THERMODYNAMICS OF PROTON DISSOCIATION
Nov. 20, 1964 [CONTRIBUTION FROM
THE
4779
DEPARTMENTS OF CHEMISTRY AND CHEMICAL ENGINEER~NG, BRIGHAM YOUNG UNIVERSITY, PROVO, UTAH]
Thermodynamics of Proton Dissociation in Aqueous Solution. 111. L-Cysteine, S-Methyl-L-cysteine, and Mercaptoacetic Acid. Determination of Cysteine Microconstants from Calorimetric Datal" BY DONALD P. WRATHALL, REEDM . IZATT,'~ AND
JAMES
J. CHRISTEN SEN'^
RECEIVEDJUNE 13, 1964 Calorimetric AH and pQ values are reported a t 25" and over the ionic strength range 0.002 to 1 for the ionization of protons from ( a ) the -SH group of mercaptoacetic acid, ( b ) the -NH3+ group of S-methyl-L-cysteine, and ( c ) the -SH and -NH3+ groups of L-cysteine. . 4 calorimetric method for microconstant determination is described and used to determine microconstant values in the case of cysteine through the ionic strength range 0.002 to 1.
Introduction Proton ionization from cysteine (CYS) has been investigated repeatedly for several decades with quite divergent result^.^^^ Cysteine is unusual in t h a t proton ionization occurs simultaneously from both the sulfhydryl and the protonated amino groups in each of two p H regions. The microconstant scheme for cysteinezp4is
I11
The relative concentrations of microspecies I1 and I11 are difficult to determine since p H measurements alone do not provide sufficient data to distinguish between them. At 25' the reactions represented by k12 and kI3 occur in the p H region 8.3-8.8 while those represented by k123 and kl32 occur in the p H region 9.510.5. The microconstants are related to the macroconstants, K2 and K3, in the 8.3-8.8 (K2) and 9.510.5 (K3) p H regions by the expressions2,3
KZ =
k12k13
(1)
and K2K3
=
k12k123 = kl3kl32
(2)
respectively. Many biologically important molecules contain cysteine or other groupings of atoms which may ionize to produce microspecies. The determination and correct interpretation of the thermodynamic data associated with proton ionization from such molecules is of vital importance to an understanding of their functioning in biological systems. In previous in(1) (a) Supported by National Institutes of Health Grant No. RG-9430. Presented in part a t t h e 145th National Meeting of t h e American Chemical Society, New York, N. Y., Sept., 1930. (b) To whom inquires should be directed. (2) For a critical review of previous work, see G . Gorin and C. W. Clary, Arch. Biochem. Biophys., 90, 40 (1960). (3) E . Elson and E . Edsall, Biochemislry, 1, 1 (1962). (4) T h e symbols k n and K , are used t o denote equilibrium constants valid a t zero ionic strength. Corresponding equilibrium constants a t finite ionic strength values are given t h e symbols k,' and Qn, respectively.
vestigations of the cysteine system the necessary calculation of the ratio, R,of the concentrations of I1 and I11 has been made from spectral (Raman or absorption) data or has been estimated from p K data involving molecules in which an inert group (e.g., CH3, CzHS, etc.) is substituted for the proton of an acidic group. Benesch and Benesch5 and Elson and Edsal13 have determined R to be approximately 2 by ultraviolet-absorption studies. However, the R values determined by these workers are uncertain since they are based on p K values which were not corrected to the pQ value corresponding to the ionic strength, p , of the solutions being studied. Gorin and Clary2 measured the concentration change of I1 by following the ionization of the sulfhydryl group spectrophotometrically. Their conclusion t h a t R does not vary significantly with p is probably not justified since they did not measure the concentration of 111, but apparently assumed i t to have the same I.( dependence a s t h a t found for 11. In the present study is described a calorimetric method for determining the relative concentrations of I1 and 111. The method is based on the fact that the AH values for proton ionization from the NH3+ group of S-methyl-I=cysteine (SMC) and the S H group of mercaptoacetic acid (MAA) differ by approximately 4 kcal./mole. This difference in AH values, if maintained by the corresponding groups in the cysteine species, makes possible a rapid, calorimetric procedure for the determination of R. However, analysis of the calorimetric data requires accurate proton dissociation constant data. Although several proton dissociation studies have been reported2x6 for cysteine, only one6a has been conducted as a function of p . It was necessary in the present study to know pQ as a function of p from = 0 to I.( = 1 in order to make meaningful comparisons with other microconstant values2, valid in high p regions. Since calorimetric AH values have not been reported previously for proton ionization from MAA, SMC, or CYS, i t was also necessary to determine these values as a function of p . In the present study are reported pQ, AHj and AS values determined a t 25' and covering the range p = 0.002 to p = 1.0 for proton ionization from the -SH group of MAA, the NH3+ group of SMC, and the combined -SH and -NH3+ groups of CYS. CYS microconstant values valid a t 25' and covering the p range ( 5 ) R. Benesch and R. E . Benesch, J. A m . Chem. Soc., 77, 5877 (1955). (6) (a) H . Borsook, E . L. Ellis, and H. M . H u f f m a n , J. Bid. Chem., 117, 281 (1934), (b) N. Bjerrum, Z . P h y s i k . Chem., 106, 219 ( 1 9 2 3 ) ; (c) R . C . Cannon and B. C. J. G . Knight, Biochem. J . ,2 1 , 1384 (1927); (d) M . A. Grafius and J. B. Neilands, J . A m Chem. Soc., 77, 3389 (1955).
