REVIEW AND PROBLEM SET. Review Question 1. If the membrane potential of a hypothetical cell is –60 mV (cell interior negative):
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1. Here we are told that the cell membrane potential is 60mV
The Nernst Equation (Nernst Equilibrium Potential)
Recall the above equation from Lecture 2. Now let’s refer the concentration on side 1 to the outside of a cell (extracellular conc.), Co and the concentration on side 2 to the inside of a cell (intracellular conc.), Ci. We can rewrite the above equation as:
Now lets simplify the equation: 2.3RT/F at 37°C reduces to ‘60’ and lets keep the valence z in the equation. We can now use this equation to calculate the answers to parts A and C.
Also, note log (10/100) = 1 and log (100/10) = +1
Ci = 1040 mM
The predicted concentration for A+ is 1040 mM but the actual (or measured) value is 7 mM. The value of 1040 mM is far greater than the actual value so this solute is not passively distributed, therefore it must actively pumped out of the cell.
Therefore, the Nernst equilibrium potential for A+ is +70.3 mV
Ci = 80 mM
The predicted concentration for B+ is 80 mM but the actual (or measured) value is 110 mM. The value of 80 mM is less than the actual value so this solute is not passively distributed, therefore it must actively pumped in to the cell.
Therefore, the Nernst equilibrium potential for B+ is 68.3 mV
Ci = 1 mM
The predicted concentration for C++ is 1 mM and the actual (or measured) value is 1 mM. Thus this solute is passively distributed.
Therefore, the Nernst equilibrium potential for C++ is 60 mV
Ci = 1 mM
The predicted concentration for D is 1 mM but the actual (or measured) value is 5 mM. The value of 1 m M is less than the actual value so this solute is not passively distributed, therefore it must actively pumped in to the cell.
Therefore, the Nernst equilibrium potential for D is 18.1 mV
Ci = 10 mM
The predicted concentration for E is 10 mM and the actual (or measured) value is 10 mM. Thus this solute is passively distributed.
Therefore, the Nernst equilibrium potential for E is 60 mV
Ci = 0.2 mM
The predicted concentration for F is 0.2 mM but the actual (or measured) value is 2 mM. The value of 0.2 mM is less than the actual value so this solute is not passively distributed, therefore it must actively pumped in to the cell.
Therefore, the Nernst equilibrium potential for F is 0 mV
G is an uncharged solute, therefore we only need to consider the chemical gradient NOT an electrical gradient. If the solute is passively distributed, at equilibrium, with an extracellular concentration of 4 mM, we would have an intracellular concentration of 4 mM. This is also the measured value for G, therefore this solute is passively distributed. Nernst does not apply.
H is an uncharged solute, therefore we only need to consider the chemical gradient NOT an electrical gradient. If the solute is passively distributed, at equilibrium, with an extracellular concentration of 1 mM, we would have an intracellular concentration of 1 mM. This is less than the measured value for H (3 mM), therefore this solute is actively transported in to the cell. Nernst does not apply
Consider a closed system bound by rigid walls and a rigid membrane separated the two compartments. Assume the membrane is freely permeable to water and impermeable to sucrose.
A) If both compartments contain pure water and a pressure is applied to the piston establishing a hydrostatic pressure difference across the membrane, which direction will water flow in? What will the initial rate of water flow depend on?
B) If no force is applied to the piston and 100 mM sucrose is placed in compartment A, which direction will the meniscus in compartment B move? What concentration of NaCl (also impermeant) would have to be added to compartment B to prevent volume displacement? What hydrostatic pressure must be applied to the solution in compartment A to prevent this volume flow?
Piston
A
B
If both compartments contain pure water and a pressure is applied to the piston establishing a hydrostatic pressure difference across the membrane, which direction will water flow in? What will the initial rate of water flow depend on?
Piston
H2O
A
B
The water will flow from side A to B
The initial rate of flow of water will depend on:
Magnitude of the pressure difference
Area of the membrane (units of pressure – force/area)
Hydraulic conductivity (or water permeability) of the membrane
If no force is applied to the piston and 100 mM sucrose is placed in compartment A, which direction will the meniscus in compartment B move? What concentration of NaCl (also impermeant) would have to be added to compartment B to prevent volume displacement?
100 mM
sucrose
H2O
Piston
B
A
The osmotic pressure of side A > B. Water will flow from low to high osmotic pressure (but high to low water concentration).
50 mM NaCl will be required to negate the osmotic effect of sucrose in side A (actually slightly more than 50 mM because of the incomplete dissociation of NaCl).
Note: (each sucrose molecule = 1 osmolyte, NaCl has 2 osmolytes per mole….MgCl2 has 3 etc. so if the question asked for the concentration of MgCl2 instead of NaCl, your answer would be approx. 33 mM)
What hydrostatic pressure must be applied to the solution in compartment A to prevent this volume flow?
Considering 100 mM sucrose, thus a concentration gradient of 100 mM, at equilibrium, = PH. The hydrostatic pressure that is required to negate the osmotic pressure ( ) required is determined from the van’t Hoff equation: = RTCS = (25.4)CS at 37°C.
(Note: With appropriate conversions one can estimate osmotic pressure using the relation 1 osmole/liter = 19,300mm/Hg = 25.4 atm.)
Therefore with an osmolarity difference of 100 mosmoles/liter = 0.1 osmoles/liter, the pressure required is 2.5 atm.
Consider two compartments of equal volume separated by a membrane that is impermeant to anions and water
A) If in addition the membrane is not permeant to Na+, what is the orientation and the magnitude of the potential difference across the membrane at 37C? What is the composition of compartment B when the system reaches equilibrium?
B) If the properties of the membrane change and now the membrane is only permeant to Na+, what is the orientation and magnitude of the potential difference?
C) If both Na+ and K+ are permeable, but PNa>PK what will be the orientation of the potential difference initially? What will be the orientation of the potential difference and the composition of compartments A and B when electrochemical equilibrium is reached?
100 mM NaCl
10 mM KCl
100 mM KCl
10 mM NaCl
A
B
If in addition the membrane is not permeant to Na+, what is the orientation and the magnitude of the potential difference across the membrane at 37C?
What is the composition of compartment B when the system reaches equilibrium?
A
B


