The cell membrane is permeable to many different ions. Therefore, the equilibrium membrane potential for the case of multiple ions will depend not only on the concentrations of the ions within and outside the cell, but also on the permeability of the cell membrane to each ion (P_i). The Goldmane equation shown, builds off of the Nernst equation to calculate the equilibrium membrane potential for the case of multiple ions. When considering Na⁺ and K⁺ ions, the equation is:

V = (RT/zF) ln((P_NaC_Na,o+P_kC_k,0)/P_NaC_Na,i+P_kC_k,i))

Where the subscripts i and o represent the inside and outside concentrations, respectively (hint: z is still equal to +1 even though two ions are considered). For a cell at rest, PNa is much smaller than PK, with PNa0.01PK. During the depolarization stage of an action potential, the sodium permeability increases drastically, such that PNa=2P_k. Determine (A) the equilibrium membrane potential for a cell at rest, and (B) for a cell during the depolarization stage. Assume the concentrations of sodium and potassium in the cell are 14 mM and 140 mM, respectively. Assume the concentrations of sodium and potassium outside the cell are 140 mM and 4 mM, respectively. Assume the system is at physiological conditions. (Ans: A = -85 mV)