4780
D. P. WRATHALL, R . M . IZATT,A N D J. J. CHRISTENSEN
Vol. 80
0.002 to 1.0 are calculated from the pQ and AH data. Extrapolation of these data to I.( = 0 gives the corresponding thermodynamic quantities in each case. Experimental Materials.-CYS hydrochloride hydrate (California Biochem. Corp., A grade, Lot No. 503233), and SMC (California Biochem. Corp., A grade, Lot KO. 671051) were used without further purification. An equivalent weight determination (carboxyl group) of C Y S agreed t o &0.1% of the theoretical value. MAA from two sources (Eastman White Label, Lot KO.2249, and Fisher Certified Reagent, 9 9 . 5 5 , Lot N o . 733405) was used in the determinations with no distinguishable difference in the pQ and AH results. T h e Eastman material was fractionally distilled, and the fraction boiling between 79.5 and 81.0' (1.0 m m . ) was taken. T h e Fisher material was used without further purification. .Ill water used in the solution preparations was recently boiled and doubly distilled. Special precautions were taken during the preparation of solutions to avoid oxygen contamination since such contamination caused oxidation of the CUS and M.4.I solutions. Other chemicals used ( S a O H , HCIO,, and NaC1) were of the highest available purity. Care was taken in the preparation of the NaOH solutions t o exclude atmospheric COS. Equilibrium Constant Determinations.-CUS solutions were titrated with standard KaOH solutions a t 25" in a water bath controlled t o f 0 . 1 ' . The solutions were allowed to equilibrate in the water bath approximately 30 min. before each titration and all titrations were carried out under a nitrogen atmosphere. T h e p H measurements were made using a Leeds and Sorthrup p H indicator (catalog no. 7401) equipped with a 1000-ohm heliopot with a microdial setting making the precision of the readings approximately f 0 . 0 0 4 p H unit. T h e Beckman E-2 glass and saturated calomel electrodes used in the determinations were calibrated against a p H 9.18 buffer solution which was prepared using borax (Sational Bureau of Standards sample no. 187a) and instructions supplied by the Kational Bureau of Standards. T h e electrodes were checked against the buffer solution before and after each run. Subsequent calculations were made using only data from runs in which the initial and final buffer readings agreed t o within 0.02 p H unit. I n these calculations the average of the initial and final buffer readings was taken as the reference buffer p H value. H e a t Determinations.-The therniometric titration apparatus used in the calorimetric determinations has been described previously.7 Solutions were prepared for the calorimetric determinations using the same precautions that were used in preparing solutions for the pQ determinations. Sufficient S a O H was added in each case to form predominantly the ionized forms of MAX, S M C , and CYS. These solutions were then titrated with standard HCIOa solution. Determinations were made using solutions having p-values comparable to those used in the pQ determinations. Calculations.-The method used t o calculate AH and AH' values from the thermometric titration data has been described.7",b Values of pQ were obtained in the following manner from the pH titration data; p was calculated in the usual manner. A Debye-Huckel equation of the forms
(3) was used t o convert p H to [H'] and ii was calculated from electroneutrality and mass-balance expressions using titration readings within 0.1 unit of half-integral ii values. For high p values, f i was taken a s equal to the mean activity coefficient of hydrochloric acid in water.8 All calculations, including a recycling process between p a n d f i until the approximation attained the desired self-consistence, were done on I B M 650 and 7040 electronic computers. pK values were determined for each acid ( 1 ) by extrapolation of pQ us. plots t o p = 0, and ( 2 ) using activity coefficients calculated from a Debye-Hiickel expression of the form8 ( 7 ) (a) J. J. Christensen anc R . M. I z a t t , J . P h y s . C h e m . , 66, 1030 (1962); (b) H . M I z a t t , el a l . , I n o v g . C h e m . , 1, 828 (1962). (8) K . G . Bates, "Electrometric p H Determinations," John Wiley and Sons, Inc., h-ew York. N . Y., 1984, p . 5 1 . (9) H . S. Harned and R . W. Ehlers, J A m . C h e m . Soc., 6 6 , 2179 ( 1 9 3 3 ) .
