Theory of the rotational contribution to facilitated diffusion

Gros and others have recently shown experimentally that the facilitated diffusion of protons carried by a form of haemoglobin is enhanced by rotational diffusion of the carrier, whereas facilitated diffusion of oxygen by the same carrier is not. In this paper the theory of facilitated transport by rotating carriers is developed from first principles. The theory confirms Gros's findings that (i) the rotational contribution appears only when the angle of rotational diffusion over the average time the proton remains bound is small and (ii) under these conditions rotation enhances the normal translational contribution by a factor 1/2 at the lowest carrier concentrations. The theory also shows that there must be a rotational boundary layer.     

On facilitated oxygen diffusion in muscle tissues.

The role of myoglobin in facilitated diffusion of oxygen in muscle in examined in a tissue model that utilizes a central supplying capillary and a tissue cylinder concentric with the central capillary, and that includes the nonlinear characteristics of the oxygen-hemoglobin dissociation reaction. In contrast to previous work, this model exhibits the effect of blood flow and a realistic, though ideal, tissue-capillary geometry. Solutions of the model equations are obtained by a singular-perturbation technique, and numerical results are discussed for model parameters of physiologic interest. In contrast to the findings of Murray, Rubinow, Taylor, and others, fractional order perturbation terms obtained for the "boundary-layer" regions near the supplying capillaries are quite significant in the overall interpretation of the modeling results. Some closed solutions are found for special cases, and these are contrasted with the full singular-perturbation solution. Interpretations are given for parameters of physiologic interest.     

Measurement of facilitated calcium diffusion by a soluble calcium-binding protein

The flux of calcium through an aqueous compartment was determined in a flow-dialysis cell in which two dialysis membranes separated the middle aqueous compartment from two outer compartments. The contribution of convection to the total calcium flux was large but could be removed by addition of 1% agar. The flux of calcium through the gelled aqueous compartment agreed with theoretical expectations. The self-diffusion coefficient for calcium from these results was calculated to be 0.81 X 10(-5) cm2 X s-1. Carp parvalbumin significantly enhanced the calcium flux at 2.3 X 10(-6)M free calcium. The calcium flux increased linearly with parvalbumin concentration. These observations are consistent with the hypothesis that the overall unidirectional calcium flux J is the sum of free calcium diffusion and protein-calcium diffusion: J = D[Ca] + D'[CaPr]. The value of D', the self-diffusion coefficient for parvalbumin, was calculated from the flux data to be 13.7 X 10(-7) cm2 X s-1.     

The facilitated diffusion of oxygen by hemoglobin and myoglobin.

We have clarified the use of Wyman's differential equation for the facilitated oxygen flux through a slab of solution of myoglobin or hemoglobin by showing that there is a unique choice of boundary condition on the carrier concentration to be employed in conjunction with it. The singular perturbation solution of Wyman's equation, due to Murrayand Mitchell and Murray, has been extended. By means of it, the paradox of Wittenberg, that the facilitated oxygen flux per mole of heme is apparently independent of the protein carrier, has been resolved.     

