Study Guide: Ion Channels & Membrane Electrophysiology

1. Overview


2. Key Equations

  1. Ohm’s Law

    V=I×R
  2. Conductance (g)

    R=1gV=Ig
  3. Weighted Sum for Membrane Potential (multiple ions)

    Vm=i(giEi)igi
    • gi: conductance of ion i

    • Ei: Nernst (equilibrium) potential for ion i

  4. Ion Current

    I=g(VmEion)
    • Net current depends on the difference (VmEion).

  5. General Flow Equation

    Flow=(concentration)×(mobility)×(area)×(driving force)
  6. Time Constant

    τ=R×C
  7. Chord Conductance

    g=IIrevVErev

3. Capacitance & RC Properties

3.1 Stored Charge

Q=C×V

3.2 Capacitive Current

Ic=dQdt=CdVdt

3.3 Time Constant (τ)

τ=R×C

4. Measuring & Calculating Membrane Properties

  1. Measure the Time Constant (τ)

    • Inject a small current step; record time to reach 63% of the final voltage.

  2. Measure Steady-State Voltage Response

    • After current injection, at steady-state:

      G=ΔIΔVR=1G
  3. Calculate Capacitance

    C=τR
  4. Determine Cell Area

    Cell Area=C1μF/cm2
    • Typical biological membranes have 1μF/cm2.

  5. Find Specific Membrane Resistance

    Rm=R×(Cell Area)

5. Membrane as an Electrical Circuit

5.1 Equivalent Circuit

5.2 Time Constant

5.3 Length Constant


6. Voltage-Gated Channels

6.1 Na⁺ Channels

6.2 K⁺ Channels

6.3 Ca²⁺ Channels


7. Current–Voltage (I–V) Relationships


8. Conductance–Voltage (G–V) Plots


9. Single-Channel Behavior


10. Protocols to Study Na⁺ Activation/Inactivation

  1. Activation:

    • Clamp the membrane at various depolarizing steps from a negative holding potential.

    • Measure how quickly and strongly Na⁺ current activates.

  2. Inactivation:

    • Use prepulses at different voltages.

    • Then step to a test voltage → measure available Na⁺ current.

    • Plot fraction of channels available vs. prepulse voltage → midpoint of inactivation.


11. Consequences of Na⁺ Channel Inactivation


12. External Ion Concentrations


13. Pathophysiology: Muscle Weakness & Inexcitability


14. Axonal Conduction

14.1 Passive Spread (Cable Properties)

14.2 Unmyelinated Axons

14.3 Myelinated Axons

PropertyUnmyelinated AxonsMyelinated Axons
Conduction TypeContinuousSaltatory
SpeedSlow (~0.5–2 m/s)Fast (~50–100 m/s)
Na⁺ Channel LocationDistributedClustered at nodes
CapacitanceHighLow
ResistanceLowHigh

15. Calcium Action Potentials


Summary

  1. Membrane potential depends on ion gradients, selective permeability, and ion channel gating.

  2. RC properties (resistance R, capacitance C) govern how quickly a cell’s voltage responds.

  3. Time constant (τ) is crucial for understanding the speed of electrical responses.

  4. Voltage-gated channels underlie action potentials and are finely regulated by voltage sensors.

  5. Ion concentrations critically affect excitability and AP amplitude.

  6. Myelination optimizes conduction velocity without drastically increasing axon diameter.

  7. Inactivation of channels (especially Na⁺) is key to the refractory period and directional AP propagation.


Properties of Voltage-Activated Calcium Channels

  1. Subunit Structure :

    • main α1 subunit

      • has 4 domains

      • the main pore-forming subunit that determines ion selectivity, conductance, and gating properties

    • γ :

      • Four-transmembrane-spanning protein, initially found in skeletal muscle calcium channels but also present in the brain (e.g., stargazin).

