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Del ays i n I nact i vat i onDevel opment and Acti vati on Ki net i csi n Myxi col a G ant Axons

L . GOLDMANand J . L . KENYONFrom the Department of Physi ol ogy, Uni versi ty of Maryl and, School of Medi ci ne, Bal t i more,Maryl and 21201

ABSTRACT Na i nacti vati on was studi ed i n Myxi col a (two-pul se procedure, 6-ms gap between condi t i oni ng and test pul ses) . I nacti vati on devel oped w th anin it ia l del ay (range 130-817 ps) f ol l owed by a si mpl e exponenti al decl i ne (t i meconst ant T, ) . Del ays (devi ati ons froma si mpl e exponent i al ) are seen onl y f orbri ef condi t i oni ng pul seswheregNe i s s l i ght l y acti vated. Hodgki n-Huxl ey kineti csw th seri es resi st ance, Rs , predi ct devi ati ons f roma si mpl e exponenti al onl y f orcondi t i oni ng pulses that substanti al l y acti vate gNe . Reduci ng I Na f i vef ol d ( i r i ssubsti tuti on) had no ef f ect on ei ther T, or del ay. Del ay i s not generated byRb orby contamnat i on fromacti vati on devel opment . The sl owest t i me const ant i nNa ta i l s i s - 1 ms (Gol dman and Hahi n, 1978) and the gapwas 6ms . Short eni ngthe gap to 2ms had no ef f ect on ei ther T, or delay. Del ay i s a true property ofthe channel . Del ay decreased w th mor e posi ti ve condi t i oni ng pot ent i al s, andal so decreased approxi matel y proport i onal l y w th t i me to peak gNe dur i ng thecondi t i oni ng pul se, as expected f or sequenti al l y coupl ed acti vati on and i nacti -vati on. I n a f ew cases the di f ference between Na curr ent val ues f or bri efcondi t i oni ng pul ses and the T, exponent i al coul d bemeasured . D f ference val uesdecayed exponent i al l y w th t i me constant ' r , , , . The i nacti vati on t i me course i sdescri bedby a model that assumes a process w th the ki neti cs of gNe acti vati onas a precursor to i nacti vati on.I NTRODUCTI ONAn i ssue of some i nterest i n the questi on of how the Na channel gat i ng

machi nery i s organi zed i s whether acti vat i on and i nacti vat i on proceed i nde-pendent l y, as suggest ed by a l i teral i nterpretat i on of Hodgki n-Huxl ey (1952)ki neti cs, or rather are coupl ed together i nto some sort of mul t i state sequence.One of a number of observat i ons bear i ng on thi s i ssue i s t he presence of ani n i t i a l del ay i n the devel opment of i nacti vat i on, as determned w th the two-Address repri nt request s to Dr . L . Gol dman, Dept . of Physi ol ogy, Uni versi ty of Maryl andSchool of Medi ci ne, 660 West Redwood St . , Bal t i more, MD21201 . Dr . Kenyon' s presentaddress i s Dept of I nt ernal Medi ci ne, Uni versi ty of Texas Heal th Sci ence Center, Dal l as, TX75235.J . GEN. PHYSI OL .The Rockef el l er Uni versi t y Press - 0022-1295/ 82/ 07/ 0083/ 20 $1 . 00 83Vol ume80 J ul y 1982 83-102

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84 THE JOURNAL OF GENERAL PHYSIOLOGY " VOLUME 80 " 1982pul se method, reported f or sever a l preparat i ons ( s e e Gol dman, 1976, f o r ar evi ew) . Del ays ar e i n gener al expect ed i f i nact i vat i on devel ops a f t e r aprecursor process . O parti cul ar i n t er e s t f o r t he i s s u e of coupl ed k i n e t i c s i s t heobservat i on, i n Myxi col a axons (Gol dman and Schauf , 1972) , that the del ay i sreduced wi t h a more posi t i ve condi t i oni ng pot ent i al . Thi s i s as expect ed i fi nact i vat i on i s sequent i al l y coupl ed t o acti vat i on, due t o t he shorter t i meneeded f or act i vat i on t o devel op at more posi t i ve potent i al s . Corr espondi ngl y,Gol dman and Schauf di d f i nd i n a si ngl e exper i ment that t he decrease i ndel ay seen wi th t he more posi t i ve pot ent i al was r oughl y para l l el ed by t hedecr eased t i me t o peak gNa dur i ng t he condi t i oni ng pul se .Recentl y, Gi l l espi e andMeves ( 1980), i n a car ef ul s t udy, report ed smal li nact i vat i on del ays i n squi d axons . I n addi t i on, they c r i t i c i z e d some of t hee a r l i e r r epor t s of i nact i vat i on del ays because agap ( a step back t o t he hol di ngpot ent i al between condi t i oni ng and t e s t p ul s e s ) as i n t he ori gi nal pr ot ocol s ofChandl er et al . ( 1965) was not i ncl uded . Agap that i s l ong r e l a t i v e t o t het i me constant of act i vat i on i s e s s en t i a l f or t hes e exper i ment s s o that t he t i mecourse of i nact i vat i on wi l l not be di stort ed by t he act i vat i on t hat devel opsdur i ng bri ef condi t i oni ng pul ses . As demonst r at ed both by si mul ati ons wi t hHodgki n-Huxl ey k i n et i c s ( Gi l l es pi e andMeves, 1980) and anal yt i cal cal cul a-t i o ns ( Kn i f f k i , 1979) , om t t i ng t he gap can ar t i f act ual l y i nt r oduce del ays i nt he t i me course of i nact i vat i on . I n t hei r exper i ments , Gol dman and Schauf( 1972) al ways i ncl uded a gap of 5mswdth i n a si ngl e exper i ment conduct edat 5 Cand 7. 5 ms wdth i n exper i ment s at 2 CThesegapwi dths ar e l ongr e l a t i v e t o t he t i me const ant of act i vat i on (Gol dman and Schauf , 1973 ;Gol dman and Hahi n, 1978) , and i t seems very unl i kel y that i nact i vat i ondel ays reported f o r Myxi col a were pr oduced by t h i s error . Wepresent experi -ments belowt hat es t abl i s h t hat t he i nact i vat i on del ays report ed i n t h i s paperar e a l s o not generated by an i nadequat e gapwdthAsecond c r i t i c i s m rai sed by Gi l l espi e andMeves ( 1980) i s that i n a gapexper i ment , f o r condi t i oni ng pot enti al s l ong enough t o substant i a l l y acti vatebut not i nact i vate gNa, there wi l l be an i nwar d t a i l of Na current f l owi ngdur i ng t he gap. Thi s current f l owi ng across any r esi dual uncompensatedpor t i on of t he s e r i e s resi stance, R, and that f l owi ng dur i ng t he condi t i oni ngpul se wi l l produce adepol ari zati on and hence addi t i onal i nact i vat i on . G i l l e s -pi e and Meves showed wi th si mul ati ons f r o m Hodgki n-Huxl ey k i n e t i c s ,i nc l udi ng R, that such e f f e c t s wi l l pr oduce an i nact i vat i on curve wi t h ani n i t i a l exponent i al decl i ne of j u s t t he Hodgki n-Huxl ey Th val ue f o r condi t i on-i ng pul ses t oo bri ef t o acti vate gNa very much, f ol l owed by aper i od of st eeperdecl i ne f or condi t i oni ng pul ses t hat t e r m n a t e when gNa i s l a r g e, f ol l owed bya return t o t he ori gi nal exponent i al f or l onger condi t i oni ng pul ses dur i ngwhi ch gN i s i nact i vat i ng . They suggest ed that such di storted curves m ghthave been m stakenl y i nt erpreted as demonst r at i ng a del ay .R errors ar e a l s o not l i ke l y t o be t he or i gi n of t he i nact i vat i on del aysreported i n Myxi col a . Fi g . 10 of Gol dman and Schauf ( 1972) presented at ypi cal r e s u l t f r o m that s e r i e s . Peak I Na duri ng t he t e s t pul se vs . condi t i oni ngpul s e durat i on di spl ayed an i n i t i a l pl at e au f ol l owed by a decl i ne rather than

