Rate Constants and Equilibrium Constants for Thiol-Disulfide ...

Szajewski. Whiresides/ Thiol-Disulfide InterchangeReacrions

I

201I

Rate Constantsand EquilibriumConstants for Thiol-DisulfideInterchangeReactions InvolvinsOxidizedGlutathionel Richard P. Szajewski2 and George M. Whitesides* Contributionfrom the Department of Chemistry, MassachusettsInstitute of Technology, . Cambridge, Massachusetts02139. ReceiuedMay 8, 1978

Abstract:The rate of reductionof oxidizedglutathione(GSSG) to glutathione(GSH) by thiolateanions(RS-) followsa Br/nstedrelationin pK"s of the conjugatethiols(RSH):pnu"- 0.5.This valueis similarto that for reductionof Ellman'sreagent:0nu"= 0.4-0.5.Analysisof a numberof rate and equilibriumdata,takenboth from this work and from the literature. indicatesthat rate constants, interchange reactions k, for a rangeof thiolate-disulfide are correlatedwell by equationsof the formlogk=C*0nu.pKunu"*0"pK""*0repKule(nuc=nucleophile.c=central,andlg=leavinggroupsulfur):eq36-38 giverepresentative valuesof the Br/nstedcoefficients. The valuesof theseBr/nstedcoefficients are not sharplydefinedby the availableexperimental data.althougheq 36-38 provideusefulkineticmodelsfor ratesof thiolate-disulfide interchange reactions.The uncertaintyin theseparametersis suchthat their detailedmechanistic interpretation is not worthwhile.but their qualitativeinterpretation-thatall threesulfuratomsexperience a significanteffectivenegativechargein the transitionstate, but that the chargeis concentrated on the terminalsulfurs-is justified.Equilibriumconstantsfor reductionoiCSSG using a,cr-dithiolshavebeenmeasured. The reducingpotentialof the dithiol is stronglyinfluencedby the sizeof the cyclicdisulfide formedon its oxidation:the moststronglyreducingdithiolsare thosewhichcan form six-membered cyclicdisulfides. Separate e q u i l i b r i u mc o n s t a n tfso r t h i o l a t e a n i o n - d i s u l f iidnet e r c h a n g(eK s - ) a n d f o r t h i o l - d i s u l f i dien t e r c h a n g(eK s H ) h a v eb e e ne s t i matedfrom literaturedata:Ks- is roughlyproportionalto2ApK. is the differencebetweenthe pKusof the two thiolsinvolved in the interchange. The contributions of thiol pKu valuesto the observedequilibriumconstantsfor reductionof GSSG with a,co-dithiols appearto be much smallerthan thoseascribableto the influenceof structureon intramolecularring formation. Theseequilibriumand rate constantsare helpfulin choosingdithiolsfor useas antioxidants in solutionscontainingpro(DMP), and 2-mercaptoethanol teins:dithiothreitol(DTT), 1.3-dimercapto-2-propanol usefulproperties. haveespecially

: 0.34).and B rockl ehurst of et al . haveexami n edr educt ions = 0.23).r2'Thes (pnu" di sul fi de e 2,2-di pyri dyl st udies indicat e rl O x idat iono f c a ta l y ti c a l l o y r s rru c tu ra l ley ssenti al cystei ne i s that thi ol ate-di sul fi de i nterchange a mech anist icaily sim ple t hiol gr oupsc a n b e a n i m p o rta n tm e c h a ni smfor enzyme but.suggest that the valuesof t he reacti on, deac t iv at ion .l It i s i mp ra c ti c ato i e x c l u d eo x ygencompl etel y S x 2 di spl acement characteristic Brpnsted sensitiveto the parcoefficients are f r om s olut io n o s f p ro te i n sd u ri n gth e i rm a n i pul ati on, and the ti cul ar The extensi o of n t hesem odel set of reactants chosen. s t r at egynor m a l l yfo l l o w e dto m i n i m i z eth e i nfl uenceof autFir st .t he studi esto GS S G w ascarri edout for tw o re asons. ox idat ionon e n z y m a ti ca c ti v i tyi s b a s e do n th e protecti on afwit h l ' or di aryl di sul fi des t ypical aliequi l i bri a reducti on of t or dedby or g a n i cth i o l s(e s p e c i a l l2y-m e rc aptoethanol and phati c l i e thi ol that e quilibr ium conthi ol s so far tow ard aryl dithiothreitola's) presentin excess. Theseaddedthiolsprobably conveni entl y. I t was t hus not stantscoul d not be measured inhibit t he ir re v e rs i b l o e x i d a ti v ed e a c ti v a ti on of protei nsby possible to explore the influence of the structure of the reducing s ev er alm ec h a n i s msT.h e y re v e rs eth e i n i ti ai sragesof the equilibria. Second,aryl thioi on the thiol-disulfide interchange proteinautoxidation protein reactions by reduction of disulfides poor protei n cyst inegr oup. for a thi ol s are arguabl y model s and s ulf enica c i d s 6to th i o l s .T h e y m a y , b y coordi nati on, m odif y t he c a ta l y ti ca c ti v i tyo f tra n s i ti o n -metal i onsi n thi ol aut ox idat ion .l T ' 7h e i r o w n o x i d a ti o nc o n s u mes R esul ts di oxvsenand hy dr ogenper o x i d eps re s e nitn s o l u ti o n Ratesof Reductionof OxidizedGlutathioneby Mono- and As part of a projectaimedat thedevelopment of techniques Dithiols.The rate of reieaseof GSH from GSSG wasdeterto permit the useof enzymesas practicalcatalystsin the synmi ned usi nga fast enzymati cfol l ow i ngreact ionat pH 7. 0 thesisof organicand biochemicals,e we havebegunto study (0.06 M phosphate buffer)and 30.0* 0.5 ' C underar gon. the relationbetweenthe structuresof organicthiolsand their CSH wasconvertedto S-lactoylglutathione(GS-lac)by reability to preventor reversethe autoxidationof proteins.The o f glyoxalase- l acti on w i th methyl gl yoxali n the presence work describedin this paperis focusedon one aspectof this (GX -l ), and the concentrati on of GS -l ac was m onit or ed pr oblem ,v iz ., ra te - a n d e q u i l i b ri u m -s tru c t ure rel ati onsfor spectrophotometri calatl y 240 nm, es 3.37 m M - l cm - i. l'1 the reductionof a modelcystine-containing pepride(oxidized EquationsI -6 list the reactionspertinentto this assay.In these glut at hione,G S SG, 7 -g l u ta my l c y s te i n y l gl yci ne) by base- equations,RSH is a monothiolreducingagent.Reaction6, the catalyzedthiol-disulfideinterchange. Oxidizedglurathione enzymaticconversion to GS-lac,is essentially of hemithioacetal wasselectedas substratein this investigation for threereasons: i rrevei si bl e.l a it is readilyavailablein pureform:its presence, as wellasthat KrRsH of reducedglutathione(GSH), can be monitoredin the pres(I) RSH_ RS- + H+ enc eof ot hert h i o l sa n d d i s u l fi d e u s s i n ge n z ymari cassays;10 and, becauseit occursin biologicalsystems,l.llinformation kt ( 2) GS S R + GSR S - + GS S G_ about its reactionswith variousthiolsshouldprovegenerally k-r us ef ul.W el2a n d H u p e e t a l .l 3h a v ea l re a d yreportedratesof k't t hiol- dis ulf id ei n te rc h a n g e re a c ti o n si n v o l v i n gE Il man' sre(3) R S - + G S S RR S S R+ G S agent(5.5'-dithiobis(2-nitrobenzoic acid))and foundthemto k-z foilowa Brlnstedcorrelation(pnu"= 0.5).Clelandet al. have p K " C S H= g . l l t S (4) carriedout relatedstudieswith 4,4'-dipyridyldisulfide(pnu" GS- + H+ GSH Introduction

