8. Electrical properties of excitable cells: Capacitance & Conductance Part 2: Conductance

Lecture 8

Why is the cell membrane called a leaky capacitor?

• Membrane = capacitor (stores charge)

• Ion channels allow current through membrane → “leak”

• Current measured in picoamperes (pA) = 1 picocoulomb per second

How do ion channels affect membrane conductance?

• Channels allow specific ions to pass → act as conductors

• Ion channels have resistance (more than ECF/ICF) → can act as resistors

  • For neuron activity, important to consider resistance of intracellular environment

• Ionic conductance depends on number of open channels

• Together with capacitance → determines electrical activity

How is current through a single K+ channel determined?

• Lipid bilayer separates charge → capacitance (Cm)

• Current depends on electrical potential difference across membrane (V_m − E_ion)

• Conductance: ability of channel to pass current

  • γion (single channel), gion (all channels of that type)

  • Measured in siemens (S); inversely proportional to resistance (R), measured in Ohms

• γ_ion = 1 / R

• Closed channel conductance = 0

  • When resistance ↑ = conductance ↓

How does Ohm’s Law apply to ion channels in cells?

• Ohm’s Law: I = V / R

• In circuits: voltage source → resistor → current of electrons.

• In cells: current = flow of ions, not electrons.

• Conductance (g_ion) = 1 / R

• Rewritten for ions:

  • I = g_ion ×V

• ⚠ Note: For ion channels, “V” isn’t just the battery voltage — it’s the driving force (membrane potential relative to the ion’s equilibrium potential).

Why is Ohm’s Law modified for ion channels?

• Current: I_ion = g_ion × (V_m − E_ion) → includes driving force

  • Depends on conductance (g) and driving force (V_m − E_ion)

• If V_m = E_ion → no net movement (i_ion = 0)

• Resting V_m≠ E_ion → driving force influences conductance of channel

• Ions flow to move V_m toward their E_ion

• Example: V_m = −68 mV → K+ efflux occurs when channels open because E_k=-81 mV

How do we calculate ion-specific currents?

• I_k = g_k(V_m − E_k)

• I_Na = g_Na(V_m − E_Na)

• I_Cl = g_Cl(V_m − E_Cl)

• Each ion has its own conductance and driving force

How do we determine driving force and direction of ion movement in non-excitable cell?

• Driving force = Vm − Eion

• Example cell: Vm = −75 mV

  • Na+: −75 − 65 = −140 mV → Na+ moves in

  • K+: −75 − (−109) = 34 mV → K+ moves out

• Larger absolute value → greater driving force

What happens to passive and active currents at steady-state (excitable cell)?

• Circuit includes conductance through passive Na+, K+, Cl− pathways and active transport (sodium-potassium pump)

• At steady-state: sum of all active & passive ionic currents = 0

• Passive and active currents balance each other

How does a negative driving force affect ion movement in excitable cell?

• Vm − Eion < 0 → positive ion moves into cell

• Example: Vm = −68 mV, ENa = 58 mV

  • Vm − Eion = (-68) - (58)

  • Driving force = −126 mV → Na+ moves in to depolarize cell

How does a positive driving force affect ion movement?

• Vm − Eion > 0 → positive ion moves out of cell

• Example: Vm = −68 mV, EK = −81 mV

  • Vm − Eion = (-68) - (-81)

  • Driving force = +13 mV → K+ moves out to hyperpolarize cell

How can we determine which ions flow through an ion channel?

• Use patch clamp technique

  • Ex: Cell attached patch clamp

• Experimentally induce depolarizing voltage step and measure current through single channel → determine ion specificity

What does an I-V (current-voltage) plot tell us about an ion channel?

• I-V plot shows how current through a channel changes with membrane voltage.

• Linear relationship: Channel behaves like an Ohmic conductor → current is proportional to voltage.

• Slope of I-V plot: Gives channel conductance (how easily ions pass).

• No current at specific voltage (e.g., 58 mV): Membrane voltage equals the ion’s equilibrium potential (ENa).

  • At this voltage, driving force = 0, so no net ion flow.

• Insight: Identifies which ion the channel is permeable to (here, Na⁺).

What does a single-channel I-V plot tell us about ion flow and membrane potential?

• The reversal potential (Eion or ER) is the voltage where no net current flows through the channel.

• Activating a channel that is selective for a specific ion moves the membrane potential (Vm) toward Eion.

• As Vm approaches Eion, the driving force decreases → less current.

• If Vm = Eion → no current

• If Vm is on the other side of Eion → current reverses direction.

• I-V plots can be:

  • Linear (Ohmic) → channel passes current equally in both directions

  • Rectifying → channel passes current more easily in one direction than other

How do electrical signals arise when ion channels open?

• Membrane potential changes during action potential

• Caused by transient changes in ion conductances:

  • Rapid, brief Na+ influx

  • Slow, prolonged K+ efflux