An analysis of the adequacy of the asymmetric carrier model for sugar transport

In 1972, Lieb, W. R.; Stein, W. D. (Biochim. Biophys. Acta 265, 187–207) in their review of sugar transport in human erythrocytes concluded that the conventional two-state carrier model was inconsistent with the experimental data available at that time. Since then, other papers have appeared which question the validity of the model. In this paper, we give a brief derivation of the equations describing the two-state carrier model, and analyze the predictions of the model in the classical experiments, i.e. zero-trans, infinite-cis, and equilibrium exchange. We show that the estimate of the half saturatiion constant of 2.8 mM for glucose at the inner face of the human red cell membrane for the infinite-cis procedure reported by Hankin, B. L., Lieb, W. R. and Stein, W. D ((1972) Biochim. Biophys. Acta 288, 114–126) is unreliable. We note that all of the other experimental findings are consistent with the asymmetric carrier model.     

An allosteric pore model for sugar transport in human erythrocytes

Glucose transport in human erythrocytes is characterized by a marked asymmetry in the $\text{V}$ and $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ values for entry and for exit. In addition, they show a high $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ and a high $\text{V}$ for equilibrium exchange but low $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ values for infinite cis and for infinite trans exit and entry. An allosteric pore model has been proposed to account for these characteristics. In this model, substrate-induced conformational changes destabilize the interfaces between protein subunits (the pore gates).Pores doubly occupied from inside destabilize the transport gates and result in high $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ and high $\text{V}$ transport parameters. This effect is less marked when pores are doubly occupied from outside and therefore transport asymmetry results.     

Analysis of protein-mediated 3-O-methylglucose transport in rat erythrocytes: rejection of the alternating conformation carrier model for sugar transport

3-O-Methylglucose (3OMG) transport in rat erythrocytes (RBCs) is mediated by a low-capacity, facilitated diffusion-type process. This study examines whether the characteristics of sugar transport in rat RBCs are consistent with the predictions of two diametric, theoretical mechanisms for sugar transport. The one-site carrier describes a transport mechanism in which sugar influx and efflux substrate binding sites are mutually exclusive. The two-site carrier describes a transport mechanism in which sugar influx and efflux substrate binding sites can exist simultaneously but may interact in a cooperative fashion when occupied by substrate. Michaelis and velocity parameters for saturable 3OMG transport in rat erythrocytes at 24 degrees C were obtained from initial rate measurements of 3OMG transport. The results are incompatible with the predictions of the one-site carrier but are consistent with the predictions of a symmetric two-site carrier, displaying negligible cooperativity between substrate binding sites. This allows reduction of the two-site carrier transport equations to a form containing fewer constants than the one-site carrier equations without limiting their predictive success. While the available evidence does not prove that rat erythrocyte sugar transport is mediated by a two-site mechanism, we conclude that adoption of the formally more complex one-site model for sugar transport in rat erythrocytes is unnecessary and unwarranted. Counterflow experiments have also been performed in which the time course of radiolabeled 3OMG uptake is measured in cells containing saturating levels of 3OMG. The results of these experiments are consistent with the hypothesis [Naftalin et al. (1985) Biochim. Biophys. Acta 820, 235-249] that exchange of sugar between intracellular compartments (cell water and hemoglobin) can be rate limiting for transport under certain conditions.     

Tests of the carrier model for ion transport by nonactin and trinactin.

The fluxes of K+ and NH+4 carried by nonactin and trinactin across thin lipid membranes have been measured as functions of ion activity, electric potential and time. In agreement with the predictions of a version of the carrier model in common use, the shape of the initial current-voltage relation is independent of the activity of the electrolyte, alpha-i, while the ratio of the initial conductance, G-o, to the steady-state conductance, G infinity, increases according to G-o/G infinity equals const1+const2 times alpha-i. For trinactin the data presented allow the estimation of the rate constants of the carrier process (in the limit of zero potential) in a manner which does not assume any particular variation with potential for the constants. Using empirically determined functions of potential, a complete set of values is also available for nonactin. The curve fitting which is necessary is described in the following paper. The data presently available for valinomycin are sufficient neither to test the model nor to determine a complete set of constants.     

Alternating carrier models of asymmetric glucose transport violate the energy conservation laws

Alternating access transporters with high-affinity externally facing sites and low-affinity internal sites relate substrate transit directly to the unliganded asymmetric “carrier” (Cⁱ) distribution. When both bathing solutions contain equimolar concentrations of ligand, zero net flow of the substrate-carrier complex requires a higher proportion of unliganded low-affinity inside sites () and slower unliganded “free” carrier transit from inside to outside than in the reverse direction. However, asymmetric rates of unliganded carrier movement, k_ij, imply that an energy source, ΔG_carrier = RT ln (k_oi/k_io) = RT ln (Cⁱⁿ/C^out) = RT ln (), where R is the universal gas constant (8.314 Joules/M/K°), and T is the temperature, assumed here to be 300 K°, sustains the asymmetry. Without this invalid assumption, the constraints of carrier path cyclicity, combined with asymmetric ligand affinities and equimolarity at equilibrium, are irreconcilable, and any passive asymmetric uniporter or cotransporter model system, e.g., Na-glucose cotransporters, espousing this fundamental error is untenable. With glucose transport via GLUT1, the higher maximal rate and K_m of net ligand exit compared to net ligand entry is only properly simulated if ligand transit occurs by serial dissociation-association reactions between external high-affinity and internal low-affinity immobile sites. Faster intersite transit rates occur from lower-affinity sites than from higher-affinity sites and require no other energy source to maintain equilibrium. Similar constraints must apply to cotransport.     