(1980).1

zjt2

Journal of the Anterican Chemical Society / 102:6 / March 12, lgB0

o

( G S S R ) > ( R S S R ) : s i n c et h e r a t e c o n s t a n t sk r , k : , k - 1 ,a n d k -2 areall of the samemagnitude,the second.third. and fourth t e r m s o f e q 8 c a n b e n e g l e c t e d ,a n d t h i s e x p r e s s i o nm a y b e combined with eq 7c and rewritten as eq 9a. For convenience, this equation was used in a form (eq 9b) involving an observed r a t e c o n s t a n t .k l o b ' d b , a s e do n t h e t o t a l c o n c e n t r a t i o no f t h i o l and thiolate anion in solution.The rate constantsll I and k robsd a r e r e l a t e db y e q 1 0 .

( F4

9. x 1

I (n

9-?

d ( G S - l a cf )d t - k r ( R S - ) ( G S S G ) = f t , o b s d t ( R s+- ) ( R S H ) l ( G S S G ) k t = k , o b s1dl + l 6 p x " n s x - p H ) ot23456789tO

(9a)

(eb) (l0)

To ensurethe accuracy of the assumptionsand approximations m a d e t o g e n e r a t ee q 9 , i t i s n e c e s s a r yt o a d j u s t t h e r e l a t i v e Figure l. Formationof S-lactoyl glutarhione(CS-tac, M) with time at 30.0 c o n c e n t r a t i o n so f t h e v a r i o u ss p e c i e sp r e s e n ti n s o l u t i o n . R e o C , * 0.5 u n d e ra r g o n i n a p H 7 . 0 p h o s p h a t eb u f f e r ( 0 . 0 6 6 M ) c o n t a i n i n g actionswere carried out using the following initial conceno x i d i z e dg l u t a t h i o n e( G S S C . 0 . 3 5 m M ) . d i t h i o t h r e i t o l( 5 . 0 7 m M ) , a n d t r a t i o n s :( R S H ) 0 = 0 . 7 7 m M , ( G S S G ) = 0 . 3 5 m M , a n d m e t h y l g l y o x a(lC H : C O C H O , 0 . 7 7 m M ) . a n d u s i n g( A ) 2 4 , ( B ) 2 . 4 .( C ) ( G X - l ) - 2 . 5 X l 0 - 4 m M ( 2 . 4 U / m L ) . 1 6 B e c a u s et h e s r a r t i n g 1 . 8 .( D ) 1 . 2 ,( E ) 0 . 3 U / m L . r e s p e c t i v e l yo.f g l y o x a l a s e - (l G X - l ) . T h e c o n c e n t r a t i o no f G S - l a c w a s d e t e r m i n e ds p e c t r o p h o t o m e t r i c a l l ay t 2 4 0 c o n c e n t r a t i o no f t h i o l i s m u c h g r e a t e r t h a n a n y o f t h e o t h e r n m u s i n ge o3 . 3 7 m M - l c m - 1 . T h e r e i s n o s i g n i f i c a n td i f f e r e n c eb e r w e e n s o l u t i o n c o m p o n e n t s ,t h i s c o n c e n t r a t i o n i s n o t s i g n i f i c a n t l y d ( G S - l a c ) / d / a t e n z y m ec o n c e n r r a r i o n o sf 24 and 1.8 U/mL: the conperturbedby hemithioacetalformation and remainsessentially c e n t r a t i o no f e n z y m eu s e dr o u t i n e l y i n t h e a s s a yw a s 2 . a U l m L . c o n s t a n tt h r o u g h o u t t h e c o u r s eo f a k i n e t i c r u n . T h e c o n c e n t r a t i o n o f C H I C O C H O u n d e r t h e s ec o n d i t i o n si s , o f c o u r s e . u nknown: although a significant fraction oi this material is K5=J6fYfla p r o b a b l . vc o n v e r t e dt o h e m i t h i o a c e t a l ,t h e v e l o c i t y o f e q u i l i GSC HO HCO CHT GSH + CH3COCHO (5) l i t h a l d e h y d ea n d h e m i h y d r a t e b r a t i o n o f t h e h e m i t h i o a c e t aw GSCHOHCOCHT + GX-I9 G S C O C H O H C H+3c x - l i s f a s t c o m p a r e d t o t h e e n z y m a t i c r e a c t i o n sw h i c h f o l l o w . r a Regardlesso[ the equilibrium concentrationof hemithioacetal. (GS-lac) ( C H I C O C H O ) o > ( G S H ) i n t h e i n i t i a l s t a g e so f t h e r e a c t i o n . (6) F o r s m a l l e x t e n t so f r e a c t i o n( i n t h e s ee x p e r i m e n t st y p i c a l l v l0-20Vo) the concentrationof CHICOCHO can be considered T o d e r i v e r a t e e x p r e s s i o n sf o r k I f r o m t h e s ee q u a t i o n s ,w e c o n s t a n t .T h u s . w i t h t h e a s s u m p t i o n si n d i c a t e d ,t h e r a t e o f r e q u i r e t h a t t h e o v e r a l l r a t e - l i m i t i n g s t e p i n c o n v e r s i o no f a p p e a r a n c eo f G S - l a c w i l l b e d i r e c t l y p r o p o r t i o n a l t o t h e G S S G t o G S - l a c b e t h e i n i t i a l t h i o l a t e - d i s u l f i d ei n t e r c h a n g e c o n c e n t r a t i o no f G S H . F o r t h e s t e a d y - s t a t ea p p r o x i m a t i o nt o r e a c t i o n( e q 2 ) . W e w i l l a s s u m et h a t t h i o l a t ea n i o n i s t h e o n l y h o l d f o r G S H , i t i s n e c e s s a r yt h a t i t b e c o n v e r t e dt o G S - l a c n u c l e o p h i l ep a r t i c i p a t i n g i n t h e t h i o l - d i s u l f i d e i n t e r c h a n g e much more rapidly than it is formed from GSSG. The rate of r e a c t i o n , l Tt h a t r e d u c e dg l u t a t h i o n e( G S H ) i s p r e s e n to n l y a t c o n v e r s i o no i G S H t o G S - l a c c a n b e a d j u s t e d o v e r a w i d e a low, steady-stateconcentration.and that glyoxalase-lfollows m a r g i n b y s i m p l y c h a n g i n gt h e