+
+
100 K
10 K

+

+

+
This is an example of an equilibrium potential for K+. At equilibrium there is no change in concentration of the BULK solution. (P.D. 60 mV negative on side B)
If the properties of the membrane change and now the membrane is only permeant to Na+, what is the orientation and magnitude of the potential difference?
A
B

+

+
10 Na
100 Na

+

+

+
This is an example of an equilibrium potential for Na+. (P.D. 60 mV negative on side A)
If both Na+ and K+ are permeable, but PNa>PK what will be the orientation of the potential difference initially? What will be the orientation of the potential difference and the composition of compartments A and B when electrochemical equilibrium is reached?
A
B
100 Na
10 Na
10 K
100 K
*** Impermeable to anions and water
BUT remember …...because PNa>PK ………the potential that develops will be governed by the Na+ permeability
This is an example of a diffusion potential (side B positive) that will collapse over time as the Na+ and K+ gradients collapse. We cannot calculate the precise value for the potential because the question gives us insufficient information….i.e., we do not know the value of the permeability. Electrochemical equilibrium will be reached when the concentration gradients, and consequently the P.D. (potential difference) have collapsed to zero. 55mM NaCl and 55mM KCl in compartments A and B (at zero electrochemical driving force).
What happens to the movement of an ion if the Vm is different from Eion
B
Nernst…..

+
10 X+
100 X+

+

+
Measured value
+30 mV
Out/B
A/in
B/out
EX+
+30
60

+
10 X+
100 X+

+

+
In/A
Even though the Nernst potential dictates the equilibrium to be at 60 mV, if the measured value is +30 mV, there is movement of X from A to B.
10 X
Out
EX
+60
In
+100
Measured value
+100 mV
+ve outward current follows the movement of +ve charge – by convention. Here X is moving IN to the cell.
10 X+
Out
EX
60
90
In
Measured value
90 mV
Here X+ is moving IN to the cell. Electrical gradient>chemical gradient.