Question

Imagine that a scientist has two compartments separated by a membrane that is permeable to ions but not to proteins. Imagine further that both compartments contain a pH 7 buffer, and in one of the compartments (compartment A) the experimenter has added proteins that all have pIs greater than 7. Next, the experimenter adds solid KCl to the other compartment (compartment B) and stirs to dissolve the salt and allow it to diffuse into compartment A until an equilibrium (a Donnan equilibrium) is established such that the concentration of potassium ions in B will be greater than that in A and vice versa for chloride ions. Nonetheless, [K+]A*[Cl-]A = [K+]B*[Cl-]B, and thus [K+]A/[K+]B = [Cl-]B/[Cl-]A. The latter two ratios equal what is called r, the Donnan ratio. Accordingly, we can use either ratio in the Nernst equation to solve for the membrane potential when a Donnan equilibrium holds. What is the membrane potential (absolute value in terms of mV to the nearest ones) when r is 1/15? Assume a temperature of 298 K.

Answer 1

The membrane potential at Donnan equilibrium with a ratio of 1/15 is approximately -58 mV, as calculated using the Nernst equation. This value is close to the typical resting membrane potential of cells, commonly -70 mV, which is maintained by the Na+/K+ pump and ion channels.

Step-by-step explanation:

The student is asking about the calculation of membrane potential when a Donnan equilibrium is established. To calculate the membrane potential when the Donnan ratio (r) is 1/15, we use the Nernst equation, which is E = (RT/zF) * ln([ion] outside / [ion] inside), where R is the gas constant, T is the temperature in Kelvin, z is the charge of the ion (for K+, z is +1), and F is Faraday's constant. In this case, the membrane potential can be calculated using the given ratio for potassium or chloride ions, since [K+]A/[K+]B = [Cl-]B/[Cl-]A = r.

Inserting the values into the Nernst equation: E = (8.314 J/mol*K)(298 K) / (1 mol e-*96,485 C) * ln(15) results in a membrane potential of about -58 mV, since we are asked for the absolute value to the nearest ones.

It's important to note that the actual resting membrane potential of cells can vary, with the commonly referenced value being -70 mV due to the actions of ion channels and the Na+/K+ pump that help maintain this potential.