This document contains 4 practice problems about membrane potentials and ion concentrations: 1. It asks the reader to calculate equilibrium potentials for Na+, K+, and Ca2+ ions in a muscle cell based on given concentrations, and asks which ion the membrane is most permeable to at the peak of an action potential. 2. It asks the reader to calculate the membrane potential across mitochondria given concentrations of a lipid-soluble ion on both sides of the membrane. 3. It asks whether a neurotransmitter that opens proton channels would be excitatory or inhibitory given internal and external pH levels and the resting potential. 4. It asks about the Nernst equilibrium potential for Cl- in skeletal muscle

1. Practice Problems
1. One use of concentration gradients of ions across cell membranes is to drive the flow
of ions during action potentials of excitable cells. A concentration gradient of ions across
a membrane may be expressed in terms of an electrical potential at equilibrium by use of
the Nernst Equation.
(a). The concentrations of some of the ions inside (I) and outside (o) of a particular
muscle cell are as follows:
Na+o = 140 mM Na+i = 10 mM
+ +
K o = 4 mM K I = 140 mM
2+
Ca2+i = 10-4 mM
Ca o = 1 mM
Calculate the equilibrium potential for each of the ions in the muscle cell.
(b). The actual measured membrane potential for the muscle cell was -90 millivolts.
From this information, what conclusion can you draw concerning the relative
permeabilities of sodium and potassium in these cells at rest (i.e. in the absence of action
potentials) assuming that sodium and potassium are the only ions that contribute to
membrane potentials. Is this last assumption valid?
(c). The value of the membrane potential at the peak of the action potential is +25 mV.
To which ion species is the membrane most permeable at the peak of the action
potential?
2. One way to measure membrane potentials in cells or organelles relies on the use of
lipid-soluble ions like TPP+, which distribute themselves passively across membranes
and achieve transmembrane concentration gradients which depend on the membrane
potential. A suspension of mitochondria is exposed to 10 µM TPP+. At equilibrium, the
intramitochondrial TPP+ concentration is measured as 3 mM. What is the membrane
potential across the mitochondrial membrane?
3. Suppose there were a neurotransmitter which selectively opened channels for
protons. If the external pH is 7.4 and the intracellular pH is 7.0, and the resting potential
is –90 mV, would the transmitter be excitatory (depolarizing) or inhibitory
(hyperpolarizing)?
4. Cl- ions permeate skeletal muscle membranes and are (almost) passively distributed.
In an unstimulated skeletal muscle fiber, where does the Nernst equilibrium potential for
Cl- lie relative to VNa and VK? Does the presence of a chloride permeability have any
effect on the shape of the action potential (assume that the chloride permeability is not
voltage dependent)? Is there a net influx or efflux of Cl- ions during the action potential?
Gamma-amino-butyric acid (GABA) is a neurotransmitter which opens chloride selective
channels (e.g. in spinal cord neurons). In a neuron with a resting potential of –80 mV,
what happens to the membrane potential when GABA is added? Will GABA change the
threshold for action potential generation (assume no direct action of GABA on any
channels other than Cl- channels)? If so, in which direction will the threshold move?