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GOLDMAN AND KENYON I nacti vati on Del ays andActi vati on Ki neti cs 85an in it ia l exponent i al decl i ne. Thi s i s qual i tati vel y di f f erent behavi or f romthat expected f or anR8error . Moreover, a second determnat i on on thi s sameaxonw th amore posi ti vecondi t i oni ng potenti al resul ted i n adecreaseddel ay,even t hough the current duri ng the mor e posi ti ve pul se rose mor e rapi dl y toa l arger peak val ue (Gol dman and Schauf , 1972) . Maki ng the condi t i oni ngpul se curr ent densi ty l arger made the del ay shorter . Thi s i s the opposi tedi recti on expected f or RS tobe thebasi s of thedel ay. We present experi mentsbel ow that establ i sh that the del ays report ed i n thi s paper are al so notgenerated by Rs errors .Wepresent here newobservati ons on thedel ay i n i nacti vati on devel opment

i n Myxi col a that were desi gned to reveal somethi ng about the process gener-at i ng i t . We f i r s t establ i sh that the del ay i s a genui ne property of the Nachannel . We then show that thedel ayari ses f roma processwhose ki neti cs arei denti cal to those of the acti vati on process . Al l of our resul ts are consi stentw th thevi ewthat i nMyxi col aNa channel s i nacti vat i on i s sequenti al l y coupl edto i nacti vati on .Aprel i mnary report of some of these resul ts has been presented (Gol dman

and Kenyon, 1981) .METHODS

Myxi col a were obtained fromMari ne Research Associ ates, St . Andrews, NewBruns-wck, Canada . Methods f or prepari ng and vol t age cl amping the axons were as i nBi nstock and Gol dman ( 1969) . Arti fi ci al sea water (ASW had the fol l ow ng compo-sit ion: 440mMNa, 10 mMCa, 50 mMMg, 560 mMCl , 5mMTri s [Tr i s(hydroxymethyl ) amnomethane], pH8. 0 0. 1 . The temperaturewas 50. 5C Al lpotenti al s are reported as absol ute membr ane potenti al s (i nside mnus outsi de) andhave been corrected f or l i qui d j uncti on potenti al s accordi ng to the val ues of Cole andMoor e ( 1960) , whi ch are sui tabl e f or Myxi col a ( Bi nstockandGol dman, 1971) .Compensat ed f eedback to reduceRwas used throughout . To f urt her reduceerrorsproducedbyanyresi dual uncompensat ed port i onofR8, al l vol tage-cl ampobservat i onsweremade i n bathi ngmedi a wth theNa concent rati on reducedby substi tuti on wthTri s to ei ther 1/2, 1/3, or 1/ 4of that i n ASWreferred to as 1/2Na ASW 1/ 3NaASW and 1/ 4 Na ASW respecti vel y) . I n nearl y al l experi ments 2mM3, 4- di am-nopyri di ne (Al dri ch Chemcal Co . , Ml waukee, W) was added to the bathi ngmedi um t o reducegK (Ki rsch and Narahashi , 1978) . The 3, 4-di amnopyri di ne sol u-ti ons weremade fresh each day and thepHwas checked I n a f ewcases the K-channelbl ocker was omttedw thout any obvi ous eff ect on the resul ts (compare Figs . 1 and 2) .For each experi ment, the hol di ng potent i al was set equal to the natural resti ngpotent i al at the start of t he f i r s t cl amp runandhel d constant thereaf ter . Each vol tage-cl amp run consi stedof a seri es of condi ti oni ng pul ses of f i xed ampl i tudeand vari abl edurati on each f ol l owed by a gap ( 6 ms i n durati on unl ess otherw se noted) and a

f i xed-ampl i tude test pul se. Each condi t i oni ng pul se-gap- test pul se sequencewas bothpreceded and f ol l owed by an uncondi ti oned test pul se, and each condi t i oned deter-mnati on was normal i zed t o the mean of the bracket i ng uncondi t i oned val ues . 15 swere al l owedbetweeneach vol tage-cl amp stepwhether condi t i onedor uncondi ti onedto mnimze the effects of sl ow i nacti vati on (Rudy, 1981) . Pul ses sent to the vol t agecl ampwere f ormed by a PDP 11/ 34computer (D gi tal Equi pment Corp. , Maynar d,MA) i n a progr ammed sequence f or each experi ment . I N was extracted by repeati ng

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86f o r each axon, t he enti re vol t agecl amp prot ocol i n t he pr esence of 1 J IMt et r odot oxi n(TTX Cal bi ochem Behr i ng Corp , San Di ego, CA), and subt r acti ng t he t wo s e t s ofcurr ent records . For t hose exper i ment s i n whi ch det er m nat i ons wer e made i n mret han one Na concent r at i on, TTXcont r ol s wer e r un i n each of t he bat hi ng medi aused . Nodi f f erences i n the cur r ent r ecords were f ound w t h anyof t he TTX-contai ni ngmedi a

RESULTSDemonst r ati on of a Del ay i n I nact i vat i onTIMECOURSEOF INACTIVATION Fi g . 1 pr esents a t ypi cal det er m nat i on .The peak val ue of IN duri ng t he t e s t pul se i s shown as a f unct i on of t hedur at i on of t he condi t i oni ng pot ent i al . I nact i vat i on developedwtha r el at i vel y

