2016 exam

Question 1

What must be true for a cell to disregard spatial variations in concentrations and adopt a non-spatial description of your system.
Name the assumption
Explain what it mean mechanistically / what is assumed

Answer 1

The well-stirred assumption

• the concentration is the same everywhere
• the probability that a molecule is found is the same everywhere
• the frequency/rate of molecular collisions are much larger than the rate of reactions

Question 2

Describe how to model sodium diffusion in a large spherical neuron and how to keep down computational work

Answer 2

Draw spherical iso-concentration cells
Use a spherical coordiante system to get only diffusion along the radial direction.
Use one-dimentional diffusion between the shells
The spherical core volume might have a different radius than the thickness of the shells
Add Na channels as Na sources to the cell membrane

Question 3

Write the stoichiometric matrix for
2A -> 2B + C
C -> 2D + E

And give the equilibrium constant

Answer 3

-2 1 1 0 0
0 0 -1 2 1

j = 0 gives All right = k1/k2 = b*c^2/a

Question 4

Ion species Inside (mM) Outside (mM)
Na+ 10 100
K+ 200 100
Cl- 100 200
A- 110 0

The plasma membrane is permeable to K+ and Cl- but not for Na+ and A-.
The cell is in electrochemical equilibrium, and space charge neutrality holds. Show this. (2p)
One aspect of the system is not in balance, which?

Answer 4

Donnan equilibrium holds:
[K_out/K_in]^1 = [Cl_out/Cl_in]^-1 e.g. 100/200 = 100/200

Space charge neutrality holds:
Charges inside: 10+200-100-110 = 0
Charges outside: 100+100-200-0 = 0

Osmotic balance is not in place:
Inside: 10+200+100+110 = 420
Outside: 100+100+200 = 400

Question 5

Give the equation that describes the current through a cloride leak channel. Leak channels are
linear channels, that is they have a purely linear (ohmic) voltage dependence.

Moreover, make a figure of the electrical equivalent circuit for a very small cell that only has
this channel.

Assume the cell above has a resting potential of -65 mV. If chloride has a reversal potential of
-65 mV in this cell, what is the effect on the cell if you close the chloride channel by adding a
chemical compund that blocks (makes the permeability zero) the channel? For this blocked case,
write the equation for the membrane time constant of the small cell above.

Answer 5

I = Gcl * (V - Vcl)

in
---------------
|        |       |
|        -    Gcl
Rm -Cm   |
|        |       - Vcl
|        |      ---
|        |       |
---------------
        |
out ---

The effect is that the total membrane resistance (input resistance) gets higher since you are closing a
conductance.
Membrane time constant tau_m = Rm * Cm

Assume the text indicates there are no other channels including leakage channels. Closing the Cl
channel thus means there is no leakage at all. This means R_m=infinity and tau thereby also is infinity.

Question 6

In a neuron, the following concentration values (in mM) have been measured

[K+]in = 168 , [Na+]in = 50 , [Cl-]in = 41 , [K+]out = 6 , [Na+]out = 337 , [Cl-]out = 340.

At rest, PK : PNa : PCl = 1 : 0.019 : 0.381. You can assume a temperature of 20 degrees C. What
concentration of external potassium [K+]out should you use to produce a depolarization of +10
mV from the potential present at rest?

Answer 6

Vrest = 58log[(16 + 0.019337 + 0.38141) / (1168+0.01950+0.381340)]=-59.6mV

We seek the concentration at Vrest = -49.6mV.

Kout = exp(-49.6/58) (0.01950+0.381340) - (0.019337 + 0.381*41) = 19.6.

Question 7

Ralls model, semi infinite

Answer 7

d(3/2, p) = ∑d(3,D)/2

Gn = 1/(lambda*ri)

Question 8

Finite cylinder, sealed end

Answer 8

Gn = 1/lambda*ri * tanh(L)
L = l v o/lambda v o + l v 11/lambda v 11 + l v 211/lambda v 211