L08 Goldmann 2011 - COPYRIGHT Mammalian Physiology BIOAP...

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1/10 COPYRIGHT Prof. Beyenbach Mammalian Physiology BIOAP 4580 2011 VOLTAGES ACROSS CELL MEMBRANES: The Goldman Equation 1) Diffusion potentials as a voltage source across cell membranes. There are two major mechanisms for generating a voltage across a cell membrane: 1) by the diffusion of electrolytes, and 2) by electrogenic pumps. Voltage generation via the diffusion of electrolytes is illustrated in Fig. 1. The high K + concentrations and low Na + concentrations one finds in the cytoplasm of eukaryotic cells stem from the activity of the Na/K pump (Na/K ATPase). The pump is an exchange pump that extrudes Na + in exchange for K + . As a result, the intracellular [Na + ] is low and the intracellular [K + ] is high. The opposite is true for extracellular concentrations, low in K + and high in Na + , largely generated by the transport activities of the kidney (Fig. 1). Together, the Na/K pump of cell membranes and the kidneys maintain transmembrane concentration differences for K + and Na + , thereby providing outward and inward gradients for K + and Na + respectively – for all cells of the body. Fig. 1. Transmembrane concentration differences generated for K + and Na + by the integrated activities of Na/K pump in cell membranes and the kidneys. At "rest" the cell membrane is primarily permeable to K + , allowing K + to diffuse out of the cell. The outward diffusion K + generates the resting cell membrane voltage (positive outside
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2/10 and negative inside). If the cell membrane were permeable to K + only, then the membrane voltage (V m ) would rise to the equilibrium voltage E K (eq. 1). (eq. 1) At typical intracellular (141 mM) and extracellular (4.7 mM) concentrations of K + , this membrane voltage would be 90.7 mV, negative inside (eq. 2). (eq. 2) (Note that the voltage in eq.2 is positive, reflecting the polarity of the compartment placed in the denominator of the Nernst equation, extracellular fluid positive). However, measured membrane voltages in eukaryotic cells are less than 90.7 mV, let us say 83.9 mV (Fig. 2). A membrane voltage V m less than stems from the fact that cell membranes are permeable to other ions as well. In particular, cell membranes offer some permeability to Na + . Hence, the entry of Na + into the cell under resting conditions lowers the membrane voltage V m towards zero mV, reaching a steady state membrane voltage of -83.9 mV when the cell is “at rest” (Fig. 2). Clearly, Nernst conditions (i.e. ideal permselectivity to just one ion and equilibrium conditions) do not hold true for biological cell membranes. Fig. 2. The dynamic range of membrane voltages. When the membrane is at rest, the membrane voltage V m approaches but does not reach the equilibrium voltage of K + ( = -90.7 mV, neg. inside). The active membrane has V m approaching (but not reaching) the equilibrium voltage of Na + ( = 69.8 mV, pos. inside). The measured membrane voltage (V
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L08 Goldmann 2011 - COPYRIGHT Mammalian Physiology BIOAP...

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