-0 s- 0 . 8-0 7, No

(mA/cm-06

-05

-0 4 L0

et 6MSI / 2 No ASW

THEJOURNALOF GENERALPHYSIOLOGY " VOLUME80 " 1982

- 70. 5 mV ~)0

2 4 6 8 10 12 14 30Condi t i oni ng Durati on(MS)

,/ /-I-

FIGURE l . Time cours e of i nacti vati on devel opment . Peak I N dur i ng a 4 . 5-mVt e s t pul se i s shownas a f uncti on of t he durat i on of a -25. 5-mVcondi t i oni ngpul se . The cur ve i s a si mpl e exponent i al w t h a t i me const ant ( T , ) of 5 . 7 1 m .I nset shows t he i n i t i a l par t of t he cur ve on anexpanded t i me s c al e . Del ay i s 285p, s . 1/ 2 NaASWNo K- channel bl ocker . 6- ms gap Hol di ng potent i al was-705mV Axon 81M6 Pul se schedul e i s shown i n l ower l e f t , where At i s t hecondi t i oni ng durat i on .br i ef i n i t i a l del ay of 285 ps f ol l owed by a si mpl e exponent i al decay of ti meconst ant, T, of 5. 7 1 m ( s o l i d cur ve) . Thi s same pat t er n, an i n i t i a l del ayf ol l owed by a si mpl e exponent i al decl i ne, was seen f or each of t he 57det er m nat i ons on 27 axons r epor t ed her e . Agai n, t hi s i s a qual i t a t i vel ydi f f er ent pattern thanexpected f or R errors . The del ays ( i . e . , devi at i ons f roma si mpl e exponent i al ) ar e seen onl y f or br i ef condi t i oni ng pot ent i al s wheregNai s l i t t l e acti vat ed . Hodgki n-Huxl ey ki net i cs i n t he pr esence of some R, , pr edi ct

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GOLDMAN AND KENYON I nacti vati on Del ays andActi vati on Ki neti csdevi at i ons f roma simpl e exponent i al onl y f or condi t i oni ng pul se durati onsl ong enough to acti vate 9Na substanti al l y (G l l espi e and Meves, 1980, Fi g 8) .Note t hat t o demonst rate a del ay, an i n i t i a l pl ateau ( i . e. , i n i t i a l sl ope ofzero) i n t he i nacti vat i on curve i s not r equi r ed . The i n i t i a l sl ope canbe posi t i ve,zero, or even negati ve, dependi ngon t he rel ati ve val ues of the t i me const ant sf or any precursor ( del ay producing) and i nacti vati on processes and on t herel ati ve val ues of the coef f i ci ents on t hese two exponent i al term . To demon-strate a del ay one onl y need showt hat the uncondi ti oned val ue f a l l s bel owt he exponenti al .The i nset i n Fi g 1 shows the ear l y par t of t he curve on an expanded t i mescal e t o i l lustrate howt he i nacti vati on del ays were operat i onal l y determnedThey are taken as t he t i me at whi ch t he uncondi t i oned I N. val ue i ntersectst he exponent i al .

DELAY I S NOT A SERI ES RESI STANCE ARTI FACT Several arguments al r eadypresented st rongl y suggest t hat t he del ay i s not an Rs art i f act . We have al soput t he i ssue t o di rect experi mental test . Fi g 2 i l l ustrates one suchexperi ment .

-1 . 05

- ae5

- 0. 65

Conditi oni ng Durati on(ma)

87

FI GURE 2 . Two i nacti vat i on det ermnat i ons on the same axon Condi t i oni ngand test potent i al s wer e - 29 and 1 mV, respect i vel y, f or bot h det ermnat i ons .T, was 7 . 49 ms and del ay 403 I t s f or bot h curves . Upper curve i n 1/ 2 NaASWand l ower curve i n 1/ 4 Na Hol di ng potent i al was -74mV and gapw dth was6ms t hroughout . 2mM3, 4- di amnopyr i di ne . Axon 81M11 .

I n thi s experi ment two det er m nat i ons weremade on t he same axon wth t hesame hol di ng potent i al , gap w dt h, and condi t i oni ng and test- pul se ampl i -t udes . As i ndi cat ed, one det er m nat i on (upper curve i n Fi g 2) was made i n1/2 Na ASWand t he other ( l ower curve) was made i n 1/4Na ASWAgai nf or both curves we see an i n i t i a l del ay f ol l owed by a simpl e exponenti aldecl i ne . The two sol i d curves are drawn accordi ng to t he same exponenti alf uncti on ( T, of 7. 49 m) . I n f act t he upper curve i s j ust t he l ower scal ed up by

I Na - 0. 45I / 2 No ASW

(mA/em2) - 0. 25- 0. 20

- 0. 20 OA 0 8 1 . 2 1 . 6- 0. 15

1/ 4 No ASW- 0. 10

'02 4 6 8 10 12 14

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88t he r a t i o of the two uncondi ti oned I N val ues . The del ays computed f or bothdet ermnati ons, t hen, ar e al so t he sam ( 0 . 40 ms) , and reduci ng t he cur r entdensi t y by nearl y f i vef ol d has no ef f ect on ei t her ' r , or t he del ay . I dent i calr esul ts were obtai ned on three other axons . I nact i vat i on del ays ar e ther ef orenot producedbyvol tage-cl amp art i f acts dependent on t he cur r ent magni tude .The experimnt of Fi g . 2was done i n t he pr esence of 2mM, 4- di amno-pyr i di ne, whereas that of Fi g . 1 was done wthout any K-channel bl ocker ,wh ch suggest s that these data have not been af f ected byKurrents . As t hedata of thi s sect i on i ndi cate that i dent i cal resul ts ar e obtai ned w th ei t her1/ 2 Na or 1/4 NaASW t he rest of t he det er m nati ons of thi s paper havebeenmade i n 1/3NaASWand i n t he presence of 2mM, 4- di amnopyr i di ne .

