L07 Volt to Conc 2011

# L07 Volt to Conc - COPYRIGHT Mammalian Physiology BIOAP 4580 2011 Prof Beyenbach THE NERNST EQUATION FROM VOLTAGE TO CONCENTRATION DIFFERENCE 1

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1/7 COPYRIGHT Prof. Beyenbach Mammalian Physiology BIOAP 4580 2011 THE NERNST EQUATION FROM VOLTAGE TO CONCENTRATION DIFFERENCE 1) Concentration differences and voltages. Under Nernst conditions, a concentration difference can give rise to a voltage difference. The corollary, a voltage giving rise to a concentration difference is considered below in Fig. 1. Compartments 1 and 2 are separated by a membrane that is selectively permeable to Na + (permeable to Na + only, i.e. Na + -selective). The membrane is placed in an electrical field of 100 mV by an external battery. Reversible Cl-electrodes (vide infra) provide electrical continuity between electron flow (current) in the external circuit (wire) and ionic current flow in aqueous solutions and across the membrane. Since only Na + ions can pass through the membrane, and since cations move to negative poles, it follows that ionic Na + current flows from compartment 1 to 2. As a result the Na + concentration in compartment 2 will rise and continue to rise until the inward electrical pull (1 to 2) is equal to the outward concentration push (2 to 1). Note, electrical pull versus concentration push. Fig. 1. A voltage gives rise to a Na + concentration difference. The membrane is permselective to Na + . Upon the application of a voltage of 100mV across the membrane, Na + moves from left to right. When the electromotion of Na + from 1 to 2 equals the diffusion of Na + from 2 to 1, the equilibrium condition is reached and there is no net movement of Na + across the membrane. The equivalence of electrical and chemical potentials is again described by the Nernst equation (eqs. 1-3). However, since voltage is the initial driving force, a concentration difference is generated. This voltage-equivalent concentration difference can be calculated by the Nernst equation (eqs. 1-3).

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2/7 (eq. 1) (eq. 2) (eq. 3) Thus, a voltage of 100 mV raises the Na + concentration in compartment 2 from 261 mM to 510 mM while reducing the Na + concentration in compartment 1 from 261 mM to 12 mM. The Na + concentration in compartment 2 is therefore 42.5 times bigger than the Na + concentration in compartment 1, which is expected for the x-fold concentration difference supported by 100 mV when a monovalent ion is at electrochemical equilibrium (Fig. 1). When solving these types of problems, be sure to have the voltage carry the sign (+ or -) of that compartment you place in the denominator of the Nernst equation (see eq. 2). 2) Electroneutrality. Solutions are electrically neutral, i.e. the number of cations equals the number of anions, and for currents of electrons and ions to flow in Fig. 1 there must be a "closed" electrical circuit. A closed circuit is provided in the example of Fig. 1 by way of reversible Ag/AgCl electrodes. Reversible Ag/AgCl electrodes provide bridges (continuity) between the flow of electrons in the wire and the flow of ions in solution. Doing so, the electrodes also serve the maintenance of electroneutrality of solutions. For each Na
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## This note was uploaded on 04/09/2011 for the course BIOAP 4580 taught by Professor Beyenbach,k. during the Spring '11 term at Cornell University (Engineering School).

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L07 Volt to Conc - COPYRIGHT Mammalian Physiology BIOAP 4580 2011 Prof Beyenbach THE NERNST EQUATION FROM VOLTAGE TO CONCENTRATION DIFFERENCE 1

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