JD

lecture thursday 8/28

Resting Potential and Ion Gradients

  • Resting membrane potential (RP) is approximately V_m \approx -70\ \text{mV}, with the inside being more negative.

  • Maintained by:

    • Potassium (K$^+$) leak channels: Many open, allowing K$^+$ efflux, making the inside more negative. If only K$^+$ permeable, RP would be near E_K \approx -90\ \text{mV}.

    • Sodium (Na$^+$) leak channels: Fewer open, allowing some Na$^+$ influx, counteracting K$^+$ efflux.

    • Na$^+$/K$^+$ pump: Actively moves 3 Na$^+$ out and 2 K$^+$ in, maintaining ion gradients and contributing to the negative RP.

Graded Potentials and the Trigger Zone

  • Definition: Local, variable changes in membrane potential (at dendrites/cell body) caused by a stimulus.

  • Key Features:

    • Variable amplitude: Proportional to stimulus strength (number of channels opened).

    • Decay with distance: Strongest at the source, dissipates due to diffusion, cytoplasmic resistance, and leak currents.

    • Can be depolarizing (e.g., Na$^+$ influx, moving towards threshold) or hyperpolarizing (e.g., K$^+$ efflux).

  • Trigger Zone (Axon Hillock):

    • Cone-shaped region where the axon originates, site of high concentration of voltage-gated Na$^+$ and K$^+$ channels.

    • Threshold: Approximately V_{th} \approx -55\ \text{mV}. If a graded potential reaches or exceeds this at the trigger zone, an action potential is initiated.

    • If threshold is not met, the graded potential dissipates without an AP.

  • NaV Channel Gates: Consists of an activation gate (opens quickly at threshold) and an inactivation gate (closes shortly after opening).

The Action Potential (AP)

  • Definition: A rapid, large, all-or-nothing depolarization-repolarization wave that propagates along the axon without decaying. Peaks around V_m \approx +30\ \text{mV}.

  • Phases:

    1. Resting: V_m \approx -70\ \text{mV}.

    2. Depolarization to Threshold: Graded potential reaches trigger zone, depolarizing it to V_{th} \approx -55\ \text{mV}.

    3. Rising Phase: Voltage-gated Na$^+$ channels (NaV) open rapidly, causing fast Na$^+$ influx and steep depolarization.

    4. Peak: NaV channels inactivate, halting Na$^+$ influx.

    5. Falling Phase (Repolarization): Voltage-gated K$^+$ channels (Kv) open, K$^+$ efflux repolarizes the membrane.

    6. Afterhyperpolarization/Overshoot: Membrane potential temporarily dips below resting due to prolonged Kv activity.

  • Propagation: Initiated at the trigger zone, the AP regenerates sequentially in adjacent axon segments by opening local voltage-gated Na$^+$ channels (domino effect).

  • Refractory Periods:

    • Absolute Refractory Period: NaV channels are inactivated and cannot reopen; no new AP possible. Ensures one-way propagation.

    • Relative Refractory Period: Some NaV channels have reset, but a stronger-than-normal stimulus is needed to trigger another AP.

AP Conduction Speed Enhancement

  • Axon Diameter: Larger diameter reduces internal resistance, increasing conduction velocity.

  • Myelination: Myelin insulation wraps around axon segments, reducing current leak.

  • Nodes of Ranvier: Gaps in myelin with high density of voltage-gated channels. The AP "jumps" from node to node (saltatory conduction), significantly increasing speed.

  • Myelination is an efficient solution to increase speed without impractical axon size.

Key Notations and Concepts

  • Resting potential: V_m \approx -70\ \text{mV}

  • Potassium equilibrium potential: E_K \approx -90\ \text{mV} (if only K$^+$ permeable)

  • Threshold for AP: V_{th} \approx -55\ \text{mV}

  • Action potential peak: V_m \approx +30\ \text{mV}

  • Time scales: NaV activation ~0.5 ms; AP duration ~1 ms.

  • Graded potentials can summate at the trigger zone to determine if an AP fires.