A muscle cell has an intracellular of 14 mM and an extracellular of 140 mM. Assuming that 2.3 /F = 60 mV, what would the membrane potential be if the muscle cell membrane were permeable only to Na+?
**Core Concept:** The membrane potential of a cell is determined by the concentration gradients and ion permeability of the cell membrane. In this question, we are asked to calculate the membrane potential in a muscle cell when it is permeable only to Na+ ions.
**Why the Correct Answer is Right:** In a muscle cell, the primary ions involved in maintaining the membrane potential are sodium (Na+) and potassium (K+). When the cell membrane is permeable only to Na+ ions, the Na+ concentration gradient will dominate the membrane potential. The Nernst equation helps us calculate the membrane potential (Vm) based on the ion concentrations and their permeability within the cell.
Nernst equation: Vm = (RT/zF) x ln([Na+]0/[Na+]i), where:
- Vm = membrane potential
- R = gas constant (8.314 J/(mol*K))
- T = temperature in Kelvin (assuming room temperature = 298K)
- z = valency of the ion (for Na+, z = 1)
- [Na+]0 = extracellular Na+ concentration (140 mM)
- [Na+]i = intracellular Na+ concentration (14 mM)
**Why Each Wrong Option is Incorrect:**
A. This option incorrectly assumes that the cell membrane is permeable to both Na+ and K+, leading to incorrect calculations.
B. This option also incorrectly assumes permeability to both Na+ and K+, resulting in incorrect calculations.
C. This option erroneously assumes the cell membrane to be permeable to K+, not Na+.
D. This option does not consider the permeability of the cell membrane to Na+ ions, which is the key factor in this question.
**Clinical Pearls:**
1. The Nernst equation is a crucial tool in understanding the membrane potential of cells, particularly neurons and muscle cells.
2. The membrane potential is essential for the proper functioning of cells, particularly neurons and muscle cells, as it influences their ability to transmit signals and contract/relax.
3. Understanding the effects of ion concentrations and permeability in determining membrane potential is essential for clinical practice, as it helps explain physiological processes such as muscle contraction and neuronal transmission.