Homeostatic regulation of synaptic strength and the safety factor for neuromuscular transmission

Transcription

1 The Life Cycle of Neuromuscular Synapses Homeostatic regulation of synaptic strength and the safety factor for neuromuscular transmission 1. Synaptic transmission, safety factor and sizestrength relationships at NMJ 2. Quantal analysis 3. Pathophysiology Synaptic transmission Synaptic recordings from the frog NMJ: B. Katz et al. MEPPs Desaki & Uehara, 1981, J Neurocytol 1,11 1

2 Transmission electron micrographs of the principal features of neuromuscular synapses. Schwann cell Nerve terminal Motor end-plate Neuromuscular Junction: postsynaptic Pre Basal lamina Post Junctional Fold Synaptic vesicle Each nachr contains two α subunits, giving an overall stoichiometry of α 2 βγδ (fetal form) or α 2 βδε (adult form). Each of the subunits contains four hydrophobic transmembrane domains. 2nm 6 nm Fetal Adult 3 nm 2 nm Bovine Muscle 9 nm Xenopus Oocyte γ subunit ε subunit 2 ms Neuromuscular Junction: presynaptic (vesicle proteins) 2, channels End-Plate Current (EPC) End-Plate Potential (EPP) 2 mv 2

3 Wood & Slater (1997) Desaki & Uehara, 1981 MEPP EPP Quantal analysis P x MEPPs The ʻSafety Factorʼ for transmission = e m m x x! Actual m Wood SJ, Slater CR. The contribution of postsynaptic folds to the safety factor for neuromusculartransmission in rat fastand slow-twitch muscles.j Physiol Apr 1;5 ( Pt 1): PMID: Threshold m EPPs Stim. Quantal Size: Quantal Content: q = MEPP m = EPP q Threshold 3

4 Vm 2.5 mv Vm Ch mv 1 mv Ch.2 31 Keyboard AC mv mv Ch.2 1 mv 1. ms 1. ms ms s Vm 2.5 mv Ch.2 1 mv 1. ms AC mv Ch.2 1 mv 5. ms s Factors affecting safety factor for synaptic transmission -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) Synaptic depression EPPs - Facilitation 1 mv 25 ms 5 ms EPPs - Short-term Depression 1 mv Gillingwater 3 ms D. Thomson Synaptic size-strength regulation maintains safety factor nt mf NMJ size and muscle fibre diameter co-vary 1 mv 2 na R in 2 ms MEPPs EPPs Kuno et al.,

5 12 end plate area (µm 2 ) fiber diameter (µm) 2 µm ms 1 mv Occupancy% Harris JB, Ribchester RR. The relationship between end-plate size and transmitter release in normal anddystrophic muscles of the mouse.j Physiol Nov;296: PMID: Costanzo EM, Barry JA, Ribchester RR. Co-regulation of synaptic efficacy at stable polyneuronally innervated neuromuscular junctions in reinnervated rat muscle. J Physiol Dec 1;521 Pt 2: PMID: Quantal Content (variance method) at NMJ of rat HD First EPP Plateau EPP (1Hz) Species Quantal content Frog 2 Frog 3 Rat, mouse Man 2-3 Rat Age Man (Based on Kelly & Roberts, 1977 and Kelly, 1978) The size of NMJ and the extent of junctional folding vary between species 2 Frog Frog Frog 15 Rat Rat Synaptic area Rat Man Man Man 5

6 4 3 2 Ch Quantal Analysis 1-5 mv 5. ms Binomial model: Binomial model: Let: n=3 p=.17 (q=1-p) m=n.p Let: n=3 p=.1 (q=1-p) m=n.p P() =? P(1) =? P(2) =? P(3) =? P() = q 3 P(1) = 3pq 2 P(2) = 3p 2 q P(3) = p 3 P(x) = n! x!(n! x)! p x.q (n! x) Let : x<<n p<<1 Then q (n-x) ~ exp(-np) P(x) = exp(!m). m x Poisson Distribution P() =? P(1) =? P(2) =? P(3) =? x! and n! (n! x)! " n x 6

