Transmembrane Potential across Cell Membranes

Up to now in this chapter, we have concentrated on the measurement via electric field sensitive dyes of the transmembrane electrical potential, which by itself should produce a linear drop in the electrical potential across a membrane. However, at least through the lipid matrix of a cell membrane, the electrical potential, /, at any point does not change linearly across the membrane. Instead, it follows a complex profile (see Fig. 6). This is due to contributions other than the transmembrane electrical potential to /. The other contributions come from the surface potential and the dipole potential. Both of these can also be quantified via electric field sensitive dyes. 

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... 

Each of their receptors transmits its signal across the plasma membrane by increasing transmembrane conductance of the relevant ion and thereby altering the electrical potential across the membrane. For example, acetylcholine causes the opening of the ion channel in the nicotinic acetylcholine receptor (AChR), which allows Na+ to flow down its concentration gradient into cells, producing a localized excitatory postsynaptic potential—a depolarization. 

The transmembrane potential of cardiac cells is determined by the concentrations of several ions—chiefly sodium (Na+), potassium (K+), calcium (Ca2+), and chloride (Cl-)—on either side of the membrane and the permeability of the membrane to each ion. These water-soluble ions are unable to freely diffuse across the lipid cell membrane in response to their electrical and concentration gradients they require aqueous channels (specific pore-forming proteins) for such diffusion. Thus, ions move across cell membranes in response to their gradients only at specific times during the cardiac cycle when these ion channels are open. The movements of the ions produce currents that form the basis of the cardiac action potential. Individual channels are relatively ion-specific, and the flux of ions through them is... 

Fig. 5. Tentative mixed potential model for the sodium-potassium pump in biological membranes the vertical lines symbolyze the surface of the ATP-ase and at the same time the ordinate of the virtual current-voltage curves on either side resulting in different Evans-diagrams. The scale of the absolute potential difference between the ATP-ase and the solution phase is indicated in the upper left comer of the figure. On each side of the enzyme a mixed potential (= circle) between Na+, K+ and also other ions (i.e. Ca2+ ) is established, resulting in a transmembrane potential of around — 60 mV. This number is not essential it is also possible that this value is established by a passive diffusion of mainly K+-ions out of the cell at a different location. This would mean that the electric field across the cell-membranes is not uniformly distributed.

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. 

The transient change in the transmembrane potential upon excitation. An action potential cycle consists of a transient depolarization of the cell membrane of an excitable cell (such as a neuron) as a result of increased permeability of ions across the membrane, followed by repolarization, hyperpolarization, and finally a return to the resting potential. This cycle typically lasts 1-2 milliseconds and travels along the axon from the cell body (or, axon hillock) to the axonal terminus at a rate of 1-100 meters per second. See Membrane Potential... 

Membranes play essential roies in the functions of both prokaryotic and eukaryotic cells. There is no unicellular or multicellular form of life that does not depend on one or more functional membranes. A number of viruses, the enveloped viruses, also have membranes. Cellular membranes are either known or suspected to be involved in numerous cellular functions, including the maintenance of permeability barriers, transmembrane potentials, active as well as specific passive transport across the membranes, hornione-receptor and transmitter-receptor responses, mitogenesis, and cell-cell recognition. The amount of descriptive material that might be included under the title of biological membranes is encyclopedic. The amount of material that relates or seeks to relate structure and function is less, but still large. For introductory references see Refs. 53, 38, 12, 47, 34, 13. Any survey of this field in the space and time available here is clearly out of the question. For the purposes of the present paper we have selected a rather narrow, specific topic, namely, the lateral diffusion of molecules in the plane of biological mem-branes.38,12,43,34 We consider this topic from the points of view of physical chemistry and immunochemistry. 

Because three Na+ ions move outward for every two K+ ions that move inward, the process is electrogenic—it creates a net separation of charge across the membrane. The result is a transmembrane potential of —50 to —70 mV (inside negative relative to outside), which is characteristic of most animal cells and essential to the conduction of action potentials in neurons. The central role of the Na+K+ ATPase is reflected in the energy invested in this single reaction about 25% of the total energy consumption of a human at rest ... 

If f<total potential difference applied across the cell is developed across the membrane capacitance. In this limit, the induced membrane potential AV across a spherical cell is AV = 1.5 ER, where E represents the applied external field. Thus the cell samples the external field strength over its dimensions and delivers this integrated voltage to the membranes, which is a few mV at these low frequencies for cells larger than 10 ym and external fields of about 1 V/cm. These transmembrane potentials can be biologically significant. 

Bioelectric Organization of Nervous Tissue. The membrane potential of 70 mV is developed across the lipid bilayer of the cell membrane. This layer is approximately 40 8 thick, so that the transmembrane electric gradient is of the order of 105 V/cm. This extraordinary dielectric strength is not easily replicated in artificial materials. It is noteworthy that the resting membrane potential maintains this dielectric bilayer within a factor of two of electrical breakdown (19). Release of neural transmitter substances from synaptic terminals on the nerve cell surface transiently shifts the membrane potential at the site of release by a few millivolts. In terms of an altered transmembrane gradient, this shift is of the order of 1.0 kV/cm. 

Action on the plasma membrane is the first and most fundamental of the bewildering array of deleterious effects of the cinnamic and benzoic acids. They reduce the transmembrane electrochemical potential with the immediacy and extent of that action depending on the concentration and lipid solubility of the compound.35,37,45,60 Rate of uptake also is concentration and pH-dependent, with transfer into and across the membrane greatest with lower pH conditions and higher external concentrations.60 Phenolic acid-induced depolarization of membranes causes a nonspecific efflux of both anions and cations accompanying the increased cell membrane permeability, and these membrane effects correlate with an inhibition of ion uptake. The phenolic acids suppress absorption of phosphate, potassium, nitrate, and magnesium ions, and overall changes in tissue... 

Notably, all these characteristic alterations are conferred by cell membranes particularly the cytoplasmic membrane that is basically a lipid-bilayer structure imbedded with certain proteins. The lipid-bilayer forms a barrier to surround and protect the cell contents and the transmembrane proteins are responsible for the cell communications with the environment. For example, receptor proteins mediate the growth signals produced by growth factors and mitogens and any other stimuli. Ion channel proteins control the flux of ions across the cytoplasmic membrane to regulate membrane potential, osmolar-ity (or cell volume), etc. 

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