Membrane potential permeability coefficient

The following factors affect net diffusion of a substance (1) Its concentration gradient across the membrane. Solutes move from high to low concentration. (2) The electrical potential across the membrane. Solutes move toward the solution that has the opposite charge. The inside of the cell usually has a negative charge. (3) The permeability coefficient of the substance for the membrane. (4) The hydrostatic pressure gradient across the membrane. Increased pressure will increase the rate and force of the collision between the molecules and the membrane. (5) Temperature. Increased temperature will increase particle motion and thus increase the frequency of collisions between external particles and the membrane. In addition, a multitude of channels exist in membranes that route the entry of ions into cells. 

The coupled processes described by Eqs. (8), (14), (17), and (22) can be added in (20) as parallel solute transport pathways across the membrane. The phenomenological coefficients (Ly) describe the membrane permeability by these pathways [potential-dependent, Eq. (8) via membrane lipid partition and diffusion, Eq. (14) carrier-mediated, Eq. (17) and convectively coupled, Eq. (22)]. These pathways define parallel resistances through the intestinal barrier in series with precellular resistances to solute transport. 

This theory of an equilibrium of one species between each side of the membrane was formulated by Donnan in 1925 and from then until 1955, it reigned as the theory of membrane potentials. Its demise came when radiotracer measurements showed that all relevant ions (e.g., K+, Na+, and Cl ) permeated more than a dozen actual biological membranes, although each ion had a characteristic permeability coefficient in each membrane (Hodgkin and Keynes, 1953). 

In this table, P represents anions of protein and organic phosphate. The membrane is permeable to the group represented by P. The mean values of the charge on P are -6.7 and -1.08 for the interior and the exterior of the cell, respectively. An electrical potential difference of At// = i/t, t// = 90 mV is measured, i and o denote the intracellular and extracellular, respectively. The activity coefficients of components inside and outside the cell are assumed to be the same, and pressure and temperature are 1 atm and 310 K. Assume that the diffusion flows in from the surroundings are positive and the diffusion flows out are negative. Using tracers, the unidirectional flows are determined as follows ... 

With all of the preliminaries out of the way, let us now derive the expression for the diffusion potential across a membrane for the case in which most of the net passive ionic flux density is due to K+, Na+, and Cl movements. Using the permeability coefficients of the three ions and substituting in the net flux density of each species as defined by Equation 3.16, Equation 3.17 becomes... 

As discussed previously, the different ionic concentrations on the two sides of a membrane help set up the passive ionic fluxes creating the diffusion potential. However, the actual contribution of a particular ionic species to Em also depends on the ease with which that ion crosses the membrane, namely, on its permeability coefficient. Based on the relative permeabilities and concentrations, the major contribution to the electrical potential difference across the plasma membrane of N. translucens comes from the K+ flux, with Na+ and Cl- fluxes playing secondary roles. If the Cl- terms are omitted from Equation 3.20 (i.e., if Pci is set equal to zero), the calculated membrane potential is -154 mV, compared with -140 mV when Cl- is included. This relatively small difference between the two potentials is a reflection of the relatively low permeability coefficient for chloride crossing the plasma membrane of N. translucens, so the Cl- flux has less effect on Em than does the K+ flux. The relatively high permeability and the high concentration of K+ ensure that it... 

Both active and passive fluxes across the cellular membranes can occur simultaneously, but these movements depend on concentrations in different ways (Fig. 3-17). For passive diffusion, the unidirectional component 7jn is proportional to c°, as is indicated by Equation 1.8 for neutral solutes [Jj = Pj(cJ — cj)] and by Equation 3.16 for ions. This proportionality strictly applies only over the range of external concentrations for which the permeability coefficient is essentially independent of concentration, and the membrane potential must not change in the case of charged solutes. Nevertheless, ordinary passive influxes do tend to be proportional to the external concentration, whereas an active influx or the special passive influx known as facilitated diffusion—either of which can be described by a Michaelis-Menten type of formalism—shows saturation effects at higher concentrations. Moreover, facilitated diffusion and active transport exhibit selectivity and competition, whereas ordinary diffusion does not (Fig. 3-17). 

