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

I
Szajewski. Whiresides
/ Thiol-Disulfide Interchange Reacrions
Rate Constants and Equilibrium Constants
for Thiol-Disulfide Interchange Reactions
Involvins Oxidized Glutathionel
Richard P. Szajewski2 and George M. Whitesides*
Contributionfrom the Department of Chemistry, Massachusetts Institute of Technology,
. Cambridge, Massachusetts 02139. Receiued May 8, 1978
Abstract: The rate of reduction of oxidized glutathione (GSSG) to glutathione (GSH) by thiolate anions (RS-) follows a
Br/nsted relation in pK"s of the conjugate thiols (RSH):pnu" - 0.5. This value is similar to that for reduction of Ellman's reagent:
0nu" = 0.4-0.5. Analysis of a number of rate and equilibrium data, taken both from this work and from the literature.
indicates that rate constants, k, for a range of thiolate-disulfide interchange reactions are correlated well by equations of the
formlogk=C*0nu.pKunu"*0"pK""*0repKule(nuc=nucleophile.c=central,andlg=leavinggroupsulfur):eq36-38
give representative values of the Br/nsted coefficients. The values of these Br/nsted coefficients are not sharply defined by the
available experimental data. although eq 36-38 provide useful kinetic models for rates of thiolate-disulfide interchange reactions.
The uncertainty in these parameters is such that their detailed mechanistic interpretation is not worthwhile. but their
qualitative interpretation-that all three sulfur atoms experience a significant effective negative charge in the transition state,
but that the charge is concentrated on the terminal sulfurs-is justified. Equilibrium constants for reduction oiCSSG using
a,cr-dithiols have been measured. The reducing potential of the dithiol is strongly influenced by the size of the cyclic disulfide
formed on its oxidation: the most strongly reducing dithiols are those which can form six-membered cyclic disulfides. Separate
equilibrium constants for thiolateanion-disulfide interchange (Ks-) and for thiol-disulfide interchange (KsH) have been estimated
from literature data: Ks- is roughly proportionalto 2ApK. is the difference between the pKus of the two thiols involved
in the interchange. The contributions of thiol pKu values to the observed equilibrium constants for reduction of GSSG with
a,co-dithiols appear to be much smaller than those ascribable to the influence of structure on intramolecular ring formation.
These equilibrium and rate constants are helpful in choosing dithiols for use as antioxidants in solutions containing proteins:
dithiothreitol (DTT), 1.3-dimercapto-2-propanol (DMP), and 2-mercaptoethanol have especially useful properties.
Introduction
Oxidation of catalytically or srructurally essential cysteine
thiol groups can be an important mechanism for enzyme
deactivation.l It is impracticai to exclude oxygen completely
from solutions of proteins during their manipulation, and the
strategy normally followed to minimize the influence of autoxidation
on enzymatic activity is based on the protection aftorded
by organic thiols (especially 2-mercaptoethanol and
dithiothreitola's) present in excess. These added thiols probably
inhibit the irreversible oxidative deactivation of proteins by
several mechanisms. They reverse the initiai srages of the
protein autoxidation reactions by reduction of protein disulfides
and sulfenic acids6 to thiols. They may, by coordination,
modify the catalytic activity of transition-metal ions in thiol
: 0.34). and Brocklehurst et al. have examined reductions of
2,2-dipyridyl disulfide (pnu" = 0.23).r2'rl These studies indicate
that thiolate-disulfide interchange is a mechanisticaily simple
Sx 2 displacement reaction, but.suggest that the values of the
characteristic Brpnsted coefficients are sensitive to the particular
set of reactants chosen. The extension of these model
studies to GSSG was carried out for two reasons. First. the
equilibria l'or reduction of diaryl disulfides with typical aliphatic
thiols lie so far toward aryl thiol that equilibrium constants
could not be measured conveniently. It was thus not
possible to explore the influence of the structure of the reducing
thioi on the thiol-disulfide interchange equilibria. Second, aryl
thiols are arguably poor models for a protein cystine group.
autoxidation.l'7 Their own oxidation consumes dioxvsen and Results
hydrogen peroxides present in solution
As part of a project aimed at the development of techniques
to permit the use of enzymes as practical catalysts in the synthesis
of organic and biochemicals,e we have begun to study
the relation between the structures of organic thiols and their
ability to prevent or reverse the autoxidation of proteins. The
work described in this paper is focused on one aspect of this
problem, viz., rate- and equilibrium-structure relations for
the reduction of a model cystine-containing pepride (oxidized
glutathione, GSSG, 7-glutamylcysteinylglycine) by basecatalyzed
thiol-disulfide interchange. Oxidized glurathione
was selected as substrate in this investigation for three reasons:
it is readily available in pure form: its presence, as well as that
Rates of Reduction of Oxidized Glutathione by Mono- and
Dithiols. The rate of reiease of GSH from GSSG was determined
using a fast enzymatic following reaction at pH 7.0
(0.06 M phosphate buffer) and 30.0 * 0.5
of reduced glutathione (GSH), can be monitored in the presence
of other thiols and disulfides using enzymaric assays;10
and, because it occurs in biological systems,l.ll information
about its reactions with various thiols should prove generally
useful. Wel2 and Hupe et al.l3 have already reported rates of
thiol-disulfide interchange reactions involving EIlman's reagent
(5.5'-dithiobis(2-nitrobenzoic acid)) and found them to
foilow a Brlnsted correlation (pnu" = 0.5). Cleland et al. have
carried out related studies with 4,4'-dipyridyl disulfide (pnu"
'C under argon.
CSH was converted to S-lactoyl glutathione (GS-lac) by reaction
with methylglyoxal in the presence of glyoxalase-l
(GX-l), and the concentration of GS-lac was monitored
spectrophotometrically at 240 nm, es 3.37 mM-l cm-i.l'1
Equations I -6 list the reactions pertinent to this assay. In these
equations, RSH is a monothiol reducing agent. Reaction 6, the
enzymatic conversion of hemithioacetal to GS-lac, is essentially
irreveisible.la
KrRsH
RSH _ RS- + H+ (I)
kt
RS- + GSSG _
k-r
GSSR + GS- (2)
k't
RS- + GSSR - RSSR + GSk-z
pK"CSH = g.lltS
GSH GS- + H+
(3)
(4)
(1980).1
201 I

zjt2
F4
9.
x
I
(n
9-?
o
(
1
Journal of the Anterican Chemical Society / 102:6 / March 12, lgB0
(GSSR) > (RSSR): since the rate constants k r, k:, k- 1, and
k -2 are all of the same magnitude, the second. third. and fourth
terms of eq 8 can be neglected, and this expression may be
combined with eq 7c and rewritten as eq 9a. For convenience,
this equation was used in a form (eq 9b) involving an observed
rate constant. k lob'd, based on the total concentration of thiol
and thiolate anion in solution. The rate constants ll I and k robsd
are related by eq 10.
d(GS-lac) f dt - k r (RS-)(GSSG)
= ft,obsdt(Rs-) + (RSH)l(GSSG)
ot23456789tO
Timc (min)
Figure l. Formation of S-lactoyl glutarhione (CS-tac, M) with time at 30.0
* 0.5 oC, kt = k,obsd 1l + l6px"nsx-pH)
under argon in a pH 7.0 phosphate buffer (0.066 M) containing
oxidized glutathione (GSSC. 0.35 mM). dithiothreitol (5.07 mM), and
methylglyoxal (CH:COCHO,0.77 mM). and using (A) 24, (B) 2.4. (C)
1.8. (D) 1.2, (E) 0.3 U/mL. respectively. of glyoxalase-l (GX-l). The
To ensure the accuracy of the assumptions and approximations
made to generate eq 9, it is necessary to adjust the relative
concentrations of the various species present in solution. Reactions
were carried out using the following initial concentrations:
(RSH)0 = 0.77 mM, (GSSG) = 0.35 mM, and
(GX-l) - 2.5 X l0-4 mM (2.4 U/mL).16 Because the srarting
concentration of GS-lac was determined spectrophotometrically at 240
nm using eo 3.37 mM-l cm-1. There is no significant difference berween
d(GS-lac)/d/ at enzyme concenrrarions of 24 and 1.8 U/mL: the concentration
of enzyme used routinely in the assay was 2.a U lmL.
concentration of thiol is much greater than any of the other
solution components, this concentration is not significantly
perturbed by hemithioacetal formation and remains essentially
constant throughout the course of a kinetic run. The concentration
of CHICOCHO under these conditions is, of course.
K5=J6fYfla
unknown: although a significant fraction oi this material is
probabl.v converted to hemithioacetal, the velocity of equilibration
of the hemithioacetal with aldehyde and hemihydrate
is fast compared to the enzymatic reactions which follow.ra
Regardless o[ the equilibrium concentration of hemithioacetal.
(CHICOCHO)o > (GSH) in the initial stages of the reaction.
For small extents of reaction (in these experiments typicallv
l0-20Vo) the concentration of CHICOCHO can be considered
constant. Thus. with the assumptions indicated, the rate of
appearance of GS-lac will be directly proportional to the
concentration of GSH. For the steady-state approximation to
hold for GSH, it is necessary that it be converted to GS-lac
much more rapidly than it is formed from GSSG. The rate of
conversion oi GSH to GS-lac can be adjusted over a wide
margin by simply changing the concentration of glyoxalase- |
or CH3COCHO. The concentration of enzyme required to
achieve steady-state conditions in GSH, at a convenient
CH3COCHO concentration, was established experimentally.
The concentration (activity) of enzyme in solution was varied,
and the value of (GS-lac) measured, holding all other parameters
constant. At values of enzymatic activity greater than
-2 UlmL, increasing the activity of enzyme in solution
shortened the duration of a non-steady-state interval at the
beginning of the reaction, but did not influence the value of
d(GS-lac)/dt once the steady-state region had been reached
(Figure I ). More generally, the validity of eq 9 requires that
d(GS-lac) ldt be zero order in GX-l and CH3COCHO and
first order in RSH and GSSG. Table I, which lists k 'obsd rn6
velocities [d(GS-lac) ldt] for formation of GSH from GSSG
using 2-mercaptoethanol as reducing agent, establishes that
these conditions are fulfilled. The data in the first line of this
table were obtained using the standard conditions employed
routinely in this work; the other runs were performed on solutions
in which these conditions were systematically varied.
Analysis of the velocity data and extraction of the rate constant
k,ob'd from these data are discussed later in the text. Under
the conditions used, the assumptions made in obtaining eq 9
seem to be justified, since large deviations from the standard
conditions have no influence on krobsd.
Equation 9 applies to monothiol reducing agents. In this
work, we were particularly interested in dithiols. In treating
reducing agents, HSRSH, containing two identical thiol
groups, we used an entirely analogous procedure, with two
additional assumptions. First, we assumed that the nucleophilicities
of the mono- and dianions, HSRS- and -SRS-,
( l0)
GSCHOHCOCHT GSH + CH3COCHO (5)
GSCHOHCOCHT+ GX-I 9 GSCOCHOHCH3 + cx-l
(GS-lac)
(6)
To derive rate expressions for k I from these equations, we
require that the overall rate-limiting step in conversion of
GSSG to GS-lac be the initial thiolate-disulfide interchange
reaction (eq 2). We will assume that thiolate anion is the only
nucleophile participating in the thiol-disulfide interchange
reaction,lT that reduced glutathione (GSH) is present only at
a low, steady-state concentration. and that glyoxalase-l follows
typical Michaelis-Menten kinetics with the hemithioacetal
CSCHOHCOCHI as its only substrate (eq 7a).te.r6'r8're
d(GS-lac)/dr
= k: (GX-llIr + Krn GSCHOHCOCHT
(ia)
(GSCHOHCOCH3) ]-
t
KsKmcscHoHCocHil- I
= k:(GX-l)(GSH)l(cSH) +
t @
(7b)
= [k3(GX-l)(CH3COCHO)/3mM2](GSH) (7c)
Substitution of the equilibrium expression for K5 (eq 5) into
eq 7a followed by rearrangement gives eq 7b. At a low
steady-state concentration of GSH, eq 7b reduces to eq 7c for
K s - 3 mM and K.cscHoHcocH: - I mM.20 The bracketed
portion of eq 7c may, in principle, be made arbitrarily large and
constant by adjusting the concentrations of either GX-l or
CH3COCHO; in practice, the quantity of GX-l used is the
more easily varied. At the pH used for the assay (pH 7.0), the
majority of the reduced glutathione is present as GSH rarher
than GS-. Assuming these conditions and a steady-srare
concentration for GSH, we'relate the rate of production of
CS-lac to k 1 by the equation
0 : d(CSH) /dt
= kr(RS-)(cSSc) + k2(RS-)(GSSR)
- k_r(cssR)(GS-) - k_z (RSSR)(GS-)
- ft3[(cx-l)(CH3COCHO)/3 mM2](GSH) (8)
We ensure that kinetics observations extend only over the
initial stages of the reaction, in which regime (GSSG) >
(9a)
(eb)