ADEQUACY OF THEGAPWDTH Thewdthof t he gapbetween condi t i on-i ng and t e s t pul ses ( 6 m) i s l ong rel at i ve t o t he sl owest t i me const ant seen i nNat a i l currents i n Myxi col a at t hesesam potenti a l s and temperature ( typi cal l y-0 8- 1 . 2 m Gol dman and Hahn, 1978) . Cor r espondi ngl y, f or t he exper i -mnts reported her e, i n each case t he t a i l currents f l ow ng duri ng t he gapwere seen t o decay t o zer o wel l bef ore t he s t a r t of t he condi t i oni ng pul se . At ypi cal record f or a condi t i oni ng pul se termnati ng at peak I Na i s shown i nFi g . 3 . Watever t he condi t i oni ng pul se dur a t i on, t hen, t he occupancy of t he

THE JOURNAL OF GENERAL PHYSIOLOGY " VOLUME 80 " 1982

0 15I mA/cm2m

FIGURE 3 . Cur r ent records f r oman i nacti vati on del ay exper i ment . Condi t i on-i ng and t e s t potent i al s wer e 13 and 8 mV, r especti vel y . Condi t i oni ng pul sedur ati on was 0.75 ms, which was t he t i me of peakgNe Cur r ent t a i l s f ol l ow ngt he condi t i oni ng pul se decay to basel i ne dur i ng t he 6- ms gap wel l bef ore thes t a r t of t he t e s t pul se . 1/3 Na ASW2mM, 4- di amnopyr i di ne . Hol di ngpotent i al -67mVAxon81M35 Scal e : 0 . 15 mA/cm, 2 m .

conducti ng state has always decl i ned t o negl i gi bl e val ues by t he start of t het e s t pul se, and contamnati on of t hi s sor t cannot be t he basi s of t he del ay .For an act i vat i on pr ocess descri babl e by Hodgki n-Huxl eymki neti cs, Nat a i l currents shoul d rel ax as t he sumof three exponent i al s of t i me constants i nt he r a t i o 3 : 2 : 1 wth t he sl owest t i me const ant bei ng j ust T , , , . Na t a i l currentsi n Myxi col a re lax as t he sumof at l east three exponent i al s (Gol dman andHahn, 1978), al though w th ti m constants not i n t he ra t i os r equi r ed bymki neti cs . Three pr ocesses ar e suf f i ci ent t o account f or t he observed del ay i n t her i s e O gNa duri ng depol ar i z i ng steps (Gol dman and Hahn, 1978), and t he

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GOLDMAN AND KENYON I nacti vati on Del ays and Acti vati on Ki neti cs

sl owest acti vati on t i me constant seen i n the ta i l currents i s about Tni . Hencei t i s unl i kel y t hat there i s any sl ower rel axat i on not resol ved i n the currentrecords as the acti vat i on processes seemto be accounted f or . Corr espondi ngl y,condi t i oni ng potent i al s t oo smal l to not i ceabl y acti vate gl va s t i l l producedcl ear i nacti vati on del ays, and a 6-m gap seem suf f i ci ent to di sti ngui sh thet i me course of i nacti vati on f romacti vat i on devel opment duri ng the condi t i on-i ngpul seWe have put thi s i ssue to di rect experi mental test al so. Two det ermnat i onswere made i n each of f our axons, wth hol di ng potent i al , condi t i oni ng andtest- pul se ampl i t udes, and sol uti on composi t i on hel d const ant . For one deter-mnati on the gap wdth was the usual 6 m, whereas f or the other i t wasreduced to 4ms . I n three of theseaxons the gapwas f ur ther reduced to 2ms .I n each case f or everygap wdth the resul ts were the same.

A typi cal experi ment i s i l l ustrated i n Fi g 4 As i ndi cated, the upper curve

0. 8

0. 6I ' D

0. 8

0. 6

0. 4

I / 3 No ASW1 . 0 0

0. 90 0. 4 0. 8 1 . 2 1 . 6

Gap wdth 2 ms0 2 4 6 e 10 12 14 ' X0

Condi t i oni ng Durati on (m)

89

FI GURE 4 . Two i nacti vati on determnati ons fromthesame axon . Condi t i oni ngand test potent i al s were - 30 and 0mV, respect i vel y, f or both determnat i ons .T, was 7. 32 ms and del ay 478As f or both curves . The upper curve had a6-mgap and the l ower curve had a 2- ms gap. Holdi ng potent i al was - 75 mVt hroughout . 1/ 3 Na ASWand 2mM3, 4- di amnopyri di ne . Axon 81M39

was determned w th a 6-m gap and the l ower curvewas determned w th a2-m gap. The two sol i d curves are drawn accordi ng to the same exponent i alf uncti on ( T, of 7. 32 m) . The l ower curve decays to a l ower st eady state val ueas l ess i nacti vati on has di ssi pated duri nga 2-m gap as compared wtha 6-mgap. The del ays are therefore the same (0. 48 m) . Hence even a 2-m gap i ssuf f i ci ent to avoi d any si gni f i cant di stort i on of t he i nacti vati on t i me course byacti vat i on devel opment . I f the del ay seen for t he6-ms gap had been producedby such di storti ons, then the del ay woul d necessar i l y have i ncreased wth the

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90

2-m gapand thedatapoints f or durati ons l ong re lat i ve to ' r m must then f a l labove the curve i n the l ower part of Fi g 4 (see si ml ati ons wth Hodgki n-Huxl ey ki net i cs i n G l l espi eandMeves, 1980) . However, no such effects areseen . For squi d at 2. 6 C, G l l espi e andMeves f ound that a 1-m gap i ssuf f i c ient t o avoi ddi s tor t i on of the i nacti vati on t i m courseTheresul t s presentedso f ar establ i sh that there i s a process precedngthedevel opment of i nacti vati on ( i . e . , i nacti vati on i s not asimp e two-state proc-

e s s ) . Siml ar resul ts have been reported i n wel l -control l ed experi mnts i ncrayf i sh axons (Bean, 1981) andsqui d ( G l l espi e andMeves, 1980) . However,theseexperi mntsprovi de l i t t l e i nformati onabout thenatureof theprecursorprocess Theexperi mnts descri bedi n the fol l owngsecti onaddress thi s i ssue .

A

z

08

06

08

06

041)

Vcond ti onng- 26mV

Vcond ti onng-I I mV

Propert i es of t he I nacti vati on Delay


L L ' : /_J-4 6 8 10 12 14 30

Cond ti onng Durati on(m)FIGURE 5 ATwoi nact i vat i on determnati ons on thesam axon Test poten-t i a l was 4mVf or both determ nat i ons . Gapwdthwas 6m andthe hold ngpotent i al was -71mVthroughout . Upper curve determnedwth a-26-mVcondi t i oni ng potent i al ( T, =5 51 m) . Lower curvewtha-11-mVcondi t i oni ngpotent i al ( T . =. 37 m) . B I n i t i a l port i ons of the two curves i nAn anexpanded ti me scal e . Delaywas 525 ps f or the upper curveand309 i t s f or thel ower curve ( i ndi cated by t he vert i cal l i ne s ) . C Current records f or the twocondi t i oni ng pul ses of thi s experimnt (-26mVrecord at top and -I 1mVbelow . Scal e : 0. 06mA/cm, 2m . 1/3NaASW2mM, 4-di amnopyri di neAxon 81M19

POTENTI ALDEPENDENCYOF THEDELAY Fi g 5Ashows the resul t s of twodetemnati ons on the same axon I n thi s experi mnt the hol d ng potent i al ,gap wdth, test- pul se amp i tude, and sol uti on composi ti on were al l hel dconstant . As i ndi cated, the cond ti on ng potenti a was -26mor the

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GOLDMAN AND KENYON I nacti vati on Del ays and Acti vati on Ki neti cs 91determnat i on shown i n the upper and -11 mV f or that shown i n the l owerpart of the f i gure . r, decreased w th amore posi ti ve condi t i oni ng potent i al i nthe usual way ( 5. 51 ms f or the upper curve and 3. 37ms f or the l ower curve) .However , as shown i n Fi g 5B, whi ch i s the earl y port i on of both parts of Fi g5Aon an expanded t i me scal e, the del ay al so decreased w th amore posi ti vecondi t i oni ng potent i al (525 I t s f or - 26mV and 309,us f or - 11mV) .