Data for the pQ u ~ p0.5 . plots were taken from the M.I.1, SMC, and CYS concentration ranges 0.0016 to 0.04 F . pQ values were also determined a t p = 0.2 and p = 1.0 (using S a C l as inert electrolyte) in order t o make comparisons with earlier work,',? a n d to test the validity of ( 4 ) for estimating activity coeJGcient\. It was found that p K values calculated using activity coeliicients derived from ( 4 ) agreed well with those obtained by extrapolation in lower p regions. Microconstants for proton ionization from the sulfhydryl and protonated amino groups of cysteine were calculated froin pi7 and AH data in the following manner. If a is the fraction of CI'S molecules in which protons dissociate from the sulfhydryl group in the lower p H region ( I = I1 H - ) then ( 1 - a i ) is the fraction of CTS niolecules in which protons dissociate from the protonated amino group in the sanne p H H I ) . The measured heats of proton dissociaregion ( I = I11 tion in the two p H regions ( A H 2and A H 3 )may be expressed by the relationships
+
+
AH,
= aAH12
AH3 = aAH123
+ (1 + (1 -
a)AHl3
(3
a)AH132
(6)
Since AH,*, AHl3, AHlaa, and AHUScannot be measured directly, values are assigned t o these quantities which are equal t o the heats of proton dissociation from the sulfhydryl ( A H , ) and protonated amino ( A H , ) groups in MA,%and SMC, respectively (i.?,, AHs is taken as equal to AHl2 or AHL3?, arid AHa as equal to A l l l a or AH123). Addition of AH3 t o both sides of ( 5 ) , AH2 to both sides of (6), and appropriate substitution of AH3 and A H a leads to
AH2
+ AH3
=
a(AH,
+ AH3) -t (1 -
AH2
+
AH3 =
a(AHa
a)(AHa
+ AHz) +
+ AH31
(7)
Since the right hand members of ( 7 ) and ( 8 ) are equal, the ratio
R=-
Ly
1- a
+
(AHs - A H a ) - ( A H 2 - AH,) ( A H 3 - AH2) f ( A H , -
AHa,
(9)
where the quantity AH2 - AH3 is the measured difference between the heats of proton dissociation in the lower and higher pH regions, respectively, and AHs - AH8 is the difference between the assigned heats of proton dissociation from the -SH and -NH3groups in CYS. I t is seen from ( 9 ) t h a t if AHa - AH, is large compared to I AH9 - AH3 1 , even relatively large errors tn the assigned values of AHs and/or A H a will not change R significantly. For 0.67 < R < 1.5, even a n error in ( A H s - AH,) = (AHis AH,,) = (AH,,? - AHlss) of f 1 kcal. would cause an error in R of less than 10Tc. T h e respective microconstants are calculated from R , K?, and K 3 using (l), ( 2 ) , and the relationship
Results I n Table I are presented pQ values as a function of 1.1 and corresponding p K values for proton ionization from C Y S , MAA, and SMC together with previous work. The estimated uncertainty of the pK values is given as the standard deviation. The pH of the buffer solutions are given by the National Bureau of Standards as accurate to *0.005 pH unit. This error is not included in the stated standard deviation. The pQ values are averages based on the indicated number of separate determinations in each case. The average pK value in each case was calculated from low ionic strength data using activity coefficient values estimated from (4). In Fig. 1 are given the AH values as a function of 1.(0.5 for proton ionization from C Y S , MA,%, and SMC.
Nov. 20, 1964
THERMODYNAMICS OF PROTON DISSOCIATION
4781
TABLE I pQ
pK VALCESFOR T H E INDICATED PROTON DISSOCIATION STEPOF C T S [ ( A ) A N D ( B ) ] , M A 4 ( C ) , A N D S M C (D)"
AKD
No. of detn.
