Facilitated diffusion: the elasticity of oxygen supply.

It is well established that the presence of oxygen-carrying proteins such as haemoglobin can facilitate the diffusion of oxygen through a solution. In this paper, it is shown that some properties of a facilitated flow are substantially different from those of unfacilitated flux, including especially the stability of the tension at which the oxygen arrives at the end of the diffusion path. The concept of the “output resistance” of the supply is introduced, and a facilitated pathway is shown to have a lowered resistance. A role for the storage capacity of the bound oxygen reservoir is also developed; it is shown that delivery oxygen tensions are stabilized against transient changes in oxygen demand. In treating the equations of facilitated diffusion, a simplified approach is used to take account of boundary layers in the solution where deviations from oxygen-protein equilibrium are significant. A measure of the thickness and importance of such boundary layers is calculated.     

Parameter dependence of myoglobin-facilitated transport of oxygen in the presence of membranes

Some physicochemical entities involved in the facilitated transport of oxygen along a transport path z1 less than or equal to z less than or equal to zn with membranes impermeable to myoglobin at zi, i = 1,...,n, were identified in an earlier paper [Math. Biosci. 95:209 (1989)]. These entities are the partition between the oxygen and oxymyoglobin flows, the flow transfers taking place near a membrane, and the membrane resistance. Expressions for these entities were obtained that explicitly involve the parameters of the system. In this paper, for the case of prescribed boundary oxygen concentrations x1 and xn, these expressions are incorporated into (i) an explicit representation for the facilitated transport value in terms of the difference, E(x1)-E(xn), between the boundary oxymyoglobin equilibrium values and the sum, gamma, of the membrane resistances, and (ii) a representation for the distribution of the membrane oxygen concentrations xi at zi, i = 2,...,n-1. This makes it possible to analyze the manner in which the facilitated transport depends on the parameters. For a physiological range of parameter values, the facilitated transport was found to increase as either the oxygen-myoglobin association rate constant k', the dissociation rate constant k, the oxygen diffusion coefficient, or the oxymyoglobin diffusion coefficient increases. Thus, the facilitated transport does not depend directly on ratios of chemical and diffusion coefficients. Although the increase in the oxygen diffusion coefficient does not per se affect the chemical conductance, it diminishes the membrane resistance through an interface feature, with a resulting increase in the facilitated transport. For a larger range of values of k' and k, the dependences of the facilitated transport on k' and on k are both biphasic and are similar in shape. However, the mechanisms involved are different: The associated changes in E(x1)-E(xn) and in gamma that result from the increase in k' are opposite to those that result from an increase in k. The use of (i) and (ii) permits, also, discrimination between the different roles of the physicochemical entities involved in a given facilitated transport change. In some cases (e.g., the decreasing phase of the facilitated transport as k' increases), this change depends in an essential manner on a secondary modification of the profile xi, i = 1,...,n, along the transport path.     

The physico-chemical mechanism of mediated transport. I. Facilitated diffusion

On the basis of the currently accepted model for the cell membrane structure, a physico-chemical model for mediated transport is developed and solved for the case of polar non-electrolyte migration through the cell membrane. The model considers the interstitial space defined by the transport protein subunits to be the migration pathway for polar solutes. A Langmuir-type adsorption equilibrium is assumed at the interfaces and a multicomponent diffusion mechanism of solute and water is postulated within the migration pathway, where the polar residues of the transport protein represent another component of the system. Membrane selectivity is governed by the adsorption constants, which are shown to affect strongly the kinetics of transport. Isosmotic transport and the volume change of the cell are important features incorporated in the model, which is shown to fulfill the peculiar properties of facilitated diffusion systems. It is concluded that the same type of pathway can be used for the transport of other polar solutes through existing or induced hydrophilic channels, for which a similar approach is suggested.     

Transfers between free and combined oxygen flows in determining facilitated transport with membranes on the transport path

The facilitated transport of a species brought about by a diffusible carrier is mediated by the sharing of the total flow between the flow of the free species (fd) and of the species-carrier compound (fc). The presence of membranes impermeable to the carrier on the transport path is accompanied by transfers between fd and fc in regions next to the membranes. These transfers are associated with differences between the current species-carrier concentration and the one that would exist at chemical equilibrium with the free species. These differences determine that the actual facilitated transport is smaller than the possible maximum. Analytic approximations to describe these differences are obtained; they are expressed in terms of physiochemical entities germane to the transport. This leads to a better conceptual understanding of the process. A relatively small system of algebraic equations for the numerical solution of the facilitated transport is formulated. A feature of this approach is that, instead of matching the values of functions at some points, the flows derived from integrals evaluated over some intervals are matched. The expressions for the physicochemical entities obtained contain the parameters explicitly; this permits analysis of the mechanisms involved in the dependence of the facilitated transport on the parameters of the system. It is shown, for instance, that the increase of the "on" chemical coefficient may result in either an increase or a decrease of the facilitated transport, depending on the current values of the parameters.     

