G. E. Clement P. Hartz
and T.
Kenyon College Gambier, Ohio 43022
Determination of the Microscopic Ionization Constants of Cysteine
cysteine is a trifunctional amino acid containing three ionizable groups: carboxyl, amino and thiol.
thiol groups have similar pK.'s, and therefore, one cannot assign a priori a definite structure to R- because of the uncertainty as to which group ionizes first. The total ionization scheme pertaining to cysteine is described by eqns. (1) and (2).
+NHa
Cysteine
It is also one of the twenty biologically important naturally occurring amino acids commonly found in proteins. Its function in the protein is to provide either a free and possibly reactive SH group or a disulfide bridge. In the protein the amino and carboxyl functional groups are involved in peptide bond formation. Examples of proteins with reactive SH groups are papain and ficin; both are plant endopeptidases. The SH group in these enzymes is a necessary part of the active site functioning as an acyl group acceptor. Alternatively, two cysteines in a protein can combine (oxidation reaction) to form a disulfide bridge. These disulfide bridges affect the primary structure of proteins by either linking two separate peptide chains together as in insulin or bringing together quite different portions of the amino acid sequence of a single chain protein as in ribonuclease. Since cysteine is one of the more important amino acids, a knowledge of its chemical and physical properties is required for an understanding of its participation in biochemical processes.l A fundamental property of'cysteine which is related to much of its chemical reactivity is the acidity of its functional groups. Equation (1) describes the ionization scheme for cysteine. HSR-COOH I NHs
+
XI 8 HS-R-COO-
I NHa
Kt + H + F?
+
ThepK, of the carboxyl group is low and easily determined and identified. However, the ammonium and The development of this experiment was supported in part by n grant from the Division of Chemical Education-DuPont Small Grants Program. ' A discussion of eysteine's role in biochemical reactions can be found in any of the current biochemistry textbooks. MAHLER, H. R., AND C ~ R D EE. S , H., "Biological Chemistry," Harper and Row, New York, 1966 pp. 193-4 give an excellent discussion of the microscopic and macroscopic ionization contitnts. BENESCH, R. E., AND BENI,:SCH, R., J . Amer. Chem. Sac., 77, 5877 (19.53).
K1, Kz, and Ka are macroscopic ionization constants determined from a simple acid-base titration curve. Since the acid strengths of the ammonium and thiol groups are similar, four ionic species of cysteine exist with four different microscopic ionization constants describing their interconversion. The determination of these microscopic constants, k,, k,, k,,, and k,,, requires additional experimental measurements, since Kz can be either k, or k , or a combination of both.2 The problem then is to experimentally determine the three macroscopic and one microscopic ionization constants. Using these data, all the ionization constants can be calculated by employing eqns. (2)-(7). From eqns. (1) and (2), the following equations can be derived.
Since the carboxyl group is approximately lo6times more acidic than the ammonium and thiol groups and is completely ionized in the pH region of interest, K1 does not appear in any of the important equations. The macroscopic ionization constants Kz and KI are determined by a routine base titration of cysteine using a pH meter. From eqns. (3) and (4) i t is clear that at least one of the microscopic constants is needed for a complete analysis. The ionization constant k, is the one which is most easily determined by spectrophotometric measurements as reported by Benesch and B e n e ~ c h . ~The absorption of crysteine in the 220250(nm) region as a function of p H is shown in the figure. From such absorbance measurements, the Volume 48, Number 6, June 1971
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mercaptoethylamine occurs between pH 9.9 and 12. 8-Mercaptoethylamine is an amino-thiol compound whose thiol group almost entirely ionizes before the ammonium group. Secondly, alanine shows almost no absorbance at either p H 7 or 12 a t 232 nm. Now that the fraction of tbiol group ionized, (a.), has been determined spectrophotometrically as a function of p H , it is used in eqn. (7) to calculate4 kIc,.
Using eqns. (3) and (4) the other three micmscopic ionization constants are calculated. The table compares these ionization constants as previously reported in the literature with those obtained herein. The Ionization Constants for Cysteine
Literature
Unm)
This work
Representative speOro of cysteine a t various pH's The rpestro were determined with a 1.6 X M solution of cyrteina on o Boskmonn DB Spectrophotometer equipped with o Sargent Recorder Model SRLG. Tho sells were 1-cm quartz cwet., and o cell containing the appropriate buffer war placed in the reference compartment.
fraction of ionized thiol group (or,) as described by eqn. (5), can be calculated a t each pH.
The absorbance spectrum at p H 12.06 represents cysteine with 100% of its thiol group ionized while the spectrum a t pH 4.63 represents just the opposite condition, 100% of the thiol group unionized. The absorbance spectra in the p H range 7.95-10.55 correspond to various degrees of ionization of the thiol group, and the spectra show tbat the ionization of the thiol group produces a large increase in absorbance. Therefore, a, can be calculated at each pH value in the range 8-11 from the absorbance values a t 232 (nm) using eqn. (6).