Szajewski, Whitesides / Thiol-Disulfide Interchange Reactions
Table I. Rate Constants (k,ou'a, M-l min-l) for Reduction of Oxidized Glutathione (CSSG) by 2-MercaPtoethanol4
k , obsd d(GS-lac)/drD IHOCH2CH25HI' lcHrcocHol. lcsscl. IGS-rld comments€
8.8
9.5
8.2
9.1
7.3
9.3
8.9
8.0
8.8
9.2
t4.4
r 5.6
13.2
t4.9
39.4
1.5
t4.7
12.6
28.3
2.5
5.07
5. l0
5. r0
5.09
14.5
0.49
5.r2
4.99
5.05
5.07
0.7 6
0.77
0.77
0.77
0.76
0.75
0.31
1.50
0.76
0.76
0.32
0.32
0.32
0.32
0.32
0.3 r
0.33
0.32
0.64
0.054
1.t
:.1
aa 1
0.48
1.2
1A
L-.+
2.1
1A
'tA
L.1
1A
L.a
2.4
201 3
standard
XIOGX-I
XO.2 GX-I
x0.5 GX-l
X3 RSH
XO.I RSH
xo.5 cHTCOCHO
x2 CH3COCHO
X2 GSSG
XO.I7 GSSG
" All kinctics lrerc run in 0.056 M phosphate buffer, pH 7.0, 30.0 * 0.5 oC, under argon, wcrc followed at 240 nm using €o 3.37 mM-l cm-t,
and were coftected for blank reactions, ii rnt. , Unir; of d(Cs-tac)/dr arc M-r min:r x 106. . Concertration units are mM. d In enzyme
units (prnol/min) pcr mL. ' This column indicctes the major changc fiom the standard mnditions.
Table II. Rate Constants (k'ou'a M-l min-r) for Reduction of Oxidized Glutathione by Dithiothreitolo
k , obsa d(GS-lac)/dt' IDTTI. lcHscocHol. IGSSGl. IGS-rld commentse
14.0
14.6
8.4
t 3.l
r3.0
t4.2
9.8
l2. r
12.7
14.0
AA'I
47.0
26.9
41.3
81.6
4.5
31.9
J t,l
80. l
5.8
4.94
4.97
4.97
4.94
9.94
0.49
5.01
4.86
4.93
1.94
0.76
0.77
0.77
0.77
0.7 6
0.7 6
0.39
L50
0.76
0.'t 6
were indistinguishable. This assumption neglects electronic
effects and a statistical factor of 2, both of which would make
the dianion more reactive than the corresponding monoanion.
The concentration of dianion will, however. be small relative
to monoanion at pH 7 for the dithiols we have examined.
Moreover, the observation (see below) that mono- and dithiols
fall on the same Br/nsted correlation line suggests that the
cumulative error introduced into estimates of rate constants
by this assumption is small. Second, we assume that, for the
concentration of dithiol used, the rate of the initial intermolecular
thiol-disulfide interchange is lower than that of a
subsequent intramolecular reaction which releases a second
equivalent of CSH (eq I l). A similar assumption. rnade in our
HSRSH + CSSG g
HSRSSG + GSH
(I IA)
fast
HSRSSG
'-"; sn3 + GSH ( I lb)
0.32
0.32
0.32
0.32
0.32
0.32
0.3 3
0.3 2
0.64
0.042
1^
'tA 1
0.48
1.8
1A
1A
.\^
1,1
1A
11
standard
XIO GX-I
XO.2 GX.I
X0.75 GX.I
X2 RSH
XO.I RSH
xo.5 cH3COCHO
x2 CHTCOCHO
X2 GSSG
XO. I 3 GSSG
d All kinetics were run in 0.05 M phosphare buffer, pH 7.0, 30.0 * 0.5
'C,
under argon. ' Velocity offormation ofGS-lac as determined
spectrophoromerrically a! 240 nm u.;ng io :.:l mM-i cm-l and corrected for blank riactions. if any. Units of d(Cslac)/d, are M min-l
i t Oo. I Con""ntr",ion unirs rre mM. ; ln unirs of enzyme acriviry per mL. ' This column indicates (he major deviation from stlndard condi!ions.
previous treatment of the reduction of EIlman's reagent. could
be justified experimentally because independent estimates of
the rate constants for release of aryl thiols from diaryl disulfides
and aryl alkyl disullides indicated a sufficient difference
to be detected.
| 2' 13 4noltsis of the equilibrium constants for
reduction of CSSG by all of the dithiols examined below, except
for glycol dimercaptoacetate, established a significant
enhancement relative to analogous monothiols. lf we assume
that the rates of intermolecular reaction of mono- and dithiols
having similar thiol pK" values on GSSG will also be similar.
the observed difference in equilibrium constants suggests that
the rate of inlramolecular thiol-disulfide interchange involving
the second thiol group of an cv,c.,.r-dithiol is probably last relative
to the first intermolecular interchange (see below). Nonethe-
Iess, since we have not been able to measure rate constants for
release oi CSH irom GSSG and GSSRSH by thiol-disulfide
interchange experimentally, and since these values are prob-
ably similar for most of the thiols examined here.ll'12 we relv
on analogy with this previous work to justiiy our assumption.
Note, however, that. if this assumption is incorrect. it introduces
an error of only a factor oi 2 in the rate constants for
dithiols.
With these assumptions. a treatment similar to that described
previously leads to the expressions in eq l2 relating the
observed rate of production of GS-lac to the rate constant of
interest, k1. Again k1 and klobso are related by eq 10.
d(GS-lac)
f dr = 2k TUHSRS-)
+ (-SRS-)l(GSSG) (l2a)
= 2krob'd[(HSRSH)
+ (HSRS-) + (-SRS-)I(GSSG) (l2b)
Table I I lists values of k,ousa and velocities [d(GS-lac)/dr] for
formation oi GSH from GSSG using dithiothreitol as reducing
agent. The first line in the table reports data obtained using
our standard conditions: the other runs were performed on
solutions in which these standard parameters were varied.
Again. under the conditions used. the assumptions made in
obtaining eq l2 seem to be justified.
Straightforward consideration of material balance and integration
of eq 9 (or eq l2) by standard methods givesrz'::
ft,obsd1 =
, (GSSG)o
(S)o -
In--
(GSSG)o ())o
*[ tslo-tc (GS-lac)/n S-lac)/n I
-
[(GSSG)o (CS+*)/rl
( l3)
The terms in the expression are defined as follows: for monothiols
So = [(RS-) + (RSH)), n = l; for dithiols So =
[(-SRS-) + (-SRSH) + (HSRSH)], r = 2. Figure 2 reproduces
typical kinetic data for reduction oi CSSC by several
mono- and dithiols as derived using the integrated rate expression
(eq l3). The crude absorbance data used to generate

20t4 Journal of the American chemical society / t 02:6 / March I 2, I gg0
ct c
\l \
o l o
!19
6l s1
(,1(J
-l
i
'ld
_q6
cnl.r,
-g
8l -e
i^l v)
YI
s
l^o
l(9
Itn
|(t
-1(9
t^
l^v
t9
(GMA)
/,1
3\(DTT)
, ,7 (ME)
!{
Figure 2. Rate-constanr prots ,",- ,*1...1"1 r.t""*, l,on*tuno ot,,n,o,,
wirh oxidizcd glutathione (GSSG) in pH 7.0 "r phosphate buffer (0.066 M)
at 30-0 + 0.5 "c under argon. The termq in the expression on the axis are
defined as follows:for monothiols, Se =
[(RS-) +'(RSHt] , n = t; for di_
rhiots. s6 =
[(-SRS-) + (HSRS-) + (ASRSH)J, lr = z'(ir. eq r3 or the
text). Reducing agenrs: r, grycor dimercaptoacerate; v, dithiothreitor:
o. 2-mercaptoethanol: r. thiogl.vcolic acid. Kinetics are sho*n .espectivery
to 60, 50, 20. and 20vo of compretion. The kinetic points sho*n here were
obtained from the experimenta I Azcoattributabre to GS-lac and are corrected
for the relativel-v slow blank reaction observed in these sysrems *hen
using phosphate buffer (see ref 24).
Tables I-lll were corrected for the slow phosphate ion cara_
lyzed reaction between methylglyoxal and thiols before analysis
to obtain values of klob'd using this equation.2a Rate
constants for reduction of GSSG by a seri'es of rnono- and dithiols
under standard conditions are listed in Tabte 11y.zr.::
Figure 3 summarizes these data as plots of log ft 1 and log k ,obsd
vs. the pK" of the reducing thiol. The arornatic thiolJwhich
were used to obtain data for values of pK"RSH ( g with Eil_
man's reagentll'13 could not be used in itudying the reduction
of GSSG, because they absorbed strongiy at ine waverength
used to monitor the concenrration oi GSI-iac (2a0 nm). For
comparison, Figure 4 reproduces analogous data for reduction
of Ellman's reagent; this plot includ.i duru both from our
workl2 and from the study of Hupe et al.r3
The Br/nsted coefficient (pnu" = 0.50, coefficient of de_
termination = 12 = 0.89) obtained by least-squares analysis of
the rate constants for GSSG is similar to tiat obtainld for
reduction of EIlman's reagent by thiols. This latter system has
now been the subject of two independent studies ( Figure 4). r:. r:
our study^analyzed a group of at[yt and aryr thiors rogether,
and gave 6nu. = 0.30, 12 - 0.g5.25 Hupe et al. anal y:zed, d,ata
for a similar set of thiors, but suggested thar alkyi and aryl
thiols
l.ll_:n
separare correlation-fines, with pnu.irkyt = 6.49
(r.l = 0.98) and Bnu"a'vl ^= 0..48 (r2 = 0.96). nnatysis of our
alkyl data alone yielded pnu"ulkrl = 0.4 | (r2'= 0.67;.Our data
for aryl thiols cover a small range of pK" values unJar" l.r,
accurate than those of Hupe.26 The value of the Brlnsted
coefficient selected from these several analyses depends in purt
9n 9uljgctive
judgmenrs concerning the ihoi". oi dutu to be
included. we agree.with Hupe et al.-that the arkyr and aryr
thiols should be analyzed separately,2T and not" th"r there is
no independent evidence which can be used to select between
values of pnu""lkrl lying between -0.4and 0.5. For simpricity,
we will take 6 - 0.5; arguments outlined later suggest that
these p values may not, in any event, translate directly into
fractional charges, and the ty,n.rtry and charge distribution
of the transition state do not -demanda
pKrs*
Figure3. Plotsof (A) log,tltuand (B) Iog &r (M-r min-r) vs. thiorpK"
for the reduction of oxidized grutarhione in pH ?.0 phosphate buffer at
30.0 + 0.5
specific ialue of
The
B.zs.n
value of pnu"alkrl = 0.5 for reduction of GSSG determined
in the presen^t s.tydy thus seems physicaily reasonabre, but, since
the range of thiol pKrs covet.a is reraiivery smail, since the
scatter in the experimentar points is significant, and since the
assay system used to follow the reactions is complex, this value
oc under argon by rhe mono- ona'aitniott tisted in Table III.
DTT is dithiothreitol. .vlE is 2-mercaproethanol. DMp is 1.3-dimercap
topropa nol, and G M A t-vc^ol
.is.e ! ! mgcaproacetate. The least_sq ua res slope
for (B) is 6n," = 0.501r2 = 0.89). The equation used ,o g.n.r.,. the rine
in (A) is log k 1oH = -_1,29 * 0-50pK. - Iog ( lgpKe-7.0 +" t ); ti,. equation
in (B) is log kr = -1.29 * 0.50pK".
Table III. Rate consranrs (t. M-r min-r) for Reducrion of
Oxidized Glutathione (GSSG) by Mono- and Dithiols"
thiol PK^ &"obsd k1
I (HSCHTCO:CH:_): (GMA) 7 .1 19.91t 90 4.9 X 102
2 HSCH2CHOHCHTSH 9.0 (10.3)b 9.3 9.3 x 102
(DMP)
3 dithiothreitol (DTT)
9.2 (10.1)6r4.l
2.2 x 103
4 DTT/DTE mixture. 9.2 (r0.1)b 8.4 l.l x t03
5 HOCH2CHOHCH2SH g.5b 7.9 2.5 x 103
6 HSCH2CH(NHCOCH3)_ g.5d 5.2 1.8 x 103
COzH
7 HOCH:CH2SH (ME) 9.6, 8.7 3.4 x 103
8 HSCH:COzH
9.8r
t.J 4.6 x l0l
9 HSCH2CHzCOzH 10.68 3.2 1.2 x 104
a All rates were derermined in 0.066 M phosphate buffer, pH 7.0,
30.0 + 0.5 oc, under argon. Data typicaily represent an average of
three determinations. The rate constants are not corrected statistically
lo11he
presence of two equivalent sulfur atoms in GSSG. Reproduiibility
in these experimenrs was * l5zo. Arrempts to measure rates for
several other representative thiols were unsuccessful. The rate of reduction
9f
GSSG by CHrcoSH was not significantly faster than the
rate of the blank reaction: k,obsd is smaller than lri-r v-' min-r.
Amino thiols (cysteine, Et2NcH2cH2sH) react quickry with the
methylglyoxal in the assay solutions to form speciis which absorb
strongly at 240 nm, presumabry s-ractoyr thioesters (see ref 24 for
a discussion of the mechanism of these blank reactions). GX-l was
inactivated by HocH2cHSHcH2sH. , Sources of these pK" valuis
are listed in ref 12. These values for DTT have also been reported by
E. L. Loechler and T. C. Hollocher. -/. Am. Chem. .Soc.,'g7,323i
q9]5i c Prepared as described in ref 12. d 2 (DMP)
From M. Friedman, J.
F. Cavins, and J. S. Wall, J. Am. Chem. Soc., g7, 3672 (1965). ' This
pK" is taken from ref 13. /Reference 15. c From R. J. Irving, L.
Nelander, and I. Wadso, Acta Chem. Scand., 18, 769 ( I964).
should not be considered'highly precise. Quaritativery more
important is the observation that reductions of GSSG and
Ellman's reagent by thiol-disulfide interchange appear to be
closely related reactions. Each is characterized by a Brf,nsted
coefficient of similar size, and neither shows any evidJnce of
curvature in the Brfnsted plots suggesting a change in mechanism
or an intermediate. Since Ellman's reagent and oxidized
E -
.o
t
ctr
o
*-
('r
o
ro
tl

