ELECTRICAL PROPERITES LEC 4

Na+ gradient and ENa?

Outside >> inside (≈10:1). ENa ≈ +60 mV.

K+ gradient and EK?

Inside >> outside (≈30:1). EK ≈ −90 mV.

Ca2+ gradient and ECa?

Outside >>> inside (≈10,000:1). ECa ≈ +120 mV.

Cl− gradient and ECl?

Outside > inside (≈10:1). ECl ≈ −60 mV.

What generates the Na+ and K+ gradients?

The Na+/K+ ATPase (3 Na+ out, 2 K+ in per ATP).

What generates the Ca2+ gradient?

Ca2+ pumps (PMCA out of cell, SERCA into ER).

What generates the Cl− gradient?

Secondary active transport, e.g. K+/Cl− cotransporter.

Calculate ENa: [Na+]o=145, [Na+]i=12 mM.

61.5 × log(145/12) ≈ +67 mV

Calculate ECl: [Cl−]o=105, [Cl−]i=30 mM.

z=−1: −61.5 × log(105/30) ≈ −34 mV

Current equation for one ion?

Ix = gx (Vm − Ex).

What is the driving force on an ion?

Vm − Ex; zero at Ex.

Three things that set an ion's current?

Its Ex, the membrane potential Vm, and its conductance gx.

At steady Vm, what is ΣIx?

Zero: inward and outward currents balance.

Chord conductance equation?

Vm = ΣEx·(gx/Σg): a conductance-weighted average of each ion's Ex.

What does high gK do to Vm?

Pulls Vm toward EK (more negative).

Worked example: EK=−91, ENa=+67, ECl=−34; gK=80, gNa=15, gCl=5 pS. Vm?

≈ −64.5 mV (weighted average by conductance fraction).

Typical resting membrane potential?

−60 to −80 mV.

Why is RMP close to EK?

At rest, gK >> gNa, so K+ efflux dominates.

Why is RMP slightly less negative than EK?

Some Na+ (and Cl−) conductance is open, pulling Vm slightly toward ENa.

What keeps ion gradients stable at rest?

The Na+/K+ ATPase continuously counters Na+ in / K+ out leak.

Depolarization vs hyperpolarization?

Depolarization: Vm less negative. Hyperpolarization: Vm more negative.

What is a passive membrane response?

A graded Vm change from small currents, with no voltage-gated channel activation.

When does a response stop being passive?

When larger currents activate voltage-gated conductances (e.g. VGSCs).

Why is Vm slower than the triggering current?

The membrane is a capacitor: current must first charge it before Vm changes.

Effect of higher membrane capacitance?

Slower change in Vm for the same current.

Electrotonic conduction, defined?

Passive spread of Vm change, not amplified by voltage-gated channels.

What happens to signal amplitude with distance?

Decays exponentially (decrement).

Why does the signal decay with distance?

Current leaks out through open channels along the way.

Length constant λ, defined?

Distance over which the potential decays to 1/e (~37%).

Length constant equation?

λ = √(rm / (ro + ra)).

Effect of more open channels on λ?

Lower membrane resistance → smaller λ (faster decay).

Effect of larger axon diameter on λ?

Larger diameter → larger λ (ra falls faster than rm).

Calc: λ=2 mm. % remaining at 4 mm?

e^(−2) ≈ 14%.

Action potential, defined?

Large all-or-none depolarizing response, peak ≈ +30 to +50 mV.

Action potential threshold, defined?

Vm at which there is a 50% chance of firing an AP.

All-or-none, meaning?

Suprathreshold stimuli give the same AP; subthreshold gives only graded passive response.

VGSC role in the AP?

Open on depolarization → Na+ influx → more depolarization (positive feedback, rising phase).

Key VGSC properties?

Fast opening (<1 ms), steep voltage dependence, fast inactivation.

Accommodation, defined?

Very slow depolarization lets VGSCs inactivate before firing, so no AP occurs.

VGKC role in the AP?

Opens on depolarization → K+ efflux → repolarizes membrane.

VGKC vs VGSC kinetics?

VGKC opens more slowly, shows little inactivation (vs fast-opening, fast-inactivating VGSC).

Phase 1: threshold?

Depolarizing input reaches threshold; VGSCs open.

Phase 2: depolarization?

More VGSCs open (Na+ influx wins); Vm rises; VGSCs start inactivating; VGKCs start opening.

Phase 3: repolarization?

K+ efflux exceeds Na+ influx; Vm falls back toward rest.

Phase 4: afterhyperpolarization?

VGKCs still open; Vm dips below RMP toward EK before channels close.

How was the ionic basis of the AP studied?

Voltage clamp with TTX (blocks VGSC, isolates K+ current) and TEA (blocks VGKC, isolates Na+ current).

Absolute refractory period?

VGSCs mostly inactivated; no AP possible regardless of stimulus strength.

Relative refractory period?

VGSCs recovering; a stronger-than-normal stimulus can fire an AP.

How does an AP propagate?

Local depolarization spreads passively to next membrane patch, which reaches threshold and regenerates the AP via VGSCs.

Relation to electrotonic conduction?

AP propagation = passive (electrotonic) spread + active regeneration by VGSCs; passive spread alone decays, active regeneration restores full size.

Why do APs only go one direction?

Membrane just behind the AP is refractory (VGSCs inactivated).

Conduction velocity, defined?

Speed an AP travels along an axon; limits information flow speed in the nervous system.

Two structural factors that raise conduction velocity?

Larger axon diameter and myelination.

Why does diameter raise velocity?

Larger diameter lowers axial resistance → larger λ → faster passive spread to threshold.

What is myelination?

Insulating wrap around axons by Schwann cells (PNS) or oligodendrocytes (CNS).

Nodes of Ranvier?

Small gaps in myelin (~2 µm) every 0.3-2 mm.

Internode?

Myelinated stretch between nodes (~300-2000 µm).

Where are VGSCs on myelinated axons?

Concentrated at nodes of Ranvier; absent under the myelin.

Effect of myelin on membrane resistance?

Increases rm → larger λ → less signal decay per internode.

Effect of myelin on membrane capacitance?

Decreases capacitance → faster electrotonic spread.

Saltatory conduction, defined?

APs regenerate only at nodes; signal jumps node-to-node via fast electrotonic spread through internodes.

Effect of demyelination (e.g. MS)?

Lower rm, higher C in internodes → slower conduction, eventual propagation failure.

Range of conduction velocities in mixed nerves?

~0.1 m/s (small unmyelinated C fibers) to ~120 m/s (large myelinated Aα fibers).

Order of fiber speed, fastest to slowest?

Aα > Aβ > Aδ > C.

What drives the speed differences between fiber types?

More myelin and larger diameter = faster conduction.

Conductance and Ohm's law?

g = 1/R; I = V/R = g × V.

Membrane as a capacitor?

Lipid bilayer separates two conductors; C = q/V, C ∝ A/d; charge must build before Vm changes.