Facilitated diffusion of oxygen and carbon monoxide in the large affinity regime

Wyman's equation for facilitated diffusion of a ligand through a solution slab containing a carrier is recast and solved by means of a regular perturbation expansion in the parameter representing the driving force for facilitation. This new solution is complementary to the previously exploited singular perturbation solution due to Murray and represents facilitation in the low facilitation parameter regime. The most significant physical realization of this regime occurs when there is a large affinity between ligand and carrier, as in the carbon monoxide-hemoglobin system.The validity domains of the regular perturbation solution and the singular perturbation solution of Mitchell and Murray and Rubinow and Dembo are delineated. The equation for facilitated diffusion is solved numerically for parameter values appropriate to the oxygen-myoglobin experiments of Wittenberg, and to the carbon monoxide-hemoglobin experiments of Mochizuki and Forster, and Wittenberg. This solution provides a norm for comparison of the utility of the perturbation solutions.We show how the theory explains the apparent contradiction between the positive observations of Mochizuki and Forster and the negative observations of Wittenberg on facilitation of carbon monoxide transport through a slab of hemoglobin solution.Supported in part by the National Science Foundation under Grant No. PCM77-03344In partial fulfillment of the Ph.D. degree at Cornell UniversityProfessor S. I. Rubinow has passed away on February 22, 1981Computations were performed at the Courant Mathematics and Computing Laboratory, supported by DOE under contract #EY-76-C-02-3077.     

Facilitated diffusion of 6-deoxy-D-glucose in bakers' yeast: evidence against phosphorylation-associated transport of glucose.

6-Deoxy-D-glucose, a structural homomorph of D-glucose which lacks a hydroxyl group at carbon 6 and thus cannot be phosphorylated, is transported by Saccharomyces cerevisiae via a facilitated diffusion system with affinity equivalent to that shown with D-glucose. This finding supports the facilitated diffusion mechanism for glucose transport and contradicts theories of transport-associated phosphorylation which hold that sugar phosphorylation is necessary for high-affinity operation of the glucose carrier.     

Facilitated transport of di- and trinitrophenolate ions across lipid membranes by valinomycin and nonactin.

The conductance of black lipid membranes in the presence of 2,4,6-trinitrophenol (or 2,4-dinitrophenol) is considerably enhanced, if the cation carriers valinomycin, enniatin B or nonactin are added. The effect is, however, largely independent of the cation concentration and is identical for the cations Li+, Na+ and Ba2+. This finding, as well as the sign and magnitude of the diffusion potential in the presence of a gradient of picrate are consistent with the assumption that the transport of picrate anions is facilitated by the above-mentioned macrocyclic compounds, but that cations are not directly involved. A model is suggested which, based on the generation of mobile defect structures by the incorporation of large molecules, allows one to explain facilitated transport without the assumption of stable chemical bonds between a carrier and its transported substrate. If K+ is present in the aqueous phase, the conductance is largely determined by the permeation of the cation complexes of valinomycin and nonactin. The conductance is, however, increases by adsorption of picrate anions to the membrane surface. The negative surface potential generated by the adsorption layer seems to be responsible for the saturation of the conductance at high picrate concentrations in the absence of valinomycin and nonactin.     

Facilitated transport of calcium by cells and subcellular membranes of Bacillus subtilis and Escherichia coli.

The level of calcium in growing cells is lower than that in the growth medium. Non-energy-dependent uptake of 45-Ca by log-phase cells of Bacillus subtilis occurs under two conditions: at 0 C or in the presence of m-chlorophenyl carbonylcyanide hydrazone. Similar uptake, but quantitatively less, occurs with Escherichia coli cells under the same conditions. Membrane vesicles prepared from B. subtilis or E. coli accumulate 45-Ca by a process that does not depend on added energy sources and is not inhibited by the respiratory poison cyanide. The properties of calcium transport in all cases is consistent with carrier-mediated, facilitated transport with specificity Ca-2+ greater than Sr-2+ greater than Mn-2+ greater than Mg-2+. Upon transfer of cells from 0 C to 20 C, pre-accumulated 45-Ca is released. Heat-killed cells do not accumulate 45-Ca and calcium is released by cells upon addition of toluene (under conditions that do not cause visible lysis). These results suggest that the facilitated uptake of calcium may be utilizing a transport system that normally is responsible for the energy-dependent excretion of calcium from the cells.     

Facilitated transport of urea across the gall-bladder luminal membrane.

