Fig. 6.12 Electrical potential distribution in the BLM and in its surroundings in .NET

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Fig. 6.12 Electrical potential distribution in the BLM and in its surroundings
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where A0 is the applied potential difference. At steady state (dr(p)/df = dT(q)/df = 0), T(P) = kd(kd + k + k) kacs(kd
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The conductivity of the membrane at the equilibrium potential (A0 = O), equal to the reciprocal of the polarization resistance value (Eq. 5.2.31), follows from Eqs (6.4.2), (6.4.3) and (4.3.5):
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where ft = kjkd is the adsorption coefficient and c the bulk concentration of the ion. Equation (6.4.4) is valid when the coverage of the electrolyte-membrane interface is small. At higher concentrations of transferred ion, the ion transfer is retarded by adsorption on the opposite interface, so that the dependence of Go on c is characterized by a curve with a maximum, as has been demonstrated experimentally. Under certain conditions, the transfer of various molecules across the membrane is relatively easy. The membrane must contain a suitable 'transport mediator', and the process is then termed 'facilitated membrane transport'. Transport mediators permit the transported hydrophilic substance to overcome the hydrophobic regions in the membrane. For example, the transport of glucose into the red blood cells has an activation energy of only 16 kJ mol"1 close to simple diffusion. Either the transport mediators bind the transported substances into their interior in a manner preventing them from contact with the hydrophobic interior of the membrane or they modify the interior of the membrane so that it becomes accessible for the hydrophilic particles. A number of transport mediators are transport proteins; in the absence of an external energy supply, thermal motion leads to their conformational change or rotation so that the transported substance, bound at one side of the membrane, is transferred to the other side of the membrane. This type of mediator has a limited number of sites for binding the transported substance, so that an increase in the concentration of the latter leads to saturation. Here, the transport process is characterized by specificity for a given substance and inhibition by other transportable substances competing for binding sites and also by various inhibitors. When the concentrations of the transported substance are identical on both sides of the membrane,
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exchange transport occurs (analogous to the exchange current see Section 5.2.2). When, for example, an additional substance B is added to solution 1 under these conditions, it is also transported and competes with substance A for binding sites on the mediator; i.e. substance A is transported from solution 2 into solution 1 in the absence of any differences in its concentration. A further type of mediator includes substances with a relatively low molecular weight that characteristically facilitate the transport of ions across biological membranes and their models. These transport mechanisms can be divided into four groups: (a) Transport of a stable compound of the ion carrier (ionophore) with the transported substance. (b) Carrier relay. The bond between the transported particle and the ionophore is weak so that it jumps from one associate with the ionophore to another during transport across the membrane. (c) An ion-selective channel. The mediator is incorporated in a transversal position across the membrane and permits ion transport. Examples are substances with helical molecular structure, where the ion passes through the helix. The selectivity is connected with the ratio of the helix radius to that of the ion. (d) A membrane pore that permits hydrodynamic flux through the membrane. No selectivity is involved here. A number of substances have been discovered in the last thirty years with a macrocyclic structure (i.e. with ten or more ring members), polar ring interior and non-polar exterior. These substances form complexes with univalent (sometimes divalent) cations, especially with alkali metal ions, with a stability that is very dependent on the individual ionic sort. They mediate