# 6.021/Notes/2006-11-17

## Myelinated axons

• Potential is not just at nodes
• 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
• $\displaystyle{ V_K = 0 \rightarrow V_m = 0 \rightarrow G_K \uparrow }$
• Inject current in one, force zero voltage drop across other side via feedback to measure node in middle
• Fitting data
• Frog
• $\displaystyle{ I_{Na}=\overline{I_{Na}}(V_m)m^2h }$
• $\displaystyle{ I_K=\overline{I_K}(V_m)n^2 }$
• $\displaystyle{ I_p=\overline{I_p}(V_m)p^2 }$ (different sodium)
• Rabbit
• $\displaystyle{ I_{Na}=\overline{I_{Na}}(V_m)m^2h }$
• $\displaystyle{ I_K= }$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 $\displaystyle{ d \propto D \propto L }$ in many different cells
• Why does this scaling hold?
• $\displaystyle{ L \approx 0.5 \lambda_c }$ tends to give the fastest conduction
• Internode is electrically small, but just barely
• The entire internode is roughly isopotential
• $\displaystyle{ v = \frac{L}{\tau_m} }$ and $\displaystyle{ \tau_m }$ 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 unmyelinated speed 100 m/s 10 m/s size 10 $\displaystyle{ \mu }$m 500 $\displaystyle{ \mu }$m