The Spectrum of a Dissociation Intermediate of Cysteine A Biophysical Chemistry Experiment A. G. Splfflgerber and L. L. Chinander Gustavus Adolphus College, St. Peter, MN 56082 Molecules having ionization constants that overlap, that is, that differ in p K by less than three units, will have two or more tautomeric forms that hear the same charge. In this case dissociation of the fully protonated molecule may follow two routes. For the amino acid cysteine the scheme for the dissociation may be written ( I )
s-
JH# I
H:N-.CH
SH
SH
CHx
I CHx
I
H:N-CH
I
I
COOH Hsysi+)
Kt +
I
H:NCH
I
COO
Hms
Y
I Hcysi-)
ll~ -SH
1
$H3
sAH> I I coocy9i-2)
HsN-CH
I
HsN-CH
I
Ryklan and Schmidt (9) and Grafius and Neilands (10) used data on cysteine analogues to estimate one microscopic constant, from which the others could he calculated. For example, one assumption was that Kg for cysteine was the same as the macroscopic constant for dissociation of the protonated amino group of S-ethyl cysteine. R values around 1.3 were found in both studies, which implies roughly equal amounts of CysH(-) and HCys(-). The approach outlined in this paper makes use of Beer's Law plots of cysteine constructed at several p H values over a broad range of wavelengths. A laboratory exercise built around this method would use the Beer's Law data to estimate R, calculate the microscopic constants, and construct ultraviolet spectra for both light-absorbing species. The method also provides insight into the reasons for the wide disparity of R values in the literature. Theory
Let T be the total concentration of amino acid such that
COO CysHi-1
where KA, Kg, KC, and KD are microscopic ionization constants, and R is the "tautomeric ratio" of the two singly charged ionicforms, that is, R = [Hcys(-)]/[CysH(-)] = KA/ KB. The macroscopic ionization constants Kz and K3 may be determined by titration of cysteine with standard base followed by mathematical analysis of the titration data using standard methods for computing overlapping ionization constants (2-5). These macroscopic constants are related to the microscopic ones by three equations:
The concentration terms in eq 4 may be expressed in terms of macroscopic constants K,, Kz, and K3: [Hcys(-)l + [CysH(-)I = [H+l[Cys(-z)lIK~ [Hzcysl = [H+I2[Cys(-2)I/K& [Hacys(+)l= [H+I3[Cys(-2)l/K1KzKs
(5) (6)
(7)
Substituting eqs 5,6,and 7 into eq 4,
T = [Cys(-2)1[1 + [H+I/Ks+ [H+I2/KzK3
+ [H+13/K~KzK31 = [Cyd-2)la
(8)
where the function ol may be calculated a t any pH from a knowledge of the macroscopic ionization constants. I t may now he easily seen that Knowledge of the macroscopic constants therefore is not sufficient information for finding the four microscopic constants, hut, if one microscopic constant (or R) can be determined independently, the others may he found. The earliest approaches to the problem used the idea that the Hcys(-) and Cys(-2) species (which contain the Schromophore) should absorb ultraviolet light, but the other species should not. For example, Benesch and Benesch (67) used s~ectro~hotometric data a t 232 nm to calculate the frartionoftotal cystrine present in the S-formsat aseriesof different pH values. The assumprion that the molar absnrptivities of the two S- forms were the same allowed calcuition of the microscopic constants and yielded an R value of 2.14, the Hcys(-) form apparently predominating. Gorin (8) made use of a spectrophotometric titration method to calculate the microscopic constants a t 274 nm. His assumption was that the absorptivity ratio acys(-2)/ ancp(-, was 1.4. This ratio was calculated from spectrophotometric data on the cysteine analogue cystine. The R value from this study was 0.54, with the CysH(-) species predominating.
and The observed absorbance Aobs of a cysteine solution is given by Aoba= aobaT= acls(-2~[Cys(-2)I
+ ac,i-~I[Hcrs(-)I + [CysH(-)ll
(11)
where a,b., the observed molar ahsorptivity, may be found from Beer's Law data. The absorptivity acy,(-) reflects the total concentration of the two singly charged forms. It may be related to a~,,(-) by the equation if the assumption is made that the CysH(-) species does not absorb ultraviolet light. Substituting eqs 9 and 10 into eq 11,
Volume 65
Number 2
February 1968
167
Figure 1. Beer's lew plot of cystelne at pH 10 and 240 nm. The slope of the plot Is 2959 L m i - ' a - 1 . the observed molar absorptivity.