c o n c e n t r a t i o no f g l y o x a l a s e |typical Michaelis-Menten kineticswith the hemithioacetal o r C H 3 C O C H O . T h e c o n c e n t r a t i o no f e n z y m e r e q u i r e d t o C S C H O H C O C H I a s i t s o n l y s u b s t r a t e( e q 7 a ) . t e . r 6 ' r 8 ' r e a c h i e v e s t e a d y - s t a t ec o n d i t i o n s i n G S H , a t a c o n v e n i e n t d(GS-lac)/dr C H 3 C O C H O c o n c e n t r a t i o nw , a s e s t a b l i s h e de x p e r i m e n t a l l y . The concentration(activity) of enzyme in solution was varied, Krn GSCHOHCOCHT (ia) a n d t h e v a l u e o f ( G S - l a c ) m e a s u r e d ,h o l d i n g a l l o t h e r p a ( G S C H O H C O C H 3] )rameters constant.At valuesof enzymatic activity greater than t s K m c s c H o H C o c H i l -I 2 UlmL, increasingthe activity of enzyme in solution = k : ( G X - l ) ( G S H ) l ( c S+H K ) shortened the duration of a non-steady-stateinterval at the t b e g i n n i n go f t h e r e a c t i o n ,b u t d i d n o t i n f l u e n c e t h e v a l u e o f (7b) d(GS-lac)/dt once the steady-stateregion had been reached = [ k 3 ( G X - l ) ( C H 3 C O C H O ) / 3 m M 2 ] ( G S H )( 7 c ) ( F i g u r e I ) . M o r e g e n e r a l l y ,t h e v a l i d i t y o f e q 9 r e q u i r e st h a t d ( G S - l a c )l d t b e z e r o o r d e r i n G X - l a n d C H 3 C O C H O a n d Substitutionof the equilibriumexpression for K5 (eq 5) into f i r s t o r d e r i n R S H a n d G S S G . T a b l e I , w h i c h l i s t s k ' o b s dr n 6 eq 7a followed by rearrangementgives eq 7b. At a low velocities [d(GS-lac) ldt] for formation of GSH from GSSG steady-state 7c 7b concentrationof GSH, eq reducesto eq for K s - 3 m M and K . c s c H o H c o c H :- I m M .2 0T h e b ra c k eted using 2-mercaptoethanolas reducing agent, establishesthat theseconditions are fulfilled. The data in the first line of this portionof eq 7c may,in principle,bemadearbitrarilylargeand table were obtained using the standard conditions employed constantby adjustingthe concentrations of either GX-l or routinely in this work; the other runs were performed on soCH3 C O CHO ; in pr ac t i c eth , e q u a n ti tyo f G X -l u s e di s the lutions in which these conditions were systematically varied. moreeasilyvaried.At the pH usedfor the assay(pH 7.0),the Analysis of the velocity data and extraction of the rate constant majorityof the reducedglutathioneis presentas GSH rarher than GS-. Assumingthese conditionsand a steady-srare k,ob'd from these data are discussedlater in the text. Under the conditions used, the assumptionsmade in obtaining eq 9 concentrationfor GSH, we'relatethe rate of productionof seem to be justified, since large deviations from the standard CS-lacto k 1 by the equation conditions have no influence on krobsd. 0 : d ( C S H )/ d t = k r ( R S - ) ( c S S c ) + k 2 ( R S - ) ( G S S R ) Equation 9 applies to monothiol reducing agents. In this - k_r(cssR)(GS-) - k_z (RSSR)(GS-) work, we were particularly interested in dithiols. In treating reducing agents, HSRSH, containing two identical thiol - f t 3 [ ( c x - l ) ( C H 3 C O C H O ) / 3m M 2 ] ( G S H ) ( 8 ) groups, we used an entirely analogous procedure, with two We ensurethat kineticsobservations extendonly over the additional assumptions.First, we assumed that the nucleo-SRS-, in i ti a l stagesof t he r ea c ti o n ,i n w h i c h re g i m e (G S SG) > p h i l i c i t i e so f t h e m o n o - a n d d i a n i o n s ,H S R S - a n d Timc (min)

= k :( G X - l l+I r

@

2013

Szajewski, Whitesides/ Thiol-Disulfide InterchangeReactions (CSSG)by 2-MercaPtoethanol4 (k,ou'a, Glutathione of Oxidized M-l min-l) for Reduction TableI. RateConstants k , obsd

d(GS-lac)/drD IHOCH2CH25HI'

8.8 9.5 8.2 9.1 7. 3 9. 3 8. 9 8.0 8.8 9.2

0 . 76 0.77 0.77 0.77 0.76 0.75 0.31 1.50 0.76 0.76

5 .0 7 5 .l 0 5 .r 0 5.09 14.5 0.49 5.r2 4.99 5 .0 5 5 .0 7

t4.4

r5.6 13.2 t4.9 39.4 1.5 t4.7 12.6 28.3 2.5

l c H r c o c H o l . lcsscl. 0.32 0.32 0.32 0.32 0.32 0.3r 0.33 0.32 0.64 0.054

IGS-rld 1 . t :.1 a a

1

0.48 1.2 1A L-.+

2.1 1A 'tA L.1 1A L.a

comments€ standard XIOGX-I X O . 2G X - I x0.5GX-l X3 RSH X O . IR S H xo.5 cHTCOCHO x2 CH3COCHO X2 GSSG X O . I 7G S S G

2.4 oC, at 240nmusing€o3.37mM-l cm-t, underargon,wcrcfollowed buffer,pH 7.0,30.0* 0.5 " All kincticslrercrun in 0.056M phosphate unitsare mM. d In enzyme ii rnt. , Unir; of d(Cs-tac)/drarc M-r min:r x 106.. Concertration and werecoftectedfor blankreactions, ' mnditions. standard fiom the units(prnol/min)pcr mL. Thiscolumnindicctesthe majorchangc Table II. Rate Constants(k'ou'a M-l min-r) for Reductionof OxidizedGlutathioneby Dithiothreitolo k , obsa

14.0 14.6 8.4 t3.l

r3.0 t4.2 9.8

d(GS-lac)/dt' 47.0 26.9 41.3 81.6 4.5 31.9

l 2 .r

J t,l

12.7 14.0

8 0 .l 5.8

IDTTI.

lcHscocHol.

