Electrostatic potential across the membrane

The potential arises from the difference in surface charges on the two sides of the two leaflets. A popular theory often employed is the Guoy-Chapman theory, which is based on a continuum model description of the solvent and employs the Poisson-Boltzmann equation. 

As the environment inside the lipid bilayer is hydrophobic, it has a low static dielectric constant and therefore the electrostatic field across the membrane does not become screened as in bulk water. 

In the same vein, the variation of the diffusion coeflBcient of species across the lipid membrane cannot be explained by employing hydrodynamic expressions, such as the Stokes-Einstein relation. Here one would need to consider the free-energy barrier for entrance into the layer for each species, charged (positive or negative) and neutral the free-energy barrier is expected to be different even for same-sized species. The lipid bilayer diffusion series (LBDS) given by Eq. (12.2) is a manifestation of such microscopic effects. 

The role of water molecule as a lubricant of life is at its best in the lipid bilayers. The large-scale motions needed for the functioning of the lipids such as the transport of large molecules would not be possible without the small size and fast motion of water molecules. Even when slow, water moves faster than all other species. 

Membrane water-penetration profiles from spin labels. Eur Biophys J., 31 (2002), 559-562. 

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Electrogenic transporters are membrane transport proteins that effect transport reactions that involve overall charge transport. Thus for electrogenic transport reactions the reaction is influenced by (and influences) the electrostatic potential across the membrane and the second term on the right-hand side of Equation (7.17) is non-zero. 

Figure 21.7 The cell membrane of a nerve acts as a capacitor. The membrane Is composed of lipids that, like oil, have a low dielectric constant. If the inside and outside solutions have different electrostatic potentials, there is a gradient of electrostatic potential across the membrane. 

But second, the additional implication of Equation (22.48) is that the electrostatic potential across the membrane can depend not only on the salt concentrations on the two sides, but also on the rates of ions flowing across the membrane. This is called a diffusion potential. Table 22.2 lists ion mobilities u in water at 25 °C. 

The electrostatic potential across cell membranes plays important roles in transport and in cell signaling. Muscle contraction is stimulated by depolarization of the cell membrane. Nerve cells communicate with other cells via propagated changes in membrane potential. Also the potential across membranes of intracellular organelles, such as mitochondria, can be central components of the function of the organelles. 

The potassium ion concentrations are approximately 140 mM within the cell and 5 mb in the plasma outside the cell. Consequently, at body temperature of 37°C the electrostatic potential across the cell membrane, referred to as the membrane potential, is... 

Donnan dialysis In Donnan dialysis, a cation-exchange membrane separates the donor and receptor solutions. Cationic metal species are transported across the membrane driven by the negative electrostatic potential (the Donnan potential) across the membrane, until equilibrium is achieved. Matching of the ionic strengths of donor and acceptor solutions is necessary. Since cationic species exchange readily compared to neutral and anionic species, it is claimed that the measurement more closely relates to the free metal ion. 

The polar lipid headgroup zone contains the phospholipid and steroid phosphorus-nitrogen, carbonyl, hydroxyl and hydration water moieties which combine to establish a substantial dipolar potential. This positive potential is of a magnitude of several hundred millivolts across the membrane headgroup zone. In the membrane hydrocarbon interior, the electrostatic field must be at least 450 to 750 mV (14) and controls ion current across the interior as we 1 1 as possibly influencing selective ion adsorption to the membrane surface. 

However, if ions move down the concentration gradient (from the inside to the outside of the cell) an electrostatic imbalance will be created, resulting in more positive charges outside of the cell than inside. The resulting electrostatic force will drive the positive potassium ions across the membrane from outside to inside. In thermodynamic equilibrium, the concentration driven potential is exactly balanced by the electrostatic potential, a situation illustrated in Figure 1.3. 

Figure 6. Schematic potential seen by a hydroxyl ion as it moves across a Nafion perfluorinated membrane in a chlor-alkali cell. This potential consists of two parts a constant sloping portion that arises from the voltage drop across the membrane and an oscillating part that arises from electrostatic restriction of the hydroxyl ions. Physically, the hills and troughs correspond to the channel and cluster regions, respectively. For simplicity, a one-dimensional, periodic, model potential is used to evaluate the membrane current efficiency although the real potential is three-dimensional and aperiodic.

The membrane is permeable for the ionic species K and the solvent, i.e. water molecules. When an uncharged membrane is placed between two solutions containing two different activities and of species K, then a phase transfer of charge carriers occurs. The direction of this transfer depends on the gradient of the electrochemical potential. This results in a charging of the phase boundary and creation of an electric field. The initially favoured ion transfer will be slowed down and in the end a further net transfer will be stopped because of electrostatic repulsion forces, and the forth and back transfer of ions will cancel. In electrochemical equilibrium both reactions have the same rate, and the potential difference is constant. Assuming that (i) no temperature or pressure gradient exists across the membrane, (ii) the solvent in both solutions is the same, e.g. water and (iii) no diffusion potential within the membrane occurs, then the electrochemical potentials in the two phases are equal in case of electrochemical equilibrium ... 

In the next section we use the Nernst-Planck equation to show that the electrostatic potentials across membranes depend not only on the difference in ion concentrations, but also on the ion mobilities. 

Integrating both sides of Equation (22.47) over x, across the membrane gradients both of concentration and electrostatic potential, gives... 

Another important class of proteins that contain water channels are the aquaporins, which regulate the flow of water in and out of cells. They will let water through but not salts or other dissolved substances, and as such, they act as molecular water filters. Water transport occurs via a chain of nine hydrogen-bonded molecules (Fig. 6.13). But if this chain were to permit rapid transmembrane proton motion, that would disturb the delicate charge balance across the membrane. So aquaporin must somehow disrupt the potential proton wire that threads through it. The mechanism has been much debated, but it now seems that the inhibition of proton transport is dominated by electrostatic repulsion by positively charged groups in a narrow constriction in the middle of the pore [72]. 

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