Molecular crowding enhances facilitated diffusion of two human DNA glycosylases

Intracellular space is at a premium due to the high concentrations of biomolecules and is expected to have a fundamental effect on how large macromolecules move in the cell. Here, we report that crowded solutions promote intramolecular DNA translocation by two human DNA repair glycosylases. The crowding effect increases both the efficiency and average distance of DNA chain translocation by hindering escape of the enzymes to bulk solution. The increased contact time with the DNA chain provides for redundant damage patrolling within individual DNA chains at the expense of slowing the overall rate of damaged base removal from a population of molecules. The significant biological implication is that a crowded cellular environment could influence the mechanism of damage recognition as much as any property of the enzyme or DNA.A significant triumph in biochemistry over the last 20 years was the ability to isolate human DNA repair enzymes and study their in vitro properties using defined DNA substrates containing damaged sites. Typically, these studies have been performed using dilute conditions, where the concentration of the enzyme, DNA and buffer components were low compared to the concentration of water. Although a wealth of insights into the thermodynamic, kinetic and structural properties of enzymes have resulted from such approaches (1–7), DNA repair enzymes act in a crowded cellular environment with quite different physical properties (8,9). Thus, an open question is how the complex intracellular milieu affects the ability of enzymes to locate and repair damage sites embedded in a large polymeric DNA substrate.The human intracellular environment has numerous physical properties that could dramatically affect enzyme activity. These include high inorganic ion and metabolite concentrations (10,11), lower dielectric properties (12–14), higher bulk viscosity (15,16), and the presence of high concentrations of macromolecules which consume available volume (‘molecular crowding’) (17,18). Indeed, the concentration of macromolecules in human cells is an astounding ∼100–300 mg/ml (9,19), which means that 10–40% of the total cellular volume is consumed by large molecules (often called the excluded volume). Taken together,­ these parameters could affect association of an enzyme with its target in complex ways. For instance, high ion concentrations are expected to shield electrostatic interactions between an enzyme and its highly charged DNA substrate (10,20,21), while a lower dielectric constant could have an opposite effect. Increases in macroscopic viscosity will slow the translational movement of macromolecules and due to entropic effects, crowded environments will push macromolecular association when the complex consumes a smaller volume than the free component species (9,22,23).Although volume exclusion largely explains the effects of crowded environments on binding equilibria, crowding has been reported to have a surprisingly small effect on the diffusion-controlled association kinetics of macromolecules (24). Indeed, it has been observed that some diffusion-controlled association reactions occur at nearly the same rates in crowded solutions and in cells as they do in dilute solution (24,25). These kinetic effects are counterintuitive, but can be understood by considering that macromolecular crowders alter the macroscopic viscosity and available volume in crowded solutions, but do not change the microscopic viscosity (26,27). Thus, over short nanometer distances, the rotational and translational diffusion of proteins is not greatly affected by crowding because the protein only feels the microscopic viscosity of the solvent that is present in the spaces between the larger crowding molecules (28). Over larger distances, hard sphere repulsion between the protein and crowding molecules increases the effective viscosity and slows translational diffusion (8,28,29). When two binding partners approach one another, they are captured within a low viscosity (high mobility) cage created by the larger crowding molecules, which increases the probability for a productive encounter event. Surprisingly, the capture of two binding partners within a high mobility cage can in some cases offset all of the negative effects of high viscosity on the overall association rate (29).The above considerations raise the interesting question of what effect molecular crowding has on enzyme association with DNA, and in particular, the property of facilitated diffusion along a DNA chain? Facilitated diffusion on the DNA chain (‘translocation’) is a distinct process that involves transient states of an enzyme and DNA that are not directly observable in equilibrium binding, steady-state or rapid kinetic measurements (1–4,30). Here, we measure the effect of inert crowding agents on the probability that the DNA repair enzymes uracil and 8-oxguanine DNA repair glycosylase will successfully translocate between two damaged sites in a DNA chain. We find that crowding increases the likelihood that each enzyme will successfully translocate between their respective target sites without dissociation to bulk solution and also increases the average translocation distance. For both enzymes, crowding biases the damage search process toward a chain tracking search mode rather than a 3D search mode. Such a crowder-induced transition in the search mode could significantly impact the effectiveness of the damage search in a crowded nuclear environment. These enzymes represent two of the largest superfamilies of glycosylases and their similar behavior in these studies suggests that the findings will be general for other related glycosylases.     

