X, Y, Z are three ions permeable through cell membrane X = –50 and Y = –30. If at RMP, when there is no net electrogenic transfer. What is the value of Z?
**Core Concept**
The resting membrane potential (RMP) is the equilibrium potential at which the membrane is electrically polarized, with the inside being negative relative to the outside. It is determined by the movement of ions across the cell membrane, primarily sodium (Na+), potassium (K+), and chloride (Cl-) ions. The RMP is influenced by the concentration gradients and permeability of these ions.
**Why the Correct Answer is Right**
The RMP is calculated using the Nernst equation, which takes into account the concentration gradients and permeability of the ions. Given that X = –50 and Y = –30, we can assume that Na+ has an equilibrium potential of –50 mV and Cl- has an equilibrium potential of –30 mV. Since there is no net electrogenic transfer, the RMP is equal to the weighted average of the equilibrium potentials of the permeable ions. Assuming that K+ is also permeable and has an equilibrium potential of –90 mV (typical for neurons), we can calculate the value of Z (equilibrium potential of the third ion) as follows: RMP = (X * PNa + Y * PCl + Z * PK) / (PNa + PCl + PK), where PNa, PCl, and PK are the permeabilities of Na+, Cl-, and K+, respectively. Rearranging the equation, we get Z = (RMP * (PNa + PCl + PK)) / PK - (X * PNa + Y * PCl) / PK.
**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it does not take into account the permeability of the ions.
**Option B:** This option is incorrect because it assumes that the RMP is equal to the equilibrium potential of the third ion, which is not necessarily true.
**Option C:** This option is incorrect because it does not consider the permeability of K+.
**Clinical Pearl / High-Yield Fact**
The Goldman-Hodgkin-Katz equation is a modified version of the Nernst equation that takes into account the permeability of multiple ions and is used to calculate the RMP in various cell types. It is an essential concept in understanding the mechanisms of neuronal excitability and synaptic transmission.
**Correct Answer:** C. 0