Lecture 9: Modeling Cell Membrane Circuits

Lecture 9: Modeling Cell Membrane into Electric Circuit

• The lipid bilayer is modeled as a capacitor.
• Cell membrane capacitance is approximately 1 µF/cm².
• Ion channels are represented as resistors with specific resistance (Conductance = 1/R).
• Equilibrium potential for each ion is modeled as a battery.
• Na+/K+ pumps are modeled as generators.

Equivalent Circuit Model

• The lipid bilayer is represented as a capacitor.
• The capacitance for a cell membrane is approximately 1 µF/cm².
• Ion channels are represented by resistors, each with specific resistance (conductance denoted as g = 1/R).
• The equilibrium potential for each ion is represented by a battery across the channel.
• Na+/K+ pumps are modeled as generators working in opposite directions to the passive currents.

Equivalent Circuit Model (Detailed)

• The plasma membrane is modeled as a capacitor (separates charge, insulator).
• Capacitance (C) = Q/V, where Q is charge and V is Voltage (Farads: F)
• Ion channels are conductors (Siemens: S), allowing charge flow through the membrane.
• Conductance (G) = 1/Resistance (R)
• Voltage (Vm) is the potential difference across the membrane.
• The source of voltage is the battery.
• Ohm's Law: Current (I) = Voltage (V)/Resistance(R) = Conductance (G) x Voltage (I = GV).

Equivalent Circuit Model Variations and Scenarios

• Scenario 1 (No concentration gradient): The only force acting on ion movement is the membrane potential (Vm).

  • Potassium ion current (iK+) = Conductance (gK+) x Membrane potential (Vm) (iK+ = gK+ Vm).

• Scenario 2 (Concentration gradient present): The equilibrium potential of the ion is the only force influencing ion motion.

  • Potassium ion current (iK+) = - Conductance(gK+) x Equilibrium potential (Ek+) (iK+ = -gK+ Ek+)

• Scenario 3 (Both concentration and membrane potentials present): Both influence ion movement.

  • Potassium ion current (iK+) = Conductance (gK+) x (membrane potential-equilibrium potential) (iK+= gK+ (Vm - Ek+))

• Na/K pump acts as a generator to create a voltage difference and this charge difference generates a driving force.