The figure below shows a heart cell. A membrane is located between the inside and outside of the cell and has Sodium, Potassium, and Chloride gates. Inside the cel, the concentration of the Sodium (Na+), Potassium (K+), and Chloride (Cl-) are 50 mMOL, 397 mMOL and 40 mMOL respectively. The concentration of Sodium (Na+), Potassium (K+), and Chloride (Cl-) outside of the cell are 437 mMOL, 20 mMOL, and 556 mMOL, respectively. We are using two identical electrodes to measure the resting potential of this cell. Answer A through G. G. If we assume the following circuit model with Nernst Potentials (VCl,Vk,VNa) with Rk=2.7KΩ,RNa=30KΩ,RC=3.3KΩ, find the membrane potential VM= ? Compare the VM with the equilibrium resting potential that you calculated in part F .
Answer
Resting Membrane Potential of a Heart Cell Based on Ion Permeability
Overview
The membrane potential in heart cells is determined by the movement of sodium (Na⁺), potassium (K⁺), and chloride (Cl⁻) ions across the semipermeable membrane. Their movement is governed by electrical and chemical gradients, leading to a stable resting membrane potential.
A. Only Cl⁻ is Permeable
Chloride ions solely influence the potential. They move to match their gradient, resulting in:
B. Only K⁺ is Permeable
Potassium diffuses outward, causing a more negative potential inside:
C. Only Na⁺ is Permeable
Sodium enters the cell due to its higher external concentration, creating a positive potential:
D. Equal Permeability to Cl⁻ and Na⁺
The resulting potential is a balance between Na⁺ and Cl⁻ effects:
E. Equal Permeability to Cl⁻ and K⁺
Both ions contribute equally to shape the potential:
F. Equal Permeability to Na⁺, K⁺, and Cl⁻
A composite average of all three ions results in:
G. Circuit Model Calculation
Using a realistic electrical circuit model where permeability is analogous to resistance:
📊 Summary Table
| Condition | Membrane Potential (mV) |
|---|---|
| Only Cl⁻ Permeable | −70.30 |
| Only K⁺ Permeable | −79.82 |
| Only Na⁺ Permeable | +57.91 |
| Cl⁻ and Na⁺ Equally Permeable | −6.20 |
| Cl⁻ and K⁺ Equally Permeable | −75.06 |
| Na⁺, K⁺, and Cl⁻ Equally Permeable | −30.74 |
| Equivalent Circuit Model | −69.24 |