transport of ions through the lipid membranes of cells and cell organelles, whence the origin of the term ion-carrier (ionophore). They ion-specifically uncouple oxidative phosphorylation in mitochondria, which led to their discovery in the 1950s. This property is also connected with their antibiotic action. Furthermore, they produce a membrane potential on both thin lipid and thick membranes. These substances include primarily depsipeptides (compounds whose structural units consist of alternating amino acid and ar-hydroxy acid units). Their best-known representative is the cyclic antibiotic, valinomycin, with a 36-membered ring [L-Lac-L-Val-D-Hy-i-Valac-D-Val]3, which was isolated from a culture of the microorganism, Streptomyces fulvissimus. Figure 6.13 depicts the structure of free valinomycin and its complex with a potassium ion, the most important of the coordination compounds of valinomycin. Complex formation between a metal ion and a macrocyclic ligand involves interaction between the ion, freed of its solvation shell, and dipoles inside the ligand cavity. The standard Gibbs energy for the formation of the complex, AG v, is given by the difference between the standard Gibbs
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Fig. 6.13 Valinomycin structure in (A) a non-polar solvent (the 'bracelet' structure) and (B) its potassium complex. O = O, o = C, # = N (According to Yu. A. Ovchinnikov, V. I. Ivanov and M. M. Shkrob) energy for ion transfer from the vapour phase into the interior of the ligand in solution, AG _^V> and the standard Gibbs energy of ion solvation, AG j : AGJV = AGj_*v ~ AGs,j ~ (6.4.5)
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As the quantities on the right-hand side are different functions of the ion radius, the Gibbs energy of complex formation also depends on this quantity, but not monotonously. The dependence of the Gibbs energy of solvation, e.g. for the alkali metal ions, is an increasing function of the ion radius, i.e. ions with a larger radius are more weakly solvated. In contrast, the interactions of the desolvated ions with the ligand cavity are approximately identical if the radius of the ion is less than that of the cavity. If, however, the ion
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radius is comparable to or even larger than the energetically most favourable cavity radius, then the ligand structure is strained or conformational changes must occur. Thus, the dependence of the stability constant of the complex (and also the rate constant for complex formation) is usually a curve with a maximum. The following conditions must be fulfilled in the ion transport through an ion-selective transmembrane channel: (a) The exterior of the channel in contact with the membrane must be lipophilic. (b) The structure must have a low conformational energy so that conformational changes connected with the presence of the ion occur readily. (c) The channel must be sufficiently long to connect both sides of the hydrophobic region of the membrane. (d) The ion binding must be weaker than for ionophores so that the ion can rapidly change its coordination structure and pass readily through the channel. The polarity of the interior of the channel, usually lower than in the case of ionophores, often prevents complete ion dehydration which results in a decrease in the ion selectivity of the channel and also in a more difficult permeation of strongly hydrated ions as a result of their large radii (for example Li + ). The conditions a-d are fulfilled, for example, by the pentadecapeptide, valingramicidine A (Fig. 6.14): HC=O I L-Val-Gly-L-Ala-D-Leu-L-Ala-D-Val-L-Val-D-Val NH-L-Try-D-Leu-L-Try-D-Leu-L-Try-D-Leu-L-Try (CH2)2 OH whose two helices joined tail-to-tail form an ion-selective channel. The selectivity of this channel for various ions is given by the series H + > NH 4 + S Cs+ > Rb + > K+ > Na+ > Li+ If a substance that can form a transmembrane channel exists in several conformations with different dipole moments, and only one of these forms is permeable for ions, then this form can be 'favoured' by applying an electric potential difference across the membrane. The conductivity of the membrane then suddenly increases. Such a dependence of the conductivity of the membrane on the membrane potential is characteristic for the membranes of excitable cells.
