1. Outline Ohm’s Law Voltage Clamp Current-Voltage Relationships
Components/ conductances of an action potential

2. Ohm’s Law
V = IR
The potential difference between two points (A, B) linked by current path with the conductance (G) and current (I) is as follows: A B

3. Definition V=IR V=voltage, I=current, R=resistance g=1/R g=conductance
g=1/R g=conductance
Vm=membrane voltage
Vr=voltage of membrane at rest

4. Permeability and Conductance
gna is low at Vr because sodium channels are closed.
gk is higher than gna at Vr because some potassium channels are open.

5. Definitions Current=net flow of ions per unit time
1 ampere of current represents movement of 1 coulomb of charge per second
Resistance- frictional forces that resists movement of ions or charges measured in ohm
Current (I)= V/R

6. Definitions
Conductance is the reciprocal of resistance and measures the ease with which current flows in an object.
Measured in siemens (S)
Capacitance refers to the ability of plasma membrane to store or separate charges of opposite signs.
Myelin has high capacitance so stores charges and ions do not move across the membrane
Measured in Farads

7. Conductance = g
How many charges (ions) enters or leaves cell (inverse of resistance)
due to:
number of channels/membrane area
Highest density at axon hillock
number of open channels
ion concentration on either side of membrane
Measured in Siemens (S).

8. Action Potential
Changes in Ion Permeability allows inward Na flux and triggers an increased outward K flux through voltage gated ion channels
Causes transient change in Membrane Potential
The change in ion permeability is triggered by transient depolarization of the membrane

10. Historical Figures
Hodgkin and Huxley won Nobel Prize for Voltage clamp in 1961
used to identify the ion species that flowed during action potential
Clamped Vm at 0mv to remove electric driving force than varied external ion concentration and observed ion efflux during a voltage step
Sakman and Nehr won Nobel Prize for Patch Clamp in 1991
measured ion flow through individual channels
shows that each channel is either in open or closed configuration with no intermediate. The sum of many recordings gives you the shape of sodium conductance.

11. Voltage Clamp Itotal = IC + Iionic where IC = C(dV/dt)
Measures the amount of current needed to hold the cell at a given potential
Itotal = IC + Iionic where IC = C(dV/dt)
when clamping the cell at a certain voltage, at steady state,
dV/dt=0, thus Itotal = II
Vhold
Battery: imposes a voltage drop across the cell membrane
V-clamp
I-clamp I

12. Voltage Clamp
Vhold
V-clamp
I-clamp
Can compensate for the capacitive current with amplifier. (ie. can force the Ic=0)
By injecting an equal and opposite amount of current
Iinj Vm
Thus have full control over the membrane potential of the cell.
Thus, can measure the conductance of the cell due to Iionic at any voltage

13. Box 3A The Voltage Clamp Technique
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14. Voltage Clamp vs. Current Clamp
glut
I-clamp
V-clamp
Upward deflections are depolarizing; downward are hyperpolarizing
Downward (negative deflections) are inward currents; upward are outward

15. Figure 3.1 Current flow across a squid axon membrane during a voltage clamp experiment (Part 1)
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16. Figure 3.1 Current flow across a squid axon membrane during a voltage clamp experiment (Part 2)
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17. Figure 3.2 Current produced by membrane depolarizations to several different potentials (Part 1)
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18. Figure 3.3 Relationship between current amplitude and membrane potential
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19. Figure 3.4 Dependence of the early inward current on sodium
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20. Figure 3.5 Pharmacological separation of Na+ and K+ currents
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21. Figure 3.6 Membrane conductance changes underlying the action potential are time- and voltage-dependent (Part 1)
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22. Figure 3.6 Membrane conductance changes underlying the action potential are time- and voltage-dependent (Part 3)
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23. Figure 3.7 Depolarization increases Na+ and K+ conductances of the squid giant axon
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24. Figure 3.8 Mathematical reconstruction of the action potential
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25. Figure 3.9 Feedback cycles responsible for membrane potential changes during an action potential
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26. Action Potentials The Hodgkin-Huxley Model
The squid giant axon action potential had only sodium and potassium currents….
Other cells’ action potentials are shaped by a number of other conductances.