B

C

Vcondi t oni ng - 26mV

0. 8 1 . 2 1 . 6 2. 0Condi t i oni ng Durati on (m)

0. 06mA/ Cm2msThe decrease i n del ay w th potent i al provi des f urther evi dence that t hedel ay i s not generated byR9 . Records of the t i me course of the current dur i ngthe -26- and - 11-mV condi t i oni ng pul ses f or thi s exper i ment are shown i nFi g 5C (upper and l ower traces, respecti vel y) . The current f or t he - 11-mV

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92pul se r i s e s more rapi dl y ( t i me t o peak, 1 . 05 m) and t o a l arger peak val ue( 214 I uA/cm) than does that f or t he - 26- mVpul se ( 1 . 50 m and82 I uA/cm) .For the enti re per i od f or which t he del ays are seen, t he i nwardcurrent at -11ms l ar ger than t hat at -26mV, but t he del ay i s l e s s at -11mThi s i s i nt he opposi t e di rect i on f or t he del ay t o be caused i n any way by R . However,i t i s j ust as expected i f acti vati on and i nacti vati on are sequenti al l y coupl edowng t o the reduced t i me f or act i vat i on to devel op at -11mCol l ected val ues of del ay as a f unct i on of condi t i oni ng potent i al are showni n Fi g 6 At negat i ve potenti al s t he del ay decr eases st eepl y wth l es s negat i ve

c 400Fa

300cc200

100

THE J OURNAL OF GENERAL PHYSI OLOGY - VOLUME 80 - 1982

O0000 00

O O

0 OO0 00 00 OO

O

OO O0 O

01-60 -40 -20 0 20Condi ti oni ng Potenti al (mV)

FI GURE 6 I nacti vat i on del ay as a f uncti on of condi ti oni ng potent i al . Datapool ed f r om27 axons . Gapw dth was 6m 1/ 3 or 1/4 NaASWnd2mM, 4-di am nopyr i di ne t hroughout .potent i al and t ends t o saturate at posi t i ve potenti al s . These del ay val ues areabout hal f those reported by Schauf andDavi s ( 1975) .Somewhat more i nf ormat i on about t he del ay process i s gai ned by pl ot t i ngi nacti vati on del ay as a f unct i on of t he t i me t o peakgN duri ngt he condi t i oni ng

08000 O

700 0 0

600000

N 00 0500 00T 080aN

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GOLDMAN AND KENYON I nacti vati on Del ays andActi vati on Ki neti cspul se. The col l ected resul ts are shown i n Fi g 7 . Del ay i ncreases w th t i me t opeak 9N. , and the two vari abl es can be descri bed as roughl y proport i onal . I facti vat i on and i nacti vati on are sequenti al l y coupl ed, then both the i nacti va-t i on del ay as wel l as t i me t o peak 9Na w l l vary w th the acti vati on t i meconst ant . I f both vari abl es remai n equal l y good measures of the acti vat i ont i me constant over thei r whol e range, then proport i onal i ty between the two i sexpected f or the si mpl est sort of sequent i al l y coupl edprocess . Consi deri ng theoperat i onal way i nwhi ch the del ay i s determned, the agr eement between thedata of Fi g 7 and the expectat i ons f or a sequent i al l y coupl ed process i s qui tereasonabl e

O

O

0

O

OL 1 10 I 2 3 4 5 6

Ti me To Peak (me)

O

93

FI GURE 7 I nacti vati on del ay as a functi on of t i me t o peak gNe duri ng thecondi t i oni ng pul se . Data pool ed from24 axons . Same determnati ons as i n Fig6TI ME CONSTANT OF THE DELAY I n seven of the determnat i ons from si x

di f ferent axons, thedi f f erence between the experi mental Na currents for bri efcondi t i oni ng pul ses and the extrapol ated T. exponenti al wereboth suf f i ci ent l yl arge i n magni tudeandsmal l i n var i ance tomeasure rel i abl y . Thesedi f f erenceval ues coul d al so be descri bed as an exponent i al and i n these f ew cases thet i me const ant of t he del ay process, Tdel ay , coul d then be determned . Tdel ayval ues are pl ot tedas a f uncti on of condi t i oni ng potent i al as the f i l l ed tri angl esi n Fi g 8. Al so i ncl uded f or compar i son (ci rcl es) arethe Myxi col a T l ( V) val uesf or this potent i al range (Gol dman and Schauf , 1973) . ' rdel . y ( V) i s i n reasonabl eagr eement w th T t (V) , agai n as expected i f acti vat i on and i nacti vati on aresequenti al .

0Y 500 00 00_O0O

400 00 00.z 0 0O O)7' 0c 300 0 8 0R1P o

20000

100

700 0

6000

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94T, n i s the acti vati on t i me const ant f or an i ndependent ki neti c model .

However, no diff icult ies are rai sed by theagreement between T,n ( V) and Tdelay( V) . Fi g 8 al so i ncl udes (open t ri angl es) acti vati on t i me constants determnedby f i t t i ng a sequenti al l y coupl ed scheme to Myxi col a vol tage-cl amp data( Gol dman and Hahi n, 1978, Fi g 5) . The scheme used was :

whereA i s the resti ng state, B andCre acti vated but not conduct i ng states,Ds the conduct i ng state, andEs the i nacti vated state. Thi s scheme di spl aysthree acti vati on t i me constants consi st ent w th the three rel axati ons seen i nNa t a i l currents, and the sl owest of these ( T3 f romGol dman and Hahi n, 1978)i s pl otted i n Fi g 8 Gol dman and Hahi n presented evi dence f rom in it ia lcondi t i ons experi ments that i t i s the T3rel axati on that i s most cl osel yassoci ated

THE JOURNAL OF GENERAL PHYSI OLOGY " VOLUME 80 - 1982

A - - B; : : t C_D_E

-40 -20 0 20 40Potent i al (mV)

