Equilibrium and membrane potentials

Donnan EG. Theory of membrane equilibrium and membrane potential in the presence of non-dialysing electrol3des A contribution to physical-chemical physiology. Z Elektrochem. Angewandte Phys. Chem. 1911 17 572-581. 

The movement of solute across a semipermeable membrane depends upon the chemical concentration gradient and the electrical gradient. Movement occurs down the concentration gradient until a significant opposing electrical potential has developed. This prevents further movement of ions and the Gibbs-Donnan equilibrium is reached. This is electrochemical equilibrium and the potential difference across the cell is the equilibrium potential. It can be calculated using the Nemst equation. 

In conclusion, it can be claimed that a combination of kinetic and equilibrium conductance and membrane potential measurements provides a powerful method for investigating the permselective properties of membranes of low fixed charge density. Such methods should be applicable also to other polymers useful in hyperfiltration if they can be prepared in the form of homogeneous membranes. 

Be able to compute the equilibrium state, osmotic pressure, and membrane potentials of proteins and other charged species (Gibbs-Donnan equilibrium) (Sec. 

DONNAN EFFECT, DONNAN EQUILIBRIUM, COLLOIDAL OSMOTIC PRESSURE, AND MEMBRANE POTENTIAL... 

Fig. 30. Regression analysis to show the linear way in which the depolarizations (AV) evoked by both GABA and 5-HT are correlated with an associated decrease in membrane resistance Rm IRm)- The slope of the line is a measure of the difference between equilibrium potential of the putative neurotransmitter ( pni) and membrane potential (Tm). In this instance, the difference is greater than 30 mV in a depolarizing direction. The similarity of the results obtained during iontophoretic applications of GABA and 5-HT raises at least two, equally likely, possibilities. Either the action of 5-HT is mediated by the opening of ionic channels similar to those activated by GABA, or a presynaptic action of 5-HT which causes GABA release. (From Assaf et al, 1980.)...

Ref. [120]. Ref. [158]. Donnan was an Irish physical chemist after whom the Donnan membrane equilibrium and Donnan potential (Sec. 12.7.3) are named. Ref [45]. 

Oyama Y, Walker JL, Eyzaguirre C. Intracellular potassium activity, potassium equilibrium potential and membrane potential of carotid body glomus cells. Brain Res 1986 381 405 08. 

Petrov, J. G. Mobius, D. Interfacial acid-base equilibrium and electrostatic potentials of model Langmuir-Blodgett membranes in contact with phosphate buffer. Colloids Surf., A 2000, 171, 207-215. 

Free Ions Versus Complexed Ions In discussing the ion-selective electrode, we noted that the membrane potential is influenced by the concentration of F , but not the concentration of HF. An analysis for fluoride, therefore, is pH-dependent. Below a pH of approximately 4, fluoride is present predominantly as HF, and a quantitative analysis for total fluoride is impossible. If the pH is increased to greater than 4, however, the equilibrium... 

Potentiometric electrodes are divided into two classes metallic electrodes and membrane electrodes. The smaller of these classes are the metallic electrodes. Electrodes of the first kind respond to the concentration of their cation in solution thus the potential of an Ag wire is determined by the concentration of Ag+ in solution. When another species is present in solution and in equilibrium with the metal ion, then the electrode s potential will respond to the concentration of that ion. Eor example, an Ag wire in contact with a solution of Ck will respond to the concentration of Ck since the relative concentrations of Ag+ and Ck are fixed by the solubility product for AgCl. Such electrodes are called electrodes of the second kind. 

At each phase boundary there exists a thermodynamic equilibrium between the membrane surface and the respective adjacent solution. The resulting thermodynamic equilibrium potential can then be treated like a Donnan-potential if interfering ions are excluded from the membrane phase59 6,). This means that the ion distributions and the potential difference across each interface can be expressed in thermodynamic terms. 

Three kinds of equilibrium potentials are distinguishable. A metal-ion potential exists if a metal and its ions are present in balanced phases, e.g., zinc and zinc ions at the anode of the Daniell element. A redox potential can be found if both phases exchange electrons and the electron exchange is in equilibrium for example, the normal hydrogen half-cell with an electron transfer between hydrogen and protons at the platinum electrode. In the case where a couple of different ions are present, of which only one can cross the phase boundary — a situation which may exist at a semiperme-able membrane — one obtains a so called membrane potential. Well-known examples are the sodium/potassium ion pumps in human cells. 

Figure 11.5 Chloride distribution and the GABAa response. The change in membrane voltage (Fm) that results from an increase in chloride conductance following activation of GABAa receptors is determined by the resting membrane potential and the chloride equilibrium potential (Fci)- (a) Immature neurons accumulate CF via NKCC, while mature neurons possess a Cl -extruding transporter (KCC2). (b) In immature neurons GABAa receptor activation leads to CF exit and membrane depolarisation while in mature neurons the principal response is CF entry and h5q)erpolarisation. This is the classic inhibitory postsynaptic potential (IPSP)...

A close analogy exists between swelling equilibrium and osmotic equilibrium. The elastic reaction of the network structure may be interpreted as a pressure acting on the solution, or swollen gel. In the equilibrium state this pressure is sufficient to increase the chemical potential of the solvent in the solution so that it equals that of the excess solvent surrounding the swollen gel. Thus the network structure performs the multiple role of solute, osmotic membrane, and pressure-generating device. 

When the original compositions of the outer phases are different, the permselective membrane will prevent the complete leveling of these compositions. Some equilibrium component distribution between phases (a) and (p) will be established, and between points A and B a potential difference called the membrane potential (or transmembrane potential) (p will develop. This potential difference is determined by... 

The equilibrium conditions for homogeneous systems with membranes were first formulated in this form by Frederick G. Donnan in 1911. Hence, such equilibria are often called Donnan equilibria, and the membrane potentials associated with them are called Donnan potentials. Sometimes these terms are used as well for the equilibria arising at junctions between dissimilar solutions (Section 5.3). 

We shall write (p) and (q) for the membrane surface layers adjacent to solutions (a) and (p), respectively. Using the equations reported in Section 5.3, we can calculate the ionic concentrations in these layers as well as the potential differences and between the phases. According to Eq. (5.1), the expression for the total membrane potential additionally contains the diffusion potential within the membrane itself, where equilibrium is lacking. Its value can be found with the equations of Section 5.2 when the values of and have first been calculated. 

Membrane permeability for the Cl ions is not in contrast to the conclusion that a simple membrane equilibrium such as that described in Section 5.4.1 is established at the membrane. In fact, the membrane potential calculated for the example above with Eq. (5.26) from the Cl ion concentration ratio is exactly -90mV (i.e., the d ions in the two solutions are in equilibrium, and there is no unidirectional flux of these ions). 

Cells of the type in Scheme 10 represent the simplest case of an ion-selective liquid cell its EMF is often called a membrane, or monoionic, potential [3]. The first term is too narrow due to the fact that the membrane potential corresponds to the behavior of a number of cells, including those of Schemes 8 to 11, and to the cells with solid membranes and with Donnan equilibrium. 

Consider the simple case where both sides of the membrane are in contact with a solution of symmetrical electrolyte BA in a single solvent and the membrane is permeable for only one ionic species. In equilibrium its electrochemical potential (Eq. (3.1.5)) in both solutions adjacent to the membrane has the same value. Thus,... 

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