Human Physiology
Homework I: Movement of molecules across cell membrane
Questions
1. Draw a simple cell in the space below.
Indicate whether concentrations of Na+ is higher inside the cell or outside. Repeat for K+, and Cl-.
Indicate the electrical potential difference across the cell membrane at equilibrium.
2. Now let us consider an artificial case. Only potassium channels are open. Sodium channels are
closed. Indicate ion distribution across the cell membrane. Why potassium ion concentration
does not equilibrate across the cell membrane?
3. Let us consider another artificial case. Now only sodium channels open. Potassium channels
are closed. Indicate ion distribution across the cell membrane. Why sodium ion concentration
does not equilibrate across the cell membrane?
4. Let us consider another artificial case. Now only chloride channels open. Other channels are
closed. Indicate ion distribution across the cell membrane. Why chloride ion concentration does
not equilibrate across the cell membrane?
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Human Physiology
Homework I: Movement of molecules across cell membrane
5. Now both potassium and sodium channels open and stay open. What would happen with
potassium ion concentration? Will it equilibrate across the cell membrane?
Yes or No
Will Sodium concentration equilibrate across the cell membrane?
Yes or No
6. Now potassium and chloride channels open and stay open. What would happen with potassium
ion concentration? Will it equilibrate across the cell membrane?
Yes or No (no calculations necessary)
Will Sodium concentration equilibrate across the cell membrane?
Yes or No (no calculations necessary)
Will Chloride concentration equilibrate across the cell membrane?
Yes or No (no calculations necessary)
7. Now potassium, sodium, and chloride channels open and stay open. What would happen with
potassium ion concentration? Will it equilibrate across the cell membrane?
Yes or No (no calculations necessary)
Will Sodium concentration equilibrate across the cell membrane?
Yes or No (no calculations necessary)
Will Chloride concentration equilibrate across the cell membrane?
Yes or No (no calculations necessary)
8. In the space below explain the conditions that give rise to the resting membrane potential.
What is the role of membrane permeability in regulating membrane potential?
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Human Physiology
Homework I: Movement of molecules across cell membrane
9. Calculate osmolarity of the following solutions:
1. 1mole of NaCl was added to 1L of water.
2. 1 mole of CaCl2 was added to 1L of water.
3. 1 mole of CaCl2 was added to 2L of water.
4. 1 mole of CO2 was added to 1L of water.
5. 1 mole C6 H12 O6 glucose was added to 1L of water.
6. 0.3 mole of NaCl was added to 1L of water.
7. 0.15 mole of NaCl was added to 1L of water.
Prove to yourself that movement of very few ions across cell membrane is
associated with dramatic changes in cell membrane electrical potential. The
solution is provided.
Optional Problem 1. Question: You have isolated a spherical cell with radius 10 µm (10*10
-6 m) filled with 100 mM K+. Calculate the number of K+ ions that have to cross cell
membrane to change membrane potential by 100mV (from 0mV to negative 100mV).
Answer: You may follow these steps to solve the problem:
A. Calculate cell capacitance.
Here is information you need. Surface of the sphere S =4 Pi * R2. Typical cell membrane
capacitance is 1 uF/cm 2
C= (1 uF/cm 2)*S
R= 10µm= 1 * 10 3 cm
S =4 Pi * R2 =4* 3.14 * (10 -3)2 cm2= 12*10-6 cm2
C=(1 uF/cm 2)*S = (1 uF/cm 2) * 12*10-6 cm2 = 12*10-6uF = 12*10 -12F
B. Calculate the charge Q that has to cross cell membrane to depolarize it by voltage V.
Recall definition of capacitance C: C=Q/V;
Note we can use this formula because positive ions don’t diffuse away from the cell. What
force holds positive ions on the outside of the cell membrane? It is electrostatic force from
negative ions located on the inside of the cell membrane.
Q = C * V = 12*10 -12 F*0.1V = 1.2 * 10 -12coulomb
This is the charge that sits across cell membrane and generates 100mV. The ions that
generate this charge have diffused from inside the cell to outside.
C. Finally calculate the number of ions N that carry this charge Q
Recall that every ion carries one elementary charge, that is the charge equal to the charge of
electron - 1.6 * 10 -19 coulomb
N = 1.2 * 10 -12coulomb / 1.6 * 10 -19 coulomb = 7.5*106 univalent ions
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Human Physiology
Homework I: Movement of molecules across cell membrane
Optional Problem 2
Question: Using the solution to the problem above calculate the proportion of K+ ion that
left the cell, that is calculate (N/Ntotal) where Ntotal is total number of K+ ions in the cell
Answer: To solve the problem recall that volume of the spherical cell V can be calculated as
V = 4/3 Pi * R3
V = 4/3 *3.14 * (10-3cm)3 = 4.2 *10-9cm3
Also recall that in 1 liter of 1 Molar solution of K+ there are 6 * 1023 K+ ions. Now you only need
to calculate the volume of the cell in liters (1 liter = (10 cm ) 3 = 103 cm3 ) and don't forget that
the cell is filled with 100mM K+ not 1M.
V = 4.2 * 10 -12 liters
If 1M solution: Ntotal = 6 * 1023 K+ ions/liter * 4.2 * 10 -12 liters = 2.5 * 10 12 ions
Since 100mM: Ntotal = 2.5 * 1011 ions
N/Ntotal = 7.5*106 / 2.5 * 1011 =3 * 10-5 = 0.003%
Note that only a small number of ions, 0.003% of all ions, have to diffuse out of the cell to
depolarize membrane potential from 0mV to negative 100mV.
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