[PPT] - Foundations I Fall, 2016 Action Potentials and Associated PowerPoint Presentation

SLIDE 1

Action Potentials and Associated Voltage-gated Ion Channels

Foundations I Fall, 2016

SLIDE 2

The Bernstein Hypothesis Part II (1912)

~”Action potential results from a breakdown in selective permeability to potassium”

J. Bernstein

SLIDE 3

1946

SLIDE 4

J. Bernstein

0 for 2 (sort of)

but correct on several dozen other key aspects (e.g, discovered the AHP, first to propose use of CRT oscilloscope !!, etc.) 1868 this finding of the AHP actually argues against his hypothesis...

SLIDE 5

L. Hermann (1838-1914)

Local circuit theory

strömchen

late 1870s

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Whitestone Bridge

SLIDE 7

Wheatstone Bridge

R and R are known. What is the value of R ?

3 4 1

SLIDE 8

adjust until the ammeter reads zero

2

R

at that point,

d

V

=

2

I

1

R =

b

V =

2

I

4

R =

1

I

3

R

Why?

SLIDE 9

According to Kirchoff’s Law, the algebraic sum of the potential rises and drops around a closed loop is zero. Since V=IR for all paths in the circuit, if there is no current flowing between d and b, there must be no potential difference between d and b. In other words, Vd=Vb.

SLIDE 10

2

I

1

R =

1

I

2

R

2

I =

1

I

2

R

1

R

1

I

2

R

1

=

1

I

3

R

4

R R

2

R

1

R

=

3

R

4

R

1

R =

2

R

4

R

3

R

d

V

=

2

I

1

R =

b

V =

2

I

4

R =

1

I

3

R

2

I =

1

I

3

R

4

R

1 ?

SLIDE 11

V = I(

electrode

R

+

m

R )

totally unbalanced

V = I

m

R

electrode balanced V I V I electrode + cell membrane balanced V I

SLIDE 12

K.S. Cole (1900 - 1984)

654 IMPEDANCE OF SQUID AXON DURING ACTIVITY amplifier was sharply tuned so that a bridge frequency as low as 20 kc. could be used. A balanced modulator was then substituted for the simple mixer and the amplifier tuning broadened as much as possible. A bridge frequency of 2 kc. could then be used and the distortion was greatly decreased. A differential resistance-capacity coupled amplifier with degeneration in the common mode was used for the action potentials. The output of either this amplifier or the 175 kc. bridge amplifier could be switched to the vertical deflecting plates of the cathode ray oscillogrsph through a single stage untuned power amplifier. The conversion of all bridge output frequencies to 175 kc. before they were impressed on the oscillograph as well as the short time intervals involved precluded

I,

" OSCILLATOR

1

I BRIDGE

, . ..

S T I M U L U S s w E E P I, V-AMPLIFIER

FXG. 2. Schematic diagram of the electrical equipment.

I I

The axon is at the left, and the balancing resistance and capacity at the right, of the bridge. The action potential and bridge amplifiers are represented by V-amplifier and Z-amplifier respectively and the cathode ray oscillograph by C. R. the use of the Nitell~ motion picture and ellipse technique, but the use of a hori- zontal sweep circuit was convenient since the axon could be stimulated between

ne and ten times per second as was usually done.

The stimulus was a short shock which was taken from the sweep circuit in such a manner that it was applied at the start of the sweep, and a shielded transformer was used in the stimulus circuit to reduce the shock artifact.

Procedure Experimental.--After the axon was placed in the measuring cell and had become

steady, the resting parallel resistance and capacity were measured at 9 frequencies

Cole and Curtis 1939

SLIDE 13

Cole and Curtis 1939 40 mS/cm

2

SLIDE 14

large decrease in transmembrane impedance (AC resistance) during action potential less than 2% change in membrane capacitance

SLIDE 15

SLIDE 16

Hodgkin and Huxely, 1939 and Cole and Curtis, 1940

SLIDE 17

at this point all of this research ground to a complete halt

SLIDE 18

and after a short interlude for killing and maiming, neuroscience resumed

SLIDE 19

during an action potential the membrane potential changed rapidly the membrane potential change was associated with a very large change in membrane conductance the membrane potential change and the conductance change occurred nearly simultaneously and interdependently how can one tease them apart?

SLIDE 20

The Voltage Clamp

Marmount, Cole, Hodgkin, Huxely and Katz (1947-49)

SLIDE 21

SLIDE 22

SLIDE 23

Hodgkin and Huxley introduced the concept of ionic conductances to study the instantaneous current-voltage relations as follows: Recall that conductance, g=1/R and that R=V/I. Thus, g=I/V Note that V here is not the resting membrane potential but the difference between the resting membrane potential and the equilibrium potential for the ion.

g =I /(E -E )

Na Na m Na

g =I /(E -E )

K m K K

and

This called the driving force.

driving force

SLIDE 24

SLIDE 25

g and g were plotted after stepping to different command voltages

Na K

The kinetics of and are both voltage and time dependent

Na

g

K

g

Text

SLIDE 26

H&H assumed that some physical event, like a molecular change, underlay the voltage and time dependent change in G. Such behavior could be accounted for if the voltage sensor consisted of

ne or more membrane bound dipoles that could be either in a permissive

(conductance on) or non-permissive (conductance off) state The K current, the onset was sigmoidal in time and the decay exponential If the probability that such a dipole particle is in the permissive state is n, then the probability that x particles are in state in is n x

