lipid molecules Experiment, as on your website,

1. Calculate the number of lipid molecules we added to each cell to make the tethered membrane. (5 marks)

Molarity of lipid = 3mM

Volume added = 8?L

2. Calculate the number of molecules of lipid in the tethered monolayer film on gold. (5 marks)

Area per tethered molecule = 1nm2

Area of gold electrode = 2mm2

3. What is the fraction of added phospholipid that is incorporated into the membrane? (3 marks)

4. Calculate the number of molecules of gramicidin in 8?l of a 50nM solution. (5 marks)

5. Assume the same fraction of gramicidin remains as part of the membrane as the fraction of lipids (they are very similar molecular weights), then how many molecules of gramicidin are there in the membrane (3 marks)

6. Calculate the approximate conductance generated per gramicidin (in pS) in the membrane. (4 marks)

Total Siemens generated = 5µS

7. One can calculate membrane thickness from the relationship below between area plate separation and permittivity of a capacitor.

The following results were obtained from the biosensor experiment.

gA (nM) Capacitance (nF)

0 17.6

40 21.9

80 26.4

For a capacitor of area, A (m2) and thickness, d (m) the capacitance, Cm (F) is given by:

Cm = ?0 x ?r x A /d

where ?0 is the permittivity of free space = 8.854 x 10-12 F/m and

?r is the relative permittivity of membrane lipid ~ 2.3 and area A = 3mm2

(a) Calculate the membrane thickness at the three different gramicidin concentrations. (9 marks)

(b) What changes occur to the membrane thickness when more gA is added? Why might these changes be occurring? (4 marks)

Part B – Questions based on calculations in lectures

Q1. The table below shows the current recorded from patch clamp experiments on potassium channels in cultured rabbit lacrimal gland cells at different stimulating membrane potentials.

Current (pA) Membrane potentials (mV)

1.9 60

0.95 50

0.05 40

-0.9 30

-1.85 20

-2.8 10

-3.8 0

-4.8 -10

-5.7 -20

-6.65 -30

-7.6 -40

-8.6 -50

Draw an I – V curve. (8 marks)

Calculate the reversal potential. (2 marks)

Calculate the conductance of this ion channel. (6 marks)

Q2. A human red blood cell has a membrane surface area of about 91µm2 and a membrane thickness of about 110 Aº. If the concentration of urea in the extracellular fluid is 1.6mM, and its intracellular concentration is 0.8mM, calculate the flux of urea in µmoles/sec across the red blood cell membrane. Assume that the diffusion coefficient of urea is 1 x 10-8 cm2/sec. (10 marks)

Q3. During the course of a neurosurgical procedure a drug is applied to the surface of the brain in order to inhibit the activity of a group of neurons that lie 3mm below the surface. Approximately how long will it take the drug to diffuse from the surface to those neurons? Assume the diffusion coefficient of the drug in brain tissue is 3 x 10-4 cm2/sec. (6 marks)

Q4. Calculate the membrane potential (Vm) of a cell, given the following resistances and equilibrium potentials. Need to show all calculations. (12 marks)

EK = – 94mV, RK = 0.5 x 106 O, ENa = 66mV, RNa = 0.5 x 106 O

Q5. If EK = -92 mV and VM = -72 mV what will be the direction and magnitude of the ECDF? (4 marks)

Q6. If ENa = 66 mV and VM = -52 mV what will be the direction and magnitude of the ECDF? (4 marks)

Q7. Draw an I-V plot for two different non-voltage dependent ionic currents IA and IB under the following conditions:

• When the conductance (?) is the same (2pS) for both ions A and B, but equilibrium potentials (-70mV for A, -50mV for B respectively) are different. Label the axes. (5 marks)

• When the equilibrium potentials for both are the same (-40mV) but they have different conductance’s (2pS for A, 4pS for B respectively). Label the axes. (5 marks)

Q8. A cell has a membrane potential of – 68 mV with the concentration of an ion [X+] inside (135mM) and concentration outside (8mM). What will be the direction and magnitude of the ECDF? (8 marks)

Q9. Consider a situation where K+ ion has an intracellular fluid (ICF) concentration of 320 mM and an extracellular fluid (ECF) concentration of 35 mM. What will be the direction and magnitude of the ECDF acting on K+ at Vm = – 82 mV? (8 marks)

Q10. If ICF (K+) ion concentration is 165 mM, what ECF (K+) concentration is required for the condition of no net passive flux of K+ across the membrane at Vm = – 66 mV ? (6 marks)

Q11. What is the Donnan Effect? Two solutions are separated by a membrane permeable to sodium and chloride ions. The concentrations on side 1 are sodium = 100 mM and proteins = 100mM and the concentrations on side 2 are sodium = 100 mM and chloride = 100 mM. At steady state approximate the concentrations of the different species and describe the different forces contributing to this steady state. (10 marks)

Q12. The concentration of carbon at 1 mm into the surface of the titanium slab is 0.25 kg/m3 and at 3 mm the concentration is 0.68 kg/m3. The temperature of the carburizing environment is 925 degrees Celsius, and the rate at which carbon is entering this 2 mm thick region is 1.27 x 10-9 kg/(m2s). What is the diffusion coefficient for this particular treatment? (6 marks)