Neuro~¢ience Letters, 15 (1979) 147--152 © Elsevier/North-Holland Scientific Publishers Ltd.

147

A STA'I~-~I'ICAL LIODEL SUPPORTS THE SUBUN1T HYPOTHESIS OF QUANTAL RELEASE D.R, M A ~ N , M,E. KRIEBEL and F, LLADOS Department o f Physiology, Upstate Medical Center, State Uni,~rsity of New York, 8yraeu~, N Y 13210 (U.S.A.) (Remived May 21st, 1979) (Revised vemion received August 14th, 1979)

(Accepted September llth, 1979)

SUMMARY

Successive frequency amplitude histograms of mixAature endplate poten(MEPPs) from mouse neuromuscular, jur,c ~ s show peaks at inte~,~-al multiples of the smallest peak (s-MEPPs). The s-MEPPs are assumed to aave normally distributed amplitudes and to represent the subunit size. A model has been derived from assumptions based on the hypothesis that MEPPs are generated by the synchronous release of transmitter subunits. The model wa~ statistically ~ on amplitude histograms and in the majority of cases the model produced extremely good fits to observed distributions. While studying miniature endplate potentials (MEPPs) from small m,~cle cells of the frog u~orilw, Kriebel and Gross [9] observed that most of the ampli'mde ~ b u t i o r ~ were not smooth, bell.shaped curves but were composed of multiple ~ ~see Krlebel and GroM, Fig. 2A, 5A and 9C. ref. 9). Them multiple peaks wet~ r~t evident in the cloMical histograms of Fatt and Katz [7], del ~ 1 o and Katz [6], Boyd and Martin [4J or Liley [12] because they were c o ~ m l fron small MEPPs which most likely were recorded from larger muscle cells. Consequently, previously publishe~ MEPP were smooth with no ,econdary peaks or shoulders. In addition, Krlebel and ~ [9] described a prominent class of small MEPPs (s-MEPPs), with an amplitude about 1/7 tha~ of the mean. These s~MEPPs were also reported by Cooke and Quastel [5] in the rat diaphragm and by Kriebel et al. [10] in the mouse diaphragm. In the mmtzemed frog preparation, these s-MEPI~ ~ only 2--5% of the total MEPPs. Their small size and low aecmmt for ~ sbsence in earli~ l~jblished h i ~ z ~ m ~ . However, challenges such as elevated tempera~Jxe [9 ] or tetanic nerve stimulation [ 5,11 ] greatly ~ the percentage of g-MF.~Ps.Ind., ~Ith zepeated cl~l~ ~it m po~hle to ~ R ~ all~ into the s.MEPP cla~. K~ebel and Grow [9] on ~ fzog ~ and Kziebel et aL [10] on the mouse diap ~ ~ that the s-MEPPs composed a definite peak in th~ MEPP ampfitude~ which w u c ~ out of the ~ k ~ o u n d no;~

