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Homeostatic regulation of synaptic strength andthe safety factor for neuromuscular transmission

1. Synaptic transmission, safety factor and size-strength relationships at NMJ

2. Quantal analysis

3. Pathophysiology

The The ‘‘Life CycleLife Cycle’’ of Neuromuscular Synapses of Neuromuscular Synapses

Synaptic transmission

Desaki & Uehara, 1981, J Neurocytol 10,101

MEPPs

Synaptic recordings from the frog NMJ: B. Katz et al.

2

Schwann cell Nerve terminal Motor end-plate

Transmission electron micrographs of the principal features of neuromuscular synapses.

Junctional Fold

Basal lamina

Synaptic vesicle

Pre

Post

http://neuromuscular.wustl.edu/musdist/dag2.htm

Neuromuscular Junction: postsynaptic

Each nAChR contains two α subunits, giving anoverall stoichiometry of α2βγδ (fetal form) or α2βδε(adult form). Each of the subunits contains fourhydrophobic transmembrane domains.

6 nm

3 nm

2 nm

2nm

9 nm

Fetal Adult

γ−subunit ε−subunit

BovineMuscle

XenopusOocyte

End-Plate Current (EPC)

2 ms

200,000 channels

20 mV

End-Plate Potential (EPP)

http://neuromuscular.wustl.edu/pathol/snare.htm

Neuromuscular Junction: presynaptic (vesicle proteins)

http://www.hhmi.org/research/investigators/sudhof.html

3

Desaki & Uehara, 1981

Wood & Slater (1997)

q = MEPP

m =EPP

q

Quantal Size:

Quantal Content:

MEPPEPP

Stim.

MEPPs

EPPs

Quantal analysis

!

Px

=e

mm

x

x! Actual m

Threshold m

Threshold

The ʻSafety Factorʼ for transmission

Wood SJ, Slater CR. The contribution ofpostsynaptic folds to the safety factor forneuromusculartransmission in rat fast-and slow-twitch muscles.J Physiol. 1997Apr 1;500 ( Pt 1):165-76.PMID: 9097941

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Factors affecting safety factor for synaptictransmission

-Probability of release

-Transmitter store size and mobilisation

-Cholinesterase activity

-ACh receptor density

-Muscle fibre diameter and ‘input resistance’

-Nerve terminal size/strength

-Junctional fold density (Na channel density)

Gillingwater D. Thomson

5 ms

EPPs - Facilitation

300 ms

10 mV

EPPs - Short-term Depression

250 ms

10 mV

Synaptic depression

Vm

Ch.2

2.5 mV

1 mV

10.00 ms

Vm

Ch.2

2.5 mV

1 mV

10.00 ms

Vm

Ch.2

2.5 mV

1 mV

10.00 ms

10 mV

2 nA

mf

0

-2

-4

-6

-8

-10

mV

AC

1

190 200 210 220 230 240 250 260 270 280 290

s

Keyboard31

6

5

4

3

2

mV

AC

1

85 90 95 100 105 110 115 120 125 130 135 140 145

s

Ch.2

10 mV

5.00 ms

Ch.2

10 mV

5.00 ms

Rin

MEPPs

EPPs

ntSynaptic size-strength regulation maintains safety factor

20 ms

NMJ size and muscle fibre diameter co-vary

Kuno et al., 1971

5

20 µm

10 ms

10 mv

fiber diameter (µm)

0end

plat

e ar

ea (µ

m2 )

300

600

900

1200

10 20 4030 50 7060

Harris JB, Ribchester RR. The relationship between end-plate size and transmitter release in normalanddystrophic muscles of the mouse.J Physiol. 1979 Nov;296:245-65.PMID: 231101

Costanzo EM, Barry JA, Ribchester RR. Co-regulation of synaptic efficacy at stable polyneuronallyinnervated neuromuscular junctions in reinnervated rat muscle. J Physiol. 1999 Dec 1;521 Pt 2:365-74.PMID: 10581308

0 10 20 30 40 50 60

0

20

40

60

Occupancy%

Quantal Content (variancemethod) at NMJ of rat HD

0 100 200 300 4000

100

200

300

400

500First EPPPlateau EPP (10Hz)

Age

(Based on Kelly & Roberts, 1977 and Kelly, 1978)

Frog 200

Rat, mouse 50-75

Man 20-30

Species Quantal content

Frog

Rat

Man

Frog

Rat

Man

The size of NMJ and the extent of junctional folding vary between species

Frog

Rat

Man

0 250 500 750 1000 1250 15000

50

100

150

200

Synaptic area

Frog

Rat

Man

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Quantal Analysis

Ch0

-5 mV 5.00 ms

1

2

3

4

0

Binomial model:

Let: n=3p= 0.17(q=1-p)

m=n.p

P(0) = ?P(1) = ?P(2) = ?P(3) = ?

Binomial model:

Let: n=3p= 0.1(q=1-p)

m=n.p

P(0) = q3

P(1) = 3pq2

P(2) = 3p2qP(3) = p3

P(x) =n!

x!(n ! x)!px.q(n! x)

Let :x<<np<<1

Thenq(n-x) ~ exp(-np)

andn!

(n ! x)!" n

x

P(x) = exp(!m).m

x

x!

P(0) = ?P(1) = ?P(2) = ?P(3) = ?