Szajewski, Whitesides
/ Thiol-Disulfide Interchange Reactions
aa
o
94
5
A
a ./
zVEEs
.-
-\
MMA
b
a-t-- O
Wilron, Boyrr.Hugr O O
Whit.lid.!,Lilburn,S:oienliat
z 3 4 5 6 7 8 9 lO ll
pKo
Figure 4. Collected rate constants (M-r s-r) for reduction oi Ellman's
reagent by thiols. Data from ref l? are represented by solid points; data
from ref l3 are represented by open points. Data for alkyl thiols are
summarized by o and O: data for aryl thiols by I and E; data flor thiol
acids by r. ME is mercaptoethanol; GMA is glycol dimercaptoacetate;
MMA is methyl mercaptoacetate. Other points are identified in ref l2 and
13. The lines represent least-squares fits to these sets of data: A (-), alkyls
(o).rr 0nu"
= 0.43, r2 = 0.91; B (- - - -), alkyls (o)r3 excluding methyl
mcrcaptoacetate. 13nu.
= 0.49, rl = 0.97.C (' -' -), alkyls (O),12 gnu" =
0.-11, rl = 0.67: D (.. - - -), aryls (u),rl dnu" = 0.41. r2 = 0.9'1.
.|
--
.o
*.I
4 5 6 7 8 9 lO ll
pKoESH
gluathione represent very different types oi disulfides, their
kinetic similarities encourage the conclusion that thiol-disulfide
interchange is, in most instances, a mechanistically
u ncompl icated reaction.
Although we have not explicitly determined Brpnsted
coefficients lor the leaving (pre) and central (d.) thiol groups
in the thiol-disulfide interchange, examination of our data, and
those of Creighton,rl yields a value f or the sum of p. * 131n. We
have determined the rates of reduction oi GSSG and Ellman's
reagent with a number of thiols: Creighton established the rate
of oxidation oi DTT in the presence of several symmetric disulfides.
Representative data are summarized in Figure 5. It
is evident that, for this heterogeneous group of disulfides, 0"
+ rjre = - 1.0. Creighton has reached the same conclusion.
Equilibrium Constants for Thiol-Disulfide Interchange
Reactions. The measurement and interpretation of experimental
values for equilibrium constants for thiol-disulfide
interchange reactions in aqueous solutions are complicated by
two considerations. First. the simplest type of equilibrium reaction
to interpret-complete reduction of a symmetrical disulfide
ESSE to a thiol ESH with concomitant oxidation of the
reducing thioi RSH to a disulfide RSSR (eq l.l)-is achieved
only in two steps by way of an intermediate unsymmetrical
disulfide (eq 15, l6). Second, both thiol and thiolate species
2(RSH + RS-) + ESSEs RSSR + 2(ESH + ES-)
( l4)
(RSH + RS-) + ESSE $ *SSE + (ESH + ES-)
( l5)
(RSH + RS-) + RSSE s RSSR + (ESH + ES-)
( l6)
6'obsd
- Klobsa6robsd: '!
(I7)
(ESSE)[(RSH)+(RS-)]2
\"'
Figure 5. Rates of reduction ,t (lv1-t min-r) of symmetrical disulfides
ESSE by thiolate anion. using dithiothreitol (DTT) or glycol dimercaptoacetate
(C MA) as reducing agent. The lines have slope
may be present in appreciable concentration in solution, and
measured equilibrium constants ordinarily contain terms in
the sum of the concentrations of thiol and thiolate species (eq
- I .0. Data for
reduction using DTT are indicated by filled symbols. and are taken from
this paper or ref l2 (r ) or from Creighton (o);22 data for reductions using
GVIA are indicated by a. The disulfldes are identified by abbreviations
for the corresponding thiols: E, Ellman's anion: MA, 2-mercaptoethylamine:
C. cysteine: GSH. glutathione: ME. 2-mercaptoethanol: A, mercaptoacetic
acid.
65-
2RS- + ESSE -i-+
r"nsn lf
KSH
2RSH + ESSE =-
RSSR + 2ES-
'Jf
*""r" (1s)
RSSR + 2ESH
ESH. while reaction with thiols (KsH) should be much less
dependent on these acidities. Qualitative analyses oi equiiibrium
data obtained in nonaqueous media in which the equilibriunr
concentration of thiolate anion is very small have
suggested that thiol-disulfide interchange is relatively insensitive
to organic structure.l0'lt ln6.Oendent examinations of
KsH and Ks- in aqueous media have not been reported.
Our primary concern in the work reported here is the influence
of ring size on equilibrium constants for interchange
reactions which involve cyclic disulfides. We have approached
this problem by measuring equilibrium constants for reduction
of a standard disulfide (oxidized lipoamide) by a number of
a.c,l-dithiols having different separations between the thiol
groups. Since these thiols have different pKrs, it is important.
in trying to understand the influence of ring size in the cyclic
disulfides on the measured equilibrium constants, to identify
the contributions to these equilibrium constants which reflect
the relative acidities of the thiols.
Separation of a vaiue for KoM (eq l7) measured at a known
pH into values of KsH and Ks- requires only knowledge of the
pK,,s for the two thiols ESH and RSH. The fact that oniy one
experimental equilibrium measurement is required to obtain
values of KsH and Ks- reflects the fact that these equilibrium
constants are not independent: the relative concentrations of
201 5
l4-17). These equilibrium constants should thus. in principle.
depend both on thiol and disulfide structures and on solution
pH. In these equations, and subsequently, an equilibrium
constant referring to a disulfide interchange involving a mixture
of thiol and thiolate species will be denoted by the superscript
"obsd". The influence of the organic groups R and E on
the position of equilibrium in interchange reactions between
disulfides and thiolate ions would not necessarily be expected
to be parallel: reaction involving only thiolate anions (Ks-.eq
l8) should be strongly influenced by the pK"s of RSH and

20l6
'Yz
CI
I
+l
a,
Y
!o
t,
A o
Y
g-2
pH -trzlpKo*, p"ott")
Journal of the American Chentical Society / 102:6 I March 12, 1980
a^
ko
or
-9
0
)<
or
?
9a"
ESSE+zRS-= RSSR+zES-
' tto
,t 6,/
"a %V,
,y't
-b-4-262468
7o
z (ptrf$-proEsH)
Figure 6. schemaric represenration of the response of log. Kob'd (defined
bfeq l7) for selected values of the Parameter pK"*s| - pKusH to
.h"ng.r in the solution pHl these curves were generated from eq 25. For
convJnience in plotting, the zero oi the log 6ou'a axis is taken to be the
mean of the logarith* oi ti,. equilibrium for thiol and thiolate ion, l/z(log
KsH + log Ks=). and the zero of the pH scale is taken to be mean of the
pK, valuei. l/z(pKuRSH * pKrsH). Each curve is tabeled with a value of
pr"nsH - pr"'esH The boldface curve is for pK"RSH - pK"ES.H = 2'0:
note that the observed equilibrium constant X'obsd fel this curve increases
by, l0a as rhe pH is changed from values sufficientll,acidic that both RSH
rna eSU are essentiallyiompletely protonated to values sufficiently basic
that both components are essentially completely ionized'
thiol and thiolate anions are fixed by the known values of pH'
pKrRSH. and pKoESH. To derive KSH and KS- from 71'obsd,
several equations are useful. Expressing the ratio of thiolate
to thiol by eq l9 and 20, and substituting into eq I7, one obtains
(ES-)/(ESH) - loPH-P^u*" = 6
(RS-)i (RSH; = lgnH-RK'Rt" = 6
KSH = !] i :l; 6obsd
(l + 0)'
76s- - *
1' :-iJ; x'obsd
(l * d-';'
Ks- =
{ ^tn
log 6s- = 2(pKrRSH - pKaESH) + log KsH (24)
(l + 6)(l + 6-r)
log 6ou'o - | lz.loe KsH + log trs-1 = log
(l +e)(l *e-r)
= (pKuESH - Figure 7. Plots of (A) log ,(sH and (B) log Ks- vs' 2(pK"RS"
:!K"tt")'
Th"e numbers refer to fable IV. (B) includes the line log 5spKoRSH)
I I * I gpH-r /2(pK"nsH+pKaEsH)-l /21px^esu-pr"RsH)]
r 2log
(2s)
the relationships between 6'obsd, KSH, and KS- summarized
by eq 21-23. Taking the logarithm of both sides of eq 23 and
expanding yields eq24. Multiplying of eq 2l and 22' taking
the square root and the logarithm of the resulting expression,
and expanding generates eq 25. This last equation, although
cumbeisome. describes the functional relations between log
Kohd, pKoRSH, pKusH, and pH in a form that is easily plotted
( Figure 6). The particular functional form of eq25 was chosen
so that the shape of the curves generated from it would depend
= 2.12'
(pK"RsH - pK"sH). which represents the best least-squares line through
ii. iointr I-Slinvolving alkyl thiols) which pass-e.l through (0.0)' The
dashed lines are included for reference: (A) log KsH = 0; (B) log KS- =
2(pK"RsH - pK"EsH).
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
were made at pH 7. Thus, typically, pH - l/2(pK,RSH +
pK,ESH) had values from -3.0 to -0.5, and pK"RSH - p6"ESH
had values between 0 and 2.5. Under these circumstances,
Figure 6 indicates that 6obsd could contain significant conrributions
from both thiol- and thiolate-disulfide interchange
equilibria.
To check the physical reasonableness and consistency of the
values of KsH and Ks- obtained by dissection of 1'trbsd, wc have
examined a number of literature equilibriun'l constants. Figure
7 shows separate plots of log KsH and log KS- vs. 2(pKuRSH
- pK,Es11) derived from the data summarized in Table IV.
The equilibrium constants in the upper plot shows no obvious
correlation with pK,s. but are inlluenced by steric effects:
sterically hindered thiols give low values of Ksl'1. We note,
however, that the data in this figure have been drawn from
several sources, and differences in experimental conditions
between sets of data, and inaccuracies in individual data, may
disguise a weak dependence of log KsH-on ApK"' fl':.lppro"ximate
linearity ol the plot of log KS- vs' 2!Ptr,*t" -
pK"ESH) indicates that Ks- is strongly influenced by the acidities
of the participating conjugate thiols. and that the data
are adequately rationaliied by the scheme of eq 18. In principle,
the slope of a plot of log KsH vs-^2ApK" should.be (/3nr"
-' gr, = I ) and that of a plot of log KsH vs' 2ApKo should be
(B^,,:- 6,,) (see below); it should therefore be possible to dei!iri".
P"";"
- ,619 experimentally from these plots. Figure 7B
includes for reference the least-squares line drawn through the
set of aliphatic thiols. and suggests that 6nu. - (le)
(20)
(21 )
(22)
(23)
fl,r- l '2' We
reiterate that the quality of the data makes this estimate uncertain
bY at least *.20Vo.
With this background, we can interpret equilibrium constants
for reduction of oxidized lipoamide by a series of
a.