148

This fact coupled with the obse~vat~ns that successive peaks in MEPP smplit u d e ~ were at integral multiples of the s-MEPP mere and that peak in~ did not change with changes in mean MEPP amplitude led them to propose tbnt the larger MEPPS are composed of mimnits. These subunits generate s-MEP~. Bevan [1] confirmed t~e existence ofs-MEPPs in the normal frog Imelmm~ion but did not observe a s-MEPP peak and found no evidence for multiple, integr~ peaks. On the other band, Wem~ ~ d SUmer [19] and Wm~g and MotelicsJieino [18] show MEPP amplitude histognms with dear multiple peaks that are integral multiples of a subunit. However, Wemig and Stirner [19] do not show the s-MgPP peak, tmflm~ because their s-MEPPs were lost to the noise and/or had a very low frequency. Nevertheless, Wemig and Stirner [19] modeled the observed multiple peaks with binonfial parameters and the model fits the data. Miller, Weinstock and Magleby [15],in a very challenging note, also report multiple peaks in histograms of miniature endpla~ current (MEPC) areas. They enumerate criteria which are useful to distinguish the 'subunit' hypothesis from the 'nmdom variat/on' hypothesis u an explnnM~n for multiple peaks. Criteria for the subtmit hypothesis ere: (1) statJonm~v of the peaks in successive time periods; (2) the spacing between peaks should be constant; (3) peaks should be integral multiples of the smallest peak; (4) the variance of the peaks should increase. The data presented by Miller et al. [15J do not meet their criteria so they concluded that the peaks in their histogrm~ arose from rsndom variations in the data resulting from a limited numb~c of ohsen,~d MEPCs. however, histograms presented by Kriebel et al. [i0] completely s a t l ~ the above criteria. Nevertheless, in this note, we have eztended out, control times in ~)rder to collect more MEPPs and thus ~ meet the crl. ~eria proposed by Miller et al. [15]. We recorded MEPPs from celk of the mouse diaphragm which showed ementtnlly no change in membrm~ potential (usually less than 5%) and showed no ~qp~icant trends in MEFP frequencies. The electrophysiologicalset-upwas conventional(seeref.10 for derma). The diap~ was bathed in a modified F,~zb buffer reline [5] and the recirculated with an air llft (95%02 -- 5% CO2). MEPPs w(=e recorded on tape and subsequently p h o ~ on moving film. The noise level was 50-1oo ~ v p e ~ e a k . MEPP amp~tudm ~ere read ~ by p r o ~ the film onto graph paper so that MEPP amplitudes and calibration signals were determined to the nearest half line (50 ~V). Therefore, a system_Ktic measuring error would result oniy in single histobar positive or negative fingers. Our systematic reading error could not produce smooth peaks composed of several ~ b e ~ . The mplitudes of the calibration signals were used to determine the combined mcozding and meammement error (a~ in the. model described later). Fig'. 1 ( A - E ) are MEP.P histoglmm of suceemive 12-rain periods. The mean MEPP ampli~des were stationary and the frequencies of each period fairly constant. Note that the sample ~ i ~ of each period k not small (about 650 MEPPs), The smalkr peaks appur at definite intervals and am integnd multiples of the smallest ~ (s~MEPPs). Moreover, the peaks in the com.

149

~8

'

em

"tk Fig. 1. C o n t ~ l h i d o g r ~ m demong~mting Jtationarity of s-MEPP mean and peak intervals. (A--E) 8uc~mmi~ 12~min ~ o m . (F) Summed histogram. Note that the number of events in each ~ t i o n is fairly large: (A) 612 M E F ~ 51 MEPPs/min, (B) 734 MEPPs, 61 ~ / m i n , (C) 725 ~ , 60 MEPI~/mLn, (D) 634 M E P ~ , 53 MEPPs/min, (E) 591 MEPI~, 49 ~ / m i n and (F) 3297 MIATI~, 55 MEFPs/min. Resting membrane p o t ~ t i a l went from --80 to - 7 8 during I h of recording. Mean MI~P s~npUtude was volt: (A) 2.46 mY, (B) 2.28 mV, (C) 2A2 mY, (D) 2.65 mY, (E) 2.75 mV and (F) 2.50 inV. Note that tim ~ t i m a t e d s-ME]FP mean (~), and therefore the estim~vd peak interval, ~ the name in (F) as in each subsection ( ~ Table I). 18~lay~ld motmv. The ~&~dated n o i ~ and nmasurement error variance (o ~) for this cell was 0.044 mY.

bined histogram (Fig. 1F) are in the same l~)sitionas in each subsection. The h ~ of Fig. 1 also show two additional i m p o ~ m t characteristics.The firstpeak representing the s-MEPPs is a clear peak out of the noise (the noise level would be repzesented by the firsttwo histobars) and the overall shape of the s.MEPP class is a Gammian curve. An additional characteristic of the

overall shape of the histogram profile is that there are two major compo. nents. The ~ MEPPs ( d i s ~ ~ the peaks) form an overall skewed disi~l~flon. The skewed distribution can be cles~ly demonstrated by combining ~ b a m by'~ or fou~. The second part of the profile consists of the lazg~ MEPPs and is 'belld~k~l'. However, both classesshow peaks that ~ integralmttltiplesof the s-MEPP peak, This ob-~rvation demonstratc~ that allMEPPs ~ than ~ P P s ate composed of the same class of subunits [10]. The sulmnit mleme m e c k ~ m and/or synchzonization mechanism for these two climes ate pzobably quite diffe~nt ~mce the mechanism releasing 'skewed MEPPs' ismorn l ~ t to bo~_ 1~ttm toxin [10] and ~-btmgazotoxin [13], In ~Idition, MF,,PPs of ~ skewed distribution are u~v_~]!ynot evoked [1~I]. Visual inspection of the peaks in Fig. ~ shows that the f~t three ~,~teria for the subunit hypothe~ ~ outlined above are satisfiecL'ITieobservation

that ~

n~.

