Calculating membrane potential (Vm) given resistance and equilibrium potentials

[NOP90]

Homework Statement

Calculate the membrane potential (Vm) of a cell, given the following resistances and equilibrium potentials (10 marks)

E(K) = -80mV, R(K) = 0.2*10^6 ohms, E(Na) = 60mV, R(Na) = 0.2*10^6 ohms

Homework Equations

Not sure

The Attempt at a Solution

In my texts I have read that they relate some of the workings of a cell to a battery. So I used an equation from my last year physics lectures on electricity:

I = E(Na) - E(K) / R(Na) + R(K)

If I plug in the values I get a current of 3.5*10^-4

The lecture then asks about potential difference, which may translate to membrane potential (given that the lecture is about electricity and not specifically a cell). So I worked out the current in hope that current is needed for another equation. It's worth 10 marks so I'm assuming more than 1 equation will be used.

 

[nate808]

To calculate the membrane potential (Vm) of a cell, we can use the Goldman-Hodgkin-Katz (GHK) equation:

Vm = (RT/F)ln(PK[K]o + PNa[Na]o + PCl[Cl]i) / (PK[K]i + PNa[Na]i + PCl[Cl]o)

Where:
- R is the gas constant (8.314 J/K/mol)
- T is the absolute temperature (in Kelvin)
- F is the Faraday constant (96,485 C/mol)
- PK, PNa, and PCl are the membrane permeabilities of potassium, sodium, and chloride ions, respectively
- [K]o, [Na]o, and [Cl]i are the extracellular concentrations of potassium, sodium, and chloride ions, respectively
- [K]i, [Na]i, and [Cl]o are the intracellular concentrations of potassium, sodium, and chloride ions, respectively

Using the given values, we can calculate the membrane potential as follows:

Vm = (8.314 J/K/mol)(298 K)ln((0.2*10^6)[K]o + (0.2*10^6)[Na]o + 0) / ((0.2*10^6)[K]i + (0.2*10^6)[Na]i + 0)

Since the concentration of chloride ions is not given, we assume it to be 0. Therefore, the equation simplifies to:

Vm = (8.314 J/K/mol)(298 K)ln((0.2*10^6)[K]o + (0.2*10^6)[Na]o) / ((0.2*10^6)[K]i + (0.2*10^6)[Na]i)

Now, we can plug in the given values for [K]o, [Na]o, [K]i, and [Na]i:

Vm = (8.314 J/K/mol)(298 K)ln((0.2*10^6)(4 mM) + (0.2*10^6)(145 mM)) / ((0.2*10^6)(140 mM) + (0.2*10^6)(12 mM))

Simplifying further, we get:

Vm = (8.314 J/K/mol