FI GURE 8 Acti vat i on ti me const ant as a f uncti on of membr ane potent i al .Ci rcl es are T,n val ues f or Myxi col a (Gol dman and Schauf , 1973) . Open tr i angl esare acti vati on ti me const ant s f i t t e d to cl amp data from a coupl ed model(Gol dman and Hahi n, 1978), and the f i l l ed tr i angl es are Tdeay val ues (thispaper)

w th the f i l l i ng of the conduct i ng state. T3 ( V) al so agrees w th TmV), and theagreement between Tdel ay ( V) andTmU i s f u l l y consi st ent w th a sequenti al l ycoupl ed process .RECONSTRUCTI ONOFTHTI MECOURSEOF I NACTI VATI ON The ci rcl es i n Fi g

9A i ndi cate experi mental i nact i vat i on val ues for the f i r s t 5ms of the deter-mnat i on on a somewhat expanded t i me scal e so that the del ay can be seencl earl y . Thi s i s the same exper i ment as the upper curve of Fi g 5A. The sol i dcurve has been computed assumng that the gate can be descri bed si mpl y asa three-state scheme, i . e . ,

Rest ; . -! Conduct i ng ; - . t I nacti vatedusi ng the Tdel ay and T, val ues determned experi mental l y f or thi s axon. Threestates are known to be i nadequate (Gol dman and Hahi n, 1979) . However , t hef i t to the data i s qui te good, and the point of the cal cul ati on i s t o i l l ust rate

oT,1 . 0 o Ti me const ant of acti vati on0 fromABCD-Eoo - ' ~EE 0 A Tdel ayc . o 06V> O 0a : _EQ 40 AAAR,0wF= 02 A gro 2C0000

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GOLDMAN AND KENYON I nacti vati on Del ays andActi vati on Ki neti cs 95that theexperi mental l y observed t i me course of i nacti vati on i s consi stent w tha sequenti al acti vat i on- i nacti vati on process . Another reconstructi on w th amor e depol ari zed condi t i oni ng potenti al ( - 8. 5 ms compared w th - 26mV) and a shorter del ay i s gi ven i n Fi g 9B The whol e i nacti vati on t i mecourse for thi s exper i ment i s shown i n Fi g 9C

Ao I . p

C

Vcondi t i oni ng - 26mV0 I 2 3 4 5Condi t i oni ng Durati on (rns)

6 8 10 12Condi ti oni ng Durati on (m)

FI GURE 9 A Earl y ti me course of i nacti vati on devel opment . Ci rcl es are ex-peri mental val ues and t he sol i d curve i s computed assumng sequenti al acti va-t i on and i nacti vati on wth Tdei . y of 583 ius and - r , , of 5. 51 ms . Same experi mentas Fi g 5, upper curves . B Earl y ti me course of i nacti vati on devel opment fromanother axon Sol i dcurvecomputed w th a Tdel ey of 2901 s anda T, of 3. 45ms .CThewhol e i nacti vati on ti me course f or theexperi ment of part B Condi t i oni ngand test pul ses were - 85 and - 35 mV, respecti vel y . Hol di ng potent i al was- 785mr , i s thesame 3. 45ms as f or part B Gap w dth, 6 I ns . 1/3NaASW2m3, 4-di amnopyri di ne Axon 81M31 .Adi f f icu l ty w th the reconstructi ons of Figs . 9A and B i s that they do not

al l owfor the addi t i onal acti vati on processes report ed for Myxi cola (Hahi n andGol dman, 1978; Gol dman and Hahi n, 1978), whi ch ought to appear as aresi dual del ay Possi bl y these mor e rapi d acti vat i on processes produce effectstoo smal l to be detected on thi s t i me scal e

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96The T, - Th Di f f e r e nc e

For each i nacti vati on del ay determnat i on i n these experi ments, a T, val uewas f i r s t obtai ned These col l ected T, val ues ( h a l f - f i l l e d tr i angl es) arepl ottedas afuncti on of membranepotenti al i n Fi g 10 Al so i ncluded i n Fi g 10 arethe ori gi nal T, ( V) val ues of Gol dmanandSchauf (1973) ( h a l f - f i l l e d c i r c l es ) .Gol dmanandSchauf di d thei r experi ments i n ful l -NaASWthout a K-channel bl ocker, whereas thepresent experi ments were done i n thepresence

NEc. Qv0cw0c0cEF=


s

s

Condi ti oni ng Pot ent i al (mV)FIGURE 10 Ti me const ant s of i nacti vati on, determnedby both the twopul se( T , ) and si ngl e pul se (Th) methods, as a f uncti on of membrane pot ent i al Theh a l f - f i l l e d c i rc l es and t he open c i rc l es are T, and Th, respecti vel y, determned i nf ul l - NaASWth no K-channel bl ocker (data f romGol dman and Schauf ,1972, 1973) . The i nvert ed open and f i l l e d tr i angl es ar e T, and Th, respecti vel y,determned i n the presence ofTTXdata f romGol dman and Hah n, 1978) .The h a l f - f i l l e d and open tr i angl es are T, and Th, respecti vel y, determned i ne it her 1/3 or 1/4NaASWnd i n t he presence of 2mM, 4-di amnopyri di ne( t h i s paper) .

of 2mM, 4-di amnopyri di neandwth 1/3NaASWr , i n a f ewcases, 1/4NaASWHowever, both ser i es of experi ments producethesame T, (V) . Thi si s consi stent wth the resul ts of Fi g 2, whi ch showdi r ec t l y that T does notdependon thecurrent densi ty Theopen, i nvert ed t r i angl e i n Fi g 10 i ndi catesa T, val ue determnedwth the peak I N duri ng the uncondi t i oned test step

Tc Th0 oASWo LowCNa] ASWv vASW+TTX

s

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GOLDMAN AND KENYON I nacti vati on Del ays and Acti vati on Ki neti cs 97reduced t o -100 t t A/ cm noww thTTX rather t han reduced Na (Gol dmanandHahi n, 1978) . I t too l ies on the same T, (V) f uncti on.Th val ues (i nacti vati on t i me const ant determned fromthe I Nadecay dur i nga si ngl e potent i al step) were al so obtai ned dur i ng the course of these experi -ment s and they are pl ot ted as the open tri angl es i n Fi g 10. The open ci rc lesare the ori gi nal Th val ues of Gol dman and Schauf . Agai n the two seri es ofexperi ment s produce thesame Th (V) .The current magni t udes encountered i n these experi ments deserve comment . For potent i al s