Poisson Distribution

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P(x) = exp(!m).m

x

x!Poisson Distribution

P(0) = exp(-m)P(1) = m.exp(-m)P(2) = m2.exp(-m)/2P(3) = m3.exp(-m)/6

Freq

uenc

y

Poisson distribution of QuantalContents of EPPs (n=100 trials)

0 1 2 3 4 5 6 7 8 9 10 11 12

0

10

20

30

40

m=1

Quantal content

Freq

uenc

y

Poisson distribution of QuantalContents of EPPs (n=100 trials)

0 1 2 3 4 5 6 7 8 9 10 11 12

0

10

20

30

40

m=2

Quantal content

Freq

uenc

y

Poisson distribution of QuantalContents of EPPs (n=100 trials)

0 1 2 3 4 5 6 7 8 9 10 11 12

0

10

20

30

40

m=3

Quantal content

Freq

uenc

y

Poisson distribution of QuantalContents of EPPs (n=100 trials)

0 1 2 3 4 5 6 7 8 9 10 11 12

0

10

20

30

40

m=4

Quantal content

Freq

uenc

y

Poisson distribution of QuantalContents of EPPs (n=100 trials)

0 1 2 3 4 5 6 7 8 9 10 11 12

0

10

20

30

40

m=5

Quantal content

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Methods of quantal analysis:

1. Direct method : m=EPP/MEPP (better, EPC/MEPPC)

2. Failures method: P(0)=exp(-m); m=Ln(Tests/Failures) ( for binomial: P(0)=(1-p)n)

3. Variance method: m = 1/(C.V.)2 i.e. m=EPP2 /var(EPP) (for binomial: var(m)=npq)

Problems

- MEPP variance

- Non-linear summation

- Non-Poisson conditions

y = exp(!(x ! µ)2 / 2" 2 ) /(" 2# )

The Normal (Gaussian) Distribution

x

yy 5

x2!( )

2 0.25"exp# $% &

0.5 2'=

(µ = 0; σ =0.5)

P(x) = exp(!m)m

x

x!k =1

n

" .1

2#k$ 2

! x ! kx ( )2

2k$ 2

%

& ' '

(

) * *

+

, - -

.

/ 0 0

m=3 quantaσ= 0.2 mvx =1.1mv

y 153!( )exp 3

x"

x!# $% &' ( 1

0.2 2)k

x 1.1k!( )2!

2k0.22# $

% &' (

exp# $% &' (

# $% &' (

k 1=

10

*=

q = MEPP

m =EPP

q

Quantal Size:

Quantal Content:

MEPPEPP

Stim.

MEPPs

EPPs

Quantal analysis

!

Px

=e"mm

x

x!

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McLachlan EM, Martin AR. Non-linear summation of end-plate potentials in the frog andmouse. J Physiol. 1981 Feb;311:307-24.PMID: 6267255

v' = v /(1! v /(Em! E

r)

m =v!

q(1 ! v!

(Em ! Er )

v' = v /(1! fv(Em ! Er )

Correction Factors

Martin (1955):

v= EPP amplitudeq= MEPP amplitudem = quantal content

McLachlan & Martin (1981)

Where f = an empirically determined ('fudge’) factor

For mouse muscle, long fibres: f=0.8For frog muscle, long fibres: f=0.55

For short muscle fibres (e.g. FDB) the correction is unknown, butf=0.3 gives a good fit to our data.

Methods of quantal analysis:

1. Direct method : m=EPP/MEPP (better, EPC/MEPPC)

2. Failures method: P(0)=exp(-m); m=Ln(Tests/Failures) ( for binomial: P(0)=(1-p)n)

3. Variance method: m = 1/(C.V.)2 i.e. m=EPP2 /var(EPP) (for binomial: var(m)=npq)

4. Convolutions; graphical methods (e.g. see Clements & Silver, TINS 23, 105-113.)

Note: For all methods except the Failures Method, it is necessary toassess and correct if required for non-linear summation of synapticpotentials. Synaptic currents sum linearly.

Pathophysiology

Myasthenia GravisBefore

After edrophonium(Tensilon Test)

Case 1•Bilateral ptosis•Double vision in all directions•Fatiguable weakness•Reflexes disappear after exercise•Sensation normal

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Myasthenic Syndrome(LEMS):

EMG

EPPs have low quantal contentand show facilitation

EPP

Normal

LEMS

Pre- and post-synaptic abnormalities have distinctive effects on EPPs

- Normal presynaptic function Normal quantal content (impaired postsynaptic function)

- Impaired presynaptic function Low quantal content (normal postsynaptic function)

Synaptic Depression

Synaptic Facilitation

MG: AChR antibodies

X X

Myasthenia gravis and LEMS are autoimmune diseases

LEMS: Ca channelantibodies

X X

Botulism: Enzymaticcleavage of SNAREproteins

Summary of electrophysiological changes inMyasthenia Gravis and Myasthenic Syndrome

(NI=Normal Individual)

Congenital Myasthenic Syndromes

Palace & Beeson (2008) J Neuroimmunol

Summary

Neuromuscular junctions operate with a high “safety-factor”, secured in part by the endplate-size to fibrediameter ratio.

Statistical analysis of synaptic potential amplitudesshows that transmitter release is “quantized”.

Defects in transmitter release, sensitivity and size-strength relationships lead to various ʻmyasthenicʼsyndromes, characterised by significant muscleweakness.