Figure 2. Ploi for ca1Cul;ltlonof molar absorptlvniesof Cys(-) and Cys(-2) according to eq 14. The slope of the plot is w-,= 2742 1.06% Lmol-'en-'. The intercept is = 4723 i 1.95%L.moi~'~cm-'.
Cancelling T and rearranging, %be= acmi-,[Htl/Ks
+ ac~c-z~
(14)
A plot of a,bu versus [H+]IKs should yield a straight line with slope a ~ ~and , intercept - ~ ac,,-2,. If some reasonable assumption can be made concerning the relative absorptivities of Cvs(-2) and Hrvs(-j, then the tautomeric ratio R may be computed from eq 12. Knowledge of R allows computation of the microscopic equilibrium constants from the definition of R (R = KAIKB)and eqs 1, 2, and 3. From the same equation (eq 12) a value of aH,,(-) (the absorptivity of the singly charged absorbing species) may also be found. Additionally, manipulation of eq 14 yields ) intercept which gives straight lines of slope a ~ ~ c - 2and ac,+]. Equations 14 and 15 may both be used a t each wavelength tested in order to find the molar absorptivities acva(-2) and aH,(-) a t each wavelength, from which spectra may be constructed. The quantity acP(-zl is available directly from is found indirectly after makthe linear plots, while aH,(;) ing some assumption that y~eldsa value for R. Procedure In order to perform the required calculations, values of K1, KP, and K3 must be known or determined in a separate experiment (2-5). Frequently quoted values for cysteine are pK1 = 1.71, pK2 = 8.33, and pK3 = 10.78 (11). Data was arcumulated according to the following procedure. Acysteine solution atf 0.001 M concentration was made by dissohing 0.1576 g cysteine hydrochloride (Sigma Chemical Co., St. Louis, MO) in 1 L of buffer. The buffer was 0.15 M ammonium chloride adiusted to the desired DHwith HCI or KOH. ~bsorbanceswere read on rhissolution at 5-nm intervals from 205 nm to 275 nm on an IBM 9430s~ectro~hotomerer. Seventy-five milliliters of the original 0.001 ~ b o l u t i o n wasadded by ~ i ~t oea tIOO-mLvolumetricflask,and25 mL of buffer o f the same pH and ionic strength added. The diluted solution was mixed thoroughly and the absorbance readings repeated. For purposes of construction of Beer's Law plots it is probably sufficient to perform five successive dilutions (six sets of absorbance readings). The entire procedure was repeated a t each pH value (pH 10, 10.5, 11, 11.5). 168
Journal of Chemical Education
Figure 3. Plot for celculatlon of molar absorptivltles of Cys(-) and Cys(-2) according to sq 15. The slope of the plot is %*-,, = 4576 1.26% Lmol-'cm-'. me intercept Is --I= 2898 1.5.52%L.mol-'rml-~'.
Resuk
A typical Beer's Law plot at pH 10 and 240 nm is shown in Figure 1.The slope of the plot (the observed molar absorptivity a.k) is indicated in the figure legend. A grid of all values of a,b resulting from plots for each p H value a t each wavelength was compiled. Values of parameters used in making linear plots according to eqs 14 and 15 are given in Table 1for wavelength 240 nm. The linear plots resulting from this data are shown in Figures 2 and 3. The resulting slopes, intercepts, and standard errors in slope and intercept from linear regression analysis are given in the figure legends. Values of ac,(-) and aCya(-P)from linear plots a t each wavelength are shown in
Table 1. pH
a
Data lor Calculation of d ~ p ( - and ~ ) -1-1 am.
ma,
[H+ll&
KsaadH'I
at 240 nrn Kd[H+l
10
7.15 10.5 2.91 11 1.60 11.5 1.19
21.16 X lo3 6.000 35.13 X 10' 0.166 3.429 X 103 9.98 X 103 1.905 52.43 X 10' 0.525 4.057 X 103 8.49 X TO3 0.600 107.73 X 10' 1.680 4.296 X lo3 5.11 X lo3 0.191 268.44 X 10U.250
Table 2.
Various Molar Absorptlvltles and Apparent RValues at Dlflerent Wavelengths
2.959 X 103
WAVELENGTH Figure 4.