IGSSGl.

0.76 0.77 0.77 0.77 0 . 76 0 . 76 0.39 L50 0.76 0.'t6

0.32 0.32 0.32 0.32 0.32 0.32 0 . 33 0 . 32 0.64 0.042

4.94 4.97 4.97 4.94 9.94 0.49 5.01 4.86 4.93 1.94

AA'I

IGS-rld 1^ 'tA

1

0.48 1.8 1A 1A

.\^ 1,1 1A 11

commentse

standard X I OG X - I X O . 2G X . I X 0 . 7 5G X . I X2 RSH X O . IR S H xo.5cH3COCHO x2 CHTCOCHO X2 GSSG X O .I 3 G S S G

d All kinetics were run in 0.05 M phospharebuffer, pH 7.0, 30.0 * 0.5 'C, under argon. ' Velocity offormation ofGS-lac as determined a! 240 nm u.;ng io :.:l mM-i cm-l and correctedfor blank riactions.if any. Unitsof d(Cslac)/d, are M min-l spectrophoromerrically ' i t Oo.I Con""ntr",ionunirsrre mM. ; ln unirsof enzymeacriviryper mL. This columnindicates(he majordeviationfrom stlndard condi!ions. w e r e i n d i s t i n g u i s h a b l e .T h i s a s s u m p t i o n n e g l e c t se l e c t r o n i c effects and a statistical factor of 2, both of which would make the dianion more reactive than the correspondingmonoanion. T h e c o n c e n t r a t i o no f d i a n i o n w i l l , h o w e v e r .b e s m a l l r e l a t i v e to monoanion at pH 7 for the dithiols we have examined. M o r e o v e r ,t h e o b s e r v a t i o n( s e eb e l o w ) t h a t m o n o - a n d d i t h i o l s f a l l o n t h e s a m e B r / n s t e d c o r r e l a t i o n l i n e s u g g e s t st h a t t h e c u m u l a t i v e e r r o r i n t r o d u c e d i n t o e s t i m a t e so f r a t e c o n s t a n t s b y t h i s a s s u m p t i o ni s s m a l l . S e c o n d ,w e a s s u m et h a t , f o r t h e c o n c e n t r a t i o no f d i t h i o l u s e d , t h e r a t e o f t h e i n i t i a l i n t e r m o lecular thiol-disulfide interchangeis lower than that of a s u b s e q u e n ti n t r a m o l e c u l a r r e a c t i o n w h i c h r e l e a s e sa s e c o n d e q u i v a l e n to f C S H ( e q I l ) . A s i m i l a r a s s u m p t i o nr.n a d e i n o u r HSRSH + CSSG

g

HSRSSG + GSH

'-"; fast sn3 + GSH HSRSSG

(I IA)

( I lb)

could previoustreatmentof the reductionof EIlman'sreagent. esti mates of bejus t if iedex p e ri m e n ta l lbye c a u s ien d e p e n d ent fo r re l e a s o e f a ry l th i o l sfro m di aryldi sul t he r at e c ons ta n ts fidesand aryl alkyl disullidesindicateda sufficientdifference for t o be det ec t ed| 2. '1 34 n o l ts i s o f th e e q u i l i b ri u mconstants , r educ t ionof CS SG b y a l l o f th e d i th i o l se x a mi nedbel ow exa significant established cept for glycol dimercaptoacetate, l f w e assume s n o th i o ls. enhanc em enr e t l a ti v eto a n a l o g o umo reactionof mono-anddithiols that the ratesof intermolecular hav ings im ilarth i o l p K " v a l u e so n GS SGw i l l a l sobesi mi l ar. that suggests differencein equilibriumconstants the observed involving thiol-disulfide interchange inlramolecular the rateof is probablylast relative the secondthiol groupof an cv,c.,.r-dithiol e e eb e l ow ).N onethet o t he f ir s t int e rm o l e c u l ai nr te rc h a n g(s for Iess,sincewe havenot beenableto measurerateconstants r eleas oi e CS H i ro m GS SGa n d GS SR SHb y thi ol -di sul fi de ex p e ri m e n ta l l ya,n d s i n c eth e s ev a l uesare probint er c hange

a b l y s i m i l a r f o r m o s t o f t h e t h i o l se x a m i n e dh e r e . l l ' 1 2w e r e l v o n a n a l o g y w i t h t h i s p r e v i o u sw o r k t o j u s t i i y o u r a s s u m p t i o n . N o t e , h o w e v e r ,t h a t . i f t h i s a s s u m p t i o ni s i n c o r r e c t .i t i n t r o d u c e s a n e r r o r o f o n l y a f a c t o r o i 2 i n t h e r a t e c o n s t a n t sf o r dithiols. W i t h t h e s e a s s u m p t i o n sa. t r e a t m e n ts i m i l a r t o t h a t d e s c r i b e dp r e v i o u s l yl e a d st o t h e e x p r e s s i o nisn e q l 2 r e l a t i n gt h e o b s e r v e dr a t e o f p r o d u c t i o no f G S - l a c t o t h e r a t e c o n s t a n to f i n t e r e s t ,k 1 . A g a i n k 1 a n d k l o b s oa r e r e l a t e db y e q 1 0 . d ( G S - l a c )f d r = 2 k T U H S R S - ) + (-SRS-)l(GSSG)

(l2a)

= 2krob'd[(HSRSH) + (HSRS-) + (-SRS-)I(GSSG)

(l2b)

T a b l e I I l i s t sv a l u e so f k , o u s aa n d v e l o c i t i e s[ d ( G S - l a c ) / d r ] f o r formation oi GSH from GSSG usingdithiothreitol as reducing a g e n t . T h e f i r s t l i n e i n t h e t a b l e r e p o r t sd a t a o b t a i n e d u s i n g o u r s t a n d a r d c o n d i t i o n s :t h e o t h e r r u n s w e r e p e r f o r m e d o n s o l u t i o n s i n w h i c h t h e s e s t a n d a r d p a r a m e t e r sw e r e v a r i e d . A g a i n . u n d e r t h e c o n d i t i o n su s e d . t h e a s s u m p t i o n sm a d e i n o b t a i n i n g e q l 2 s e e mt o b e j u s t i f i e d . S t r a i g h t f o r w a r d c o n s i d e r a t i o no f m a t e r i a l b a l a n c ea n d i n t e g r a t i o n o f e q 9 ( o r e q l 2 ) b y s t a n d a r d m e t h o d sg i v e s r z ' : :