Lactic acid excretion via carrier-mediated facilitated diffusion in Lactobacillus helveticus

Summary During growth on a complex medium containing 2% (w/v) lactose, Lactobacillus helveticus produced about 180 mm lactate. Due to the acidification, the external pH decreased to 3.7. The pH remained constant at a level of 0.5–0.7 units (40 mV), and µ_Lac decreased gradually from –60 to 0 mV. The mechanism of lactate extrusion was studied with resting cells. Upon dilution of lactate-loaded cells in a buffer containing [¹⁴C]-lactate, a typical counterflow was observed, suggesting that a carrier system was employed in lactate excretion. Influx of lactate could not be driven by an artificial membrane potential, indicating that lactate was electroneutrally transported. By examining efflux under various lactate anion and lactic acid concentrations, the undissociated form of the acid was shown to influence the velocity of the transport process. A pH-dependent apparent K _m value of the carrier system was observed in efflux experiments with increasing internal lactate concentrations. It was concluded that the mode of end-product excretion can be defined as a carrier-mediated facilitated diffusion with the undissociated lactic acid or the lactate anion in symport with one proton, respectively, as the object of transport.Abbreviations L _tota total lactate - L _undissb free lactic acid - L _dissc lactate anion - pH_ed external pH - pH_ie internal pH - pH transmembrane H⁺ gradient - µ_Lacf transmembrane gradient of total lactate - µ_HLg transmembrane gradient of the free lactic acid - µ_Lh transmembrane gradient of the lactate anion - V _Effii efflux velocity Offprint requests to: G. Gottschalk     

Mechanisms for the facilitated diffusion of substrates across cell membranes

Two classes of theoretical mechanisms for protein-mediated, passive, transmembrane substrate transport (facilitated diffusion) are compared. The simple carrier describes a carrier protein that exposes substrate influx and efflux sites alternately but never both sites simultaneously. Two-site models for substrate transport describe carrier proteins containing influx and efflux sites simultaneously. Velocity equations describing transport by these mechanisms are derived. These equations take the same general form, being characterized by five experimental constants. Simple carrier-mediated transport is restricted to hyperbolic kinetics under all conditions. Two-site carrier-mediated transport may deviate from hyperbolic kinetics only under equilibrium exchange conditions. When both simple- and two-site carriers display hyperbolic kinetics under equilibrium exchange conditions, these models are indistinguishable by using steady-state transport data alone. Seven sugar transport systems are analyzed. Five of these systems are consistent with both models for sugar transport. Uridine, leucine, and cAMP transport by human red cells are consistent with both simple- and two-site models for transport. Human erythrocyte sugar transport can be modeled by simple- and two-site carrier mechanisms, allowing for compartmentalization of intracellular sugars. In this instance, resolution of the intrinsic properties of the human red cell sugar carrier at 20 degrees C requires the use of submillisecond transport measurements.     

The role of facilitated diffusion of oxygen in tissue hypoxia

The evidence that cytochrome P-450 can act as a tissue oxygen carrier is outlined, and a new experimental approach to the measurement of the fraction of oxygen carried this way is described. This fraction is increased when cytochrome P-450 concentration is increased, which occurs on exposure of the experimental animal to hypoxia. This appears to be a new mechanism of tissue acclimation to hypoxia.Presented at the Seventh International Biometeorological Congress, 17–23 August 1975, College Park, Maryland, USA.     

The glucose transport in retinal pigment epithelium is via passive facilitated diffusion

The glucose transport across the bovine retinal pigment epithelium (RPE) was studied in a modified Ussing chamber. Unidirectional fluxes were recorded with radioactive tracers L-[14C]-glucose (LG) and 3-O-methyl-D-[3H]-glucose (MDG). There was no significant difference between the unidirectional MDG fluxes (retina to choroid, and choroid to retina directions) with or without ouabain. The effects of two glucose transporter inhibitors, phloretin and cytochalasin B, on the glucose fluxes from choroid to retina cells were also investigated. The MDG flux was found to be inhibited by 45.5% by phloretin (10(-4) M) and 87.4% by cytochalasin B (10(-4) M). These inhibitory characteristics resembled the facilitated diffusion mode of glucose transport. The glucose transporter protein in the plasma membrane of RPE was located by means of photolabeling [3H]-cytochalasin B. The labeled plasma membrane enriched fraction was analysed by SDS-PAGE. The glucose transporter of bovine RPE was found to have a molecular weight range of 46-53 kDa. The molecular weight range of this transporter protein agreed with those of facilitated glucose transporters in other tissues indicating a molecular similarity between them. The results indicated that the glucose transport across the RPE is via passive facilitated diffusion.     

