Ion concentrations   Ion Axoplasm (inside)  Blood (outside)
 Potassium  400 mM  12 mM
 Sodium  55 mM  450 mM
 Calcium  0.0001 mM  10 mM
 Chloride  56 mM  550 mM

Question 1.

a) Calculate the Nernst equilibrium potential for each of the above ions. The temperature is 20oC.
1 mark each: 4 total

EX = RT ln [X]o
.........zF.....[X]i

EX = (1.987 cal/deg.mol)(293 deg) ln [X]o
.........z(23,062 cal/volt.mol)................[X]i
OR
EX = (8.315 joules/deg.mol)(293 deg) ln [X]o
.........z(96,485 joules/volt.mol)................[X]i

EK+ = 0.025 ln(12/400) = -0.088 V = -88 mV
ENa+ = 0.025 ln(450/55) = 0.053 V = 53 mV
ECa+2 = 0.0126 ln(10/0.0001) = 0.145 V = 145 mV
ECl- = -0.025 ln(550/56) = -0.058 V = -58 mV

 

b) Calculate the membrane potential (Vm) for a neuron using the Hodgkin-Goldman-Katz equation, the above ion concentrations and the following ion permeabilities:
P(K+) = 1.0
P(Na+) = 0.05
P(Cl-) = 0.55
1 mark.
Vm = RT ln PK[K+]o + PNa[Na+]o + PCl[Cl-]i
.........zF......PK[K+]i + PNa[Na+]i + PCl[Cl-]o

Vm = 0.025 ln 1(12) + 0.05(450) + 0.55(56)
........................1(400) + 0.05(55) + 0.55(550)
= 0.025 ln(65.3/705.25)
= -60 mV

 

c) What would happen to the membrane potential of the neuron if the external K+ concentration was increased to:
24 mM
48 mM
96 mM
1 mark for each calculated Vm and 1 mark for explanation.
At K+ external of 24 mM:
Vm = 0.025 ln 1(24) + 0.05(450) + 0.55(56)
......................1(400) + 0.05(55) + 0.55(550)
= -56 mV

At K+ external of 48 mM:
Vm = 0.025 ln 1(48) + 0.05(450) + 0.55(56)
......................1(400) + 0.05(55) + 0.55(550)
= -49 mV

At K+ external of 96 mM:
Vm = 0.025 ln 1(96) + 0.05(450) + 0.55(56)
......................1(400) + 0.05(55) + 0.55(550)
= -39 mV

Explanation: The resting membrane potential is most dependent on K+ ions. As the external K+ concentration rises the Nernst potential for K+ becomes less as the internal and external K+ concentrations come closer. Therefore as external K+ increases the resting potential becomes more depolarzied away from the original Nernst potential for K+

 

d) Calculate the membrane potential (Vm) for a neuron using the Hodgkin-Goldman-Katz equation, the above ion concentrations and the following ion permeabilities:
P(K+) = 1.0
P(Na+) = 30
P(Cl-) = 0.55
Explain why d) is different than your answer in a) in terms of what is happening to the neuron.
1 mark for calculation and 1 mark for explanation
Vm = 0.025 ln 1(12) + 30(450) + 0.55(56)
......................1(400) + 30(55) + 0.55(550)
= + 44 mV

Explanation: The resting membrane potential is dependent on Na+ ions. As the permeability for Na+ has increased the membrane will now move towards the Nernst potential for Na+

 

e) Poor old calcium is totally ignored in the Hodgkin-Goldman-Katz equation which was designed to calculate the resting membrane potential. Why do you think this is?
1 mark
Calcium is ignored becuase there is little to no leak of Ca+2 across the membrane at rest. Therefore even though there is a strong "driving force" on Ca+2 at rest because there is no permeablity (no conductance), there is no Ca+2 current (flow) into the cell
 

Question 2.

The sensory axons of the five toed dragon (the non-firing breathing species) contain voltage-gated Na+ channels, voltage-gated K+ channels (delayed rectifying) and the regular complement of neuronal leak channels. Scientists at the National Equirer Scientific Academy have been studying these very interesting axons. Use your calculations of Nernst potential and resting membrane potential from Question 1a and 1b for the following questions.
 

a) The scientists depolarize the membrane by 2 mV. Draw the membrane potential response in the axons. (don't forget to label your X and Y axis). Explain your answer in terms of any changes that may occur in membrane conductance/permeability.
1 mark for diagram. 1 mark for explanation.
A diagram shown a small depolarization without an action potential.
Explanation: The depolarization is subthreshold and thus the voltage-gated Na+ channels do not open. There is no change in ion conductance so the membrane potential decays rapidly.
 

b) The scientists depolarize the membrane by 30 mV. Draw the membrane potential response in the axon. (don't forget to label your X and Y axis). Explain your answer in terms of any changes that may occur in membrane conductance/permeability.
1 mark for diagram. 2 marks for explanation. The diagram should show a rising phase after stimulation towards ENa+ then a falling phase back to resting membrane potential. See example in Figure below.
Explanation: a strong depolarizating of 20 mV opens the voltage-gated Na+ channels allowing Na+ influx, which futher depolarizes the membrane and sets up a regenerative cycle of depolarization and Na+ channel opening. As the voltage-gated Na+ channels inactivate then the Na+ influx becomes reduced and the membrane is now more permeable to K+ due to the presence of the leak K+ channels.

 

c) The scientists then alter the external Na+ concentration and then depolarize the membrane by 30 mV. Draw the membrane potential responses in the axon and explain your answers for the following external Na+ concentrations:
225 mM
148 mM
2 mark for diagrams. 2 marks for explanation.
The diagram should show decreasing amplitudes of the action potential peak. As the external Na+ concentration decrease so does the Nernst potential for Na+. Therefore the peak of the action potential becomes lower. At 225 mM Na+: ENa+ = +36 mV. At 148 mM Na+: ENa+ = 25 mV.

 

d) The same scientists take a new prep and add drug X to this preparation. The resting membrane potential goes to the Nernst potential for K+. There are a number of explanations for this interesting observation. Give one explanation, detailing what the drug is affecting and why this changes the resting membrane potential.
2 marks
There are two equally valid answers to this question:
1. The drug blocks the leak Na+ channel. Less Na+ leak/influx means that the resting potential is now completely dominated by K+ and thus the resting potential goes towards the Nernst potential for K+.
2. The drug increase the permability of the membrane to K+ either by increasing conductance through the leak channels or by increasing the number of leak channels. More K+ permeability means that the membrane potential will go towards the Nernst potential for K+.