~

of the

The

sppe~ to ~ h ~

been an ~ m ~ -

~ o f

would b e r e ~

~

in t h e ~

mnp~

purred

Uffit t h e

~ee of ~ ~ would ~ relatively more dependent on t ~ unit vKiance ~ the number of subunits i n ~ The following three usumptions were used to derive a model (a prolmbility densi~, function of MEPP amplitudes), to test the hypothesk that MEPPs sre c o ~ of ~ : (I) ~ E l ' l ' s result from the r e k u e of a mbunit of trsmmitteL The subunit amplit~e is ~ t o be, normally, ~ ~mesa (~) sad re~~

m~.

more mbuai~ Subun/~ ~ e m i m e d t o a u n ~ , mid k d , ~ d e n t ~ , therefore, the r e ~ of / mbm~tJ would produce a nonmily d k t ~ b u ~ 1 po~on of M_EPP~ p ~ with ~ ¢j/~)~ ~ (jo 2 ÷ o~/). (8) The over~ mpl/tude ~ t r J b u ~ ~, t l ~ o r e , e o ~ of ~ ture of these subpopu_iations. ~ ~ b p o p u l M / ~ must ~ m u l ~ by a weighting ~ (~'j) which ~ t s the p r ~ that a M E ~ belonm to ~e jth pop~Jlation. The probability density funet/on of k s u ~ o n s is, therefore, u follows: f(x) = W, • N, (x) + W2 . N2 (x) + • • • + %

where f rude Fc

(

x

)

~

~ty

• IVh(x)

~ o ' ~ , density ~ n

(I)

a ~ P P of ~ l i with m (j~)

151

TABI~ I MAXIMUM LIKEI2[HOOD E ~ T E S

OF THE PARAMETERS IN THE

MULTIMODALMODEL ~

~,(mV) ~(mV) W~

W~ W, W4 W. W,

W, W, W, W~, W, W~z

W~ W~, W, W~, W,, W,, W~, W~, ~ y ,

fx~m Fig, 1

A

B

C

D

E

F

0.30 0.049 0.1209 0.0859 0.0596 0.0463 0.0315 0.04~ 0.0285 0.0431 0.0"/26 0.6899 0.0776 0.1175 0.0943 0.0512 0.036~ O.O~U 0.0157 0 0 0.0098~

0.30 0.046 0.1180 0.0982 0.0/38 0.0468 0.0470 0.0362 0.0555 0.0285 0J.;445 0.0904) 0.1102 0.0510 0.1154 0.0138 0.0473 0.0110 0 0.00~/ 0.00~5 0.00~94

0.29 0.048 0.0996 0.0811 0.0550 0.0560 0.0351 0.0473 0.0222 0.0630 0.0~94 0.1110 0.0657 0.1191 0.0942 0.0217 0.0512 0 0.0107 0 0.00653 0.0111

0.30 0.041 0.0756 0.0883 0.0618 0.0445 0.C~39 0.0332 0.0303 0.0668 0.0521 0.0699 0.0762 0.1276 0.0997 0.0107 0.0663 0.0250 0.0156 0 0.0526 0

0.30 0.040 0.0700 0.0897 0.0443 0.0454 0.0311 0.0330 0.0423 0.0438 0.0621 0.0668 0.0631 0.1226 0.0815 0.0441 0.0740 (~.0244 0.0253 0.0193 0.0083~ 0.00885

0.30 b.046 0.0974 0.0888 0.0577 0.0477 0.0379 0.0385 0.0357 0.0475 0.0565 0.0828 0.0768 0.1058 0.0998 0.0225 0.0549 0.0157 0.0126 0.00764 0.00394 0.00975

f~e above m ~ ~

model w~m ~

egaip~t the following

reduced (bimodal) model: f ( x ) = w/.J(2~o| ) . ~ p (--(x--~,)~/2o] + (1-w)/V(2~o])

model tJ simply the weighted eu~ of two ~ e ~ ftmctio~. It ~.tld

(2)

• ~p (-(~-p~)~/2o~

p r o d u c e a good fit t o ~

probability density

amplitude ~ b u t i o r ~

if

the ~ ( ~ ~ ) ~PPs ~ from the r e ~ of a single quantum of t z m m i t t ~ ~ size k no~.~dly ~ a t e d w~h ~ ~ ~ variance o | , emd t ~ ~ M]gP~ remit from ~ mleaN of a s m a r t 'qu~tten' w'em~ ~ k noczally ~ with melm p~ and ~ ~]. The multimodal model w ~ tested a~mst this ~iuced bim~el model by using the lemmdtzed~~ test cr~'~.~ (for ~ d~'~ see ref. 14).

