Question

1. At the peak of an action potential, the membrane potential of a human motor neuron reaches about +30mV. What value for “alpha”, the ratio of PNa/PK, allows this to occur. Use an online calculator/simulation to find a value for alpha that approximates what happens to reach this membrane potential, and write out the entire GHK equation (the version with just sodium and potassium) that can produce this membrane potential, including normal ion concentrations and temperature.

Answer 1

If we take two electrodes and place on either side of the cell plasma membrane we can observe potential difference across membrane. mostly resting potential difference is about 30 to 90 mV. inside of cell is more negative .

Thus, resting membrane potential is -30to – 90 mV

Nernst equation can no longer be used to calculate potential, When a membrane is permeable to two different ions, then we can now apply the GHK equation. This equation describes the potential across a membrane which is permeable to   Na+ and K+

Vm = 60log   [K+]0+α[Na+]0                                            [K+]i+α[Na+]i

                                                                                                           

Where α = PNa/Pk

If permeability of membrane to Na+ is 0, then alpha in the GHK is 0, and the Goldman-Hodgkin-Katz equation reduces to the Nernst equilibrium potential for K+. If the permeability of the membrane to Na+ is very high and the potassium permeability is very low, the [Na+] terms become very large, dominating the equation compared to the [K+] terms, and the GHK equation reduces to the Nernst equilibrium potential for Na+.

If membrane potential is more positive at rest the membrane ids depolarized, if negative membrane is hyperpolarized. Thus potential of + 30 indicates depolarization.