driving forces. These findings obviate most postulates of special mechanisms in cotransport: e.g., stoichiometry changes, ion wells, carrier-mediated leakage, and gating - at least as explanations for existing transport kinetic data. They also provide a simple interpretation of certain kinds of homeostatic regulation, and lead to speculation that the observed diversity in cotransport kinetics reflects control-related selection of reaction rate constants, rather than fundamental differences of mechanism.

Proton-sulfate co-transport: mechanism of H+ and sulfate addition to the chloride transporter of human red blood cells

Proton and sulfate inhibition of the obligatory chloride-chloride exchange of human erythrocytes was measured at 0 degrees C to determine their mechanism of reaction with the anion transporter. The proton and sulfate that are co-transported by this mechanism at higher temperatures behaved as nontransported inhibitors at 0 degrees C. We analyzed the data in terms of four molecular mechanisms: (1) HSO4- addition to the transporter; (2) ordered addition with the proton first; (3) ordered addition with the sulfate first; (4) random addition to the transporter. The Dixon plots of 1/MCl vs. [SO4] at different proton concentrations were not parallel. Thus protons and sulfate ions were not mutually exclusive inhibitors. The slope of these Dixon plots was independent of pH above 7.0, which indicates that sulfate could bind to the unprotonated carrier and excludes the first two mechanisms. Protons were inhibitors of chloride flux in the absence of sulfate, which indicates that protons could bind to the unloaded carrier and excludes mechanism 3. The KI for sulfate was 4.35 +/0 0.36 mM. The pK for the protonatable group was 5.03 +/- 0.02. The binding of either a proton or sulfate to the carrier decreased the KI of the other by ninefold. The only simple mechanism consistent with the data is a random-ordered mechanism with more transporters loaded with a sulfate than loaded with a proton at the pH and sulfate concentrations of plasma.

A general kinetic analysis of transport. Tests of the carrier model based on predicted relations among experimental parameters

The analysis of transport kinetics has lacked both a unified treatment in which general rate equations are written entirely in terms of experimental parameters, and a convention by which these parameters may be designated in a concise yet immediately recognizable manner. Such a treatment is presented here in an easily accessible form, and a simple system of nomenclature is proposed resembling that in use in enzyme kinetics. The treatment is independent of assumptions about rate-limiting steps in transport, and applies to both active and facilitated systems, including obligatory exchange. A single substrate is characterized by twelve different parameters, only five of which are required in theory to calculate the others. If a second substrate is present on the trans side of the membrane there are six more parameters. All eighteen parameters are linked by multiple relationships which provide a complete set of rejection criteria for the generalized form of the mobile carrier. Relationships among parameters are also defined that give information on the rate-limiting steps in transport. Equations governing any individual experiment, involving only experimental parameters, are easily written out from the general expressions, for example under conditions of zero trans and infinite trans flux, equilibrium exchange, or competitive inhibition.

Transport kinetics of 6-deoxy-D-glucose in Candida parapsilosis

The strictly aerobic yeast Candida parapsilosis transports the nonmetabolizable monosaccharide 6-deoxy-D-glucose by an active process (inhibition by 2.4-dinitrophenol and other uncouplers but not by iodoacetamide), the accumulation ratio decreasing with increasing substrate concentration. Measured accumulation ratios are in agreement with those predicted from kinetic constants for influx and efflux. Energy for transport is probably required in the translocation step. The maximum rate is temperature-dependent with a transition point at 21 degrees C. the accumulation ratio is not. The uptake is most active at pH 4.5--8.5. It appears not to involve stoichiometric proton symport. The transport system is shared by D-glucose, D-mannose, D-galactose and possibly maltose but not by fructose, sucrose or pentoses. The apparent half-life of the transport system was 3.5--4 h.