Experimentally, it has been observed that many substances are transported across plasma membranes by more complicated mechanisms. Although no energy is expended by the cell and the net flux is still determined by the electrochemical potential, some substances are transported at a rate faster than predicted by their permeability coefficients. The transport of these substances is characterized by a saturable kinetic mechanism the rate of transport is not linearly proportional to the concentration gradient. A facilitated mechanism has been proposed for these systems. Substances interact and bind with cellular proteins, which facilitate transport across the membrane by forming a channel or carrier. The two basic models of facilitated diffusion, a charmel or a carrier, can be experimentally distinguished (1,2). 

In addition to the ion-clustered gel morphology and microcrystallinity, other structural features includes pore-size distribution, void type, compaction and hydrolysis resistance, capacity and charge density. The functional parameters of interest in this instance include permeability, diffusion coefficients, temperature-time, pressure, phase boundary solute concentrations, cell resistance, ionic fluxes, concentration profiles, membrane potentials, transference numbers, electroosmotic volume transfer and finally current efficiency. 

A good relationship has been established between the number of hydrogen bonds of small model peptides and their permeability coefficients, determined using Caco-2 cell monolayers (Burton et al. 1992). The method reflects the ability of the molecule to form hydrogen bonds with the surrounding solvent. The more bonds the molecule forms with water (luminal fluid), the less potential it has to diffuse into a lipid phase of a membrane. 

Performances of PV membranes are represented by parameters such as separation factor, flux of permeates, and service life. The separation factor of a membrane is a measure of its permeation selectivity (permselectivity) and is defined as the ratio of the concentration of components in the permeate mixture to that in the feed mixture. The component flux is the amount of a component permeating per unit time and unit area, and is given by the product of the permeability coefficient of the membrane and the driving force. The driving force is the gradient in the chemical potential of the components between the feed and the permeate side of the membrane. These values are influenced by operating variables such as temperature, composition of each component in the feed mixture, and permeate side pressures (see Fig. 107). 

In facilitated transport of metal ions through LM, the metal ions are transported through the membrane against their own concentration gradient, termed as the uphill transport. The driving force in such processes is provided by the chemical potential difference of the species other than the diffusing ones on either side of the membrane. The permeability of the transported species is decided by the parameters such as membrane thickness, pore structure, aqueous diffusion coefficient of the species, aqueous diffusion layer thickness, and distribution and diffusion coefficients of the transported species in the LM phase. The diffusion of the species in the carrier solvent depends on the membrane characteristics (viz., porosity and tortuosity) and viscosity of the solvent, while the aqueous diffusion of the metal ions depends upon the flow rate and diffusivity of metal species in the aqueous phase. On the other hand, the overall transport rates of the species can be controlled through various parameters such as feed composition, carrier concentration, and receiver phase composition. 

Proton to alcohol membrane selectivity was first defined by Pivovar et al. [12] as the ratio of proton (ff-V ) to alcohol (F-Vc) flows, which depends chi the protcni membrane conductivity, a, and the permeability coefficient of the alcohol, P, and the corresponding potential and concentraticni gradients through the membrane. 

Whether these discrepancies are due to a lower activity coefficient of potassium inside of the cell as compared with the activity coefficient outside of the cell, or whether they are due to leakage of potassium outside and penetration of sodium inside the cell is not certain. Better agreement between theoretical and actual values can sometimes be obtained by calculating the potential by the Goldman equation rather than the Nernst equation. The Goldman equation does not express the membrane potential in function of the intracellular movements of potassium, but it takes into consideration the participation of other cations, particularly sodium. Thus, in Goldman s equation the potential is expressed as a function of the relative permeabilities and the electrochemical gradients of each ion. 

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