Table 2. These listed values represent a compromise hetween the values resulting from the two plotting methods, taking into account the standard errors. Table 2 also contains R values a t each wavelength calculated from eq 12, based on the assumption that acy,(-2)= an,(-) (the assumption of Benesch and Benesch (6)). These R values are included under the heading "Apparent R Values" because they show a wide variation with wavelength, whereas the true R value must be a constant invariant with wavelength as well as pH. These results may explain the large variation of R values in the literature. The literature value (6) of 2.14 a t 232 nm compares to apparent R values (Table 2) of 2.11 at 235 nm and 2.94 a t 230 nm. The literature value of 0.54 at 274 nm (8) compares with the Table 2 value of 0.544 a t 275 nm, although the assumntions made differ slightly - - in the two cases. Even so, thecorrespondence between the literatureand theapparent R values of Table 2 is reasonably good. Estimation of R
Table 2 shows that the apparent R values become rather constant at high wavelength, and i t may therefore be asr,,(-~ sumed that the absorptivity ratio a ~ ~ , ( - ~ ~ / a )becomes constant. The assumption that the ratio is unity (6) means that the "true" and "apparent"R values become the same a t high wavelength, and a value of 0.5 is reasonable, based on these two assumptions. If eq 12 is divided through by [CysH(-)] and solved for an,(-). one finds a,,.+) = ac,,-,(l+ R)IR
(16)
Values of an,(-) a t each wavelength may then be found. These are included in Table 2. Inspection of these an,,((-) values shows that an,(-) becomes approximately twice as great as acys(+)a t high wavelengths. I t is difficult to see why this should be so since the two species differ by only a proton. A better assumption ( 8 )is that the ratio ac,(-2)/a~,(-) is approximately 1.4 a t high wavelengths as described previously. This assumption leads to a new "true"R value of 0.94
Spectra of Hcys(-) and Cys(-2) assuming R = 0.94.
and a different set of values for an,,(-), which are also included in Table 2. Spectra for Hcys(-) and Cys(-2) based on this R value are shown in Figure 4. The molar absorptivities of Hcys(-) and Cys(-2) are now more similar in magnitude at low wavelength. Microscopic constants may be calculated from theR value according to K,, = K&(l+ R)
(17)
Using R = 0.94, the constants are KA = 2.26 X Kg = 2.41 X 10-9, Kc = 3.42 X lo-", and KD= 3.22 X lo-". Values of the macroscopic constants used in these calculations are and K3 = 1.66 X 10-l1 (11). Kz = 4.68 X Conclusion
Since 1970 the problem of whether Hcys(-) or CysH(-) predominates has been approached by methods such as I3C NMR. circular dichroism. and laser Raman s~ectroscouv. with the NMR method p;obably being of greatest value; clarifvine the situation (13). These results indicate that the thiol g r G p of cysteine dissociates slightly before the amino group, implying an R value slightly greater than 1, although the actual value was not calculated in these studies. Although no assumptions need bemade with the NMRmethod (one need only assign the observed peaks in the NMR spectrum to the proper carbon atoms), the method outlined in the present paper does have the advantage of revealing something of the optical spectrum of the Hcys(-) species. If the method is used as a student experiment, a recording spectrophotometer is convenient but not essential. If the spectra a t several dilutions can be recorded, the Beer's law absorbance data can be read directly, and five or six such spectra would provide sufficient data to make the necessary plots. Two laboratory periods would suffice for collecting data a t four DH values. Other am&othiols such as glutathione, homocysteine, or penicillamine could also be examined. Other possibilities Volume 65
Number 2
February 1988
169
include aminophenols such as tyrosine, although the ultraviolet spectra of these compounds is more complex than the aminothiol spectra, owing to the presence of the phenyl ring system.
4. Rametta, R.W. Ckmieo! ~quilibriumondAw1ysia;Addison-Wesley: Reading, MA, 1981: ~ 3 6 9 . 5. Li, N. C.: Gswmn, 0.;Baacuaa, G. J. Am. Chem. Soe. 1954.76.226 6. Bcnesch. R. E.; Beneseh, R. J,Am. Chem. Soe. L955.77.5877. 7 flrmm+. ~ EHart.7.T. I P.LChsm.Educ. 1971.48.395.
Literature Clted 1. Edsd1.J. T.;Wyman, J. BiophyaieolChemistry; Academic: New York, 1958; Vol. I, p 496. 2. Jensen, R. E.: Garuey,R. G.; Pau1aon.B.A. J. Chem. Educ. lW0,47,147. 3. Noyes. A. A. Z.Phyaik. Chem 1893.11.495.
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Journal of Chemical Education
Phyaio!. Chem. 1972,353,1159
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