, (GSSG)o In-())o ( S ) o- ( G S S G ) o ( GS S - l a cc))//nn * [ t s l o - -t c( C S + * ) / r lI ( l 3 ) [(GS S G)o are definedas follows:for moThe terms in the expression n o t h i o l sS o = [ ( R S - ) + ( R S H ) ) , n = l ; f o r d i t h i o l sS o = = 2 . F i g u r e2 r e p r o [ ( - S R S - ) + ( - S R S H ) + ( H S R S H ) ] ,r ducestypi calki neti cdata for reducti onoi C SSC by sever al mono-and di thi ol sas deri vedusi ngthe i nte gr at edr at e exdatau sedt o gener at e (eq l 3). The crudeabsorbance pressi on f t , o b s d 1=

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w i r h o x i d i z c dg l u t a t h i o n e( G S S G ) i n p H 7 . 0"r p h o s p h a t eb u f f e r ( 0 . 0 6 6 M ) at 30-0 + 0.5 "c under argon.The termq in the expression on the axis are d e f i n e da s f o l l o w s : f o r m o n o t h i o l sS , e= [(RS-) +'(RSHt] , n = t; for di_ r h i o t s .s 6 = [ ( - S R S - ) + ( H S R S - ) + ( A S R S H ) J , l r = z'(ir. eq r3 or the t e x t ) . R e d u c i n ga g e n r s :r , g r y c o rd i m e r c a p t o a c e r a t ev;, dithiothreitor: o. 2-mercaptoethanol: r. thiogl.vcolic acid.Kineticsare sho*n .espectivery t o 6 0 , 5 0 , 2 0 . a n d 2 0 v oo f c o m p r e t i o nT. h e k i n e t i c p o i n t s sho*n herewere o b t a i n e df r o m t h e e x p e r i m e n t Ia A z c o a t t r i b u t a b r teo GS-lacand are corrected for the relativel-vslow blank reactionobservedin thesesysrems*hen u s i n g p h o s p h a t eb u f f e r ( s e er e f 2 4 ) .

2 (DMP)

pKrs* F i g u r e 3 .P l o t s o f( A ) l o g , t l t u a n d ( B ) I o g & r ( M - r m i n - r ) v s .t h i o r p K " f o r t h e r e d u c t i o no f o x i d i z e dg r u t a r h i o n ei n p H ? . 0 p h o s p h a t eb u f f e r at 3 0 . 0 + 0 . 5 o c u n d e ra r g o nb y r h e m o n o -o n a ' a i t n i o t t i s t e di n T a b l e III. D T T i s d i t h i o t h r e i t o l . v l E i s 2 - m e r c a p r o e t h a n oD l.Mp is 1.3-dimercap topropanol, and G M A t-vc^ol mgcaproacetate. The least_sq uares slope .is.e ! ! f o r ( B ) i s 6 n , " = 0 . 5 0 1 r 2 = 0 . 8 9 ) .T h e e q u a t i o nu s e d, o g . n . r . , . t h e rine in (A) is log k 1oH = -_1,29* 0-50pK. - Iog ( lgpKe-7.0+" t ti,. equation ); i n ( B ) i s l o gk r = - 1 . 2 9 * 0 . 5 0 p K " .