    • β :

      • Cytoplasmic protein that binds to the α1 subunit’s intracellular I-II linker, helping with trafficking to the plasma membrane and modulation

    • α2 :

      • Derived from a single gene and proteolytically cleaved into an extracellular α2 portion and a membrane-spanning δ portion, which stabilizes the channel at the plasma membrane.

    image-20250225110436989

  2. Gate / Voltage Sensor :

    • S4 segment :

      • Contains positively charged amino acids , arginine and lysine , every 3rd or 4th residue

      • unctions as the voltage sensor

    • Depolarization causes deformation in P-loops , creating a pore

  3. Selectivity Filter for Calcium ( Ca+2 ) :

    • Calcium selectivity is determined by the pore loop ( P-loop ) glutamates :

      • Glutamate residues ( E ) are conserved in each of the four domains ( I-IV ) of the α1 subunit

      • These residues form a high-affinity binding site for Ca2+ ,

        • ensuring preferential permeability over other ions

    image-20250225110821908

    image-20250225110845126

  4. How would you classify or identify different subtypes of calcium channels ?

    • Voltage-gated calcium channels are classified into :

      • High-Voltage Activated ( HVA )

      • Low-Voltage Activated ( LVA ) ( T-type ) channels

    • These subtypes can be distinguished using :

      • Pharmacological blockers ( e.g., ω-Agatoxin IVA for P/Q-type channels )

      • Genetic expression ( different subtypes are present in different tissues )

      • Electrophysiology ( LVA T-type channels activate at lower voltages than HVA channels )

    Channel TypeClone (CaV)FunctionBlockers
    L-typeCaV1.1 - CaV1.4Skeletal, cardiac muscle contraction, secretionDHP (nifedipine), verapamil
    P/Q-typeCaV2.1Neurotransmitter release (central)ω-Agatoxin IVA
    N-typeCaV2.2Neurotransmitter release (peripheral & central)ω-Conotoxin GVIA
    R-typeCaV2.3UncertainSNX 482
    T-typeCaV3.1 - Cav3.3Cell excitabilityMibefradil, ethosuximide (controversial)

image-20250225111012696

α1 Subunits

SubunitTypeFunction
α1AP/Q-typeCNS neurotransmitter release
α1BN-typeNeurotransmitter release (peripheral & central)
α1CL-typeCardiac contraction
α1DL-typeHormone secretion
α1SL-typeSkeletal muscle contraction
α1GT-typePacemaking, excitability

  1. Q: Explain why the resting Vm is usually closer to EK than ENa in typical neurons. A: The cell is more permeable to K+ at rest (many K+ leak channels), so Vm lies near EK.

  2. Q: Sketch/describe an RC charging curve and label τ. What if you double Cm? A: An RC curve rises toward its final voltage, reaching 63% of the total change at t=τ. Doubling Cm doubles τ, slowing the voltage response.

  3. Q: On an IV plot, identify the slope and reversal potential. A: The slope is conductance (g). Where I=0 is the reversal potential (Erev), usually near Eion if one ion dominates.

  4. Q: How does changing [Na+]out affect AP shape/amplitude? A: Higher [Na+]out → larger driving force for Na+ → bigger, faster upstroke and more positive peak. Lower [Na+]out does the opposite.

  5. Q: Absolute vs. relative refractory periods in terms of Na+, K+ channel states? A: Absolute: most Na+ channels are inactivated → no new AP possible. Relative: some Na+ channels have recovered but K+ conductance is high → requires stronger stimulus.

  6. Q: Why might a muscle fiber at 90 mV fail to fire if channels become inactivated? A: If resting Vm is shifted or channels are in a state with fewer available Na+ channels, normal stimuli might not reach threshold.

  7. Q: Raising [K+]out from 4.5 mM to 25 mM: effect on resting potential? A: Depolarizes it (less negative) because EK becomes more positive, so Vm shifts closer to that new EK.

  8. Q: A short current pulse doesn’t reach threshold, but a longer one does. Why? A: The membrane (RC circuit) needs enough time to charge up to threshold. A short pulse may end before hitting threshold.

  9. Q: Multiple myelin wraps: effect on conduction velocity?

    A: Myelin greatly reduces Cm (and increases Rm) in internodes, so fewer charges are needed to depolarize each segment. Conduction is much faster.