Counterflow experiments demonstrate the existence of urea counter-transport on the epithelium luminal surface. This phenomenon disappears when 10(-4) M phloretin is added to the perfusion fluid. Moreover counterflow experiments made using thiourea as elicitor, demonstrate that the phenomenon is specific for the urea.     

Facilitated transport of di- and trinitrophenolate ions across lipid membranes by valinomycin and nonactin

The conductance of black lipid membranes in the presence of 2,4,6-trinitrophenol (or 2,4-dinitrophenol) is considerably enhanced, if the cation carriers valinomycin, enniatin B or nonactin are added. The effect is, however, largely independent of the cation concentration and is identical for the cations Li⁺, Na⁺ and Ba²⁺. This finding, as well as the sign and magnitude of the diffusion potential in the presence of a gradient of picrate are consistent with the assumption that the transport of picrate anions is facilitated by the above-mentioned macrocyclic compounds, but that cations are not directly involved. A model is suggested which, based on the generation of mobile defect structures by the incorporation of large molecules, allows one to explain facilitated transport without the assumption of stable chemical bonds between a carrier and its transported substrate.If K⁺ is present in the aqueous phase, the conductance is largely determined by the permeation of the cation complexes of valinomycin and nonactin. The conductance is, however, increased by adsorption of picrate anions to the membrane surface. The negative surface potential generated by the adsorption layer seems to be responsible for the saturation of the conductance at high picrate concentrations in the absence of valinomycin and nonactin.     

Facilitated diffusion and active transport systems for glucose in metacercariae of Clinostomum marginatum (Digenea)

Metacercariae of Clinostomum marginatum excysted from yellow perch, Perca flavescens, appear to have two systems for transporting glucose across the tegument, facilitated diffusion and active transport. These systems were distinguished by their differential sensitivities to Na⁺, phlorizin and phloretin. In Ringer's saline for cold-blooded vertebrates, 0.1 mm phlorizin and phloretin were incomplete, but similarly effective inhibitors of glucose uptake in 3 min incubations; worms accumulated in 1 h nonmetabolized 3-O-methylglucose against an apparent concentration difference demonstrating the active transport component. In Na⁺-free saline, phlorizin sensitivity and active transport capacity disappeared, but a phloretin sensitive, Na⁺-independent component remained. The V_max and K₁ of the Na⁺-independent system were 3.0 ± 0.54 μmol/g ethanol-extracted dry wt/h, and 0.8 ± 0.36 mm, respectively. V_max and K₁ of the Na⁺-dependent system, estimated by subtracting the Na⁺-independent values from those obtained in Ringer's saline, were 1.3 ± 0.27 μ mol/g ethanol-extracted dry wt/h, and0.7 ± 0.36mm, respectively.     

Facilitated diffusion of a DNA binding protein on chromatin.

Facilitated diffusion accounts for the rapid rate of association of many bacterial DNA binding proteins with specific DNA sequences in vitro. In this mechanism the proteins bind at random to non-specific sites on the DAN and diffuse (by 'sliding' or 'hopping') along the DNA chain until they arrive at their specific functional sites. We have investigated whether such a mechanism can operate in chromatin by using a bacterial DNA binding protein, Escherichia coli RNA polymerase, that depends on linear diffusion to locate initiation sites on DNA. We have measured the competition between chromatin and its free DNA for the formation of initiation complexes. Only the short linker segments exposed by the removal of histone H1 are available for interaction with the polymerase, but the sparsely distributed promoter sites on the linker DNA of such a polynucleosome chain are located at the same rate as those on DNA. We conclude that the polymerase is free to migrate between the separate linker DNA segments of a polynucleosome chain to reach a promoter site. This chain thus permits the 'hopping' of proteins between neighboring linker segments in their search for a target site on the accessible DNA.     

An overview of oxygen transport in plants: diffusion and convection

The movement of gases within plants is crucial for species that live in flood-prone areas with limited soil oxygen. These plants adapt to hypoxia/anoxia not by using oxygen more efficiently, but by ensuring a steady oxygen supply to their cells. Wetland plants typically form gas-filled spaces (aerenchyma) in their tissues, providing a low-resistance pathway for gas movement between shoots and roots, especially when the shoots are above water, and the roots are submerged. Oxygen movement in plant roots is mainly through diffusion. However, in certain species, such as emergent and floating-leaved plants, pressurized flows can also facilitate the movement of gases within their stems and rhizomes. Three types of pressurized (convective) flows have been identified: humidity-induced pressurization (positive pressure), thermal osmosis (positive pressure with air flow against the heat gradient), and venturi-induced suction (negative pressure) caused by wind passing over broken culms. A clear diel variation in pressurized flows exists, with higher pressures and flows during the day and negligible pressures and flows during the night. This article discusses some key aspects of these mechanisms for oxygen movement.