Ta b l e sI - lll wer ec or r e c te d fo r th e s l o wp h o s p h a te i o n cara_ lyzedreactionbetweenmethylglyoxal and thiolsbeforeanalysi s to obt ain v aluesof k l o b ' du s i n gth i s e q u a ti o n .2 a T a b l eI I I . R a t ec o n s r a n r (st . M - r m i n - r ) f o r R e d u c r i o o R ate nf constantsfor reductionof GSSG by a seri'es O x i d i z e dG l u t a t h i o n (eG S S G )b y M o n o -a n d D i t h i o l s " of rnono-and dith i o l su nders t andar dc o n d i ti o n a s re l i s te di n T a b te 1 1 y .zr.:: thiol &"obsd Figure3 summarizes k1 PK^ thesedataasplotsof log ft 1and log k ,obsd vs. th e p K " of t he r educi n gth i o l .T h e a ro rn a ti cth i o l J w hi ch : M A ) 7. 1 1 9 . 9 1 t 90 I ( H S C H T C O : C H : _()G 4.9X 102 were usedto obtaindata for valuesof pK"RSH( g with 2 HSCH2CHOHCHTSH 9 . 0( 1 0 . 3 ) b 9 . 3 9 . 3x 1 0 2 Eil_ (DMP) ma n 'sre agent ll' 13 c ouldn o t b e u s e di n i tu d y i n gth e re d u cti on of GSSG, becausethey absorbedstrongiyat ine waverength 3 d i t h i o t h r e i t o( lD T T ) 9 . 2( 1 0 . 1 ) 6 r 4 . l 2 . 2x 1 0 3 4 DTT/DTE mixture. 9 . 2( r 0 . 1 ) b 8 . 4 l . l x t 0 3 use dto m onit ort he c on c e n rra ti ooni G S I-i a c(2 a 0 n m). For g.5b 5 HOCH2CHOHCH2SH 7 . 9 2 . 5x 1 0 3 comparison, Figure4 reproduces analogous datafor reduction 6 H S C H 2 C H ( N H C O C H 3 ) _ g . 5 d 5 . 2 1 . 8x 1 0 3 o f El l man' sr eagent t; hi s p l o t i n c l u d .i d u ru b o th fro m our COzH w o rkl 2and f r om t hes t ud yo f H u p e e t a l .r3 7 H O C H : C H 2 S H( M E ) 9.6, 8 . 7 3 . 4x 1 0 3 The Br/nsted coefficient(pnu"= 0.50,coefficientof de_ 8 HSCH:COzH 9.8r t.J 4 . 6x l 0 l termination= 12= 0.89)obtainedby least-squares 9 HSCH2CHzCOzH analysisof 10.68 3 . 2 1 . 2x 1 0 4 the rate constantsfor GSSG is similar to tiat obtainld for a All rateswerederermined in 0.066M phosphate buffer,pH 7.0, reductionof EIlman'sreagentby thiols.This lattersystemhas 30.0+ 0.5 oc, underargon.Data typicailyrepresent an averageof nowbeenthesubjectof two independent r:. r: studies( Figure4). threedeterminations. The rateconstantsarenot correctedstatistically our study^analyzed a groupof at[yt and aryr thiorsrogether, of two equivalent sulfuratomsin GSSG.Reproduilo11hepresence an d g a ve6 nu.= 0. 30,12- 0 .g 5 .2 H 5 u p ee t a l . a n a yl :z e dd,, ata ibility in theseexperimenrs was* l5zo.Arremptsto measureratesfor for a similar set of thiors,but suggested severalotherrepresentative thar alkyi and aryl thiolswereunsuccessful. The rateof rethiols duction separare correlation-fines, GSSG by CHrcoSH wasnot significantlyfasterthan the pnu.irkyt = with 6.49 l.ll_:n 9f (r.l = 0.98) and Bnu"a'vl 0..48(r2 = 0.96).nnatysis rate of the blank reaction:k,obsdis smallerthan lri-r v-' min-r. of our ^= Amino thiols (cysteine,Et2NcH2cH2sH) react quickrywith the alkyl dataaloneyieldedpnu"ulkrl = 0.4| (r2'= 0.67;.Our data methylglyoxalin the assaysolutionsto form speciiswhich absorb for aryl thiolscovera smallrangeof pK" valuesunJar" l.r, stronglyat 240 nm, presumabrys-ractoyr thioesters(see ref 24 for accuratethan thoseof Hupe.26The value of the Brlnsted a discussion of the mechanism of theseblank reactions).GX-l was coefficientselectedfrom theseseveralanalysesdependsin purt inactivatedby HocH2cHSHcH2sH. , Sourcesof thesepK" valuis judgmenrsconcerningthe ihoi". oi dutu to be are listedin ref 12.Thesevaluesfor DTT havealsobeenreportedby 9n 9uljgctive incl u d e d w . e agr ee. wit hH u p e e t a l .-th a tth e a rk y ra n d a ryr E. L. Loechlerand T. C. Hollocher.-/. Am. Chem..Soc.,'g7,323i thiolsshouldbe analyzedseparately,2T q9]5i c Preparedas described and not" th"r there is in ref 12. d From M. Friedman,J. no independent F. Cavins,andJ. S. Wall, J. Am. Chem.Soc.,g7, 3672(1965).' This evidence whichcan be usedto selectbetween valuesof pnu""lkrl pK" is taken from ref 13./Reference 15. c From R. J. Irving, L. lying between-0.4and 0.5.For simpricity, w e w i l l ta ke6 - 0. 5;ar gu m e n ts Nelander,and I. Wadso,Acta Chem.Scand.,18, 769 ( I964). o u tl i n e dl a te rs u g g e sthat t thesep valuesmay not, in any event,translatedirectly into fractionalcharges,and the ty,n.rtry and chargedistribution -demanda s h o u l d n o t b e c o n s i d e r e d ' h i g h l yp r e c i s e .Q u a r i t a t i v e r y m o r e of the transitionstatedo not specificialue of B.zs.n important is the observation that reductions of GSSG and The valueof pnu"alkrl = 0.5 for reductionof GSSG determined Ellman's reagent by thiol-disulfide interchange appear to be in the presen^t s.tydythusseemsphysicailyreasonabre, but, since closely related reactions. Each is characterized by a Brf,nsted the rangeof thiol pKrs covet.ais reraiiverysmail, sincethe coefficient of similar size, and neither shows any evidJnce of scatterin the experimentar pointsis significant,and sincethe curvature in the Brfnsted plots suggestinga change in mechassaysystemusedto followthe reactions is complex,thisvalue anism or an intermediate.Since Ellman's reagentand oxidized

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pKo F i g u r e 4 . C o l l e c t e dr a t e c o n s t a n t s( M - r s - r ) f o r r e d u c t i o no i E l l m a n ' s r e a g e n tb y t h i o l s . D a t a f r o m r e f l ? a r e r e p r e s e n t e d b y s o l i d p o i n t s ;d a t a f r o m r e f l 3 a r e r e p r e s e n t e db y o p e n p o i n t s . D a t a f o r a l k y l t h i o l s a r e s u m m a r i z e db y o a n d O : d a t a f o r a r y l t h i o l s b y I a n d E ; d a t a f l o rt h i o l a c i d s b y r . M E i s m e r c a p t o e t h a n o lG ; MA is glycoldimercaptoacetate; MMA is methyl mercaptoacetate. Other pointsare identifiedin ref l2 and 13.The linesrepresentleast-squares fits to thesesetsof data: A (-), alkyls ( o ) . r r 0 n u "= 0 . 4 3 ,r 2 = 0 . 9 1 ;B ( - - - - ) , a l k y l s( o ) r 3 e x c l u d i n gm e t h y l m c r c a p t o a c e t a t1e3. n u=. 0 . 4 9 ,r l = 0 . 9 7 . C ( ' - ' - ) , a l k y l s( O ) , 1 2g n u "= 0 . - 1 1r,l = 0 . 6 7 :D ( . . - - - ) , a r y l s ( u ) , r l d n u "= 0 . 4 1 .r 2 = 0 . 9 ' 1 .

g l u a t h i o n e r e p r e s e n tv e r y d i f f e r e n t t y p e s o i d i s u l f i d e s ,t h e i r k i n e t i c s i m i l a r i t i e se n c o u r a g et h e c o n c l u s i o nt h a t t h i o l - d i s u l f i d e i n t e r c h a n g ei s , i n m o s t i n s t a n c e s ,a m e c h a n i s t i c a l l y u n c o m p li c a t e d r e a c t i o n . Although we have not explicitly determined Brpnsted c o e f f i c i e n t sl o r t h e l e a v i n g( p r e )a n d c e n t r a l ( d . ) t h i o l g r o u p s i n t h e t h i o l - d i s u l f i d ei n t e r c h a n g ee, x a m i n a t i o no f o u r d a t a , a n d t h o s eo f C r e i g h t o n , r ly i e l d sa v a l u e f o r t h e s u m o f p . * 1 3 1 W n.e h a v ed e t e r m i n e dt h e r a t e so f r e d u c t i o no i G S S G a n d E l l m a n ' s the rate r e a g e n tw i t h a n u m b e r o f t h i o l s :C r e i g h t o ne s t a b l i s h e d o f o x i d a t i o n o i D T T i n t h e p r e s e n c eo f s e v e r a ls y m m e t r i c d i s u l f i d e s .R e p r e s e n t a t i v ed a t a a r e s u m m a r i z e d i n F i g u r e 5 . I t i s e v i d e n tt h a t , f o r t h i s h e t e r o g e n e o u g s r o u p o f d i s u l f i d e s ,0 " + r j r e = - 1 . 0 .C r e i g h t o n h a s r e a c h e dt h e s a m e c o n c l u s i o n . Equilibrium Constants for Thiol-Disulfide Interchange R e a c t i o n s .T h e m e a s u r e m e n ta n d i n t e r p r e t a t i o n o f e x p e r i m e n t a l v a l u e s f o r e q u i l i b r i u m c o n s t a n t sf o r t h i o l - d i s u l f i d e i n t e r c h a n g er e a c t i o n si n a q u e o u ss o l u t i o n sa r e c o m p l i c a t e db y t w o c o n s i d e r a t i o n sF. i r s t . t h e s i m p l e s tt y p e o f e q u i l i b r i u m r e a c t i o n t o i n t e r p r e t - c o m p l e t e r e d u c t i o no f a s y m m e t r i c a l d i sulfide ESSE to a thiol ESH with concomitantoxidation of the r e d u c i n gt h i o i R S H t o a d i s u l f i d e R S S R ( e q l . l ) - i s a c h i e v e d o n l y i n t w o s t e p s b y w a y o f a n i n t e r m e d i a t eu n s y m m e t r i c a l d i s u l f i d e ( e q 1 5 , l 6 ) . S e c o n d ,b o t h t h i o l a n d t h i o l a t e s p e c i e s

