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BME 314 Lecture 14 2010

# BME 314 Lecture 14 2010 - Krish Roy PhD Associate Professor...

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Bioelectric Phenomena II Krish Roy, PhD Associate Professor Biomedical Engineering

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Learning Objectives At the end of this lecture you should be able: Describe Donan equilibrium Solve ion concentration problems across membranes at Donan equilibrium Discuss the Goldman-Hodgkin-Katz equation Explain simplified models of cells as electrical circuits Solve membrane potential problems using electrical equivalent cell models
Donnan Equilibrium A typical cell is permeable to multiple ions (e.g., K+, Na+, Cl- for the neuron). The Nernst potential for each ion in a cell can be computed individually. However, the membrane potential of the cell is due to the presence of all the ions. Suppose a membrane is permeable to only 2 ions (K+ and Cl-), but not to R+:

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Donnan Equilibrium At equilibrium, the Nernst potentials for K+ and Cl- must be equal (E K = E Cl ) or: E k = kT q ln K + [ ] o K + [ ] i = E Cl = - kT q ln Cl - [ ] o Cl - [ ] i K + [ ] o K + [ ] i = Cl - [ ] i Cl - [ ] o
Example Problem A membrane is permeable to K+ and Cl-, but not to a large cation R+ (like in the figure above). Find the steady-state equilibrium concentration for the following initial conditions:

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BME 314 Lecture 14 2010 - Krish Roy PhD Associate Professor...

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