BSCI 426/BIOL 622      Fall '14                          Problem Set 3

assigned:     9/18/14
due:           9/25/14

Membrane electrical potentials:

 1. Plot the pH as a function of distance from a membrane with a surface potential of -100 mV. The salt concentration of the medium is 50 mM KCl and 5 mM MgCl₂. The pH of the medium is 7.0.

2. a) Calculate how many Na⁺ ions would have to be pumped out of a mammalian cell by sodium pumps in the plasma membrane (transfer of 1 net charge per 3 Na⁺ ions) in order for the membrane potential to go from zero to -60 mV, negative in the cytosol. Assume a spherical cell with a diameter of 10 µm. If the [Na⁺] in the cytosol prior to pumping were 20 mM, what would be the final [Na⁺] when the potential reached -60 mV? Assume that there is no other ion flow through the membrane.

b) Calculate how many ions would have to be pumped out of a bacterial cell by the proton pumps in the plasma membrane (1 net charge per proton pumped) in order to increase its membrane potential from zero to -180 mV assuming all other ions are impermeant and that this pump is the only proton permeability pathway through the membrane. Assume the bacterium is a sphere 1micrometer in diameter. How does this number of protons compare with the number of protons in this cell at an intracellular pH of 7? In view of your results, is it possible to generate the potential? Explain.

Note that each sodium ion and each proton carries 1.6x10^-19 Coul. worth of charge.