Question

If compartment A represents the inside of a cell and compartment B the extracellular fluid, then with [K]i = 100 mM and [K]o = 10 mM as in the example above calculate the equilibrium potential for potassium.

Answer 1

To find the equilibrium potential for potassium, known as EK, the Nernst equation is used. Given the concentrations, [Ki] = 100 mM and [Ko] = 10 mM, the calculated equilibrium potential for potassium is -58 mV.

Step-by-step explanation:

The question asks for the calculation of the equilibrium potential for potassium (K+), given the intra- and extracellular concentrations. The equilibrium potential can be found using the Nernst equation, which is EK = (RT / F) * ln([Ko] / [Ki]). In this formula, EK is the equilibrium potential for potassium, R is the universal gas constant, T is the temperature in Kelvin, F is the Faraday constant, [Ko] is the extracellular potassium concentration, and [Ki] is the intracellular potassium concentration. We'll assume physiological temperature (310K), and since we know [Ki] = 100 mM and [Ko] = 10 mM, we can plug these into the Nernst equation.

First, we convert the natural logarithm to base 10 (EK = (58 mV) * log([Ko] / [Ki])) because the ln to log conversion involves multiplying by a factor of (RT/F) that, at body temperature, equates to approximately 58 mV. Doing this calculation:

EK = 58 mV * log(10 mM / 100 mM)

EK = 58 mV * log(0.1)

EK = 58 mV * (-1)

EK = -58 mV

The equilibrium potential for potassium is -58 mV, indicating that potassium will move in such a way to pull the membrane potential toward this value. In the context of a cell, this contributes to the resting membrane potential and plays a crucial role in cellular functions such as neuron signaling and muscle contraction.