Szajewski, Whitesides
/ Thiol-Disulfide Interchange Reactions
Tabfe tV. Separation of Literature Vaiues fe1 5obsd into Ks- and KsH Using Equations 2l and 22
no.
I
2
J
4
5
6
7
8
9
l0
lt
t2
IJ
t4
r5
l6
t7
l8
r9
20
thiol (RSH)
cHCONHCHzCHzSH
NH2CH2CH:SH
CHTCONHCHuCHzSH
NH2CH2CHzSH
NH2CH2CHzSH
glutathione-SH
HSCH2CO2H
HSCH2CO2H
CoHsSH
HOCH2CH2SH'
CHTCHzCH(CH3)SH
(cH3)3csH
dithiothreitol
cysteine
glutathione-SH
N HzCHzCHzSH
NHzCHzC(CHr)zSH
NH2CH(CH3)CH(CrH7)SH
NHZCHZCH(CH3)SH
NH2CH(CH3)C(CHr)25H
disulfide
(ESSE) pH gobsd a KS- O 6'SH a ref
cystine
cystine
glutathione
glutathione
glutathione
cystine
cystine
glutathione
(cHr(cH2)5s)2
(CHr(CHz)sS)z
(cHr(cH2)2s)2
(cH3(cH2)3s)2
lipoamide
BSSBi
BSSB
BSSB
BSSB
BSSB
BSSB
BSSB
7.4
7.4
t.)
7.4
6.5
6.0
6.0
6.0
T
.f
'7.0
6.0
6.0
6.0
6.0
6.0
6.0
6.0
3.1
3.6
0.80
1.7
1.4
3.0
3.3
1.7
0.16
0.28
0.98
0.54
31.
0.98
l.l
2.1
0.33
0.14
0.36
0.09
8.0 x tOl
3.6
1.9 x 102
0.r8
0.15
28.
5.6 X 104
2.7 X t02
(4.4 x t0-s
(1.4 x l0-3
(le.
(4.0
3.0
1.2 x 104
1.3 x 105
2.6 X t04
2.2 X t03
1.1 x 103
2.3 X 103
6.2 x t02
20t7
2.4 b
3.6 b
0.75 b
2.t b
1.4 c
3.0 d
3.3 e
1.7
0. t6)
0.28)
0.e8)
0.54)
31.
0.r2
e
s
s
s
s
h
j
0.14
0.26
0.04
0.02
0.05
0.0r
i
i
i
i
i
i
o Equilibrium constanr5 arc dimensionless. t L. Eldjarn and A. Pih l. J. Am. Chem. Soc., 79, 4589 ( 1957). ' L. Eldjarn and A. Pihl, "/. aior'
Chen.: 2?5,4gg (t957 ). I C. corin and c. Doughty. Arch. Bioihem. B{ophys., 126, 547 (1968). ' t. M. Kolthoff. W. Strick, and R. C. Kapoor.
J. Am. Chem. Soc.,77, 4733 ( 1955). / These cquilibrations were perfo.med in hyd.ocarbon solvents and are included for rcference. For each.
ir was assumed that KsH in water would equal the listed value of,(ot"d. s Rcference 31. ' Reference 4. i RSSB is 4.4'-dithiobis(b€nzenesulfonic
acid). i G. Gorin, G. Doughty, and R. Gideon../. Chem. Soc- B,729 (1961).
poamide by several mono- and dithiols were determined experimentally
using a procedure developed by Cleland:a details
of this procedure are summarized in the Experimental Section.
In the simplest case. reDresented bv eq 26 and exemplified bv
HS-R-SH +
(cH,).coNHr
Kupoobtd
i- s-R-s +
5H
SH
( 26al
(cH:)..coNH.,
.Aqp, Iff;a'j;"*" s
\ ^,,
)--SH
.I
^\11!/
-
-
.-_
pH7
\
\
o
b
tl
(cH,,).co\H (cHr).,coNHr
+ NADH + H+ ('/lat
HS-R-SH + NAD' : S-R-S + NADH + H'
K=
-'77
(lipoox)(NADH) = 0.0858
(lipored)(NAD')
KNeDobd = (s-R-S X NADH)
(HS-R-SHXNAD')
KtipoobdK.,,
for K1;o,rub'd from a particular set of starting and observed
concentrations depends on the choice of equilibrium equation.
Equation 26 assumes that the product of o.xidation of an
cr.co-dithiol HS-R-SH is the corresponding cyclic disulfide.
In principle. this reaction might also generate dimeric or higher
oligomeric cyclic poly(disulfides), or linear polymeric disulfides.
The experimental procedure used here measures directll
only the concentration of NADH (and by inference that of
reduced lipoamide); it does not identify the structures or
concentrations of the disulfides present. We have not attempted
to resolve the ambiguity concerning the structures of the disulfides
produced in these thiol-disulfide interchange equilibria
by their isolation: since all of the plausible types of products
can interconvert, there is no guarantee that any species identified
in concentrated, isolated form would be that present at
equilibrium under the conditions used to measur. K,,*oo'd.
Instead. we have examined the concentration dependence (or
independence) of equilibrium constants calculated from experimentai
data measured at different concentrations oi dithiols.
for three equilibrium expressions: eq 26 (for formation
of a cyclic monomeric disulfide), 29 (ior reaction generating
a cyclic oligimer of n members). and 30 (for [inear polymerization
to a higher molecular weight a,or-dithiol). The second
pq{ il_gg_2c is derived from eq 29b by assuming that
(SRISSR]n- rS) = Kliooobtd =
(S-R-SXliPorea)
(HS-R-SH )(liPoox;
(%b)
HS-R-SH = DTT (see below), reaction of I equiv of d,ordithiol
with oxidized lipoamide generated reduced lipoamide
and the cyclic disulfide formed by intramolecular oxidative
coupling of the a and c.'r thiol groups. This equilibration was
carried out in the presence of NAD+ and lipoamide dehydro-
-qenase (eq 27). The concentration of NADH at equilibrium
was measured, and straightforward calculations based on
know n initial concentrations of a,r,.r-di thiol, oxidized li poamide,
and NAD+ yielded the concentrations required to calculate
K,,*oo'o (eq 26b). Multiplication of K"*olo by Kzt gives the
biochemically relevant quantity Kr,rDob'd (eq 27,28). In eq
27b, (lipou^) and (lipo"d) are respectively the concentrations
ol oxidized and reduced lipoamide. By convention, Kn and
Kr,rDub'd are defined for a particular value of solution pH
(here, pH 7) and are dimensionless (eq 27b and 28b). The
balanced equations to which they refer (eq 27a and 28a) involve
protons: thus K27 and K5lnpobsd ;n'tp1l6itly incorporate
a term in hydrogen ion concentration, and depend on solution
pH. Kripuob'd, K7j, KNn Dobtd, and K655cobtd (see below) are
all based on calculations which utilize the totalconcentrations
of thiol and thiolate species derived from each SH-containing
compound. We take the value of Kzt to be 0.0858.32
The numericai value of the equilibrium constant calculated
| I n(liporco) (that is, in a s!'stem originally
containing only a.c,.r-dithiol and oxidized lipoamide. the
( 28a)
(27b)
(28b)

2018 Journal of rhe American chemical society / 102:6 / March 12, rg80
Table V. Equilibrium Constants for Thiol-Disulfide Interchange Reaction and Derived Constantsa
compd
chain
length thiol PK,
K,,*o* t
l4
HOCH2CHSHCH25H (BAL)
25
HSCH2CHOHCH2SH (DMP)
35
HSCH2CH2CH25H
45
lipoamidc (lipo'd)
56
dithiothrcitol (DTT)
66
dithioerythreitol ( DTE)
76
HS(CH2)4SH
87
(HSCH2CH2)20
97
(HSCH2CHOH)2CH2
l0 8 (HSCH2CONH)2'
n8
(HSCH2CHOHCH2)2CH2
t2 t0 (HSCH2CO2CHz)z (GMA)
t3 monothiolHSCH2CH2OH
(ME)
14 monothiolglutathione
(GSH)
o
8.6 ( I 0.5).
9.0 (10.3)"
9.8 (r0.9/
r0.7 (r0.7)r
9.2 (10.1)"
9.2 (10.1)a
10.0 (10.7)"
e.2 (e.e),
9.I ( r0.6)/
8.0 (9.6/
e.3 (r l.ly
7.7 (8.9).
9.U
8.7 k
5.8
0.51
0.12
I
l5
ll
22
0.68
0.88
0.50
9.2 x l0-l
2.0 X l0-l
1.8 x l0-l
disulfidc
form KxeDoH
cyclic dimer
cyclic monomer
cyclic monomcr
cyclic monomer
cyclic monomcr
cyclic monomcr
cyclic monomcr
cyclic monomer
cyclic monomcr
cyclic monomer
cyclic monomer
polymer
dimcr
dimcr
cyclic monomer 6.4
6 KcsscoM' Kcsscs- t KcsscsH "
4.2 X l0-2
4.4 X l0-2
1.6 x l0-2
8.6 x,t0-2i
1.3
0.95
1.9
0.64
5.8 x t0-2
?.6 X l0-2
2.9 x 102 -0.298 1.0 X 103 5.8 x t02
3.1 x 102 -0.279 3.8 X I0r 6.2x t02
l.l x l0l -0.296 7.8 X 105 2.0 X l0l
5.9 x 102 -0.288i l.l x 107 1.3 x t03
8.8 x t03 -0.323 6.0 X t05 1.8 x t04
6.6 x l0l -0.319 5.2 X t05 1.4 x I04
1.3 x 104 -0.328 9.6 X 106 2.6 X 104
4.4 x 103 -0.3t4 8.0 x t0'1 8.9 x tol
4.0 x 102 -0.283 4.6 X l0r 7.8 x t02
5.2 x 102
4.3 x l0-2 3.0 x 102
7.9 x l0-4 5.4
1.7 x l0-. t.2
1.5 x l0-4 I
-0.286 4.4 X tOr 1.2 x t03
-0.279 8.4 X l0r 6.0 x 102
-0.227 4.0 X 102 3.9
-0.207 7.1 x l0r t.2
-0.205 I I
-0.344 8.6 x 104 /
" All equilibrations werc carricd out in 0.05-0.02 M phosphate buffer at pH 7.0, 30.0 + 0.5 oC, undcr argon using thc lipoamide-lipoamide
delydrogenasc couple. 'i(1pooH and Kp4Dos havc units oi M-l for entries l, 12, 2, 13, and 14; l4; for all of ofthc the
'
other oher thi;k. thiols, they the; arc are dimensionless.
dimensiontcss.
(csscobd, .Kcsscs-, and K6556ss for entries l, 12, 13, and 14 are dimensionless; for all the orher thiols they havc units of M. Rcference
36 dcsc.ibes the calculation of /(qss6s-.and-,(6gs6sH from Kq556oH. d.Eg (V)
oC
vaiues vs. srandard hydrogen ilectrode at pH i.0 and 30.0
(see fef 32). ' These p,(. values arc takcn,from rif tZ. / Octcrmined by the methods described in ref li. c IlM. Gascoigne and G. K. Radda,
&ioc.him. BioPhvs. Acta, l3l,498 (1967). ' Standa.d valuc; see ref 32. i Synthesis of this material is described in ref-41. I This pK" value
is takcn from rcf 13, r Refercncc 15. r O*idiz€d dithiodiketopiperazine was cquilibrated against HS(CHr)dH in CHCl3, and an equilibrium
ofK = 3.3 determined by lH -'-
NMR spectroscopy. This value corrcsponds to kqss6sH =-A.e x IOo M.
aHSRSH + nlipo* ,- f,p]ffirt;,J * rlipo."d (29a) lution, the dcrived equilibrium constanr should be invariant
,#.--ll3
tflioo..at,
with changes in the starting concenrration of dirhiol. Exami-
K".-,,-.b'd = I:Il!!5Lr
"c,c'c - (HSRSH).*;;.)"' (2eb)
ffi[:"*hiTT|*'J:H]:,,1T;::]".,**:,";o#*l
.. fSTf SSn i-l];sl r/n{rin^,cd\ with concentration. ( '(":,.ri.obd) !/" is also invariant. Equation
( K.."ri"uo.d) r
'
/, l9c differs from that for K1,pooM (eq 26b) only in rhe
(HSRSH)(lipoo\)
e xponent
of the rerm (lipo'"d) and ru.ior, ior K1;*ofu rhis
"ion*uni
_ [l I n]t / '(lipo*d\t+ | / " ,.^^,
expone nt is_-2: for formation of a cyclic d imer (eq 26i, n = 2),
(
tzvct
HER-SE!1-1*-|
it is 3/2. Thus, equilibrium expiessions for glneration oi
r i ouru =
R,sH + R-sH + ripoox : R,ssR- + ripo,d
( R,SSR-)( lioo.d)
( R'SH)(R"SH)(lip
,-
- - (E:SSRj')( liPo'd)
[2(HSR" SH)]r(lipoo')
(3oa) fliil:ffT:li1',1"Jf,1'.:ilh:jlX.,j"J_::1$:f|'""$.
60b) - '
perimenrally
difficutr ro disringuish.
K*5;,* u, u tuncrron ot rhe concenrrarion ofsraning d.&rdiihiot
for rhree dithiols spa n n ing rhe ra nge of inrrathiol separations
examined: 2,3-dimercaptopropanol (BAL), DTT, ana
number of disurnde bonds formcd from the formcr must equa, fl:illjjT,1T,Xl"T::1H?#,tl fi:::riil'j1)'i;: t;iT
the number of lipoamide disulfide bonds reduced). Taking the As expected, this figure contlritt iial DTi forms a cyclic
n th root ofeq.29b and conve.ting the numerator by substitution monomer, and not aiincar polymer. Thc data for GMA indito
an exprcssion containing only thc concentration of reduced catc that this material forms a linear polymer. The range of
Iipoamide generatcs the final expression in eq 29c. usable thiol concentrations in this latter case is limited on the
. Equation 30 assumcs that all SH groups present in the so- low end by thc limited reducing ability of C MA and on the
Iution arc equally rcactive in each thiol-disulfide interchange; high end by its low solubility. Tie data for BAL are not com_
that is' it.assumes that the thiol groups of an a,

