1. This PowerPoint shows circuit diagrams superimposed on the membrane in order to illustrate current flow in three of the tutorials:
The Membrane Tutorial (diagrams of current flow that accompany the steps of the tutorial)
The Unmyelinated Axon Tutorial
The Myelinated Axon Tutorial
Ann E. Stuart

2. c Patch Membrane Tutorial outside inside Vm = 0 mV
stimulating electrode inserted Vm
outside
inside c
Current may be injected through a microelectrode.

3. c Patch Membrane Tutorial outside inside Vm = 0 mV Ach-gated channels
Current may also be injected by the opening of a channel.

4. Patch Membrane Tutorial steps 1 & 2
Vm = 200 mV at end of current pulse Vm
electrode injects positive charge
(20nA current pulse) Vm
injected current pulse

5. Patch Membrane Tutorial steps 1 & 2
Vm = 200 mV at end of current pulse Vm
electrode injects positive charge
(20nA current pulse) Vm
injected current pulse

6. Patch Membrane Tutorial steps 1 & 2
Vm = 200 mV at end of pulse Vm
Q = CV
V = 1/C [Q]
dV/dT = 1/C [dQ/dt];
dQ/dt = Icap
dV/dT = 1/C [Icap]
Icap = C [dV/dt]

7. Patch Membrane Tutorial step 3: add leak channelVm c
rleak 1 2 Vm t

8. Time constant tau = Rm Cm
tau = the time it takes for voltage to rise to 67% (1-1/e) or fall to 33% (1/e) of its final value Vm
tau = Rm Cm Vm
tau
tau t

9. Patch Membrane Tutorial step 4: add HH Na & K channels
Na channels (fast)
Depolarizing (positive) current is injected.
K channels (slow) Vm
K channels then open, allowing the K battery to drive positive current out through these channels (inward Icap).
The current first flows out through the capacitance C.
As the voltage builds up across C, current flows out through leak channels.
Na channels open, allowing the Na battery to drive positive current inward through these channels (outward Icap).

10. Passive Axon Tutorial: add longitudinal resistancesro
(usually negligible) ro rm
rm ( = rleak) ri ri

11. Length constant (L)
L = the distance over which a voltage step decays to 1/e (33%) of its original value.
If rm is large compared to ri, current will flow down the inside of the axon and L will be large.
L tracks the (square root of the) rm/ri ratio:
L = √ rm / ri mV L
distance x

12. Unmyelinated Axon Tutorial: add HH Na & K channels
the AP

13. Myelinated Axon Tutorial: add myelin
the AP
time constant:
tau = RmCm
Cm decreases because of many capactors in series
Rm increases because of equivalent # of resistors in series
tau does not change
length constant:
L = √ rm/ri
rm becomes very much larger
L becomes very much longer