6.021/Notes/2006-11-17

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)