Szajewski, Whitesides / Thiol-Disulfide Interchange Reactions
:<
or
I
o
-l
-2
-5
otz
Kil:.
ftr LS Ko!..
t
''lcal
| "-. *#
| (- '\
a
a ^^l
'
AE F.-/\^
r
o o.l
t.
I
^t
)-)
)*il.
aa
roe
fxsnsn] (mM)
Figure 8. Plots of log K as a function of the concentrarion of reducing thiol
IHSRSH J calculated on rhe assumption thar oxidation of the dithiols yields
(o) cyclic monomeric disulfides (KripooM,eq 26); (r) cyclic dimeric disulfides
(K"y.ti.obd, eq 29): or (O) polymeric disulf'ides (K*i"oM, eq 30).
K"y"ri"obtd and Kpu"obd have units of M: K1;*obtd is dimeniionless. AII
equilibrations were carried our in 0.05-0.2 M phosphate buffer, pH 7.0
at i0.0 + 0.5 oC under argon. Dara are shown ior (A) dithiothreitol ( DTf.
5, Table V); (B) 2,3-dimercapto-t-propanol (BAL. l. Tabte V); (C) gtycol
dimercaptoacetate (CMA, 12, Table V).
is the equilibrium constant for eq 31, and is obtained by dividing
KNRoobtd by I .5 X l0-4 tr- r (the value of Kx.roobd for
glutathione); Eo for each of the thiols is related to the half-cell
potential for the N4D+/NADH couple (eq 32) by eq 33;
KcsscS- and KcsscSH are calculated from K6556;ubJ and the
thiol pK. values using eq 2l and 22.36
I
x4 ..F
'lD-':'
aa
a
o
oo
o ooo
-f-
I
L|
.*l
HS.R.SH + CSSG #E"Y
pH7
S. + 2GSH (3I)
2e- * NAD+ + H+ E'NAD = 0'320 vr2
NADH
vs. SCE. pH 7
(32)
foRsn - EoNno : #log K;*1apub*d
(JJl
s(e
\z
oi
-9
3
I
143
gz
er 2:
I
si-:
o.g
o3
,r :: 's :lo
r e rl
I
stS
s87
"6 08
o3
'z -tt
678
os 3lo
Choin Lenglh
Figure 9. Plots of log K6556obsd on6 log K6556sH vs. chain length for the
reduction of oxidized glutathione (GSSG) by a series of dithiols at 30.0
+ 0.5 oC in pH 7.0 phosphate buffer under argon. The numbers refer ro
Table V. All dithiols are believed to form cyclic disulfides on oxidation.
with the exceprion of 2,3-dimercaptopropanol (o, r, l), which may form
a cyclic dimer (see the text), and glycol dimercaproacerate (0. O, l2),
which forms a linear polymer. The poinr for the dithioketopiperazine (v.
l5) was obtained in an organic solvent. The units of K6556obd and
KcsscsH are M. The equilibrium constants for these dithiols cannor be
contrasted directly for that with monothiols, since the unirs are different.
For comparison. however. addition of a small quanrity of GSSG to a I M
solution ol 2-mercaptoethanol, a 0.22 M solurion of glycol dimercaptoacetate.
and a 1.4 X l0-'t M solution of DTT would produce rhe same
ratio of (CSH)/(CSSG).
For comparison, Table V includes a value for a conforma-
tionally rigid dithiodiketopiperazine',vhich forms a six-membered
cyclic disulfide
'uble
on oxidation. This compound is nor solin
water. and its equilibrium constant was measured in
chloroform by equilibration of the diketopiperazine disulfide
against butane-1,4-dithiol. The derived consranr KcsscsH
should. however. be comparable to those obrained in aqueous
solutions. since these constants are probably relativelv insensitive
to medium.rl
Figure 9 illustrates the variation in Kcsscob'd and K6556sH
(from Table V) with intrathiol chain length. The former data
(pH 7.0) are useful in the practical problem of choosing a reducing
agent for pH 7 aqueous solution. The plot gives only
upper limits for a,c,.r-dithiols connected by chains of two (BAL)
and eight (GMA) atoms. Since these compounds appeared to
form respectively a cyclic dimer and polymer, it is nor possible
to establish equilibrium constants for intramolecular disulfide
formation. It is, however, possible to esrimate what these
equilibrium constants would have had to have been for the
product of intramolecular coupling to have been predominant
under the reaction conditions. These constanrs are indicated
on the figure as upper limits. The plot of log KcsscSH vs. chain
length is useful in establishing the structural basis of the reducing
ability of the dithiols. These data contain no contribution
from the relative acidities of the thiol groups. The close
qualitative similarity between the plots of log X'obsd and log
KSH vs. chain length suggests that differences in the acidities
of the thiol groups are relatively unimportant in determining
the reducing ability of these dithiols.
Several features of the data summarized in Figure 9 warrant
discussion. First. the equilibrium constant K6556SH = 3.9 for
glycol dimercaptoacetate (GMA) is approximately that for
monothiols (for example, KcsscSH = I for -elutathione. and
KcsscsH = 1.2 for mercaptoethanol). The fact that a solution
oi GMA is not significantly more reducing than a solution
containing an equal concentration of monothiol SH groups is
t2l
'29
t
t
201 9

2020 Journal of the American Chenticar society / 102.6 / March 12, Igg0
t, C)
o
()
*
8.O
7.O
6.O
5,O
4.O
3.O
2.O
l.o
Ctt
o 8.O
7.O
= l6 M-r;(ll) = l5 M-r.Theseconstanrsareca. l0ahigher
than those for other thiols which form intramolecular dimers
(GSH, ME) or polymer (GMA). Since all of the evidence from
the work suggests that this constant is not very sensitive to
structural variations in the starting thiol, we conclude either
that dithiols having seven or eight bonds separating the thiol
groups show anomalously high reactivity in polymer formation
or that they form cyclic disulfides. The latter alternative seems
the more probable. It is more difficult to distinguish intramolecular
disulfide formation from formation of a ivclic dimer
for reasons discussed above. Third, the observation that a solution
of BAL is much more strongly reducing than a solution
of a monothiol containing an equal concentration of thiol
groups supports the hypothesis that BAL forms a cyclic di_
meric disulflde: an initially formed. half-oxidized dimer from
BAL enjoys the same advantage in closing to an eight-membered
ring as does an a,or-dithiol of similar structure, but the
initial formation of the half-oxidized dimer requires a bimolecular
step.
OH
t^..
"'-{::v'"
( _Jn
Y RSsR
| --2RSH
\ -sH
6.O
RssR
.--
-z,.r'n
HO s-s -\
\ /-
- #
\r-r/
oH
/
Discussion
The rare of reducrion of oxidized grutathione, GSSG, by
thiol-disulfide interchange in aqueous solution follows a
Brpnsted relation. The analytical method used to follow these
rates was less general than that employed in our previous study
of the rates of reduction of EIlman'r i.og.nt, and fe*er thiols
were examined as reducing agents. Nonetheless, the close
parallel between the resurts of these two studies. and the sim_
ilarity of the Bnu. values derived from them suggesrs that a
correlation between the proton basicity of the tn]itate nucleophile
and the rate of its attack on a sterically unemcumbered
sulfur-sulfur bond is characteristic of thioi-disulfide interchange.
A picture of thior-disuriide interchange as a
mechanistically uncomplicated reacrion is in accird with
theoretical results, which suggest a Sr,.r2 transition state in_
volving little d-orbital participation by the central sulfur,rT and
with X-ray srudies, which indicate that the preferred direcrion
for-approach of nucreophircs to a disurfide bond is arong the
sulfur*sulfur axis.38
two, B,r/nsted coefficients
,_ Il:
determined experimentally
In thts work (pnu". - 0.5: 13.^ * 0E
ft,nuc5- + R.SSRtr l pnu"5SR. +
-SRre
(3a)
! - 1.0) difiei in their ac_
curacy. The first is derived fromi rarge number of data, and
seems reliable. The second is based on a smaller set, and depends
heavily on exampres invorving Eilman's reagent: the
generality of this coefficient is not yer defined. we-have nor
explicitly determined separare valuei for B"and B1_*. we have,
however, estimated varues for these parameters, using rate
constants from this work and frorn literature sources for reactiors
involving unsymmetrical disulfides having both Rnr"SH
and R"SH aliphatic. Assuming that these rates are described
by an equation of the form of eq 35, imposing the conditions
that Bnu. = *0.5 and B" = - 5,O
4.O
3.O
2.0
l.o
t.o ?.o 3.O 4.O 5.O 6.0 7.0 g.o
log k (expr)
Figure 10. (A) PIor of rare constants for thior-disurfide interchange (k)
calculated using eq 36 against corresponding experimental rare consranrs:
units for rate constants are M-r min-1. poinis r-g (o t ur. t"t.n
work:
from rhis
9-13 (v) from ref 22: l4-27 and 4g_50 (r) from ref l2: 2g_35 (O)
from Table lv, footnote j of G. Gorin, c. Doughty. unJ n.'cioeon. -/.
9!"^.
1.0 -
0,*,and sol-ving for the un-
uld
lno*lj
0,, by least-squares anaTysis *e esririar. ti,"r
= -0.72, Bj,
0, = -0.27, and C = 7 .0. The ability of the l-esultin!
equation (eq 36, k = M-r min-r) to fit the available data ii
s,u.mmarized by Figure l0A as a plot of log k(exptl) vs. log
k(calcd).
Soc. B, 729 (t96j):36-4: (v) from ref r3:"5 r_S j
i"
jirorn w"U"r.
Hartter, and Flohe (ref 2r). points 42-s2refer to un.y,n,n.,ricar disur_
fides; all others are symmetricar. The least-squares correra[ion line shown
l:r It =.9'?8' slope = 0.98.^and inrercept = 0.l r. (B) simirar prot for
38. Detailed
eq
identification of the points ii given in ,uppr.r.niuri material
in the microfilm edition (see paragraph a"t end of paper).
compatible with our contention that the thiols of GMA act
independently and that cMA forms porymers on oxidation.
If oxidation of GMA generated a cycric disurfide. we wourd
expect it to be a stronger reducing agent than a monothiol.
second, a,c.r-dithiols capabre of foriring five-, six-. seuen-. and
eight-membered rings are stronger redicing agenrs than monothiols.
The stability of many cyclic five- a-ndiix-membered
disulfides is well known. nttnougi, we have not explicitry established
the form of.tlrg equilibrium reactions inuotuing sevena
nd eight-mem bered disu rfi de-containing ri ngs, .^ur] nu tion
of the magnitudes,of equilibrium constants calculated using
the various equilibrium expressions (eq 26, 29, and30) suggesrs
that intramolecular disurhde formation is occurring. in p"rticular,
equilibrium constants calculated for compo"und g, 9,
10, and lI (Table v) assuming that oxidation yierds a porvmeric
disulfide are Kpry-ohd (8) = 26 M-r. 19) ='2g trtj,, (lO)