Such a calculation requires the assumption that the absorbance spectra of
be identical. Benesch and Benesch3 cite two pieces of evidence supporting this assumption. First tbat no significant change in the molar absorptivity of p396
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Reference in footnote 4, extrapolated to eero ionic strength. Reference in footnote 3.
agreement between the two sets of data is quite good. It is readily apparent from inspection of the table that both the ionizations of the tbiol and ammonium groups make a contribution to Kz. The thiol group, being more acidic, makes the larger contribution. This direct approach to the determination of the microscopic ionization constants of cysteine completely settled all discussion as to the relative influence of the thiol and ammonium groups on the macroscopic ionization. I n summary, the complete determination of all the ionization constants of cysteine requires a combination of a direct acid-base titration with a series of spectrophotometric measurements. Experimental
Delemination of pK,, pK1, pKs A d - B a s e Titration. AU experimental measurements were done a t 25'C. Dissolve 0.005 mole, 0.88 g of cysteine hydrochloride (Eastman Kodak white label) in 30 ml of distilled water and titrate this solution with a 0.500 N sodium hydroxide solution. Use s pH meter to record the pH of the solution after the addition of each 1/2 ml of titrant. Repeat this procedure on a. 30-ml sample of distilled water which is to he used as s. blank titration. T h a e titrations should he done under a. nitrogen atmosphere in order to eliminate Con ahsorption s t the higher pH's and oxidation of the thiol group. Plot the milliliters of sodium hydroxide titrant versus pH for both the cysteine and blank samples. Draw a smooth curve through the experimental points. Subtract the blank reeding from the corresponding cysteine titrant reading and EDSALL,J. T., AND W ~ A J., N "Biophysical Chemistry," Academic Press, New York, 1958.Vol. 1,pp. 496-504. We have written a relatively simple program for an IBM 1130 comnuter which will calculate the first and second derivatives of titration curve. This program is a v d ~ h l l eupon request. Analysis of this derivative data allows one to easily pick out the second and third end points for the cysteine titration. Of course the volume of titrclnt required to reach an end point can always he calculated from the following equation: Normality X volume = equivalents = g cysteine~HCl/molecularweight. =BATES,R. G., AND BOWER,V. E., Anal. Chem., 28, 1322 (1966).
make a second plot of the difference in milliliters of tit,rant required to completely titrste cysteine versus pH. Since the second and third ionizations are so close together, definite breaks in tlie t,itrat,ion curve are difficult to judge by eye. Satisfactory end points for the second and third ionizations can be obtained from a computer analysis using a program written to calculate the first and second derivatives of the titration curve.' An accurate knowledge of ihe end points is required since PIC = pH a t half ne~~.tltrdir;ation. Speclrophotomelric Delenximtion of (a,). Prepsre n stock 111) dissolved in solnt,ian of cysteine hydrochloride (1.6 X water and a scriea of borax buffers in the pH range 8-1L6 Far the pH range 8-9.10 mix 30 ml of 0.023 At borax with S ml of 0.10 If hydrochloric acid and dilute to 100 ml, and for the pH range 0.2-10.4, mix 30 ml of 0.025 M borax with X rnl of 0.10 M sodinm hydroxide and dilute to 100 ml with water. n pH 4.3, 0.03 Pl acetate buffer and x 0.016 M Finally, sodium hydroxide solution. Take l-ml nliqnots of the stock cysteine hydrochloride solution and dilute to 10 ml (use a volumetric flask) with the above borax, acetate, and sodium hydroxide buffer solutions. Borax bnffers deteriorate on standing so they should be stored in the cold and used as soon after preparation as possible. Determine the spectra of these salotkm in l-crn path length cells in the wnvelength region 220-230 nm (see the figure). I t is most important la take the pH of each of these solutions since the ~ d d i t i o nof the cysteine hydrochloride solution to the stock buffers will lower their pH. From the absorbance vnhes a t 232 nm calculate a series of a ' s a t the varions pH values. 1Jse these nverage a, values in eqn. (7) to calculate s series of k,. The other three rnicroscapic ionisabion constants can now be calculated using nn average k, value with eqns. (2) and (4). If a recording speetrophotorneter is not avaihble. the same calculstions can be made from absorbance measurement* taken only a t 232 nm on n Uerkmann U U or Spectronic 20.
Additional Problems and Comments
This spectrophotometric method for the determination of the ionization constants of -SH groups is completely general and can be applied to all thiols. An interesting extension is to determine the ionization constants for cysteine ethyl ester. For this compound an inversion of the microscopic constants occurs where the ammonium group is now a stronger acid than the thiol group.4 This compound could provide the student with an additional experimental challenge. It is also instructive to answer the question of v h y the inversion in the magnitude of microscopic ionization constants.
There are a number of other questions and calcnlations which are not answered herein. 1) Why does the peak absorbance maximum of cysteine shift to longer wavelength with increasing pH? 2) I n the analysis of the spectrophotometric data why was it, necessary to assume that
exhibit the same molar nbsorptivities? 3) From the ionisalion scheme shown in eqns. (1) and (2) derive eqns. (3), (4), (6), and (7). Hint: Equations (3) and (4) can be obtained using a procedure similar t,o ihnt described in footnobe 3. Equ.ztiun (7) can be oblained by srtbstituting the appropriate micmscopic oqdibrin inla eqn. (3) so that (a,) is R. function of only ke,kn, k,,, k,,,IIt, and I
sa
\
The concentration term is then eliminated and k,, k,,, and k,, are replaced by I
