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 in Heart Cells | Ion Permeability Explained

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:

Membrane Potential: −70.30 mV

B. Only K⁺ is Permeable

Potassium diffuses outward, causing a more negative potential inside:

Membrane Potential: −79.82 mV

C. Only Na⁺ is Permeable

Sodium enters the cell due to its higher external concentration, creating a positive potential:

Membrane Potential: +57.91 mV

D. Equal Permeability to Cl⁻ and Na⁺

The resulting potential is a balance between Na⁺ and Cl⁻ effects:

Membrane Potential: −6.20 mV

E. Equal Permeability to Cl⁻ and K⁺

Both ions contribute equally to shape the potential:

Membrane Potential: −75.06 mV

F. Equal Permeability to Na⁺, K⁺, and Cl⁻

A composite average of all three ions results in:

Membrane Potential: −30.74 mV

G. Circuit Model Calculation

Using a realistic electrical circuit model where permeability is analogous to resistance:

VM = (E_K/R_K + E_Na/R_Na + E_Cl/R_Cl) ÷ (1/R_K + 1/R_Na + 1/R_Cl)

Calculated Membrane Potential: −69.24 mV

📊 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

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