S:ajewski, Whitesides
/ Thiol-Disulfide Interchange Reactions
log k + C + gnu"pK"nut
* p.pK"c * dp*pK,ls (35)
logk = 7.0+ 0.5OpK,,nu'-0.21pK, -0.73pK.,rs (36)
log k: 5.5 * 0.63pK.nuc - 0.30pK,c - 0.63pK,rB (37)
logk=6.3+0.59pK,nu" - 0.40pK"'- 0.59pK"rs (38)
log /gou'o = log k - (l + l0PKrnuc-PH) (3e)
lf the attacking thiolate anion and the leaving thiolate anion
are both derived from aromatic thiols, the only change in eq
36 is that the constant C has the value 7.9.
Figure l0A establishes that eq 36 provides a good model for
a large number of rates. In fact, the quality of the correlation
is probably higher than indicated by the coefficient of determination
(rl = 0.98), because most of the points rvhich fall far
off the tine (points 13. 26, 40, 46, and 50) involve either
thioglycolic acid (or its anion) or methyl thioglycolate (RO-
COCHzSH, R = H, CH3). Hupe et al. have summarized evidence
that these compounds behave anomalously in other
Brpnsted correlations. I l
Although eq 36 fits the experimental data well, there remains
some ambiguity concerning the mechanistic significance
oi the value of dre used in it. This equation implies that Bnu. -
,J,*:0.50 + 0.73 - 1.2, and both the inequality in the magnitudes
of these Brlnsted coefficients and the fact that their
difference is greater than 1.0 are reasons to consider the possibility
that they might reflect some element of experimental
or analytical artifact. In principle, it should be possible to estimate
the parameter /3nr. - d', independently from the slopes
of Figure 7,re but. for reasons discussed previously, experimental
estimates based on these slopes are too uncertain to be
of great value. Further, it is possible to find other combinations
of Br/nsted i3's rvhich give good correlations. For example. if
*. ro'lu. for the set of i'r ruii.h best fit the data summarized
in Figure l0 under the imposed conditions that d. = -0.30 and
dnu. = -d'*, we obtain the parameters summariz-ed in eq 37
(rl = 0.96). We have also explored solutions to eq 35 in which
,dnu.
= -ptg and in which d. is allowed to assume values other
than 0.3. The best solutiona0 with these constraints is given by
eq 38 (r2 = 0.96): the agreement between experimental rates
and those calculated using this equation is also summarized
in Figure 10.
The observation that all three of these correlations give
similar coefficients of determination indicates that the
Brpnsted coefficients are not sharply defined by the available
data. Further, the population of thiols and disulfides represented
by the experimental rates is sufficiently heterogeneous
that great precision is not expected. For a more limited set of
thiols and disulfides, it would probably be possible to develop
a Brpnsted equation which would correlate experimental rates
more closely than eq 36-38, but for semiquantitative estimation
of rate constants for thiol-disulfide interchange given
known values for the pK.s of the participating thiols, or for
kinetic measurements of thiol pKos using rate constants for
thiol-disulfide interchange, any one of these equations should
prove equally useful (and equally accurate).1r We routinely
use eq 36 and 38. and find little difference between the two. We
emphasize, however, that these equations should be considered
primarily as kinetic models for thiol-disulfide interchange,
and that detailed mechanistic interpretation of the 0 coefficients
should wait on simultaneous, direct, experimental determination
of these coefficients using a carefully limited set
of thiols and disulfides.
Although quantitative discussion of the charge distribution
in the transition state for thiol-disulfide interchange based on
the coefficients in eq 36-38 is not justified, qualitative discussion
certainly is. Hydrogen and sulfur have similar electronegatives
(Xn = 2.20,XS = 2.44),12 and there is no evidence
of curvature in the Br/nsted plots suggesting an intermediate
2021
or chanree in rate-limiting step. Thus the transition state appears
to be svmmetrical. rvith significant effective negative
charge on all three sulfurs. but concentrated on the terminal
positions.rl Hupe et al. have reached similar conclusions.ll
An important objective of this work. unrelated to questions
of transition-state structure, was that of trying to understand
the relationships between the structures of the thiols and their
reducing potentials in thiol-disulfide interchange reactions:
especially, what structural features characterize strongiy reducing
thiols? Four useful conclusions emerge from this work.
First. as anticipated, many a,ro-dithiols capable of forming
cyclic disuliides are more strongly reducing than the corresponding
monothiols. This effect is attributable in major part
HS.R-SH + ESSE$
k-1
"S.N.SSE
+ HSE
-
kz
2RSH+ESSE$NSH+RSSE
k'-t
t-*-S + 2HSE (40)
+ HSE 5 nssR + 2HSE (41 )
to a much higher forward rate for the second step of eq 40 than
for that oi eq 4l . reflecting the high effective concentration of
thiol groups in the intramolecular thiol-disulfide interchange
step.r5 We have not been able to compare the rate constants
kl and t'1 directly, so that we cannot presently judge rvhether
other structural features of the intermediate mi.red disulfide
oi eq .l I might contribute to its rapid conversion to products.
Second. there is a clear correlation between the reducing potential
of an a.c,:-dithiol and the size of the cyclic disulfide
formed on its oxidation. The maximum equilibrium advantage
is observed ior dithiols capable of forming six-membered rings.
although seven-membered and five-membered rings can also
have good stability. All-carbon systems seem to favor sixmembered
rings in a wide variety of cases.a6 We were surprised
to iind that the same apparently holds true for cyclic disulfides,
since a CSSC dihedral angle of 90" is tavored both experimentally'*6
and theoretically,aT and elemental sulfur itself
forms eight-membered rings. The relative stabilities of six- and
seven-membered cyclic disulfides seems to represent a delicate
balance between CSSC angle strain and entropy of ring closure.47
Third. a large contribution to thiol-disulfide interchange
equilibrium constants can, in principle, arise from the
relative pK,s of the reducing thiol and the thiol derived from
the disulfide. This contribution is proportional to the difference
between the thiol pK"S, and is largest when both thiols are
present entirely as thiolate anions (i.e., when the equiiibrium
considered is a thiolate-disulfide interchange). For the systems
considered here-aqueous solution. pH 7, thiols having pK"
values between 8 and l0-contributions 1s (obsd from this
source are less important than those due to intramolecular
disuliide bond formation. Fourth. the rare of reduction of a
disulfide by a thiol does not necessarily correlate with the
equilibrium constant for the reduction. The former is determined
by the relation of thiol pK" to solution pH, with the most
rapidly reacting thiols normally being those having pK, values
close to the solution pH;12 the latter is determined by factors
unrelated to thiol pK", except in solutions sufficiently basic that
the interconverting thiols are significantly ionized. Dithiols are
ordinarily more rapidly reducing than monothiols of the same
pK,, especially in dilute solution: although the initial conversion
of starting disulfide to an intermediate mixed disulfide
proceeds equally rapidly with either, the conversion of the
mixed disulfide to products is more rapid rvith the dithiol.
Within the group of dithiols, the selection of rate and equilibrium
constant can usually be made on the basis of the thiol
k'-2

2022
Journal of the American Chemical sociery / 102:6
/ March t2. rgg0
il
t3579ttt3
/,) El \ ,iit
g=:RE EgE
Compound
Figure ll. Concenrrarions of thiors required to reduce by harf the concentrarion
of the indicated disurfide group in sorurions
"i,gi#iL" containing
oxidized Iipoamide ( I 0-3 M, r ) ox-idized glutathione tj O:i pf . O ). and
oxidized lipoamide ( l0-6 M, o). Compound numbers refer ro Table V.
The schemaric srrucrures at the top of the figure represenr the type of disulfide
believed to be formed from ihe thior re-ducing'ug.ni (..u.ric dimeric,
cycl ic monomcric, a nd i n tcrmolecu la r. respect iveiy).*
pK,1 and of the ring size that would be formed on oxidation
of the dithiol to a disulfide. Thus, DTT (p,

Szajewski, Whitesides
/ Thiol-Disulfide Interchange Reactions
perature under water aspirator vacuum. Argon-degassed methanol
(30 mL) and 2 mL of a I N solution of HCI in diethvl ether were
added, the mixture was refluxed under argon for 5 h and cooled. and
erher, methyl acetate, and methanol were removed by disrillation at
atmospheric pressure. The residual oil was distilled bulb to bulb at
130-150 "C (0.05-0.1 Torr) togive 1.86 g (10.2 mmol) oi 1,6-dimercapto-2,5-hexanediol
as a clear, foul:smelling liquid: IR (neat)
3450,2920, 2860, 1050 cm-r; NMR (CCl4) 6 4.1-3.9 (m. 2),3.5-3.3
(m, 2), 2.8-2.4 (m, 4), 2.4-1.8 (m, 4), 1.6 (t, 2. J = 9 Hz). The epimeric
composition of this material was not determined. The pK"s of
the thiol groups in this material were measured as previously described:l2PKar
= 9.3,pK^2= ll.l
Anal. Calcd for C6HlcOzSz: C,39.56; H,7.75. Found: C,39.75:
H. 7.63.
1,5-Dimercapto-2,4-pentanediol. Application oi the epoxidation,
thioacetylation, and transesterification sequence as described above
to 3.4 g (50 mmol) of 1,4-pentadiene gave 3.16 g (19 mmol) of 1,5dimercapto-2,4-pentanediol
as a clear, odiferous oil: IR (neat)
3400-3200,2920,2550. t420, 1050 cm-{; NMR (CCla) d 3.8-i.2
(m.2), 2.8-2.2 (m,6),2.2-1.8 (m.2), 1.4 (br t,2,J = 9 Hz); pKur =
9.1, pKu, = 10.6.
Anal. Calcd for C5H12O2S2: C,35.72: H,7.19. Found: C,35.39;
H. 6.91.
Kinetics of Reduction of Oxidized Glutathione (GSSG) by Thiols.
one representative kinetic run using the coupled enzymatic indicator
reaction will be described in detlil as will the corresponding control
experiments. other runs were performed in an analogous rnanner. To
t 000 pL of 0.2 M phosphate buffer, pH 7.0, containing 0.t%o egg albumin,
under argon ar 30.0 * 0.5 oC in cuvette I was added Ze00 pL
of a 7.6 mM solution (as determined by Ellman's assayae) of dithiothreitol
prepared by dissolving I I 7 mg of that thiol in t 00 mL of
water. To this solution was added 50pL of a freshly steam distilled
solution of methylglyoxal (47 mM) in water. The concentration of the
stock solution of methylglyoxal was determined by enzymaric conversion
to s-lactoyl glurathione using an excess of rey'uced glutathione
and glyoxalase-1.s0 A blank solution. in cuvette 2, was prepared similarly.
A slow blank reaction berween methylglyoxal and added thiot
was noted under these conditions. To cuvette I was added 20 gL of
a glyoxalase-l solution exhibiting 0.37 UlltL activity. The activity
of stock glyoxalase- [ was determined in a separate experiment utilizing
reduced glutathione and merhylglyoxal following a literature procedure.So
Comparison of the blank reacrions in cuvettes I and 2 over a
5-min period showed no difference. thus establishing thar, under rhese
conditions, glyoxalase-l did not mediate the redox coupling of the
added thiol with methylglyoxai. To borh cuvettes were simultaneously
added l0-pL aliquots of a 99 mM stock solution of GSSG prepared
by dissolving 68.3 mg of GSSG in 1000 1tL of 0.2 M phosphate buffer.
pH 7.0. The end poinr of the kinetic run. after correcrion for the slow
blank reaction, indicated a concenrration of S-lactoyt glutathione of
0.69 mM in the assay. This value corresponds to a concentration of
106 mM GSSG in the stock solution prepared as above. The concentration
could be further checked by oxidation of NADPH by GSSG
utilizing the enzyme glutathione reductase.t0 The absorbance in both
cuvettes was followed simultaneously by appropriate repositioning
o[ the cuvette holder (at 240 nm. the tr-u* for GS-lacla) until the slopes
of both curves were again parallel. As a further control, the above
assay was repeated, the only difference being in the use of 100 pL of
the glyoxalase-l solution. The absorbance curves produced were essentially
identical. Figure l2 illustrates this experiment. The quantities
added correspond to the following initial assay conditions: 66 mM
phosphate. 5.07 mM dithiothreitol. 0.'11 mM methylglyoxal, 2.4
U lmL glyoxalase-1, 0.35 mM GSSG. The final pH of the assay so-
o 2 4 6I lo tor,,'." 3o
(,r,in)
40
Figure 12. Plot of A2a6 vs. time in 0.066 M phosphate buffer, pH 7.0, at
30.0
lution was 7.02. The raw data were refined by subtraction of the blank
from the reaction curve, determination of the CS-lac concentration
using ee240n- = 3.37 mM-l cm-l,la and substitution into the integrated
form of the appropriare rate equation (eq I 3 ). These data are
illustrated in Figure 2. Alternatively, subtraction of the blank from
the reaction curve, extrapolation ro time 0 (past the short initial rog
phase), determination of the initial slope, and division by e6 gave an
approximation of the initial velocity, d(GS-lac)/dr, of rhe reaction
in units of mM min-r. Division of this velocity by the initial GSSG
and RSH concentrations gives a value of k,obsa indistinguishable from
that obtained using eq I 3.
Determination of Relative Reducing Ability of Mono- and Dithiols
toward NAD+ Utilizing a Coupled Enzymatic Assay. One representative
equilibration using the coupled enzymatic indicator reaction
oC under argon with 5.07 mM dithiothreitol as reducing agent and
0.77 mM methylglyoxal as enzyrne cosubstrate. Curve I is the reacrion
mixture;curve 2 is a blank. The arrows indicate (a)addition of glyoxalase-l
Q.a U lnL) to cuvette l; (b) simultaneous addition of oxidized glutathione
(GSSG, 0.32 mM) to cuvettes I and 2: (c) attainment of steady-stare
concentrations ol reduced glutathione in cuvette l. Use of larger amounts
of glyoxalase-l (12 U/mL) gave curve 3. The rangenr used to calculate
d(GS-lac)/dt is indicated by the broken line (. -. -).
with DTT as reducing thiol will be described as will the corresponding
control experiments. Other runs were performed in an analogous
manner. To 2900 pLof 0.2 M phosphate buffer. pH 7.0. containing
O.lVo egg albumin. at 30.0 + 0.5 oC r.o
o.8
o.6
o.4
o.2
o.o
under argon, was added l0 pL
of a 48 mlvl NAD+ stock solution prepared by dissolvin g 32.4 mg of
NAD+ in i000 pL of 0.2 M phosphate buffer, pH 7.0. To the resulting
solution were added l0 pL oi9.0 mM lipoamide solution (prepared
by dissolving 3.68 mg of oxidized lipoamide in 2000 pL of degassed
methanol) and 50 pL of a 105 mM dirhiothreitol stock solution in 0.2
M phosphate but'fer. pH 7.0. The initial concenrrarion of the dithiothreitol
stock solution was checked by Ellman's merhod,l8 and
the initial concentration of NAD+ could be checked by total conversion
of NADH using a large excess of thiol. The absorbance ar 340
nm was noted and 30 pL of solution containing approximately I U lpL
of lipoamide dehydrogenase was added. The absorbance ar 340 nm
was followed until it became constanr. Controls indicated that no
formation of NADH occurred when lipoamide. lipoamide dehydrogenase.
or organic thiol was absent. From the absorbance ar 340 nm,
the concentration of NADH was obtained. The concenrration of
NAD+ is given by (NAD+; = (NAD+)o - (NADH), where
(NAD+)o is the concentration of NAD+ present before adding the
lipoamide dehydrogenase. The ratio of oxidized to reduced lipoamide
given by inse rting values ior (NAD+) and (NADH) into eq
irr:n""
(lipoo*)
_
(NAD+)o - (NADH)
Kzt
- = ^YKz'r
(lipo,d) (N=-=-
Q2a)
(lips'.4) =
[l + 7Kn]-r(lipo)s
(42b)
(lipoox) =
7i(27(lipo'ed)
G2c)
This equation yields values for (lipoo^) and (lipo'"d), since their sum
is (lipoo*)e, the known concentration of oxidized lipoamide before
addition of lipoamide dehydrogenase. The sum oi (NADH) and (lipot"d)
equals (DTTox), the concentration of oxidized DTT present at
equilibrium. Since the original concenrration of DTT betore addition
of lipoamide dehydrogenase is known. (DTT)0, the concentration of
(DTT) at equilibrium, is easily calculated. Combination of these
concentrations yields eq 43 and 44 which directly relate K1;*oBd rnd
KNeDHobd to known quantities.
oxa-
I (NADH)( | t :yKzt) * (lipo)o
Ktipo
7K27 [(DTT)6
- (NADH)l(l * TKzt) - (lipo)o
KNeDHobtd' DTT = (43 )
KzrKri*obtd
(44)
In the particular experiment used here for illustration, the initial
concentrations of materials were 0.2 M phosphate. pH 7.0: 0.166 mM
2023