2 ( R S H+ R S - ) + E S S E s

R S S R+ 2 ( E S H+ E S - ) (l4)

( R S H+ R S - ) + E S S E$

* S S E+ ( E S H+ E S - ) (l5)

( R S H+ R S - ) + R S S Es

R S S R+ ( E S H+ E S - ) (l6)

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(I7) \"' (ESSE)[(RSH)+(RS-)]2

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pKoESH F i g u r e 5 . R a t e s o f r e d u c t i o n, t ( l v 1 - t m i n - r ) o f s y m m e t r i c a l d i s u l f i d e s E S S E b y t h i o l a t ea n i o n . u s i n gd i t h i o t h r e i t o l( D T T ) o r g l y c o l d i m e r c a p t o a c e t a t e( C M A ) a s r e d u c i n ga g e n t .T h e l i n e sh a v es l o p e- I . 0 . D a t a f o r r e d u c t i o nu s i n g D T T a r e i n d i c a t e db y f i l l e d s y m b o l s .a n d a r e t a k e n f r o m t h i s p a p e ro r r e f l 2 ( r ) o r f r o m C r e i g h t o n( o ) ; 2 2d a t a f o r r e d u c t i o n su s i n g G V I A a r e i n d i c a t e db y a . T h e d i s u l f l d e sa r e i d e n t i f i e db y a b b r e v i a t i o n s f o r t h e c o r r e s p o n d i n gt h i o l s : E , E l l m a n ' s a n i o n : M A , 2 - m e r c a p t o e t h y l : E . 2 - m e r c a p t o e t h a n oAl :, m e r : S H . g l u t a t h i o n eM a m i n e :C . c y s t e i n eG c a p t o a c e t i ca c i d .

l 4 - 1 7 ) . T h e s ee q u i l i b r i u mc o n s t a n t s h o u l dt h u s . i n p r i n c i p l e . d e p e n db o t h o n t h i o l a n d d i s u l f i d es t r u c t u r e sa n d o n s o l u t i o n p H . I n t h e s e e q u a t i o n s ,a n d s u b s e q u e n t l ya, n e q u i l i b r i u m c o n s t a n tr e f e r r i n gt o a d i s u l f i d ei n t e r c h a n g ei n v o l v i n ga m i x t u r e o f t h i o l a n d t h i o l a t es p e c i e sw i l l b e d e n o t e db y t h e s u p e r s c r i p t " o b s d " . T h e i n f l u e n c eo f t h e o r g a n i cg r o u p s R a n d E o n t h e p o s i t i o no f e q u i l i b r i u m i n i n t e r c h a n g er e a c t i o n sb e t w e e n d i s u l f i d e sa n d t h i o l a t e i o n s w o u l d n o t n e c e s s a r i l yb e e x p e c t e d t o b e p a r a l l e l :r e a c t i o ni n v o l v i n go n l y t h i o l a t ea n i o n s ( K s - . e q l 8 ) s h o u l d b e s t r o n g l y i n f l u e n c e db y t h e p K " s o f R S H a n d

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E S H . w h i l e r e a c t i o nw i t h t h i o l s ( K s H ) s h o u l d b e m u c h l e s s d e p e n d e n to n t h e s ea c i d i t i e s .Q u a l i t a t i v ea n a l y s e so i e q u i i i b r i u m d a t a o b t a i n e d i n n o n a q u e o u sm e d i a i n w h i c h t h e e q u i l i b r i u n r c o n c e n t r a t i o no f t h i o l a t e a n i o n i s v e r y s m a l l h a v e s u g g e s t e dt h a t t h i o l - d i s u l f i d e i n t e r c h a n g ei s r e l a t i v e l y i n s e n s i t i v e t o o r g a n i c s t r u c t u r e . l 0 ' l t l n 6 . O e n d e n te x a m i n a t i o n so f KsH and Ks- in aqueous media have not been reported. Our primary concern in the work reportedhere is the inf l u e n c e o f r i n g s i z e o n e q u i l i b r i u m c o n s t a n t sf o r i n t e r c h a n g e reactionswhich involve cyclic disulfides.We have approached this problem by measuring equilibrium constants for reduction o f a s t a n d a r d d i s u l f i d e ( o x i d i z e dl i p o a m i d e ) b y a n u m b e r o f a.c,l-dithiols having different separations between the thiol groups. Since thesethiols have different pKrs, it is important. i n t r y i n g t o u n d e r s t a n dt h e i n f l u e n c eo f r i n g s i z e i n t h e c y c l i c d i s u l f i d e so n t h e m e a s u r e de q u i l i b r i u m c o n s t a n t s ,t o i d e n t i f y the contributions to theseequilibrium constantswhich reflect the relative acidities of the thiols. Separationof a vaiue for KoM (eq l7) measuredat a known pH into valuesof KsH and Ks- requiresonly knowledgeof the pK,,s for the two thiols ESH and RSH. The fact that oniy one e x p e r i m e n t a le q u i l i b r i u m m e a s u r e m e n ti s r e q u i r e d t o o b t a i n valuesof KsH and Ks- reflectsthe fact that theseequilibrium c o n s t a n t sa r e n o t i n d e p e n d e n t :t h e r e l a t i v ec o n c e n t r a t i o n so f

