How quickly can $V_m$ change?

• Represented by a resistor-capacitor system
• $\lambda = \sqrt{\dfrac{r_m}{r_a}}$, $\tau = r_a\cdot c_m$
• Speed $\propto \dfrac{1}{r_a \cdot c_m}$
• Speed $\propto$ diameter
• Speed $\propto$ thickness

Nodes of Ranvier

• Start action potential at axon hillock. Peak to peak voltage will decay (due to axial and membrane potential)
• Between myelin sheaths—very dense in voltage gated ion channels, will activate positive feedback loop
• Axon hillock is the “first node of ranvier”
• Question: are nodes of ranvier created due to gaps between myelin sheaths?

Ion flow through voltage-gated channels

• Ion conductance high during AP
• There is an ion flux through membrane channels, but what membrane?
• $V_m$ and conductance change at same time—host to experiment with conductance?
• Voltage clamp decouples $V_m$ from conductance by keeping it at a certain level
• Experiments
  • A: 10 mV depolarization step wrt resting value
    • Turn on, Spiking current, then constant current, turn off, negative spike, 0
    • $I_I$: current termed leakage (resting ion channels)
    • $I_C$: capacitive current
  • B: 60 mV depolarization
    • Larger $I_c$ and $I_I$
    • Short time later, large inward current
    • Shortly after that, large outward current
  • C: 60 mV depolarization: use toxins to block either potassium or sodium ion channels
    • K+ current goes up
    • Na+ current goes down, but then up due to inactive IC
• Channel conductance kinetics
  • Step up membrane to different voltages
  • Na, K similarities:
    • Depolarizing $V_m$ channels open up
    • Larger depolarizing steps, probability and rate of opening increases (rise times down)
  • Na, K differences:
    • Rates of opening: Na > K
    • Responses to prolonged
      • Na+ opens, closes (inactive)
      • K stays open
• Short-term vs. long-term depolarization
  • Short-term: allow Na and K return to rest in state
  • Long-term: Na becomes inactive
  • Reactivating after a short time doesn’t open as many ion channels
  • Absolute refractory period: 2-4 ms, won’t spike in between
  • Relative refractory period: 15 ms, can generate another action potential, but some are still closed and potassium still flowing in, so harder to generate