2024
Journal of the Anterican Chenrical Sociery'
/ t02;6 / March t2. tgg0
NA D+: 0.030 mM lipoamide; | .6g mM dithiothreitol; l0
poamide
U/mL li-
dehydrogenase. The concentrarion, of ;p.;;", presenr
equilibrium
at
were 0.0146 mM NAD+;0.153 mM frieOff ; 1.49
DTT'd:
mM
0.183 mM DTTo*; 0.OZg71nt,t tipo."o. -3 X l0--3 mM lipoox.
In other runs. higher concentrations of oigunic tr,iotr-*ere necessary
ro achieve comparabre reductions of NRb+. ln tt," reast favorabre
case. 540 mM 2-mercaptoethanor was required. For severar
proved
runs it
more convenient to start with known mixtures oioxidized
reduced
and
thiol. Thus, a stock sorution prepared by dissorvin g
(-0.132
23.7 mg
mmol) of a mixture of oxid'ized and ,.ou..J dimercapto_
acetvlhvdrazide ( r0. Tabre v) in 2.0 mL of 0.2 M
pH ;;;;phate buffer,
7.0' showed a dithiorconcenrrarion of 44.5 n.,M *hJn assayed by
Ellman's method.ae The composition of the mixed stock sorution
then
is
44.5 mM in dimercaptoicetyrhydrazicilercd
mM in dimercaptoacetylhydrazideox.
The remainder of the
"nazl.:
equilibration *as
carried out as described above. Initial concentrations of materials were
0.2 M phosphate, pH 7.0; 0.162 mM NAD+; l+.g mia dimercaptoacetylhydrazide'd;
6.9g mM dimercaptoacetylhydrazideor; 0.00367
mM lipoamideo*; I O Lt lmL tipoamide d.hyd;;;;;r". ir... concen_
l.1tl?lr
of species.pr..r:1t at equitibriu, *..."0.139 mM NAD+;
0.0223 mM NADH: 14.7 mM dimercaptoacetylhydrazider"d; 7.01
mM dimercaptoacetylhydrazideox; 0.001 2g 111M li;;;iA-."-, O.OOZ:q
mM liPoaml6.rcd.
Equilibration of l.,4-Dimercaptobutane and Dithiodiketopiperazine.
Easily monitored
.physicar
properties of r,+-oimercap,olur"n"
l'2-dithiane are^their 'H NM-R spectra which are. for r,4-dimer- "no
captobutane (CD^Ct:),6 2.6_2.4 im, q, CCH25), f .S_r.6 (m,4,
9CHrC), 1.3 (t, 2. J ^= 8_Hz. -SH), and for t.2-dithiane (CDCl3),
q 3.0-2 8 (m, 4, CCH2S), z.A:s (m, 4, CCH'6; !i Oxidized
d.ithiodiketopiperazine shows (CDCt3i d 4.1 _t.t
iur;, q, 3.1_2.6
(br m, 2), 2.s-2-0 (br m, 6). This ratter NMR spectrum is rittre
changed on reduction to the disurfide. A mixture oi ql.s mg (0. rg5
mmol) of oxidized. dithiodikeropiperazine and 29.0 mg (0.23g mmor)
of-I.4-dimercaptobutane in r.0 mL of cDCr3 under ,;g';". at 30.0 *
0.5 oc, showed initiaily a I H N M R spectrum which w-as just the su_
perimposition of the specrra of the consriruenrs. The,p..*u, of this
mixture was monirored.over a period of 7 days ouring *trich signars,
6 3-0-2.8. characreristic of 1,2-dithiane appeared while signars. d
I .8- I .6. characteristic of. r ,4.-dimercaptobutane disappeared in equar
amounts as determined by integration. After 5 days, the spectrum
became static. The integrated ralio of signal intensiiv at 6 r .g- r .6 to
that at d 3.0-2.8 is equivatenr to (HS(Cit2)oSH)/({-H2)iS). i;;
rario of oxidized ro reduced diketopiperazine ma.v be cariurated bv
the law of mass barance since the ln'itiar quantities
"i a;;-it_ii
mercaproburane and dith.iodiketopiperazine are known. Multiplication
of these ratios gives a value of 3.3 as the equilibrium constant for reduction
of 1,2-dirhiane by dithiodiketopiperazine; this value corresponds
to KNeooM = 7.1 X l0-l and KcsscsH = 4.6 X 105 mM. The
definirions and interconversions of ttrese constanrs in Table
V and in the text.
"pp""i
Experimentalchecks of Carcurated Data in Figure r r. Four equiribrations
were carried out to verify representative calculations included
in Figure I l. In each instance, a quanrity of thior carcurared to be
sufficient to reduce 50vo of GSSG io GSH (or lipoo' ioiipo-ay *ui
added to a solution containing GSSC (or lipoox) and the'final concentrations
of thiols and disulfides were measured. These experiments
we re semiquantirative: the difficulties in measuring small quantities
of air-sensitive thiols. and the low solubility of oxidlzeJ iipJamiae in
water. precluded high precision. They nonetheless served io establish
that the data in Figure r r were not grossry in.error. Representative
experimenral details follow, and reiults are summarized in Table
vt.
The absorbance of a solution of 0.003 g4 g of DTT in 50.0 mL of
q.0i M phosphate at pH 7-0. 30 + 0.5 oc, Table VI. Initial and Equilibrium Concentrarions (mM) in Thiot_
Disulfi de lnterchange Reactions
expt initial
0.5 l3 0.5r4
0.000 0.004
0.994 0.986
0.497 0.493
0.497 0.231
7.22 6.92
0.507 0.809
0.254 0.405
0.540 0.538
0.031 0.028
0.500 0.s03
0.500 0.503
0.538 0.497
50r
500.
0.502 0.545
0.502 0.545
" Conducted in aqueous buffer sorution.
wis monitored ar 290 nm,
the tr,n", for 1,2-dithianes,sa before and after the addition of 0.030g
g.of oxidized glutathione. After equilibration, 0.0304 g of oxidized
glutathione was added and the absoibance again measur.? to establish
a blank correction for thar quanrity of glutathione. Initial conccntrarions
used in this experim.nt *eri o.+gz mtr4 Drr unJ i.007 mM
cssc. The absorbance change at 290 nm indicatea tn.
olilr::9 DTT present at equiribrium. From this varue concenrrations
"o,ount-6i
of GSH' GSSG. and DTT at equiribrium courd be carcurated. The
concentrarions achieved at equiribrium are listed in Table VI.
Equilibrations against ripoamide were performed by.Jai"g known
quanritities of oxidized lipoamide to solurions of BAL. DTi:or ME
in I : I MeoH- H20 buffer and measuring the absorbance at 330 nm
6 conducted in r:r
methanol-aqueous buffer solution.
before the addition of lipoamide and after equilibrium had been obtained.
Extinction coefficients €2es =290 M-r cm-r for 1.2-dithianes
(DTTo*; and e33e =147 M-l cm-l for 1,2-ditholanes (oxidized lipoamide)
were used in the work.3a
Acknowledgment. our colleagues John Deutch and James
Barber provided us with most usefur discussions of the separation
op 6'obsd into KsH and Ks-, and of the compatibilitv of
the kinetic and thermodynamic equations. we also thank
william Rastetter and Robert wiiliams for the gift of the
dithiodiketopiperazine used in these studies. anI Edward
Solomon and AI H.pp for determination of Raman specrra.
ze'ev Shaked provided dara concerning rares of thiol-disulfide
interchange reactions involving proteins used to test some of
the Brfnsted equations summarized here. we thank especially
Professor w. w. cleland for detailed readings of several versions
of this paper and for exceptionaily useful suggestions and
criticisms. Professors w. Jencks and D. Hupe alsoiontributed
substantially in correcting errors in these early versions.
supplementary Material Available: Identification and sources of
the data in Figure l0 (4 pages). Ordering informarion is given on any
current masthead page.
References and Notes
( 1) Parts of this research were supported by NrH (GM 26543, 24o2s, and
091 12CT).
cA
(2) NIH Postdoctorat Feltow, 1976-1978 (Feilowship A j05337).
(3) M. Friedman, "The chemistry and Biochemistry of the Surfhydryr Group",
.1st
ed.,, Pergamon press, Elmsford, N.y., rgzSi p. C. .tocetyn,
:igiochem_
istry of the SH Group", Academic press, New york, 1972: yu. M. Torchinskii,
"surfhydryl and Disulflde Groups of proteins", plenum piess, New
York' 1974; A. L. Flaharty in "The chemistry of the Thior cr-up';, s. patai,
Ed., Wiley, New york, 1974, p 589.
(4) W. W. Ctetand. Biochemistry,3, 480 (1964).
(ll y Konigsberg, Methods Enzyrnot.,25, 185 (19721.
(6) W. S. Ailison, Acc. Chem. Bes., 9, ZSg (rSZb).
(7)
E. S. G. Barron, Adv. Enzymot., ,fi,2O1(rgSr);
A. K. Ahmed, S. W.
Sciraffer, and D. B. Weflaufer, J. Biol. Ctrcm, ZSO, gqZt (1975); t. G. D"nce,
R. C. Conrad, and J. E. Cline, J. Chem. Soc., Chem. iommun., 13
( 1s74).
(8) Hyeogen peroxide_is generated duing rnost oxidations of thiors by diorygen:
P. P. Trotto, L. M. pinkus_ and A- MeiJrer, J. Biot. Clpm., Zcg, tgts
M.
t$iql:
Costa, L. Pecci. B. pensa, and C. Cannella, Biochem. biopnys. Resi.
Commun., 78, 596 (1977\.
(9) A. Pollak, R. L. Ba,ghn,.and G. M. Whiresides, J. Am. CEm. fu.,99, 2366
ll9l1l,-1.L.Baughn, 0. Aroarstetnsson, and G. M. Whilesioes, iora, rOo,
30a (1978); Y.-S. Shih and G. M. Whilesides,,t. Org. Chem.,42,4165
(19771.
(10) E. Bernt and H. U._Bergmeyer in "Methods of Enzymatic Analysis", Vor.
4,Znd ed., H. U. Bergmeyer, Ed., Academic press, New yori

