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Myelinated axons

  • Potential is not just at nodes
    • Is greatly spread out
    • Reacts very slowly
  • Voltage clamp
    • 3 barriers to separate 3 nodes
    • Test one node by shorting out the 2 adjacent nodes with KCl in bath
      • [math]\displaystyle{ V_K = 0 \rightarrow V_m = 0 \rightarrow G_K \uparrow }[/math]
    • Inject current in one, force zero voltage drop across other side via feedback to measure node in middle
  • Fitting data
    • Frog
      • [math]\displaystyle{ I_{Na}=\overline{I_{Na}}(V_m)m^2h }[/math]
      • [math]\displaystyle{ I_K=\overline{I_K}(V_m)n^2 }[/math]
      • [math]\displaystyle{ I_p=\overline{I_p}(V_m)p^2 }[/math] (different sodium)
    • Rabbit
      • [math]\displaystyle{ I_{Na}=\overline{I_{Na}}(V_m)m^2h }[/math]
      • [math]\displaystyle{ I_K= }[/math]small
  • Model of myelinated fiber
    • Core conductor model with cable model at internodes and Hodgkin-Huxley like model at nodes
  • Internode parameters
    • inner diameter d, outer diameter with myelin D, length L
    • Experimentally find [math]\displaystyle{ d \propto D \propto L }[/math] in many different cells
    • Why does this scaling hold?
    • [math]\displaystyle{ L \approx 0.5 \lambda_c }[/math] tends to give the fastest conduction
      • Internode is electrically small, but just barely
      • The entire internode is roughly isopotential
    • [math]\displaystyle{ v = \frac{L}{\tau_m} }[/math] and [math]\displaystyle{ \tau_m }[/math] is independent of shape
  • Fault tolerant: safety factor
    • Several nodes (amplifiers) can fail and still give an action potential (but takes longer -- more delay)
  • Myelinated fiber advantages
myelinated unmyelinated
speed 100 m/s 10 m/s
size 10 [math]\displaystyle{ \mu }[/math]m 500 [math]\displaystyle{ \mu }[/math]m
  • myelinated fibers also use less energy (only nodes use energy)