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98 THE JOURNAL OF GENERAL PHYSI OLOGY " VOLUME80 " 1982the test step . Thi s effect cannot be reconci l ed w th any model i n whichacti vat i on and i nacti vat i on are s t r i c t l y i ndependent ( i . e , descri bed bymono-toni cal l y i ncreasi ng or monotoni cal l y decreasi ng vari abl es, respecti vel y) , andappear as a product , nomatter what the number of states assumed f or ei therprocess . However, i t i s not i n pri nci pl e i nconsi stent w th amodel i n whi chonl y those channel s that acti vate can i nacti vate, al though addi t i onal assump-t i ons are al so needed . For Myxi col aNachannel s, therefore, the avai l abl e ki neti cdata are most si mpl y accounted f or i f acti vat i on and i nacti vati on are noti ndependent but are coupl ed together such that i nacti vati on i s, at l east i npart, sequent i al t o acti vat i on .Resul ts fromother preparat i ons that suggest coupl i ng are reports of T, -Th di f f erences i n l obster (Oxf ordandPool er, 1975), crab axons (Connor, 1976),andcul tured heart cel ls (Ebi hara and J ohnson, 1980), and i nacti vat i on del aysi n careful studi es i n squi d (Gi l l espi e and Meves, 1980) and crayf i sh (Bean,1981) . Bezani l l a andArmt rong (1977) al so f ound an i nacti vat i on del ay i nsqui d by compari ng I N. before and after r emovi ng i nact i vat i on. Conti et al .(1980) foundthat f l uctuati onpower spectra frommyel i nated f i bers were f i t t edsomewhat better by coupl ed than by Hodgki n-Huxl ey k i net i cs . I n squi d( Armst rong and Bezani l l a, 1974, 1977 ; Meves and Vogel , 1977), myel i natedf i bers (Neumcke et al . , 1976 ; Nonner et al . , 1978), Myxi col a axons (Rudy,1976 ; Bul l ock and Schauf , 1979), andcrayf i sh axons (Swenson, 1980 ; Starkuset al ., 1981), the asymmet r i cal di spl acement current i s reduced by depol ar i za-ti ons that produce i nacti vati on, so that charge di spl acements w th acti vat i onk i net i cs ( Armst rong andG i l l y , 1979) are affected by i nacti vat i on . Ca currentsi n Hel i x neurons showboth the h ( l ~ shift anda T, -Th di f f erence ( Akai keet al . , 1978), and Ca channel i nacti vat i on i n snai l neurons seems t o be ani nherent l y coupl ed process (Eckert and Ti l l otson, 1981) at l east i n part f orHel i x (Brown et al . , 1980), i n that Ca i nacti vati on i s dependent onCa entryt hrough the conduct i ng channel . These observati ons do not al l suggest thati nacti vat i on i s obl i gatori l y sequenti al to acti vati on, but they al l do suggestcoupl i ng to some degree.Sequent i al coupl i ngwas not seen, however, by Horn et al . (1981) i n curr entsfromsi ngl eNa channel s i n cul tured rat myotubes where i nacti vat i on occurredat the same rate whether channel s opened earl y or l ate, which suggests thatchannel openi ng and i nact i vat i on proceed i n paral l el . These resul ts do noti ndi cate i ndependent acti vat i on and i nacti vat i on but onl y that these channel sneed not open before i nacti vat i ng . Al so, not al l preparat i ons di spl ay thephenomena reported f or Myxi col a (Bezani l l a andArmst rong, 1977 ; Chi u, 1977 ;Bean, 1981), and there i s a range of Na channel propert i es among di f f erentpreparati ons i ncl udi ng i nacti vat i on at l east t o some degree sequent i al tochannel openi ng (e. g . , Myxi col a), i nacti vati on paral l el to channel openi ng (e. g . ,cul tured rat muscl e), and possi bl y i ntermedi ate cases (e. g ., crayf i sh axons,Swenson, 1980 ; Bean, 1981) .A scheme represent i ng a way to summari ze these di verse behavi ors i spresented bel ow

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/ 3m pm 2,8. 38m L______-

kAB kBC kco kDEA ; : . t B#tC; _t Dr=Eksa k, B kDC kED

99

Vari ous states of t he channel are shown mohl i s the resti ng state, anddepol ari zat i on f avors tr ansi ti ons to the ri ght al ong both rows so t hat MA i stheconducti ng state. Depol ari zat i on al sof avors tr ansi ti ons f romtop to bottomand al l the states i n t he bottomrow are i nacti vated. As shown, wth f i xedrati os between the a,. and f . terms, the f t h term al l i dent i cal , and the ahterm al l i dent i cal , thi s i s j ust mh Acti vat i on and i nacti vat i on are then s t r i c t l yi ndependent as the probabi l i t y of an h parti cl e tr ansi ti on i s i ndependent ofthemstate, and s imlar ly mparti cl e transit i ons are i ndependent of the h state.Thi s scheme al so i l l ustrates the speci al case nature of mh ki net i cs . I ndepen-dence ari ses f romthe constr ai nt t hat eachof the at and / 3t term are i dent i cal .Rel axi ng thi s constr ai nt by, f or i nstance, maki ngone or more of the ah termdi f f erent fromthe others produces a process t hat i s coupl ed to some degree .Another speci al case of i nterest i s obtained by set ti ng the three l ef t- handah and ah term to zero . I f theMA- _ m3ho tr ansi ti on i s al so f orbi dden, as i sconsi stent wth gat i ng charge i mmobi l i zati on, we are le f t w th the fi ve states

encl osed wthi n the dashed l i nes . Fur t her rel axi ng the requi rement of f i xedrati os between the acti vati on rate const ant produces t he s t r i c t l y sequent i al l ycoupl ed scheme:

Hence one can obtai n the two l i m t i ng cases of strictly i ndependent, paral l elacti vat i on and i nacti vati on, and ful l y coupl ed, sequenti al acti vati on ari di nacti vat i on by the adjustment of r at e const ant s . Cl earl y, any vari ety ofi nt ermedi ate cases w th a mx of paral l el and sequent i al processes can al so beobtai ned by a sui tabl e adjustment of rate const ant s . Such pi ctures provi de asi mpl e way t o summari ze a di verse body of experi mental resul ts . However,t hey i mpl y a consi derabl e compl exi ty i n the mol ecul ar organi zat i on of t hegate, and of ' course i t remai ns ful l y possi bl e that Na channel s i n di f f erentpreparat i ons di f fer fromone another more than quant i t at i vel y .What seem fa ir ly cl ear i s that, consi dered separatel y, the acti vati on processi s mul t i state . Thi s i s basedon observati ons of Na tai l currents i ncl udi ng i n i t i a lcondi t i ons ef fects (Gol dman and Hahi n, 1978; Oxford, 1981) , other i n i t ia lcondi t i ons effects (Neumcke et al . , 1976; Hahi nandGol dman, 1978) , mul t i pl e