' l:-
L
S:ajewski, Whitesides
/ Thiol-Disulfide Interchange Reactions
E. M. Kosower in "Free Radicals in Biology", Vol. ll' W. A. Pryor' Ed.' Academic
Press, New York, 1976, Chapter ll; l. M. Arias and W- B. Jakoby'
"Glutathione: Metabolism and Function", Raven Press, New York,
1976.
(12) G. M. Whitesides, J. Lilburn, and R- P. Szalewski , J. Org- Chem., 42, 332
(1e77).
(13) J. tvt. Witson, R. J. Bayer, and D. J. Hupe, J. Am- Chem. Soc-, 99, 7922
(1977): C. E. Grimshaw, R. L- Whistler, and W. W. Cleland, ibid','1O1,1521
irgz9); M. Shipton and K. Brocklehurst, Biochem' J-, 171,389 (1978): K.
Brocklehr.nst ano C. Uttle, rbrd., 128, 471(1972). The vah.p of 0.,c - 0'45
has been reported for the reaction of amines with disulfides: H. Al-Rawi,
K. A. Stacy, R. H. Weatherhead, and A. William, J- Chem. Soc', Perkin
Trans.2,663 (1978).
(14) The substrate for glyoxalase I is the hemithioacetal formed between gl|Jtathione-SH
and an-a-keto aldehyde. See E. E- Cliffe and S. C' Waley'
Biochem. J..79,475 (1961); M. V. Kester and S. J. Norton, Biochim' Biophys.
Acta, 3g'1.,212 (1975): L.-P. B. Han' L- M. Davison, and D' L' Vander
|lagt, ioia-,445, 486 (1976); D. L- Vander Jagt, E Daub..J' A' Krohn' and
f-.-F. A. Han, Biochemistry, 14, 3669 (1975). For a discussion of the
magnih.des of equilibrium constants between GSH and aldehydes, see M.
S. (anchuger and L D- Byers, J. Am. Chem. Soc., 101, 3005 (1979)'
(15) O, M. E. Reuben and T. C. Bruice, J. Am. Chem- Soc', 98, 114.(1976)'
Robenstein [D. L Rob€nstein , J. Am. Chem. fuc.,95'2797 (1973)] reports
microscopiC pK.s of 8.93 (amino group protonated) and 9'08 (amino group
unprotonated) blsed on NMR chemical shifts. and Jung [G. Jung, Eur. J.
Biochem., 24,438 (1972)] reports pKr= 9.2. M. S. Kanchuger and L. D.
Byers, J. Am. Chem. Soc., 101, 3005 (1979), Indicated pK" = 9.1 by alkylation.
The origin of the differences between these values is not entirely
clear. In any event, the estimate of Bruice (pK' = 8.7) is compatible with
our data, and is used throughout this paper.
(16) The maximum specific activity reported for this enzyme is -103 pmol of
product mg-t 61n-t. Using a molecular weight of 48 000t4 for GX-|, this
value gives a turnover number of -5 X 10s mol of product min-r (mol of
enzyme)-! as the maximum value of k"., (k3). Typically, kinetic runs were
performed using enzyme with specific activity ol -200 U mg-t.
(17) N. Kharasch, "Organic Sulphur Compounds", Vol. l, Pergamon Press,
Efmsford. N.Y., '1961: A. Fava. l. llliceto, and E. Camera. J. Am. CEm. Soc.,
79, 833 (1957); L. Eldiarn and A. Pihl, J. Biol. Chem., 225, 499 (1957).
(18) H. U. Bergmeyer in ref 10, Vol. 1, p 95 ff.
(19) H. R. Mahler and E. H. Cordes. "Biological Chemistry", Harper and Row,
New York, 1966, p 237 tl.
(20) R. H. Weaver and H. A. Lardy, J. 9iol. Chem.,236, 313 (1961)'
iZrt ff'e values of klob$ in this work are comparable to rates (1.9-33 M-1
min-11 observed for the formation ot GSSG from GSH and GSSR at pH 7'0:
U. Weber, P. Hartter, and L. Flohe, Hoppe-Seyler's Z. Physiol. Chem.,351,
1389 (1970). fhe values of k1 in this work are also comparable to those
found by 'S-S J.-R. Garel, FEBS Lett.,79, 135 (1977), tor the reduction ot a
cystine OonO in ribonuclease A of 3.0 X 102 M-r min-r at pH 8.5.
(221 T E. Creighton, J. Mo|.9iot.,96,767 (1975). Several corrections were
applied to Creighton's data before they were incorporated into Figure 5.
First. the pK" values are those used consistently throughout this paper'
and do not always match those used by Creighton. Second, Creighton's
rate constants are calculated on the basis of the appearance of oxidized
DTT, and ours on the appearance of reduced thiol by reaction of a disulfide
with a monothiol. Creighton's rate constants were multiplied by a factor
of 4 to make them compatible with ours: a factor of 2 to account for the
dilterence in the rates of appearance of oxidized DTT and reduced thiol
(2dIDTTo']/dt = d[Rs-]/dt), and a second factor of 2 to account for the
presence of two symmetry-equivalent thiol groups in DTT.
(23) A. A. Frost and R. G. Pearson, "Kinetics and Mechanisms", 2nd ed., Wiley,
New York, 1961.
(24) S. S. Hall, A. M. Doweyko. and F. Jordan, J. Am. Chem. Soc., 100, 5934
( 1978).
(25) The value of pnr" given in ret 12 was calculated from the rate constants
incorrectly, and is in error.
(26) The data ot Hupe et al. also show some small sensitivity to the particular
data inch.rded in the analysis- Two sels of experiments were carried out
in obtaining rate constants for reductions with aryl thiols: one used the
reducing agent in excess, one had Ellman's r^eagent in excess. Leastsquares
analysis of the first set of data yielded =
Fn*nv'
0.48 (l = 0.96);
anatysis of thb second se!of data yielded a =
in 0.41 1F = 1.0); analysis
of both together yielded d*-ry'
= 0.44 1ts = 0.97). Inclusion. o1 a point for
methyl mercaptoacetate in Hupe's analysis changes Fn,-"'*v' to 0.43 (ts
= 0.91).
(27) Although the data for alkyl thiols in these studies are in good agreement,
there is a small but real difference in the data for the aryl thiols. The similarity
in the alkyl thiol rate constants suggests that no consistent experimental
difference accounts for this difference. All ot orr data were obtained
using the same procedure, although their experimental precision was lower
for the more rapidly reacting thiols. Hupe et al. used slightly different procedures
for alkyl and aryl thiols. Either this difference in procedure, or
differences in the compositions of solutions (especially ionic strengith and
buffer composition), might confibute to fie consistent tactor ot ca. 2 which
separates these sets of rate constants.
(28) We note that the values of 0^* derived from these two-independent investigations
are. in fact, experimentally indistingnristraole (Fo.ry = 0.4112
vs. 0.4313) if the datum for methyl mercaptoacetate is included in the calculation
of the latter point- Hupe et al. point out frat this compound shows
deviations in analyses of rate constants derived from both thioesters and
disulfides, and exclude it on that basis.
(29) C. O. Johnson, Chem. Rev., 75,755 (1975).
(30) H. A. Smith, G. Doughty, and G. Gorin, J. Org. Chem.,29,1484 (1964).
(31) G. Dafman, J. McDermed, and G. Gorin, J. Org. Chem.,29, 1480
(1964).
(32) O. R. Sanadi, M. Langley, and R. L. Searls, J. Biol. Chem., 234, 178 (195-9)'
report Eq' tor the reduciion of lipoamide to be -0.294 V at pH 7.1' 22 oC,
2025
vs. the standard hydrogen electrode. This correspords to a vah.re of -o.2gg
V at pH 7.0,30 "C. V. Ma,ssey, Biochim. Eiophys- Acta,3Z,314 (1960),
reports a value ol -0.288 V vs. standard hydrogen electrode at pH 7.0.
30 oc. we have repeated the equilibrations described by Dandi et at. .r,o
obtained the same value for this potential. These potentials were all ou
tained by equilibration against an NAO+/NADH couple. We have used a
vah.p of E9' = -0.30 V at pH 7.0, 30.0 oC, vs. standard hyctogen electooe
for this couple: K. Brton and T. H. Wilson, BirJpm. J., 54, 86 (1953). Aq,
values and equilibrium constants were interconverted using eq 33; Kr, =
(lipoo'[NADH)/(lipddXNADH+) = 0.08_58 at.pH 7.0, 3O-"C. rc)ri;t
Kn^od'i are thus pH dependent but K27[H+]-' (and Kxeo@ [H+]--riare
pH independent.
(33) UV spectra of solutions obtained by mixing BAL and Ellrnan's reagent
showed only those features attributable to Ellman's anion and to acyclic
S-S bonds (Ellman's reagent). However, consideration of the trerds observed
in the UV of various disulfidesJ'(acyclic, €ru 480 at tr 250 nm;
1,2{ithiepan€. €mar 444 al tr,,la, 258 nm; 1,2{ithiane. €m.r 290 at tr,*-,
290 nm; 1,2{ithiolane , enex 147 at tr,.", 330) suggest that the e,r,., torfour-membered
cyclic disulfide might be vanishingly srnall. Rarnan specta
of an identical mixture of BAL and Ellrnan's reagent show, in addition to
the expected absorptions, a new band at 510 cm-r. This position is consistent
with there being no special st'ain in ft€ S-S bord and is substantially
diflerent from the y 500 cm-r predicted for a l,2dithietane.$ Thus. these
spectral data are compatible with formation of either a cryclic dimer or
higher oligomer o( a polymer on oxidation of BAL. The isolation of a dithietane
has not been reported, but stable disulfide-containing rings containing
seven or more members are well established: A. E. Asato and R.
E. Moore, Tetrahdron Lett., 4841(1973); G. H. Wahl. J. Bordner, D. N.
Harpp, and J. G. Gleason. J. Chem. Soc. Chem. Commun'985 (1972); T.
C. Owen, J. M. Fayach, and J. S. Chen, J. Org. Chem.,38, 937 (1973).
(34) J. A. Barltrap, P. M. Hayes, and M. Calvin, J. Am. Chem. Soc., 76, 4348
(1954).
(35) H. E. Van Wart and H. A. Scheraga, J. Phys. Chem.,80, 1812, 1823
( 1976).
(36) We assume in doing these calculations that the pf. ol HSR-SSR' eqtnls
that of HSRSH (see Discussion section in text). The calculated values of
Kosscs and K6556sH include a statistical factor of 2 whenever a dithiol
reducing agent is involved.
(37) J. P. Snyder and L. Carlsen, J. Am. Chem. Soc., 99, 2931 (1977).
(38) R. E. Rosenfield, Jr., R. Partfiasarathy, and J. D. Dunitz, J. Am. Chem. Soc.,
99, 4860 (1977).
(39) In principle. it should be possible to estimate 0n,. * grs from a plot of the
sort shown in Figure 7, assuming that 36 (with constant parameters)
characterized all the thiol-disulfide reactions in an equilibrating mixture
of RSH and ESSE (eq 18). At equilibrium, defining the equilibrium constant
in terms of rate constants for forward and back reactions:
xs- = 2(dn,- - p'gXpK""sH - pKaESH)
The data in Figure 7 cover both alkyl and aryl thiols and disulfides' and tying
tofitthema||toasing|eequation'naynot|eadtousefu|parameters.||we
analyze. however, oity tfte group oi points 1-8 corresponding to thiol-
OisuitiOe interchange involving aliphatic thiols. and force the le.ast-squares
line to go hrough (d,O), we estirrnie trat do- - 0,n.= 1'?7. n tJ's= -O'7'l'
This va-lue is in quaiitative agreement with the vilue of grc = -0'73 generated
by analyzrng rates. R. Freter, E. R. Pohl, J. M. Wilson, and,,D. J. Hupe.
J- Org. Chem.', 44: fl70(1979), have independently estirnated /J" = -o'3
for dlsplacement of Ellman's anion from mixed disulfides of the form
RSS-Ellman's.
t+ol viies';ilj: : -0.30 (0n* =
=g,g= 0.63, C = 5'5.1)' 0"-= -0'35 (0'"*
''-'
_:d; =b.oz. C= S.Sir'jlndP::0.40(t,.,8 = -d'n = 0.!1- C= 6.29)
arl nale ts = 0.96 for plots of the type shown in Figure 10' The values
-orresponolng to d. = -O'40 were chosen as "best" becausa the slope
a of the correlatlon line and the intercept b in the eguation-log K4itcd
- a
log A-'ot * bwereclosest to the values of a = 1'0, b = 0'0 expected for
a oerlect conetatioi:-1i.: :o'50 (a = 0'93' a = 0'34); 0' = -0'35 (a =
o.'gO, o = 0.20)i dc = -0.40 (a = 0'98' b = 0'09)'
(41) In practice, in apptications of these equalions to the determination of the
pK's of protein ttiolg-toupi u"ing thiol-disulfide intercfrange-rates' we find
that fre difference-be-t*# G p"r"s estirnated using eq.3F3.8 is less than
the uncertainty from other aspectl of the experimental *9fr'^^"
(42) A. L. Af lred ano E. G- Rocnow' J. lnorg' Nuci' Chem'' 5' 26.4' 269 (1958);
E. Clementi, F. Cavallone, and R. Scordamagli a' J' Am' Chem' Soc" 99'
5531 (1977).
(43) The relative magniMes of the Bronsted coefficients used in eq 36 can'
in principte, o" |'"tloi-"ii.Jt ,rig itnodrl for the transition state in which
RSre and RS'c have eqtral charge, provided that the substituent on ona
sulfur significantty intGnces thi ability of an adiacent.sulfur to acconrmodate
charge. An;;;Gi;;iti."tt a distribution based on this
"Ltg"
modef , and on u.,e aoaitionaf assumption that fre rnagniMe. of p.is lircarly
related to the difference in charga on sulfur in the -ground and transition
state, lead. however, to physically unreasonable results'
(44) R. P. Bell, "fne p;ln l[ Crremijtry " , 2nd ed" Cornell University Press'
Itfraca. N.y.. 1973; Ui. F..l*"f", "Cit"rV"S in Ci=mist y ancl Enzynptogy"'
McGraw-Hill, New York' 1969'
(45)Theef|ectivemotarityotthiotinintramo|ecularattackonthecarbony| is 1' 4
moiety of fnitrophenyl M(2

2026
Journal of the American Chemicar societl, / r02.6 / March r2, tgg0
8,29 (1e6s).
(49) c. L. Eilnran. Arch; Bjo_chgm. Biophys., gZ,
(S1) H. U. Bergmeyer,
ZO (1959); K. Gawehn,
A. F. and
Methods
S,
Enzymot.,
A' l'{abeeb' M. Grassl in
25, 457 (19i2f.
(52) ref 10, Vol. 1, p N- r. 469.
crrairoeilain
(50) K. Crawehn and H. U. Bergmeyer
"no
in ref 10, Vol. 3, p 1496.
J.l. n. Reed;; -'rilJin"irti""t and chemisry lts or Sutrur
Compounds", Part lll, "Nr.rclear tutagnetic nesonance
Compounds',,
Data of Sulfur
J. H. Karchmer, Ed., Wit"V]frr-.i york. j971.