Intracellular Extracellular

Na+ 12 mM 160 mM
Cl- 7 mM 110 mM
K+ 140 mM 5 mM

1.How do you calculate the equilibrium potential for potassium, K+, under these conditions?

2. Assuming that Na+ is the only ion the plasma membrane of this cell is permeable to, at what voltage will there be no net flux of any ions? Can you give the equation along with how you go about it?

3.Can you calculate (predict) the resting Vm for a neuron with these ion concentrations above (at 37°C). Assume now that the membrane is 20x more permeable to K+ than to Na+, and 100x more permeable to K+ than to Cl-. Again with the equation first.

4. Why is the Vm of this neuron, calculated in #3, closer to EK+, than to ENa+?

5. Assume now that the plasma membrane of this neuron undergoes a rapid change in ion permeability so that it is now 20x more permeable to Na+ than to K+, and 100x more permeable to Na+ than to Cl-. Predict (calculate) the membrane potential under these conditions. Again with the equation first.

I don't know how to do these problems. I need help severly!

For #1, I got E(K+) = 60/+1 * log (5mM/140mM) = -87mV I think this is right but I don't the rest

No problem! I'll walk you through each of the questions step by step.

1. To calculate the equilibrium potential, you can use the Nernst equation:

EK+ = (RT/zF) * ln([K+]out/[K+]in)

Where:
- EK+ is the equilibrium potential for potassium
- R is the gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin (37°C = 310 K)
- z is the valence of the ion (in this case, +1 for potassium)
- F is Faraday's constant (96,485 C/mol)
- [K+]out is the concentration of potassium outside the cell (5 mM)
- [K+]in is the concentration of potassium inside the cell (140 mM)

Plugging in the values:
EK+ = ((8.314 J/(mol·K)) * (310 K) / (1 * 96,485 C/mol)) * ln(5 mM / 140 mM)
EK+ = 58.5 mV * ln(0.036)

Use a calculator to evaluate ln(0.036), then multiply it by 58.5 mV to get the equilibrium potential for potassium (EK+).

2. If only Na+ can pass through the plasma membrane and there is no net flux of any ions, the membrane potential (Vm) will be equal to the equilibrium potential for sodium (ENa+).

ENa+ is calculated using the same Nernst equation, but with the concentrations for sodium:

ENa+ = (RT/zF) * ln([Na+]out/[Na+]in)

Given the concentrations:
[Na+]out = 160 mM
[Na+]in = 12 mM

Plug these values into the equation above to calculate ENa+. The resulting value will be the voltage at which there is no net flux of any ions.

3. To calculate the resting membrane potential (Vm) for a neuron, you can use the Goldman-Hodgkin-Katz (GHK) equation:

Vm = (RT/F) * ln((PNa+[Na+]out + PK+[K+]out + PCl-[Cl-]in) / (PNa+[Na+]in + PK+[K+]in + PCl-[Cl-]out))

Where:
- Vm is the resting membrane potential (the value you want to calculate)
- R is the gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin (37°C = 310 K)
- F is Faraday's constant (96,485 C/mol)
- PNa+ is the permeability of the membrane to sodium
- PK+ is the permeability of the membrane to potassium
- PCl- is the permeability of the membrane to chloride
- [Na+]out, [K+]out, [Cl-]in, [Na+]in, [K+]in, [Cl-]out are the respective ion concentrations inside and outside the cell

Given the permeability ratios and ion concentrations, plug them into the equation and evaluate it to get the resting membrane potential (Vm).

4. The Vm of the neuron calculated in #3 is closer to EK+ because the membrane is more permeable to potassium (20x more permeable to K+ than Na+). As a result, potassium ions have a greater influence on determining the Vm compared to sodium ions. Therefore, the Vm is closer to the equilibrium potential for potassium (EK+).

5. To calculate the membrane potential under the new conditions where the membrane is more permeable to Na+ than K+, you will need to use the Goldman-Hodgkin-Katz equation again, but with updated permeability ratios for sodium and potassium. Consider the given ratios and ion concentrations, and use the equation to calculate the new membrane potential (Vm) under these conditions.

I hope this helps clarify the process for you! Let me know if you have any further questions.