The influence of uncouplers on facilitated diffusion of sorbose in Saccharomyces cerevisiae

Sorbose uptake in Saccharomyces cerevisiae, strain Delft 1, proceeds via mediated passive transport. In the cell sorbose is distributed in at least two compartments. Efflux studies showed that sorbose uptake in one of these compartments is not readily reversible. Uncouplers of oxidative phosphorylation inhibit both transport velocity and steady-state uptake level. It could be shown that these two effects are caused by different modes of action of the uncouplers. None of these two effects could be ascribed to changes of the electrochemical H+ gradient or of the intracellular pH. It is suggested that the inhibition of uptake velocity is caused by binding of the uncoupler to the sorbose translocator, thus lowering the transport activity. The uncoupler binding site is probably located at the intracellular fragment of the carrier. The second effect, reduction of the steady-state uptake level, is probably due to blocking of sorbose influx into the compartment that exhibits poor reversibility.     

Transport of glucose by Bifidobacterium animalis subsp. lactis occurs via facilitated diffusion

Two strains of Bifidobacterium animalis subsp. lactis were indistinguishable by several nucleic acid-based techniques; however, the type strain DSMZ 10140 was glucose utilization positive, while RB 4825, an industrially employed strain, was unable to grow rapidly on glucose as the principal carbon source. This difference was attributed to the presence of a low-affinity facilitated-diffusion glucose transporter identified in DSMZ 10140 but lacking in RB 4825. Uptake of D-[U-(14)C]glucose in DSMZ 10140 was stimulated by monovalent cations (ammonium, sodium, potassium, and lithium) and inhibited by divalent cations (calcium and magnesium). When competitor carbohydrates were included in the uptake assays, stereospecific inhibition was exhibited, with greater competition by methyl-beta-glucoside than methyl-alpha-glucoside. Significant inhibition (>30%) was observed with phloretin, an inhibitor of facilitated diffusion of glucose, whereas there was no inhibition by sodium fluoride, iodoacetate, sodium arsenate, sodium azide, 2,4-dinitrophenol, monensin, or valinomycin, which typically reduce energy-driven transport. Based on kinetic analyses, the mean values for K(t) and V(max) were 14.8 +/- 3.4 mM D-glucose and 0.13 +/- 0.03 micromol glucose/min/mg cell protein, respectively. Glucose uptake by several glucose-utilizing commercial strains of B. animalis subsp. lactis was also inhibited by phloretin, indicating the presence of facilitated diffusion glucose transporters in those strains. Since DSMZ 10140 has been previously reported to lack a functional glucose phosphoenolpyruvate phosphotransferase system, the glucose transporter identified here is responsible for much of the organism's glucose uptake.     

The role of facilitated diffusion in glucose transport across the apical membrane of enterocytes

In chronic experiments on Wistar rats, glucose and galactose absorption in the isolated loop of the small intestine considerably decreased in presence of both phloridzine am phloritine (inhibitors of the glucose transporters SGLT1 and GLUT2). The load of the isolated loop with glucose or galactose solutions scarcely influenced the absorption of 2-deoxi-D-glucose (substrate for GLUT2). According to the immunocytochemical analysis by means of confocal microscopy, after the load of the isolated loop with glucose (75 mM) the labels to GLUT2 and proteinkinase C (PKC betalI) were concentrated mainly in the apical part of the enterocytes, whereas after the load with the Ringer solution--in the basal part of the enterocytes. It was shown on the mathematical model that the part of the facilitated diffusion in the total glucose absorption was considerably lesser in comparison with the active transport mediated by SGLT1. Thus the findings support the hypothesis about a recruitment of the transporter GLUT2 into the apical membrane of the enterocytes and its involvement in glucose transfer across this membrane. However, under natural conditions, the active transport is the main mechanism of glucose absorption, whereas the facilitated diffusion plays a certain role only at high carbohydrate loads.