0.5 µm · 20 µm 10 ms 10 mv fiber diameter (µm) e 0 n d p l a t e a r e a (µ m 2) 300 600 900...
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Gillingwater 0.5 µm
Transcript of 0.5 µm · 20 µm 10 ms 10 mv fiber diameter (µm) e 0 n d p l a t e a r e a (µ m 2) 300 600 900...
Gillingwater
0.5 µm
MEPPs
Synaptic recordings from the frog NMJ: B. Katz et al.
Ca2+
Mg2+
EPP
MEPP
5 mV
10.00 ms
5 mV
10.00 ms Log Vepp
Log Ca 2+o
Slope ~ 4
Synaptic responsesfluctuate randomly inresponse to constant
excitation
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(2) = 3p2qP(1) = 3pq2
P(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
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
0 1 0 0 0 0
0 0 0 0 1 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 1 0 0 0 1
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 1 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
1 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 1
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
1 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 1 0 0 0
0 1 0 0 1 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 1 0
0 0 0 0 0 1
0 1 0 0 0 0
0 0 0 0 0 0
0 0 0 1 0 0
1 0 0 0 0 0
1 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
1 0 0 0 1 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 1 0 0 0
0 0 1 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
1 0 0 0 0 0
0 0 0 0 0 0
0 0 1 0 0 0
“God does not play dice ”
--> Simulation:Excel
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:
Px=e!m.m
x
x!MEPPEPP
Stim.
MEPPs
EPPs
Quantal analysism=Ln (Trials/Failures)
m=1/C.V.(EPP)2
Actual m
Threshold m
Quantal analysis of EPPs shows a “safety factor” of 2-5
Wood SJ & Slater CR. (1997) The contribution of postsynaptic folds to the safety factor forneuromusculartransmission in rat fast- and slow-twitch muscles. J Physiol.;500:165-76
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 necessaryto assess and correct if required for non-linear summation ofsynaptic potentials. Synaptic currents sum linearly.
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.
Gillingwater D. Thomson
5 ms
EPPs - Facilitation
300 ms
10 mV
EPPs - Short-term Depression
Frog 200
Rat, mouse 50-75
Man 20-30
Species Quantal content
Quantal content varies in differentspecies
0
50
100
150
200
250
0 500 1000 1500
Synaptic Area (?m2)
Qu
an
tal
Co
nte
nt
man
rat, mouse
frog Frog
Rat
ManSynaptic area (µm2)
Fibre diameter, synaptic area and quantal content are correlated
Kuno, Turkanis & Weakley (1971); frog nmj
0 10 20 30 40 50 600
250
500
750
1000
1250R6/2
Wild type
Fibre Diameter (µm)
20 µm
…likewise in mice:
Wilkinson RS, Son YJ, Lunin SD.Release properties of isolated neuromuscular boutons of the garter snake.J Physiol. 1996 Sep 1;495 ( Pt 2):503-14.PMID: 8887760
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
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60
Occupancy%
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
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-10
mV
AC
1
190 200 210 220 230 240 250 260 270 280 290
s
Keyboard31
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5
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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
Stain Destain
hνHydrophobic Hydrophilic
“FM” styryl dye structure and function
Bewick
Bewick
250 ms
10 mV
Synaptic depression
…. but just 5 simple Principles of Chemical Synaptic Transmission:
Synthesis
Storage
Release
Action
Inactivation
A host of molecules...
Neuromuscular transmission/Quantal Analysis Problems
1. In an experiment on a partially curarised frog neuromuscular junction,
acetylcholine (ACh) was applied to the endplate by iontophoresis, using 1 nA, 1 ms
current pulses at a frequency of 2 Hz. A train of five endplate potentials (EPPs) was
then evoked by stimulating the muscle nerve at 50Hz. The iontophoretic pulses were resumed within 20 ms of the end of the stimulus train.
The following data were obtained:
Mean ACh response before EPP train = 1.53 + 0.12 mV (mean ± S.D.; n=10) Mean ACh response after EPP train = 1.51 + 0.10 mV (mean ± S.D.; n=7)
EPP number 1 2 3 4 5
Amplitude (mV) 2.2 2.7 2.1 1.3 0.9
a) calculate the amount of charge delivered by each of the iontophoretic current
pulses;
b) sketch the characteristic responses to ACh and nerve stimulation indicating the
time course of the responses;
c) how might the iontophoretic responses to ACh change, if a low concentration
of ACh (1 M) were also continuously present in the medium?
d) is the hypothesis that short-term synaptic depression is caused by desensitisation
of ACh receptors supported or refuted by these data? Give your reasoning
2. Intracellular recordings were made from a mouse neuromuscular junction. The
nerve supply was stimulated 150 times at 1Hz. The mean size of the EPP evoked was 1.00 mV. Five of the stimuli evoked no response (i.e. there were 5 'failures').
a What was the mean quantal content at this neuromuscular junction?
b What do you predict for the quantal size, the amplitude of the uniquantal event
(MEPP)? c How many of the EPPs would you predict to have quantal contents of 1,2,3 and 4
quanta?
d What do you predict would be the standard deviation of the EPP amplitudes? e If the baseline ‘noise’ level peak-to-peak was 500 !V, how would this affect the
accuracy of your estimates?
3. In an experiment on an isolated flexor digitorum brevis nerve-muscle preparation
dissected from a mouse, intracellular microelectrode recordings were made of spontaneous miniature endplate potentials (MEPP). Endplate potentials (EPP) were
then evoked by nerve stimulation at a frequency of 1 Hz. In total, 97 of the stimuli
applied to the nerve evoked an EPP but 3 stimuli failed to evoke any EPP. The
following mean data with their standard deviations were obtained:
Mean MEPP amplitude (± SD) : 1.20 ± 0.72 mV
Mean EPP amplitude (± SD) : 4.25 ± 2.42 mV
I. Speculate on the ratio of C a2+ to Mg2+ ions in the medium bathing this
preparation. II. Calculate the mean quantal content of the EPP using the Direct, Variance and
Failures Methods.
III. What does the standard deviation of the MEPP amplitude (quantal size)
indicate and how might this affect the estimation of mean quantal content? A. Give one other possible reason for a low quantal content, in the contexts of
health and disease.