Infinite-cis kinetics support the carrier model for erythrocyte glucose transport

It has been claimed that the Km for infinite-cis uptake of glucose in human erythrocytes is so low that the carrier model for transport must be rejected. We redetermined this parameter for three experimental conditions and found instead that the Km values were in good agreement with the model. For each of a variety of cis glucose concentrations, cells were preequilibrated with various concentrations of glucose, and the apparent Km was determined as the intracellular concentration reducing the initial rate of net uptake by half. The dependence of the apparent Km values on the cis glucose was as predicted by the carrier model; the infinite-cis Km was determined from both this concentration dependence and the extrapolated value at infinite cis glucose. The resulting values were 15 mM for fresh blood at 0 degrees C, 39 mM for outdated blood at 0 degrees C, and 11 mM for outdated blood at 25 degrees C. Previous measurements of the Km at room temperature yielded values of 2-3 mM. These earlier studies used a time course procedure that indicated rapid changes in rates during the initial 10 s of uptake but did not directly measure such changes. We examined the uptake of 60 mM glucose at 20 degrees C into cells containing 0 and 5 mM glucose; rapid changes in rates were not observed in the first few seconds, and the time courses were more consistent with our higher Km values. Our new values, together with other initial rate measurements in the literature, support the adequacy of the carrier model to account for the kinetics of glucose transport in human erythrocytes.     

Phosphate transport in rat liver mitochondria--a mobile carrier model.

The possibility of a mobile carrier model for phosphate transport in rat liver mitochondria was examined on the basis of counterflux experiments. The rate of P_i uptake and P_i exchange were identical and depended on the external pH value. The alkalization of the suspending medium of P_i-preloaded mitochondria induced an efflux of P_i. The induction of a net P_i efflux by alkalization of the external medium stimulated the rate of ³²P_i uptake. Arsenate was shown to be an alternative substrate for P_i-carrier. A net efflux of inorganic arsenate (As_i), induced by alkalization of the external medium, also supported an acceleration of the ³²P_i uptake. When mitochondria were first preloaded with As_i and ³²P_i and then diluted into a more alkaline buffer free of Asi, a transient uptake of ³²P_i was observed. These results are discussed in terms of reorientation of the active site of the P_i carrier under the conditions where a net efflux of P_i or As_i occurred. This conclusion was supported by a change in the accessibility of the SH groups of the carrier toward poorly permeant thiol reagents during that process.     

Tests of the carrier model for ion transport by nonactin and trinactin

The fluxes of K⁺ and NH₄⁺ carried by nonactin and trinactin across thin lipid membranes have been measured as functions of ion activity, electric potential and time. In agreement with the predictions of a version of the carrier model in common use, the shape of the initial current-voltage relation is independent of the activity of the electrolyte, $\text{a}{}_{\mathrm{<mtext>i</mtext>}}$ while the ratio of the initial conductance, $\text{G}{}_0$, to the steady-state conductance, $\text{G}{}_{\mathrm{\infty }}$, increases according to $\text{G}{}_0\text{/G}{}_{\mathrm{\infty }}\text{=}\text{const}{}_1\text{+ const}{}_2\text{× a}{}_{\mathrm{<mtext>i</mtext>}}$. For trinactin the data presented allow the estimation of the rate constants of the carrier process (in the limit of zero potential) in a manner which does not assume any particular variation with potential for the constants. Using empirically determined functions of potential, a complete set of values is also available for nonactin. The curve fitting which is necessary is described in the following paper. The data presently available for valinomycin are sufficient neither to test the model nor to determine a complete set of constants.     

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.     

Hydrogen ion-coupled transport of D-glucose by phlorizin-sensitive sugar carrier in intestinal brush-border membranes

In rabbit intestinal brush-border membrane vesicles, Na+-independent D-glucose uptake in the presence of an inside-negative transmembrane potential was found to be stimulated by an imposed pH gradient. Na+-independent, pH-dependent and phlorizin-sensitive D-glucose-evoked potentials could be recorded from isolated toad intestine. The obtained data suggest that phlorizin-sensitive D-glucose carriers of intestinal brush-border membrane can interact with H+ when Na+ is absent.     

Cytochalasin B and the kinetics of inhibition of biological transport. A case of asymmetric binding to the glucose carrier

Cytochalasin B inhibits glucose transport in human erythrocytes by competing with glucose for the carrier on the inner surface of the cell membrane, but there is no cytochalasin site associated with the outward-facing form of the carrier. Such asymmetry may be demonstrated by zero trans exit and entry experiments, whereas Sen-Widdas exit experiments are not easily interpretable. The orientation of the transport system appears to be reversed in certain other cell types: chick embryo fibroblasts, Novikoff hepatoma cells and HeLa cells. Here the cytochalasin site is present in the external but not internal carrier form.