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F i g u r e6 . s c h e m a r i c r e p r e s e n r a t i oonf t h e r e s p o n s eo f l o g .K o b ' d( d e f i n e d - pKusH to b f e q l 7 ) f o r s e l e c t e dv a l u e so f t h e P a r a m e t e rp K " * s | . h " n g . r i n t h e s o l u t i o np H l t h e s ec u r v e sw e r eg e n e r a t e df r o m e q 2 5 . F o r c o n v J n i e n c ei n p l o t t i n g , t h e z e r o o i t h e l o g 6 o u ' a a x i s i s t a k e n t o b e t h e l/z(log m e a no f t h e l o g a r i t h * o i t i , . e q u i l i b r i u mf o r t h i o l a n d t h i o l a t ei o n , K s H + l o g K s = ) . a n d t h e z e r o o f t h e p H s c a l ei s t a k e n t o b e m e a n o f t h e * p K r s H ) . E a c h c u r v e i s t a b e l e dw i t h a v a l u eo f pK, valuei. l/z(pKuRSH = p r " n s H - p r " ' e s H T h e b o l d f a c ec u r v e i s f o r p K " R S H p K " E S . H 2 ' 0 : n o t e t h a t t h e o b s e r v e de q u i l i b r i u mc o n s t a n tX ' o b sfde l t h i s c u r v e i n c r e a s e s b y ,l 0 a a s r h e p H i s c h a n g e df r o m v a l u e ss u f f i c i e n t l l , a c i d i ct h a t b o t h R S H rna eSU are essentiallyiompletelyprotonatedto valuessufficientlybasic t h a t b o t h c o m p o n e n t sa r e e s s e n t i a l l yc o m p l e t e l yi o n i z e d '

-b-4-262468 z (ptrf$-proEsH) F i g u r e7 . P l o t so f ( A ) l o g , ( s H a n d ( B ) l o g K s - v s ' 2 ( p K " R S " : ! K " t t " ) ' = 2.12' T h " en u m b e r s r e f e r t o f a b l e I V . ( B ) i n c l u d e st h e l i n e l o g 5 s t hrough l i n e l e a s t s q u a r e s b e s t t h e w h i c h r e p r e s e n t s (pK"RsH pK"sH). (0.0)' The i i . i o i n t r I - S l i n v o l v i n g a l k y l t h i o l s ) w h i c h p a s s - et.hl r o u g h = (B) log KS- = d a s h e dl i n e sa r e i n c l u d e df o r r e f e r e n c e (: A ) l o g K s H 0 ; p K " E s H ) . 2(pK"RsH only on the differences in the characteristics (pK,. KsH' Ks-) of the thiols involved. rather than on their absolute values. The thiols with which we are concerned in the following have pr(" values between 7.5 and I 1.0.and experimental measurements

w e r e m a d ea t p H 7 . T h u s ,t y p i c a l l yp, H - l / 2 ( p K , R S H+ - p6" ESH pK ,E S Hhad ) val uesfrom -3.0 to -0.5, andpK " R S H ci rcumsta nces, these t h i o la n dt hiolat eanionsa refi x e db y th e k n o w nv a l u e so f pH ' U nder 2.5. and 0 had val uesbetw een T o d e ri v eKS H a n d K S- fro m 7 1 ' obsd, Fi gure6 i ndi cates p KrRSHa. nd pK oE S H. that 6obsdcoul dcontai nsi gni fi cantc ong e ra ti o o f th i o l ate rri buti onsfrom boththi ol - andthi ol ate-di sul fi de . p re s s i nth ar e us e fu l Ex i nterchange s e ve rael quat ions intoeq I7, oneobtains e q u i l i b r i a . to thiolby eq l9 and 20,andsubstituting of t he andconsi stency reasonabl eness To checkthephysi cal (le) ( E S - ) / ( E S H ) - l o P H - P ^ u * "= 6 wc have of 1'trbsd, valuesof KsH andKs- obtainedby dissection Figure constants. ( 2 0 ) examineda numberof literatureequilibriun'l ( R S - ) i ( R S H ; = l g n H - R K ' R t "= 6 pl otsof l og K sH and l og K S - vs. 2(pK uRSH 7 show sseparate - pK ,E s11) deri vedfrom the data summari zedi n Tabl e I V. ( 2 1) KSH= !] i :l; 6obsd i n the upperpl otshow sno obvious The equi l i bri umconstants (l + 0)' pK,s. are inlluencedby steric effects: but with correlation - 1' * :-iJ; x'obsd (22) 76ssteri cal l yhi nderedthi ol sgi ve l ow val uesof K sl ' 1.W e n ot e, (l * d-';' how ever,that the data i n thi s fi gurehavebeendraw n from several sources,and differencesin experimentalconditions (23) Ks- = { ^tn in individualdata,may betweensetsof data,and inaccuracies ApK"' fl':.lpKsH-on log of weak dependence disguise a (24) log 6s- = 2(pKrRSH - pKaESH)+ log KsH pro"ximate linearityol the plot of log KS- vs' 2!Ptr,*t" by the acithat K s- i s strongl yi nfl uenced pK " E S Hi)ndi cates ( l + 6 ) ( l+ 6 - r ) conj ugatethi ol s.and that the d at a di ti esof the parti ci pati ng log6ou'o- | lz.loeKsH+ logtrs-1= log ( l + e ) ( l * e - r ) are adequatelrati y onal i i edby the schemeof eq 18.In pr inshould.be(/3nr" ciple,the slopeof a plot of log KsH vs-^2ApK" = (pKuESH - pKoRSH) -' gr, = I ) and that of a plot of log KsH vs' 2ApKoshouldbe I I * I gpH-r /2(pK"nsH+pKaEsH)-l/21px^esu-pr"RsH)] e de(B ^,,:- 6,,) (seebel ow );i t shoul dthereforebe possi blto r 2log experimentallyfrom theseplots.Figure7B i!iri". P"";"- ,619 line drawn throughthe (2s) includesfor referencethe least-squares that suggests and thiols. 6nu.- fl,r- l '2' We setof aliphatic unKSH,and KS- summarized rei teratethat the qual i tyof the data makesthi s esti mate between6'obsd, the relationships *.20Vo. least bY at certain and eq 23 of sides both of logarithm by eq 21-23.Taking the w e can i nterpretequi l i bri umc onW i th thi s background, exp a n d i n gy ieldseq24.M u l ti p l y i n go f e q 2 l a n d 2 2 ' ta k i ng lipoamideby a seriesof oxidized of reduction for stants expression, the squareroot and the logarithmof the resulting both by differentseparationsbecharacterized a.