SLIDE 27

α βn

n n 1-n

K

I

=

4

n

k

g (

m

V

−

k

V )

where the voltage and time-dependent changes of n are given by

For the K conductance, based on the sigmoidal shape of the rise in current, the best fit was obtained by

SLIDE 28

τn= 1 αn+β n

n∞= αn αn+βn

as an alternative to using rate constants, H-H defined a voltage dependent time constant, and a steady state value for n, n

τ

n

∞

dn dt = n∞ − n τn

Then the change of n with time, which is formally equivalent to the changes in the K+ conductance is calculated by solving the ODE

dn dt = α n(1− n) − βnn

The change in n over time is given by

SLIDE 29

Similarly, the Na conductance was formalized as The extra term h is required for the inactivation

Na

I

=m 3h

Na

g

(

m

V

−

k

V )

Na

SLIDE 30

dm dt

=

∞

m −m

m

τ

dh dt

=

∞

h −h

h

τ

The values for the sodium conductance are obtained by solving these

m

τ =

1

m

α +

m

β

h

τ =

1

h

α +

h

β

∞

m =

m

α

m

α +

m

β

∞

h =

h

α

h

α +

h

β

where

SLIDE 31

h is actually 1- probability of inactivation

r probability that the gate is not inactivated

SLIDE 32

Predictions of the H-H Model

1. refractory period

SLIDE 33

The absolute refractory period is due to Na+ channel inactivation The relative refractory period is due to partial Na channel inactivation and the delayed rectifier K+ conductance

SLIDE 34

Predictions of the H-H Model

1. refractory period
2. threshold

SLIDE 35

20 mV 2 nA 40 ms

SLIDE 36

As the membrane depolarizes, m increases, but so do n and h, according to their voltage dependence and their voltage dependent time constants Individual channels have no fixed threshold For a particular K channel, if its 4 n particles are in the permissive state, it will open - this is a probabilistic thing Threshold is that voltage at which the inward currents just

verbalance the outward currents. At the point the inward

current becomes regenerative and the action potential takes

ff.

Threshold

SLIDE 37

SLIDE 38

SLIDE 39

Dai et al., NYAS, 1998

SLIDE 40

Predictions of the H-H Model

1. refractory period
2. threshold
3. accomodation and adaptation

SLIDE 41

ISI1 ISI10

10 mV 50 ms

S1 S10 ISI1 ISI10

spike frequency adaptation

accommodation

SLIDE 42

SLIDE 43

Predictions of the H-H Model

1. refractory period
2. threshold
3. accomodation
4. gating currents

SLIDE 44

Armstrong and Bezanilla, 1974

step to positive +TTX step to positive

SLIDE 45

SLIDE 46

Action Potential Conduction

Mechanism of propogation

SLIDE 47

SLIDE 48

SLIDE 49

SLIDE 50

Conduction Velocity ...in unmyelinated axon, depends on electrotonic properties

f axon

Action Potential Conduction

conduction velocity is inversely proportional to τ = r c

i m

ri r

m

note that this tau is based on , the axial resistance, not , the membrane resistance Recall from last lecture)

m

r

i

r

=

m

R

i

R

⋅ a 2

Larger axons have smaller axial resistance, a faster time constant and faster conduction velocity

SLIDE 51

Conduction Velocity II

Action Potential Conduction

Conduction velocity also depends on the length constant, λ From last lecture,

λ = rm ri =

m

R

i

R

⋅ d 4

Thus λ dictates how far the local depolarizations that underly action potential conduction spread - and the farther they spread, the fewer times they need to re- initiate at a different membrane location The larger the diameter, the larger λ is and the faster the action potential spreads

SLIDE 52

Conduction Velocity III - Saltatory Conduction

Action Potential Conduction

Myelination increases conduction velocity by increasing λ to the internodal distance, and by decreasing τ

C=eeoA/d

SLIDE 53

Normal Saltatory Conduction

Hugh Bostock at Institute of Neurology, University of London

The graphics represent membrane current at various sites along nerve fibers derived from recordings of external longitudinal current in undissected fibers from rat spinal roots – in some cases demyelinated with diphtheria toxin. Outward membrane current is represented as upward, inward membrane current as downward.

SLIDE 54

Hugh Bostock at Institute of Neurology, University of London

Normal Saltatory Conduction (smaller diameter fiber)

SLIDE 55

Hugh Bostock at Institute of Neurology, University of London

Interrupted myelination

SLIDE 56

“The action potential is ‘all-or-none’”

What does this mean, exactly?

SLIDE 57

Paré et al., 1998

SLIDE 58

2 ms 2 ms 2 ms

SLIDE 59

SLIDE 60

10 mV 1.0 nA 40.0 ms

SLIDE 61

SLIDE 62

Text

SLIDE 63

SLIDE 64

... it means that it has a threshold

SLIDE 65

Antidromic Action Potentials

10 ms

1. fixed latency
2. high frequency following
3. only one response per stimulus
4. collision

SLIDE 66

SLIDE 67

5 superimposed sweeps

Prensa and Parent, 2001

SLIDE 68

Kocsis and Vandermaelen, 1979

SLIDE 69

Swadlow et al., 1980

ARP RRP Supernormal Period Subnormal Period