At a temperature of 10∘C, the concentrations of ions are:
IonIntracellularExtracellular
Na61485
K28010
Cl51485
The transmembrane potential is -30 mV.
How many ion species (Na, K, or Cl) are NOT in equilibrium?
To determine which ion species (Na, K, or Cl) are not in equilibrium, we need to compare their actual transmembrane potentials with their equilibrium potentials. The equilibrium potential for an ion can be calculated using the Nernst equation:
Equilibrium potential (Eion) = (RT/zF) * ln([ion]outside/[ion]inside)
where:
- R is the gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin (10°C = 283.15 K)
- z is the charge of the ion
- F is the Faraday constant (96485 C/mol)
- [ion]outside is the concentration of the ion outside the cell
- [ion]inside is the concentration of the ion inside the cell
Let's calculate the equilibrium potentials for Na, K, and Cl.
For Sodium (Na):
- z = +1
- [Na]outside = 1485 mM
- [Na]inside = 614 mM
Using the Nernst equation:
E_Na = (RT/zF) * ln([Na]outside/[Na]inside)
= (8.314 J/(mol·K) * 283.15 K)/(1 * 96485 C/mol)) * ln(1485/614)
≈ (2.659/96.485) * ln(2.416)
≈ 0.027 * 0.88
≈ 0.024 V
For Potassium (K):
- z = +1
- [K]outside = 10 mM
- [K]inside = 280 mM
Using the Nernst equation:
E_K = (RT/zF) * ln([K]outside/[K]inside)
= (8.314 J/(mol·K) * 283.15 K)/(1 * 96485 C/mol)) * ln(10/280)
≈ (2.659/96.485) * ln(0.036)
≈ 0.027 * (-3.314)
≈ -0.089 V
For Chloride (Cl):
- z = -1
- [Cl]outside = 1485 mM
- [Cl]inside = 514 mM
Using the Nernst equation:
E_Cl = (RT/zF) * ln([Cl]outside/[Cl]inside)
= (8.314 J/(mol·K) * 283.15 K)/(-1 * 96485 C/mol)) * ln(1485/514)
≈ (2.659/96.485) * ln(2.886)
≈ 0.027 * 1.05
≈ 0.028 V
Now, we know the equilibrium potentials for Na, K, and Cl:
- E_Na = 0.024 V
- E_K = -0.089 V
- E_Cl = 0.028 V
To determine which ion species are not in equilibrium, we compare their actual transmembrane potentials with their equilibrium potentials.
Given that the transmembrane potential is -30 mV, we can compare it with the equilibrium potentials to determine which ions are not in equilibrium:
- For Na: -30 mV < 0.024 V (not in equilibrium)
- For K: -30 mV > -0.089 V (in equilibrium)
- For Cl: -30 mV > 0.028 V (in equilibrium)
From this comparison, we see that the Na ion is not in equilibrium. Therefore, only one ion species, Na, is not in equilibrium.