Models of Transmembrane Transport

Various models describing the motion of molecules across membranes have been proposed in the literature (see reviews [186,187]). In 1949 Zwolinsky, Eyring and Reese [188] proposed that we should consider the membrane as being a structureless medium and to characterize the migration of molecules across membrane by the isotropic diffusion coefficient, D. The same assumption was used by Hardt [189] to derive the expressions for the characteristic time, t, of the particle diffusion from one side of the spherical membrane to the other  

however that the concepts about the lipid membrane as the isotropic, structureless medium are oversimplified. It is well known [19, 190] that the rates and character of the molecular motion in the lateral direction and across the membrane are quite different. This is true for both the molecules inserted in the lipid bilayer and the lipid molecules themselves. Thus, for example, while it still seems possible to characterize the lateral movement of the egg lecithin molecule by the diffusion coefficient D its movement across the membrane seems to be better described by the so-called flip-flop mechanism when two lipid molecules from the inner and outer membrane monolayers of the vesicle synchronously change locations with each other [19]. The value of D, = 1.8 x 10 8 cm2 s 1 [191] corresponds to the time of the lateral diffusion jump of lecithin molecule, Le. about 10 7s. The characteristic time of flip-flop under the same conditions is much longer (about 6.5 hours) [19]. The molecules without long hydrocarbon chains migrate much more rapidly. For example for pyrene D, = 1.4x 10 7 cm2 s1 [192]. 

The lipid membrane is not only anisotropic, but also inhomogeneous in the transmembrane direction. It contains relatively hydrophilic polar layers adjacent to the membrane // water interfaces, which include the polar heads of lipid molecules, and highly hydrophobic non-polar central core, containing the hydrocarbon chains. 

Trauble [193] made an interesting attempt to take into account the influence of the membrane molecular structure on the transmembrane transfer of small molecules. The transmembrane motion of these molecules was considered under the assumption that the thermal motion of the hydrocarbon chains of the membrane lipid leads to the appearance of the mobile structural defects (so called kinks ) in the membrane. The kinks are small free volumes in the hydrocarbon phase of the membrane diffusing in the membrane. The molecules from the aqueous phase may be captured by these kinks and, moving together with them, transferred to the other side of the membrane. Such a model was shown to describe satisfactory the translocation of small neutral molecules such as water. 

For the transmembrane transfer of ions containing hydrophobic substituents the model was proposed that takes into account the variations of dielectric properties across the membrane. According to this model [194-200] the lipophilic ions are adsorbed at the minima of the potential energy near to the membrane // water interface (see Fig. 6b). The transfer of the ions across the membrane is considered to be monomolecular reaction of the ion s surmounting of the hydrophobic barrier in the center of the membrane with the first order rate constant k,. 

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Figure 8.3 A model of iron transport across the intestine. Reduction of ferric complexes to the ferrous form is achieved by the action of the brush border ferric reductase. The ferrous form is transported across the brush border membrane by the proton-coupled divalent cation transporter (DCT1) where it enters an unknown compartment in the cytosol. Ferrous iron is then transported across the basolateral membrane by IREG1, where the membrane-bound copper oxidase hephaestin (Hp) promotes release and binding of Fe3+ to circulating apotransferrin. Except for hephaestin the number of transmembrane domains for each protein is not shown in full. Reprinted from McKie et al., 2000. Copyright (2000), with permission from Elsevier Science.

The ideas of Overton are reflected in the classical solubility-diffusion model for transmembrane transport. In this model [125,126], the cell membrane and other membranes within the cell are considered as homogeneous phases with sharp boundaries. Transport phenomena are described by Fick s first law of diffusion, or, in the case of ion transport and a finite membrane potential, by the Nernst-Planck equation (see Chapter 3 of this volume). The driving force of the flux is the gradient of the (electro)chemical potential across the membrane. In the absence of electric fields, the chemical potential gradient is reduced to a concentration gradient. Since the membrane is assumed to be homogeneous, the... 

Today, there are a wide variety of laboratory protein expression systems available, ranging from cell-free systems over bacterial and yeast cultures to eukaryotic models including the Xenopus oocytes or insect and mammalian cell cultures, some of which even form polarised epithelial-like cells layers. In Table 24.1, an overview of the most important systems, as well as their particular strength and weaknesses in the expression of transmembrane transport proteins is provided. 

With the widespread availability of cell culture facilities, the reduced costs of media and reagents and above all, the commercialisation of a variety of transfection and expression kits, mammalian cells have now become probably the standard for functional studies of transmembrane transporters. Unsurpassed predictivity of the mammalian models may outweigh the higher costs and the lengthiness of the process, compared with bacterial cultures or Xenopus oocytes. Nevertheless, structural studies may require larger amounts than those easily produced in mammalian cells and the appeal of insect cell cultures for... 

The theoretical description of the kinetics of transmembrane transport through a liquid membrane should be based on the principles of solvent extraction kinetics. It should be determined by the processes at both water/membrane interphases and should also involve the intermediate step of diffusion in the membrane. Thus the existence of all these three steps makes the membrane system and its description much more complicated than the relatively simple water/organic phase. However, even the kinetics mechanism in simpler extraction systems is often based on the models dealing only with some limiting situations. As it was pointed out in the beginning of this paper, the kinetics of transmembrane transport is a fimction both of the kinetics of various chemical reactions occurring in the system and of diffusion of various species that participate in the process. The problem is that the system is not homogeneous, and concentrations of the substances at any point of the system depend on the distance from the membrane surface and are determined by both diffusion and reactions. The solution of a system of differential equations in this case can be a serious problem. 

All of the transport systems examined thus far are relatively large proteins. Several small molecule toxins produced by microorganisms facilitate ion transport across membranes. Due to their relative simplicity, these molecules, the lonophore antibiotics, represent paradigms of the mobile carrier and pore or charmel models for membrane transport. Mobile carriers are molecules that form complexes with particular ions and diffuse freely across a lipid membrane (Figure 10.38). Pores or channels, on the other hand, adopt a fixed orientation in a membrane, creating a hole that permits the transmembrane movement of ions. These pores or channels may be formed from monomeric or (more often) multimeric structures in the membrane. 

The amino acid sequences of the glutamate transporters show a high degree of similarity with between 40-60% of amino acid residues identical between subtypes. At present, the three-dimensional (3D) structure of the transporters is unknown and indirect methods based on amino acid sequence hydropathy plots and amino acid accessibility methods have been employed to predict the transmembrane topology of the transporters. Two similar models developed by the groups of Amara (12,13) and Kanner... 

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