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Membrane Potentials: 10 point assignment:

1) What is a membrane potential? (in your own words)

Membrane potentials are created when opposite charges are stacked across the plasma membrane, as a result of the action of differing Na+ and K+ permeabilities and the ubiquitous Na+/K+-ATPase. In short the membrane on the inside of a cell (intracellular) is slightly negative and the outside (extracellular) is a bit positively charged. This stacking of charge creates a voltage that can be detected by voltage gated channels in excitable cells.

2) Give an example of an excitable and non-excitable cell? How do they differ with respect to voltage gated-ion channels?

All cells have a membrane potential (pump Na+ out of cytosol and K+ into the cytosol). Excitable cells (i.e. neurons or skeletal muscle cells) have large numbers of voltage gated channels on their plasma membranes and can create self-propagating waves of depolarization, called action potentials using these channels. In contrast, non-excitable cells, for example glial cells that create the myelin sheath around an axon or an epithelial cell) lack the ability to create an action potential when depolarized because they lack the required voltage gated channels.

3) Describe (10-20 words each) three different ways membrane potentials are important for cellular function or for that matter cellular dysfunction?

Many examples exist- here are a few

1) When your heart fibrillates it is unable to depolarize and contract in an organized fashion, therefore to fix the problem “defibrillation” may be needed. This entails depolarizing all heart cells, resetting all voltage-gated channels and hoping that the heart returns to its correct pattern/pathway of depolarization and contraction.

2) If a poison prevented Na+ voltage gated channels from opening, you could not create an action potential and could not get your skeletal muscle to contract…..you would not inhale.

3) If you administered excess potassium (K+) by IV drip to a person, it would acutely cause their cells to become much more excitable. Therefore heart cells would be more likely to depolarize and contract.

4) What is a voltage gated channel with respect to membrane potential, permeability and the threshold voltage for its achieving the open state?

Voltage gated channels (VGC) exist for many ions, those for Na+, K+ and Ca++ are most important. The Na+-VGC allows depolarization associated with an action potential, the Ca++VGC permits calcium to enter a cell for exocytosis or contraction, and the K+ VGC is important for return the membrane potential to its hyperpolarized state (around -80 to 130 mv) following an initial depolarization. Hyperpolarization is required to return the VGC to their original resting state before they can be opened again.

5) Why is the Goldman-Hodgkin-Katz equation important for predicting what an excitable cell will do it the intra and extracellular concentration of Na+ and K+ change?

GHK lets you calculate ion concentrations and environmental temperature and make an accurate prediction of what the membrane potential will be. This can be important clinically and this is part of the reason why the doctor carefully monitors the blood plasma concentrations of K+ , Na+ and Ca++ in persons who have either kidney disease (poor ability to regulate these plasma ion concentrations) or heart disease (cells are very sensitive to alterations in these ion concentrations).

Use these values to calculate the following for cell in your body:

Convert log to natural log (ln) --? X 2.303

R- Gas constant R= 1.987 (cal/mole-K)

T= Temperature K= 0C+ 273

F= Faraday constant F= 23,062 (cal/volts-mole)

Remember to convert millimolar to molar (i.e. 19 mM = 0.019 M)

Use the intra/extracellular ion concentrations from your notes for baseline values to answer the questions below. Use the permeability values provided. (show all math)

6) What if you ate a Banana: assume blood plasma K+ changes to 15 mM and plasma Cl- changes to 135mM

Vm=2.303RT/F log 1.0( )o+0.04( )o+0.45( )i

1.0( )i+0.04( )i+0.45( )o

7) What if you ate a Banana: assume plasma K+ changes to 15 mM and Cl- changes to 135mM

But your body temperature was 21 C (yes you would be in severe hypothermia)

Vm=2.303RT/F log 1.0( )o+0.04( )o+0.45( )i

1.0( )i+0.04( )i+0.45( )o

8) Salty Chips: assume plasma Na+ changes to 160mM and Cl- changes to 145 mM

Vm=2.303RT/F log 1.0( )o+0.04( )o+0.45( )i

1.0( )i+0.04( )i+0.45( )o

9) What happens to Vm if a toxin increases PNa (sodium permeability; PNa+) to 0.40? How is this similar to what happens during an action potential?

Vm=2.303RT/F log 1.0( )o+0.40( )o+0.45( )i

1.0( )i+0.40( )i+0.45( )o

10) What happens to PNa+ (sodium permeability) in an excitable cell when the membrane potential changes to the point where it is equal to the threshold for voltage gated sodium channels? Why is this significant? What happens to Vm, when the potassium channels open? Why is it good that the potassium voltage gated channels open “after” the sodium voltage gated channels?

Threshold for a VGC is the membrane potential that it detects as signal to open its gates and become permeable to a specific ion. When this occurs the P-value (permability) to the specific ion changes and the GHK calculation changes. Because Na+ permeability it typically very low, an increase in Na+ permeability has a dramatic effect on the membrane potential (mVolts). Opening of K+ VGC returns the potential to its hyperpolarized state, so all gates can return to their native closed state and this way they are available for a second round of opening. NOTE: it is also very important to remember that VGC only remain open for a very short time and that converting the closed gates to a re-usable closed-gate state only occurs if the VGC can be hyperpolarized again.

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