27. Squid Axon Action Potentials
Current clamp
Voltage clamp
Assymetrical currents w/ depol or hyperpol V-steps
ie. non-Ohmic I-V relationship

28. Ion Permeability Changes during action potential
The plasma membrane becomes permeable to sodium ions
Permeability increases from 0.02 to 20=1000 fold increase
Causes Em aka Vr to approach Ena at positive voltages = +20mV

29. 6 Characteristics of an Action Potential
#1 Triggered by depolarization
a less negative membrane potential that occurs transiently
Understand depolarization, repolarization and hyperpolarization

30. #2 Threshold
Threshold depolarization needed to trigger the action potential
10-20 mV depolarization must occur to trigger action potential

31. #3 All or None Are all-or- none event
Amplitude of AP is the same regardless of whether the depolarizing event was weak (+20mV) or strong (+40mV).

32. #4 No Change in Size
The shape (amplitude & time) of the action potential does not change as it travels along the axon
Propagates without decrement along axon

33. #5 Reverses Polarity
At peak of action potential the membrane potential reverses polarity. Becomes positive inside as predicted by the Ena Called OVERSHOOT
Return to membrane potential to a more negative potential than at rest Called UNDERSHOOT

34. #6 Refractory Period
Absolute refractory period follows an action potential. Lasts 1 msec
During this time another action potential CANNOT be fired even if there is a transient depolarization.
Limits firing rate to 1000AP/sec

35. Nerve Impulse Conduction
Conduction of action potentials is not like conduction of charge along a wire conductor.
The axon is a poor conductor of electrical charge and is leaky to charge in the form of ions.
Within a short distance, the flow of electrical charge is greatly diminished.
However, this passive electrotonic spread of charge in an axon is an important component of the propagation of action potentials down the axon.

36. Propagation of the Action Potential
The action potential is regenerated all along the axon like a series of relay stations.
Localized flow of current from the region undergoing an action potential depolarizes the adjacent membrane.
Voltage gated Na+ channels in the adjacent membrane respond by opening their activation gates.
A new action potential is triggered in the adjacent membrane.
This sequence is repeated down the length of the axon.
Action potentials don’t decay in strength as they are conducted down the axon.

40. Unidirectional Propagation
Propagation of the action potential only moves in one direction, from the axon hillock to the axon terminals.
The region just recovering from an action potential (K+ outflow region) cannot be stimulated by local current flow.
During the repolarizing and undershoot phases, the inactivation gates of the Na+ channels are still closed, blocking any Na+ influx even if the activation gates were to open.
Refractory period

41. 2 ways to increase AP propagation speed
Increase internal diameter of axon which decreases the internal resistance to ion flow.
Increase the resistance of the plasma membrane to charge flow by insulating it with myelin.

42. Myelinated Neurons
Many vertebrate peripheral neurons have an insulating sheath around the axon called myelin which is formed by Schwann cells.
Myelin sheathing allows these neurons to conduct action potentials much faster than in non-myelinated neurons.

45. Saltatory Conduction in Myelinated Axons
Myelin sheathing is interrupted by bare patches of axon called nodes of Ranvier where ion channels are concentrated.
Action potentials jump from node to node without depolarizing the region under the myelin sheath - called saltatory conduction.
Myelin sheathing improves the ability of electrical charge to flow far enough down the axon to reach the next node.

46. Myelinated Neurons Conduct Faster Than Non-myelinated
Myelin sheathing and saltatory conduction improves the speed of nerve impulse conduction.
This allows small diameter neurons to conduct impulses rapidly.
Invertebrates, which don’t have myelinated neurons, have to increase axon diameter to speed up conduction.
The larger the cross-sectional area of a neuron, the further it can conduct electrical charge along the axon.
Giant axons are found in some invertebrates like earthworms and squid that need to rapidly conduct nerve impulses to distant muscles for escape responses.