Membrane potential Goldman equation

Equation (3) suggests that the membrane potential in the presence of sufficient electrolytes in Wl, W2, and LM is primarily determined by the potential differences at two interfaces which depend on charge transfer reactions at the interfaces, though the potential differences at interfaces are not apparently taken into account in theoretical equations such as Nernst-Planck, Henderson, and Goldman-Hodgkin-Katz equations which have often been adopted in the discussion of the membrane potential. 

This Goldman-Hodgkin-Katz voltage equation is often used to determine the relative permeabilities of ions from experiments where the bathing ion concentrations are varied and changes in the membrane potential are recorded [5],... 

An equation (also referred to as the constant field equation, the Goldman-Hodgkin-Katz equation, and the GHK equation) which relates the membrane potential (Ai/r) to the individual permeabilities of the ions (and their concentrations) on both sides of the membrane. Thus,... 

If any one ion has a significantly greater permeability than any of the other ions, then the Goldman equation reduces to the Nernst equation for membrane potential. 

If the permeability of one ion is altered, while all concentrations and other permeabihties remain unchanged, the Goldman equation permits one to predict the changes in the membrane potential. For example, consider the... 

Thus, a 10 1 transmembrane gradient of a single monovalent ion, say potassium, will generate a membrane potential of 58 mV. See Resting Potential Action Potential Depolarization Threshold Potential Nernst Equation Goldman Equation Patch-Clamp Technique... 

PERMEABILITY PERMEABILITY CONSTANT MEMBRANE POTENTIAL ACTION POTENTIAL DEPOLARIZATION GOLDMAN EQUATION NERNST EQUATION RESTING POTENTIAL THRESHOLD POTENTIAL PATCH-CLAMP TECHNIQUE Membrane protein dynamics,... 

Goldman equation. An equation expressing the quantitative relationship between the concentrations of charged species on either side of a membrane and the resting transmembrane potential. 

If the permeability is significant for both potassium and sodium, the Nernst equation is not a good predictor of membrane potential, but the Goldman-Hodgkin-Katz equation may be used. 

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

The magnitude of the spike potential is around a hundred millivolts, (a) Following the spirit of the H-H theory, use the Goldman equation to calculate the change in ionic concentration between the outside and inside of the axon that is needed to explain this spike, (b) From this result, calculate the flux of cations per square centimeter of membrane that would have to pass across the membrane to bring about the concentration change. 

The transmembrane potential difference can be described by the Goldman equation that relates t tm to the permeabilities of the membrane to specific ions and the concentrations of such major ions on either side of the PM ... 

Figure 3-7. Passive movements of K+, Na and Cl- across a membrane can account for the electrical potential difference across that membrane, as predicted by the Goldman equation (Eq. 3.20). Usually K+ fluxes make the largest contribution to Em-...

In certain cases, all of the quantities in Equation 3.20 —namely, the permeabilities and the internal and the external concentrations of K+, Na+, and Cl- —have been measured. The validity of the Goldman equation can then be checked by comparing the predicted diffusion potential with the actual electrical potential difference measured across the membrane. 

As a specific example, we will use the Goldman equation to evaluate the membrane potential across the plasma membrane of Nitella translucens. The concentrations of K+, Na+, and Cl- in the external bathing solution and in its... 

Thus, we expect the cytosol to be electrically negative with respect to the external bathing solution, as is indeed the case. In fact, the measured value of the electrical potential difference across the plasma membrane of N. translucens is —138 mV at 20°C (Table 3-1). This close agreement between the observed electrical potential difference and that calculated from the Goldman equation supports the contention that the membrane potential is a diffusion potential. This can be checked by varying the external concentration of K+, Na+, and/or Cl and seeing whether the membrane potential changes in accordance with Equation 3.20. 

Similarly, ENk is -179 mV and ENa is 99 mV (Table 3-1). Direct measurement of the electrical potential difference across the plasma membrane (Em) gives —138 mV, as indicated earlier in discussing the Goldman equation (Eq. 3.20). Because En differs from EM in all three cases, none of these ions is in equilibrium across the plasma membrane of N. translucens. 

Now what s the molecular basis of different permeabilities for different ions This is where the channels come in. Without a specific channel, no ion can effectively cross the membrane, so its permeability will be very small only ions for which specific channels exist will therefore have a say in determining the membrane potential. Furthermore, as ion channels open and close, the changing permeabilities can shift the weight from one ion to the other. The most important example is the transient opening of sodium channels, which according to the Goldman equation will cause the... 

Figure 4.13. Top Gradients of anions, because of their opposite charge, have effects on the membrane potential that are opposite to those of cations. Bottom The Goldman equation for sodium, potassium, and chloride.

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 ... 

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