1. Nerve Excitation
Topic II-2
Biophysics

2. Neurons Nerve signals due to modulations of membrane potential
Motor neuron
Sensory neuron
Nerve signals due to modulations of membrane potential
Motor Neurons have dendrites

3. History
Action potential is electrical pulse that travels much slower than electrical current
K+ and especially Na+ play big role
Hodgkin and Katz: as [Na+] decreases velocity of action potential decreases
Calamari
Alan Lloyd Hodgkin
Andrew Fielding Huxley
Hodgkin and Huxley observe membrane potential reverses during pulse and goes to +100 mV
They also see that conductance of membrane increases 40X and propose have transient changes in Na and K conductance → Nobel Prize

4. Voltage Clamp Measure current to keep voltage constant
Positive current: + ions out of axon
VK = -72 mV,
VNa = + 55 mV
DV = Vin - Vout
Measure current to keep voltage constant
INa = gNa(Vm – VNa), IK = gK(Vm -VK), IL = gL(Vm – Vk)
Voltage Clamp makes IC = Cm dV/dt = 0
Itot = INa + IK + IL (with clamp)
Vm = Vh = 1/gtot (gKVK + gNaVNa + gLVL + I), clamp and look at I
See notes on conventions re current etc.

5. Voltage Clamp experiments
Set concentrations of ions so can get Nernst potentials equal membrane potential and reduce variables
gNa, gK ~ 0 at resting potential and they are only activated when the axon is depolarized (becomes less negative). H&H get gL when hyperpolarize
I = IL = gL (Vm – VL), VL < Vresting (-60 mV)

6. Action Potential Resting Na m gate closed h gate open; n-gate closed
Sufficient initial depolarization →
open m-gate, Vm → VNa;
h gate closes (inactivation) and K n-gate opens, Vm → Vk
n-gate closes and h-gate opens (de-inactivation), Vm → Vrest h
Do Axon 1 Dynamics

7. Axon 1 Dynamics

8. H&H Voltage Clamp experiments
When depolarize, get early negative current and later positive current
As DV increases
Amplitude of Ineg decreases; DV = 115 have Ineg = 0; DV > 115 have early positive current
Rate of current development increases (both + and -)
Switch from negative current to positive gets earlier
Note: VK = -72 mV, VNa = +55 mV, Vresting = -60mV; INa = gNa(Vm – VNa), IK = gK(Vm – VK)
So IK always positive; INa negative for small DV but becomes positive for DV>115 mV
I reversal could be due to cessation of early I- or stronger/earlier I+
H&H isolate currents by setting Vm = VNa so get voltage dependence of IK
Deduce voltage dependence of INa since Itot = INa + IK
Do axon 1 and 2
Then 3
Do Axon 2&3 Voltage Clamp Currents

9. Axon 2&3 Axon 2 – Voltage Clamp and Currents
Screen shows graph with membrane potential steps and currents vs time. Current is sum of Na and K currents. Ieak is subtracted out.
1. Run. Start at -60 mV. Have Vstep = 10 mV.
2. Step up Vstep by 20 mV up to 140 mV). What do you see?
3. Find voltage when only have positive current. (~115 mV). What is happening here?
Axon 3 – Voltage Clamp and Separate Currents
4. Repeat Vsteps like in Axon 2. Set Vstep to 60 mV just to show general currents. Why no sodium current at 115 mV?
5. Go to parameters in top parameters window. See that VNa is 55 mV (so when step 115 mV = = 55 mV).
6. Now, like H&H, can change VNa (would be changing Na concentrations) and study voltage dependence of gk alone. Take both VNa and Vstep down by 20 (go to 35 mV and 95 mV).
7. Could keep doing this. H&H get INa by subtracting IK from Itotal.

10. Na activation and inactivation and deinactivation
DV  activation , time inactivation  deinactivation deinactivation is also voltage dependent
H&H use conditioning steps:
Brief conditioning depolarization  reduced INa during 2nd step
As Dt for conditioning step increases  INa 2nd step decreases (more sodium channels inactivated during conditioning step)  H&H find time and voltage dependence of inactivation
ex – conditioning step + 29 mV  tinactivation = 2 ms (nearly complete) step + 8 mV  tinactivation > 8 ms (less inactivation)
They found that even at resting potential, many sodium channel are inactive.
H&H used long conditioning steps to study de-inactivation This turned off (closed) Na channels then set 2nd voltage to recovery voltage – vary time to 3rd voltage to look at current.
Axon 4
Do Axon 4 Voltage Clamp Na Inact

11. Axon 4 Voltage Clamp Na inactivation

12. Empirical Equations
Generally dg/dt = a(1-g) – bg; a = opening (fwd rate), b = closing
Potassium, have gk = gkmaxn4; gkmax = max conductance (all open)
Sodium, have gNa = gNamaxm3h, m is like n for K, h describes inactivation
Each has time dependence like n
m3 = fraction activated, h is fraction de-inactivated
Do Axon 5 Voltage Clamp Na K conductance
Axon 5
Do axon 6 and review
Do in Maple?
If know parameters (max g, taus, nernst potentials etc) can get action potential and explain all observed phenomenon.

13. Axon 5 Na K conductances
This is like previous exercises except, now look at conductances which you would get from the currents divided by the potential. Remember can get g from I = gV.
Play. Have 10 mV Vstep. See nothing in gNa and small effect on gK.
Increase step 30, 50 , 70, 115 [Vstep in middle parameter – increase]. What is happening here? Why is gNA so high so big when Vm = VNa (Vstep = 115 mv)?

14. Action Potential Do Axon 6 Impulse conductance
Note that at resting 40% Na channel inactivated
Do axon 6
Do Axon 6 Impulse conductance

15. Axon 6 Current clamp Summary
Hit Stop/Go
Explain what you see.

16. Threshold and Refractory Period
Axon 7 and 8
There is a minimum initial depolarization you need to get action potential – this is the threshold. “All or none” aspect of action potential
After action potential, threshold is infinity (Na h gates closed), this leads to a refractory period.
Do Axon 7&8 Impulse Threshold and Refractory

17. Axon 7 Impulse Threshold

18. Axon 8 Absolute and Refractory Periods

19. Spread of Action Potential
Na comes in and causes depolarization at neighboring sites. Refractory period insures unidirectional event.
Want current to go along axon, not out of axon
Invertebrates: large radius → small R
Vertebrates: large R along axon (myelin sheath and nodes of Ranier)

20. Have ligand gated channel (eg Ach receptor that needs two Ach to open).
When open both Na and K can get through → get depolzarization