+60zlog10( outsideinside )
V=IR
R=1g
V=Ig
Vm=i( giEi )i( gi )
I=g( VmNernstion )
Flow=(concentration)×(mobility)×(area)×(driving force)
τ=RC
Chord Conductance ( g )=IIrevVErev


Capacitance


Time constant ( τ )

τ=RC

Steps to Calculate Electrical Properties

  1. Measure the time constant (τ) – time to reach 63% of steady state.

  2. Measure steady-state voltage response to injected current.

    • Use G=ΔI/ΔV to find conductance.

    • Resistance: R=1/G.

  3. Calculate capacitance using:

    C=τR
  4. Determine cell area:

    Cell Area=C1μF/cm2
  5. Find specific membrane resistance:

    Rm=R(Cell Area)


Voltage-Gated Channel Structure



Membrane as an Electrical Circuit


Equivalent Circuits & Passive Electrical Properties

  1. Membrane as an RC Circuit

    • Capacitance (Cm): lipid bilayer stores charge.

    • Resistance (Rm): ion channels in parallel.

    • Ohm’s Law: ΔV=I×R.

  2. Input Resistance

    Rin=ΔVI.
    • Higher Rin = bigger voltage change for a given current.

  3. Time Constant

    τ=RmCm.
    • Governs how quickly membrane voltage responds to current steps. Numerically, the time to reach ~63% of the final voltage after a step.

  4. Length Constant

    λ=RmRi
    • Determines how far a passive potential spreads along a cable-like structure (dendrite/axon) before decaying significantly.



Current-Voltage ( I / V ) Plots


  1. Chord Conductance

    g=IVmEion.
    • Evaluate at various voltages to map how channels open with depolarization.

  2. Separating Na/K Currents

    • Under voltage clamp, set gNa=0 to isolate IK, or gK=0 to isolate INa.

    • Examine each current’s activation, inactivation, reversal potential, etc.


Conductance-Voltage ( G / V ) Plots

G=IVENa

Single-Channel Events & Stochastic Gating

  1. Microscopic Currents

    • Individual channels open in discrete, square-step events.

    • The macroscopic current is the sum of many channels.

  2. Na+ vs. K+ Channels

    • Na+: open quickly upon depolarization, then inactivate.

    • K+: slower to open but often remain open longer with minimal inactivation (in classical models).

  3. Voltage Dependence

    • Higher depolarization usually increases open probability (especially for K+ channels).

  4. Open-Time / Closed-Time

    • By repeated single-channel recordings, you measure average open times, closed times, gating rate constants, etc.


Studying Na⁺ Channel Activation


Studying Na⁺ Channel Inactivation


Consequences of Na⁺ Channel Inactivation

  1. Transient Na⁺ currents:

    • Even with sustained depolarization, Na⁺ channels inactivate.

  2. Refractory period:

    • Prevents immediate reactivation of Na⁺ channels after an action potential.

  3. Unidirectional action potential propagation:

    • Ensures nerve impulses travel in one direction.

  4. Prolonged depolarization leads to paralysis:

    • Na⁺ channel inactivation prevents further excitation.



Influence of Ion Concentrations


Voltage Clamp Protocols (Activation/Inactivation)

(Relevant to Guides #6, #7)

  1. Voltage-Step Protocols

    • Condition at a certain potential (e.g. -90 mV), then step to a test potential (e.g. -20 mV).

    • Measure current amplitude to see how many channels activate or remain inactivated.

  2. Midpoint of Activation

    • The Vm where g is half of gmax. Determined from gV curves.

  3. Midpoint of Inactivation

    • The conditioning Vm that inactivates half the channels.

    • Found by applying various prepulses, then stepping to a fixed test potential.

  4. Na vs. K

    • Na+ channels typically show both strong activation and inactivation; K+ channels require stronger depolarization, often show little inactivation.


Skeletal Muscle Weakness & Inexcitability

  1. Shifts in Resting Vm

    • Disease can produce abnormal channel gating, changing Vm from e.g. -70 to -90 mV and making it harder to fire or causing partial channel inactivation.

  2. Input Resistance & Time Constant

    • If Rin or Cm are altered, the fiber’s response changes. Could need bigger/longer stimuli to reach threshold.

  3. Pathophysiological Relevance

    • Small disruptions in channel function or ion gradients can cause muscle weakness or periodic paralysis.


Electrical Propagation in Axons

  1. Passive Spread (Cable Properties)

    • Voltage decays with distance if no regenerative channels are involved.

    • Larger diameter reduces Ri, bigger λ. Lower Cm or gleak can help signals travel faster/farther.

  2. Unmyelinated Axons

    • Conduction velocities can be a few to ~20 m/s (like in squid giant axon).

    • Speed often scales with axon diameter.

  3. Myelinated Axons

    • Myelin drastically lowers Cm and raises Rm in internodes → saltatory conduction (jump node-to-node).

    • Can reach 100+ m/s in large vertebrate axons.

  4. Experimental Observations

    • Changing diameter, Cm, or gleak changes conduction speed.

    • More “wraps” (myelin) → less internodal capacitance → faster conduction.


Passive Axon Properties


Squid Giant Axon: An Evolutionary Solution


Comparing Myelinated vs. Unmyelinated Axons

PropertyUnmyelinated AxonsMyelinated Axons
Conduction typeContinuousSaltatory
SpeedSlow ( ~0.5–2 m/s )Fast ( ~50–100 m/s )
Na⁺ channelsSpread along axonClustered at nodes
CapacitanceHighLow
ResistanceLowHigh

Myelin decreases capacitance and increases resistance:



Calcium Action Potentials

  1. Ca2+ Channels

    • Open upon depolarization but often inactivate slower, leading to longer-duration APs (plateau-like phases).

  2. Replacing Na+ with Ca2+

    • Produces slower, longer spikes if Ca2+ is the main inward current. Peak amplitude might be smaller, but duration is often larger.

  3. Cardiac-Like APs

    • Characterized by a plateau due to sustained Ca2+ current, slower repolarization.

    • Increasing gCa → prolongs plateau.

    • Increasing gNa → faster upstroke, higher peak.

  4. Role of K+ Channels

    • Eventually repolarize the membrane, but if Ca2+ channels remain open, the net outward current is delayed, prolonging the AP.


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.