p
x
103
+
HzCYS ( I ) = 11, 111 H+; 2 1000 4 160 (~150)~ (-160jC (-llO)d 1 81.2 4 41 2 2 14 4 3 7 2 3 1 6
PK
PQ
4.5 A,, Bi 8.071 8.142 ( 8 . 14)b (8.30y (8.17jd 8.176 8.234 8.293 8.317 8.354
=
(Ole Av. of all p K determinations in the p range 0.0016-0.0412
=
0.1 ( A ) 8.385 8.386
9'5
8.372 8.388 8.395 8.393 8.392 ( 8 . 3 3j"
8 . 3 9 2 f 0.006 6.5
2 4
995 (~320)~ 176
(~160)~ (-llOjd 3 79 4 2 29.3 3 13 0 3 2 7 (0)" Av. of all pK determinations in the p range 2.1-29.3 HM.4A- = H +
H S M C - - = H' 3 3
+ SMC-;
998 194 (-160)' 3 7.1 3 5.0 3 4.0 Av. of all pK determinations in the p range 4.0-7.1
3,
oi
1 I
I
I
0.2
10.765 10.770 10.751 10,761 (10.78)e
= 0.1 ( C )
9.67 9.84 10.24 10.39 10.42
10.60 10.49 10.57 10.57 10.56
ai = 4 , @ 1=
0.1 ( D ) 8.99 8.95 8.97 8.96 8.97
8.97 f 0.01
a Values are valid a t 25 f 0.1". Uncertainties of the p K values are given as standard deviations. Values of ai and p i (see eq. 4) are given for each system. The reaction for which the data are valid is indicated in each case. Previous pQ and pK data are given in parentheses. Ref. 6c, temperature = 30". Ref. 6d. G. Gorin, J . A m . Chem. SOL.,78, 767 (1956); Gorin's values have been converted to concentration constants using the activity coeficient of HCL9 e Ref. 6a.
The brackets represent the range of the experimental A H data. The A H o values obtained by extrapolation have the estimated uncertainties indicated by the arrows in each case. Considerable difficulty was experienced in obtaining consistent AH values for MAA proton ionization. The AH values reported in Fig. 1 were obtained using different calorimeters and different sources of RIAA. It was never possible to obtain a set of determinations which had the precision of the S M C or CYS determinations. The reasons for the observed data scatter in the case of MAA are not known.
I
I
I
I
0.6
0.4
p
I
I
1
I.o
0.8
0.1
Fig. 1.-Plot of A H (kcal./molej us. pO.6 for proton ionization from SMC, CYS, and MAA. Range of the experimental AH and estimated uncertainty of the AH" values are indicated by brackets and arrows, respectively Temperature = 25".
In Fig. 2 pn.5is plotted v s . (a) R,(b) pk12' and pk13', and (c) pk123' and pk132' for CYS ionization. The estimated uncertainty of the R and pk' values is indicated by the brackets. Previously reported R values are also given in Fig. 2a. TABLE I1 A S VALUES(E.W.)AS A FUNCTION OF p FOR PROTON IONIZATION FROM CYS, MAA, AND SMC"
10.56 f 0 . 0 2
8.65 8.69 (8.75)' 8.89 8.90 8.91
MAA=+HL
T
10.747
10.761 f 0.010 =
HMAA--
L
10.771
9.947 (10.34)b 10.213 (10 40)" (10. 32)d 10.382 10.504 10.557 10.664
+ M A X " ; ai
3 1051 2 236 4 38 2 9.8 3 5.5 Av. of all pK determinations in the p range 2.1-38
t
--
A S values Reaction
+ +
p =
0
p
= 0.04 p = 0.16
I = (11,111) H+ -9.5 -9.2 H+ -21.9 -19.9 (11, 111) = IV HMAA- = MAA-" Hf -27.6 - 2 6 . 1 HSMC+- = SMCH-7.2 -6.4 Values are valid a t 25", and are estimated to 1 e.u.
+ +
Q
p =
1.0
1 -9.6 -18.6 - 1 5 . 8 -25.1 -23.6 -5.8 -5.0 to be accurate -9
I n Table I1 are presented A S values as a function of for proton ionization from CYS, MAA, and SMC. The estimated uncertainty of these values is f 1 e.u. A S values for proton ionization from the CYS microspecies cannot be calculated from the present data. p
Discussion The pQ data in Table I are generally in good agreement with previous data where these were determined under the conditions used in the present study. A rough check can be made on the assumptions made in calculating the microconstants, i.e., A H a = AH12 = AH132, and AHs = AH13 = AH1g3, since, if these assumptions are true, A H a AHs = A H 2 AH3. At 1.1 = 0, the difference between these two sums (Fig. 1) is 0.45 kcal. /mole, indicating the validity of the assumptions. It should be pointed out, however, that an alternate explanation is t h a t the heats of proton ionization from the sulfhydryl and protonated amino groups in CYS differ in opposite directions one higher and one
+
+
D. P.WRATHALL,
4782
21.8o
I
I
2.4
1
R.h l . IZATT. A N D J. J . CHRISTENSEN
I
1
I
t