GOLDMAN AND KENYON I nacti vati onDel ays andActi vati on Ki neti cs

3a , 2am amoh . ' mh,~ mh, ' m3h, III Nm 2l m 3/3mpf th ah pf th ah

IIf th ah I Rh ahI I

I I

3am 2am IIIam Imoho mho MAO. ~ MAO II

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100acti vat i on rel axat i ons i n the gati ng current ( Armst rong and G l l y , 1979 ;Nonner, 1980; Starkus et al ., 1981), and di f f erenti al D20 effects on I N andgat i ng current t i me courses (Meves, 1974; Schauf and Bul l ock, 1979) . Si m-lar ly , consi dered separately, the i nacti vati on process i s al so mul ti state, basedon the observat i ons of mul t i pl e i nacti vati on rel axati ons (Chi n, 1977; Kni f f kiet al ., 1981 ; Oxford and Pool er, 1975 ; Connor , 1976) and t he del ay i n i tsdevel opment . Al so suggested i n anumber of cases i s that these twomul t i stateprocesses are coupl ed together i nto a si ngl e gat i ng structure, but t he t i ghtnessof the coupl i ngmayvary w del y frompreparat i on to preparat i on .We are grateful t o Mr . Mark Pohl f or excel l ent technical assi stance. Thi s work was support edby Nati onal I nsti tutes of Heal t h research grants NS 07734 andNS 14800Recei vedf or publ i cati on 4November 1981 and in revisedf orm29J anuary 1982

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THE J OURNAL OF GENERAL PHYSI OLOGY " VOLUME 80 " 1982

AKAIKE, N, KS LEE, and A MBROWN 1978. The cal ci umcurrent of Hel i x neuron . J . GenPhysi ol . 71:509-531 .

ARMSTRONG, CM, and F . BEZANI LLA 1974 . Charge movement associ ated w th t he openi ngand cl osi ng of t he acti vati on gates of t heNa channel s . J . Gen Physi ol . 63: 533-552ARMSTRONG, CM, and F BEZANI LLA 1977 . I nacti vati on of the sodi umchannel . I I . Gati ngcurrent experi ments . J . Gen Physi ol. 70:567-590 .ARMSTRONG, CM, andWF GI LLY. 1979 Fast and sl ow st eps i n t he acti vati on of sodi umchannel s . J . Gen Physi ol . 74: 691-712 .BEAN, B P 1981 . Sodiumchannel i nacti vati on i n t hecrayf i sh gi ant axon . Must channel s openbef ore i nacti vat i ng? Bi ophys J . 35:595-614 .BEZANI LLA, F ., andC MARMSTRONG 1977 . I nacti vati on of the sodi umchannel . I . Sodiumcurrent experi ments . J . Gen Physi ol . 70: 549-566 .BI NSTOCK, L ., and L . GOLDMAN 1969 . Curr ent andvol tage-cl amped studi es on Myxicol a gi antaxons . Effect of tetrodotoxi n . J . Gen Physi ol . 54: 730-740 .

BI NSTOCK, L . , and L . GOLDMAN 1971 . Recti f i cati on i n i nstantaneous potassi umcurr ent- vol tagerel ati ons i n Myxicol a gi ant axons. J . Physi ol. (Lond) . 217: 517-531BROWN, AM, N AKAI KE, Y TsUDA, andKMORI MOTO 1980 . I on mgrati on and i nacti vati oni n t he cal ci umchannel . J . Physi ol . (Pari s) . 76: 395-402 .BULLOCK, J . O, andC L . SCHAUF . 1979 . I mmobi l i zati on of i ntramembranecharge i n Myxicol agiant axons . J . Physi ol . ( Loud) . 286: 157-172 .CHANDLER, WK, A L . HODGKI N, andHMEVES 1965 . The effect of changi ng the i nternalsol uti on on sodi umi nacti vati on and rel ated phenomena i n gi ant axons . J . Physi ol . (Loud ) .180: 821-836 .

CHI U, S. Y 1977. I nacti vati on of sodi umchannel s . Second order ki net i cs i n myel i nated nerve.J . Physi ol . (Lond ) . 273: 573-596COLE, K S. , and J . WMOORE. 1960 . Li quidj uncti on andmembrane potenti al s of the squi dgiant axon . J . Gen Physi ol . 43: 971-980.

CONNOR, J . A 1976 Sodiumcurrent i nacti vati on i n crustacean axons . Bi ophys J . 16:24a (Abstr . ) .CONTI , F ., B NEUMCKE, WNONNER, and R STAMPFLI 1980 . Conductance f l uctuat i ons fromthe i nacti vati on process of sodi umchannel s i n myel i nated nerve f i bers . J . Physi ol . (Loud) .308: 217-239 .

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GOLDMAN AND KENYON I nacti vati onDel ays andActi vati on Ki neti cs 101EBI HARA, L. , and E A J OHNSON 1980 . Fast sodi umcurrent i n cardi acmuscl e . Aquant i tat i vedescri pti on. Bi ophys . J . 32: 779-790 .ECKERT, R, and D L . TI LLOTSON 1981 . Cal ci ummedi ated i nacti vati on of the cal ci umconductance i n caesi uml oaded giant neurons of Apl ysia cal i forni a . J . Physi ol . (Loud ) . 314: 265-280

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102 THEJOURNAL OF GENERAL PHYSI OLOGY " VOLUME80 " 1982OXFORD, G S 1981 . Some ki neti c and steady-state propert i es of sodi umchannel s after removal

of i nacti vati on . J Gen Physi ol . 77: 1- 22.OXFORD, GS , and J . P POOLER. 1975 . Sel ecti ve modi f i cat i on of sodi umchannel gat i ng i nl obster axons by 2, 4, 6- tri ni tr ophenol . Evi dence f or two i nacti vati on mechani sm . J . GenPhysi ol . 66: 765- 780 .

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SCHAUF, C L . , and J . OBULLOCK 1979 . Modi f i cati ons of sodi umchannel gat i ng i n Myxi col agi ant axons by deuteri umoxide, t emperature and i nternal cat i ons . Bi ophys . J . 27 : 193-208 .SCHAUF, C L . , and F A DAM. 1975 . Further studi es of acti vati on- i nacti vati on coupl i ng i nMyxi col a axons . I nsensi ti vi ty t o changes i n cal ci umconcent rat i on . Bi ophys. J . 15: 1111-1116

STARKUS, J . G , B D FELLMETH, andMDRAYNER. 1981 . Gati ngcurrents i n the i ntact crayf i shgi ant axon Bi ophys. J . 35: 521-533 .SWENSON, RP 1980 Gat i ng charge i mmobi l i zati on and sodi umcurrent i nacti vati on i ni nternal l y perf used crayf i sh axons . Nature (Loud) . 287: 644-645 .

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Golman Et Al., 1983