Membrane potential Nemst equation

Cells create potential differences by pumping ions across membranes. The Nemst equation defines the electrical potential arising from differences in ionic concentration created by the various pumps. It relates the membrane resting potential to the charge and concentration of ions on either side of a membrane. 

The transmembrane potential derived from a concentration gradient is calculable by means of the Nemst equation. If K+ were the only permeable ion then the membrane potential would be given by Eq. 1. With an ion activity (concentration) gradient for K+ of 10 1 from one side to the other of the membrane at 20 °C, the membrane potential that develops on addition of Valinomycin approaches a limiting value of 58 mV87). This is what is calculated from Eq. 1 and indicates that cation over anion selectivity is essentially total. As the conformation of Valinomycin in nonpolar solvents in the absence of cation is similar to that of the cation complex 105), it is quite understandable that anions have no location for interaction. One could with the Valinomycin structure construct a conformation in which a polar core were formed with six peptide N—H moieties directed inward in place of the C—O moieties but... 

Otherwise it has been shown that the accumulation of electrolytes by many cells runs at the expense of cellular energy and is in no sense an equilibrium condition 113) and that the use of equilibrium thermodynamic equations (e.g., the Nemst-equation) is not allowed in systems with appreciable leaks which indicate a kinetic steady-state 114). In addition, a superposition of partial current-voltage curves was used to explain the excitability of biological membranes112 . In interdisciplinary research the adaptation of a successful theory developed in a neighboring discipline may be beneficial, thus an attempt will be made here, to use the mixed potential model for ion-selective membranes also in the context of biomembrane surfaces. 

If the membrane is permselective for a i rticular ion (i), a potential develops ross the membrane which depends on the ratio of activities of the ion on either side of the membrane as describ l by the Nemst equation... 

The principle of pH electrode sensing mechanisms which are based on glass or polymer membranes is well investigated and understood. Common to all potentiometric ion selective sensors, a pH sensitive membrane is the key component for a sensing mechanism. When the pH sensitive membrane separates the internal standard solution with a constant pH from the test solution, the potential difference E across the membrane is determined by the Nemst equation ... 

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 the case of 100% selective membrane and negligible water transport, the membrane potential is given by the Nemst equations (46), respectively (47). 

In general it may be said that for the normal ion exchange membranes there is a concentration area for which the Nemst equation holds true. At high electrolyte concentrations deviations occur due to the participation of the co-ions in the transport. At very low concentrations deviations are found too. As causes are here mentioned the influence of unstirred surface layers and hydrolysis of the charged groups. With membranes of a high permeability to the solvent, the Nemst potential is not reached, because the transport of the solvent reduces the membrane potential. The decrease is some per cent at most. 

The measurement of ion activities assumes chemical equilibrium between the PVC membrane and the electrolyte bearing solutions. The time domain chemical and dielectric space charge changes that occur are minimized by membrane composition and sensor design and are considered negligible during the measurement period. Hence, the potential dependence of the ion activity is characterized by the Nemst equation. The following thermodynamic expressions describe the potentials of the... 

E. Goldman,./. Gen. Physiol. 27 37 (1963). Equation for membrane potentials based on application of the Nemst-Planck equation. 

Thus, because Iresting membrane potential. If this potential does depend only on Cl- ions, the Nemst equation should predict how the membrane potential will change. 

The unequal distribution of K+ and Na+ across plasma membranes gives rise to an electrical potential difference AE. It can be calculated by the Nemst equation (see Chapter 2) ... 

Equation (36) suggests that the membrane potential in the presence of sufficient electrolytes in Wl, W2 and M is primarily determined by the potential differences at two interfaces that depend on ion transfer reactions at the interfaces, although the potential differences at interfaces are not apparently taken into account in theoretical equations such as Nemst-Planck, Henderson and Goldman-Hodgkin-Katz equations which have been often adopted in the discussion of the membrane potential [19,22-25]. 

In the potentiometric-type sensor, a membrane (glass, solid state, liquid) selectively extracts a charged species into the membrane phase, generating a potential difference between the internal filling solution and the sample solution (enzyme layer). This potential is proportional to the logarithm of the analyte concentration (activity) following the well-known Nemst equation. 

K, too), so that the potential is essentially a function of the ion concentration gradient alone. However, this simple relationship will hold only when there is only one diffusible ion species. In a cell, we have several ion species, and finite permeabilities for several of them. The two dominant cations, Na and K, have roughly opposite distributions across the plasma membrane. Application of the Nemst equation to Na and would yield membrane potentials of -1-60 mV and -90 mV, respectively. Yet, the actual resting... 

Figure 4.4. Driving forces in ion diffusion across selectively permeable membranes, a Entropy promotes diffusion down a con-centrationgradient,regardlessof charge, b Electroneutrality will oppose entropy, c The Nemst equation describes the membrane potential that ensues when entropy and electroneutrality are in equilibrium.

An ISE consists of a membrane, an internal reference electrode, and an internal reference electrolyte of fixed activity. The ISE is immersed in a sample solution that contains the analyte of interest, along with a reference electrode. The membrane is chosen to have a specific affinity for a particular ion, and if activity of this ion in the sample differs from that in the reference electrolyte, a potential develops across the membrane that is dependent on the ratio of these activities. Since the potentials of the two reference electrodes (internal and external) are fixed, and the internal electrolyte is of constant activity, the measured potential, E, is dependent on the membrane potential and is given by the Nemst equation ... 

This equation is similar to the Nemst equation except that it simultaneously takes into account the contributions of all three permeant ions. It indicates that the membrane potential is governed by tw o factors (1) the ionic concentrations, which determine the equilibrium potentials for the ions, and, (2) their relative permeabilities, which determine the relative importance of a particular ion in governing where lies. For many cells, including most neurons and immune cells, this equation can be simplified the chloride term can be dropped altogether because the contribution of chloride to the resting membrane potential is insignificant. In this case, the Goldman equation becomes ... 

Note that this equilibrium involves only the membrane potential, and is independent of the pH gradient. Estimation of membrane potential from this Nemst equation involves the determination of the equilibrium concentration gradient of the indicator ion across the membrane, either by the use of isotopes, or by using an electrode in the medium responsive to the decrease in external concentration as the ion is accumulated by the organelle [13,24]. 

The diffusion of charged ions is more complicated because of the law of electroneutrality, which states that the sum of the positive charges on each side of the membrane must equal the sum of the negative charges. In addition to the concentration gradient, the electrical potential difference determines the Bnal equilibrium of a substance across the membrane. Therefore at equilibrium, the concentration of an ionic species may be unequal across the membrane and this gradient will balance the electrical difference across the membrane. The driving force for transport in this situation is defined as the electrochemical potential. The Nemst equation describes the equilibrium situation for ions... 

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