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Fig. 6.14 A gramicidin channel consisting of two helical molecules in the head-to-head position. (According to V. I. Ivanov)
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If a small amount of gramicidin A is dissolved in a BLM (this substance is completely insoluble in water) and the conductivity of the membrane is measured by a sensitive, fast instrument, the dependence depicted in Fig. 6.15 is obtained. The conductivity exhibits step-like fluctuations, with a roughly identical height of individual steps. Each step apparently corresponds to one channel in the BLM, open for only a short time interval (the opening and closing mechanism is not known) and permits transport of many ions across the membrane under the influence of the electric field; in the case of the experiment shown in Fig. 6.15 it is about 107 Na+ per second at 0.1 V imposed on the BLM. Analysis of the power spectrum of these
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Fig. 6.15 Fluctuation of the conductivity of BLM in the presence of gramicidin A. (According to D. A. Haydon and B. S. Hladky)
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449 stochastic events (cf. page 373) has shown that the rate-detemining reaction of channel formation is the bimolecular reaction of two gramicidin molecules. A similar effect has been observed for alamethicin I and II, hemocyanin, antiamoebin I and other substances. Great interest in the behaviour of these substances was aroused by the fact that they represent simple models for ion channels in nerve cells. Some substances form pores in the membrane that do not exhibit ion selectivity and permit flow of the solution through the membrane. These include the polyene antibiotics amphotericin B, OH O HOOC OH OH OH OH O
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nystatin and mycoheptin, forming pores in the membrane with a diameter of 0.7-1.1 nm. Proteins also form pores, e.g. the protein from the sea anemone Stoichactis helianthus or colicin El. In all these systems, the energy source is an electrochemical potential gradient and transport occurs in the direction grad /i, (i.e. in the direction of decreasing electrochemical potential). It is often stated in the literature that this spontaneous type of transport occurs in the direction of the electrochemical potential gradient; this is an imprecise formulation. Transport occurring in the absence of another source of transport energy is termed passive transport. Active transport. The definition of active transport has been a subject of discussion for a number of years. Here, active transport is defined as a membrane transport process with a source of energy other than the electrochemical potential gradient of the transported substance. This source of energy can be either a metabolic reaction (primary active transport) or an electrochemical potential gradient of a substance different from that which is actively transported (secondary active transport). A classical example of active transport is the transport of sodium ions in frog skin from the epithelium to the corium, i.e. into the body. The principal ionic component in the organism of a frog, sodium ions, is not washed out of its body during its life in water. That this phenomenon is a result of the active transport of sodium ions is demonstrated by an experiment in which the skin of the common green frog is fixed as a
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membrane between two separate compartments containing a single electrolyte solution (usually Ringer's solution, 0.115 MNaCl, 0.002 M K C I and 0.0018 MCaCl2). In the absence of an electric current a potential difference is formed between the electrolyte at the outside and at the inside of the skin, equal to about 100 mV, even though the compositions of the two solutions are identical. This potential difference decreases to zero when electrodes on both sides of the membrane are short-circuited and a current flows between them. If the compartment on the outer side of the skin contains radioactively labelled 22Na, then sodium ions are shown to be transported from the outer side to the inner side of the skin. Sodium ion transport in this direction occurs even when the electrolyte in contact with the inside of the skin contains a higher concentration of sodium ions than that at the outside. When the temperature of the solution is increased, then the current as well as the sodium transport rate increase far more than would correspond to simple diffusion or migration. When substances inhibiting metabolic processes are added to the solution, e.g. cyanide or the glycoside, ouabain, OH CH3
the current decreases. For example, in the presence of 10" 4 M ouabain, it decreases to 5 per cent of its original value. The rate of the active transport of sodium ion across frog skin depends both on the electrochemical potential difference between the two sides of this complex membrane (or, more exactly, membrane system) and also on the affinity of the chemical reaction occurring in the membrane. This combination of material flux, a vector, and 'chemical flux' (see Eq. 2.3.26), which is scalar in nature, is possible according to the Curie principle only when the medium in which the chemical reaction occurs is not homogeneous but anisotropic (i.e. has an oriented structure in the direction perpendicular to the surface of the membrane or, as is sometimes stated, has a vectorial character). It is assumed that the chloride ion is transported passively across the membrane. Using an approach similar to the formulation of Eqs (2.1.2), (2.3.26) and (2.5.23), relationships can be written for the material fluxes of sodium and chloride ions, 7Na+ and Jcr (the driving force is considered to be the electrochemical potential difference), and for the flux of the chemical reaction, / ch : Jcr = / ch = LrlAjUNa+ L22AfiCr + LrrA (6.4.6)
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451 where A/2Na+ and A/2 cr designate the electrochemical potential difference between the inner and outer sides of the skin and A is the affinity of the chemical reaction. As the material flux in the direction from inside to outside is considered as positive, then the coefficients Lu and L22 will also be positive. On the other hand, the coefficients LXr and LrX will be negative. When the electrolyte concentration is identical on both sides of the membrane and A0 M = 0, then AjUNa+ = AJUC, = 0 and Eqs (6.4.6) yield the equation for the current density, 7 = F / N a + = ^ / c h = L1H4
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