7 P(x) = exp(!m). m x Poisson Distribution P() = exp(-m) P(1) = m.exp(-m) P(2) = m 2.exp(-m)/2 P(3) = m 3.exp(-m)/6 x! Frequency Poisson distribution of Quantal Contents of EPPs (n=1 trials) Quantal content m=1 Poisson distribution of Quantal Contents of EPPs (n=1 trials) Poisson distribution of Quantal Contents of EPPs (n=1 trials) 4 m=2 4 m=3 Frequency 3 2 Frequency Quantal content Quantal content Poisson distribution of Quantal Contents of EPPs (n=1 trials) Poisson distribution of Quantal Contents of EPPs (n=1 trials) 4 m=4 4 m=5 Frequency 3 2 Frequency Quantal content Quantal content 7

8 Methods of quantal analysis: 1. Direct method : m=epp/mepp (better, EPC/MEPPC) 2. Failures method: P()=exp(-m); m=ln(tests/failures) ( for binomial: P()=(1-p) n ) 3. Variance method: m = 1/(C.V.) 2 i.e. m=epp 2 /var(epp) (for binomial: var(m)=npq) Problems - MEPP variance - Non-linear summation - Non-Poisson conditions The Normal (Gaussian) Distribution y = exp(!(x! µ) 2 / 2" 2 ) /(" 2# ) n + P(x) = " exp(!m) mx.- k =1 x!,- 1 %!( x! kx ) 2 (. 2#k$ 2 ' & 2k$ 2 * )/ y (!x 2 ) # % exp $ & 2".25 y = 5.5 2' (µ = ; σ =.5) 1 ' exp (! 3) " 3 x y 15 % ' & ( 1 '! ( x! 1.1k) 2 ( % ' exp # x! $.2 2)k # % 2k.2 2 $ & & ( ( = * % & # # $ $ k = 1 m=3 quanta σ=.2 mv x =1.1mv x Quantal analysis MEPP EPP P x = e"m m x x! MEPPs EPPs Stim. Quantal Size: Quantal Content: q = MEPP m = EPP q 8

9 Correction Factors Martin (1955): v' = v /(1! v /(E m! E r )! v m = q(1! v! (E m! E r ) v= EPP amplitude q= MEPP amplitude m = quantal content McLachlan & Martin (1981) v' = v /(1! fv(e m! E r ) Where f = an empirically determined ('fudge ) factor For mouse muscle, long fibres: f=.8 For frog muscle, long fibres: f=.55 McLachlan EM, Martin AR. Non-linear summation of end-plate potentials in the frog and mouse. J Physiol Feb;311:37-24.PMID: For short muscle fibres (e.g. FDB) the correction is unknown, but f=.3 gives a good fit to our data. Methods of quantal analysis: Pathophysiology 1. Direct method : m=epp/mepp (better, EPC/MEPPC) 2. Failures method: P()=exp(-m); m=ln(tests/failures) ( for binomial: P()=(1-p) n ) 3. Variance method: m = 1/(C.V.) 2 i.e. m=epp 2 /var(epp) (for binomial: var(m)=npq) 4. Convolutions; graphical methods (e.g. see Clements & Silver, TINS 23, ) Note: For all methods except the Failures Method, it is necessary to assess and correct if required for non-linear summation of synaptic potentials. Synaptic currents sum linearly. Myasthenia Gravis Before After edrophonium (Tensilon Test) Case 1 Bilateral ptosis Double vision in all directions Fatiguable weakness Reflexes disappear after exercise Sensation normal 9

10 Myasthenic Syndrome(LEMS): EMG EPP Pre- and post-synaptic abnormalities have distinctive effects on EPPs Synaptic Depression Normal - Normal presynaptic function Normal quantal content (impaired postsynaptic function) Synaptic Facilitation LEMS EPPs have low quantal content and show facilitation - Impaired presynaptic function Low quantal content (normal postsynaptic function) Myasthenia gravis and LEMS are autoimmune diseases Botulism: Enzymatic LEMS: Ca channelcleavage of SNARE proteins antibodies Summary of electrophysiological changes in Myasthenia Gravis and Myasthenic Syndrome X X X X MG: AChR antibodies (NI=Normal Individual) Congenital Myasthenic Syndromes Summary Neuromuscular junctions operate with a high safetyfactor, secured in part by the endplate-size to fibre diameter ratio. Statistical analysis of synaptic potential amplitudes shows that transmitter release is quantized. Palace & Beeson (28) J Neuroimmunol Defects in transmitter release, sensitivity and sizestrength relationships lead to various ʻmyasthenicʼ syndromes, characterised by significant muscle weakness. 1