~uced ~

i ~

~

~

his ~

~

~ ~ ~

ry~ptic

152 REFER]~CE8 1 Bevan, S., SubminiaL~ end-pkte ~ t i s k ~ ~ ~ tio~,,1, l'hy,~_ (Loud.), 25~ (19'76) 145--155.

fr..~ mmmm,,meudm"jm~c-

(Lo~.), S,tS (]L~4) 5:Ze-,e,31. s aonmtein, a.C.,a~x,nt,a m o ~ m u ~ i q m m ~ d i e w a t . , ~ , m i ~ ,mte~-pie~ ipmslia; ~ that release am occur ~ bmmW,J. ~ . (T.,~d.), ?SS (1978) 375-'-~,95. 4, ]k,yd, 1-~ and bba'tin, A.R., 8pontaNoun ~ I d activity at ~ ~,~,junetfm~, J. P h y M . (Lond.), 132 (1956) 61--73. b Cooke, J.D. u d ~ , D~MJ., T r s m m t t ~ ~ by mamm,l i ~ ~ mm~eterin mmome to ~ , a. ~ . (Z,emd.), SSS ( l ~ S ) ~ 7 - - , ~ 5 . 6 del ~ , J. sad K ~ . , B . ~ ,eompoNm~ of the end-plate Vot,amt/sl, J. Phy. eioL (l,o~d.). 124 (1954) 560--575. 7 F~d~,P. m~d Ksl~, B., 9pooSaemn m ~ ~ ~ m o ~ emne ee~lb~m.J. Fhyaioi. {T,ood.), 117 (1959-) 109-128. 8 gat,z, B. In G.A. CotCreHand P.N.R. Usherwood (Eds.), Synapses, ~ Press, Few Yozk, 1977, pp. 1"5. 9 Kriebel, M.E. and Gross, C~B., M ~ distri~ of frog minisgwe en~plate potentials in adult, denermted, amt tadpole leg mmcle, J. lte~. Physkd., 64 (1974) 85-103. 10 Kflebel, M.E., Llad~, F. and Matteson, D.R., ~)ntmn~ous eubmmkdu~ end-plate potentiab in mo~e d i a p b r ~ : evidence for ,ejnehroem~ rehle, J. Pl~aioi. (I,ond.), 262 (1976) 553.-581. 11 K.rtebel, M.E., Bmmll mode mLedatm,oead-phd,e ~ m ' e ~ aandevoked in bttmaad p,.~mm#o~ a.d In h i ~ MS m ~ , ~ ~em., 14s O ~ S ) ~Sl--~SS. 12 Lacy, A.W., An tnve~J~mn of spontaneou~ settvity st the ~ u m d a r ~ u of the r~t, a. ~ 1 . (Lond.~ ZSS (~gSe) 65o-ee~. ~s ~ , W., bl~t, uon, D,R. s . d KzJebeJ, M,g., p ~ z i n ~ bto,~ one elm of mlnlataue e n d ~ potm#ab, Nsture (Lond,), (19"70)Lo pm~. 14 P/~tteeon, D.R., A stetlstic~ model indicates tha~ meppe u d mslt~y evokad eppe ~ . c~nl)need of s u b ~ , Ph.D. Thesis, UpaeSe ~ Cuter, 6fete L i l y of York, 8yraeuN, New York, 1979. 15 MAiler,D.C., Weinstock, M.M. and Msgk~y, LL., Is the quantum of ~ t t ~ cornpond of subunits?, Nature (Lond.), 274 (1978) 388--090. 16 Z~ood, A.M., GzaybUl, F.A. en~ Bo~, D.C., lntrodu~tkm to the theory of s~tl~k~, McGraw-HiU, New York, 197~, pp. 276--283 sad 440"--442. 17 Steel, R.G.D. and Torfle, J.H., Prin¢/piN snd proeadu~s ot statist~, McGraw-HilL New York, 1960, pp. ~19--~L50. 18 Wern.~8,A. ~td ~ - H e i n o , L, On the Wesynoptie mt,~e of the qmmt,~l su~u~;,

s (l

s) ss]-sa4.

19 Wern~, A. and 8t/rr,er, H., Qumttr~ amplitude dJstsdbuff~o~ point of unity of the rynaptie 'active zone', Nature (Loud.), 269 (19"7) 8~)---~2~.