DISSOCIATION OF AMINO ACIDS
893
T H E EFFECTS OF CERTAIN SALTS ON T H E DISSOCIATION OF ASPARTIC ACID, ARGININE, AND ORNITHINE' A. C. BATCHELDER A N D CARL L. A. SCHMIDT
Division of Biochemistry, University of California Medical School, Berkeley, California Received November 16, 1999
The present experiments dealing with the effects of salts on the dissociation of ttspartic acid, arginine, and ornithine were carried out with the same technique as described in the previous paper (1). These amino acids were chosen since one, aspartic acid, represents the group of dicarboxylic amino acids, while the other two are representative of the predominantly basic amino acids. CALCULATION OF RESULTS
A . Aspartic a d : K: and K; The equilibria H0OCCHaCHNH:COOH
$
HOOCCH2CHNH:COO-
$
+ HOOCCHzCHNH$COOH+ + -OOCCHzCHNH$COOH+
(1) (2)
described by the apparent constants K: and K: , respectively. These wristants are defined by
:LIT
Actually the zwitter ion and the cation are in equilibrium between the various possible structures. 'The charges have been placed on particular groups for convenience only. The constants are therefwe over-all constants, obtained by considering the total concentration of the various species of ions, each species being differentiated by the net electrical chargc and not by the spatial location of the charge. The above two constants are "overlapping" (4). Therefore they have been calculated from the experimental data by an adaptation of the method suggested by Neuberger (7). In two solutions of aspartic acid that have different pH values, the amino acid will exist in the three forms that are given in equations 1 and 2, 1 The authors were aided by 3 grant from the Research Board of the University of California and by Eli Lilly and Company. They are indebted t o the Cyrus M. Warren Fund of the American Academy of Arts and Sciences for the loan of the Type K potentiometer.
894
A . C. UATCHELDEH .IND CAHL L. A . SCHMIDT
provided the pH of both solutions is such that the concentration of the divalent anion is negligible. Or, in mathematical terms,
where CR+ , c R + - , and cR- refer to the concentrations of the aspartic acid cation, zivitter ion, and monovalent anion, respectively. cT indicates the total concentration of the aspartic acid, regardless of form. The subscript cy refers to the first solution and @ to the second. The divalent anion of aspartic acid need not be considered, since -log K 3 is about 6.0 units greater than -log K z . In the present experiments, solution 01 was made up by adding hydrochloric acid to isoelectric aspartic acid, and solution @ by adding sodium hydroxide. The following are therefore obtained upon consideration of the electrical neutrality of the solutions:
CB
= CR-
-
cE+
- CR+
(8)
where C A and CB refer to the added concentration of hydrochloric acid and sodium hydroxide, respectively, and c H + indicates the hydrogen-ion concentration. If both solutions have been brought to the same value of the ionic strength by the addition of the same neutral salt to each, cR+-cH+
cRt-cH+
CRf
CRf
K { = u= S A
Division of equations 5 and 6 by cR,+- and following : CR:-
CR:-
CR:-
cR+-,
CR2-
(9)
respectively, gives the
(11)
By combination with equations 9 and 10, the ratios in the left-hand sides of equations 11 and 12 may be expressed in terms of hydrogen-ion concentration and the apparent constants. After performing this substitution and rearranging, the following equations are obtained:
895
DISSOCIATION OF AMINO ACIDS (cH;)'
+c cH;
(cH;)'
+
~ ~ KK:K: : -~c T ~ K: CRt-
(13)
+ c ~ ; K +: K:K: -- _ _ c T ~
cH;
K:
(14)
CR+-
Analogous operations on equations 7 and 8 result in two additional equations that are similar to equations 13 and 14. Combination of these four equations results in the following pair of equations :
1.9-
Y
Q1.4\ t
3 -
0.9
I
I
I
I
FIG.1. The effects of varying amounts of sodium chloride and potassium chloride on the hydrogen-ion concentration of partially neutralized solutions of aspartic acid. Curve I, potassium chloride, A = -4; curve 11, sodium chloride, A = - 4 ; curve 111, potassium chloride, A = - 3 ; curve IV, sodium chloride, A = - 3 . Kote: 0.3 X units have been subtracted from the experimental values for curve I1 to place thc curve on the graph.
- (cH;)'
~CA
- CH+
_Q-6_ _-- (cH;)' CE
f
cH$
+
K:cH:
(cHb+)*
+
+ K:K;
- K:K:
K:cH;
+KX
K:K; - ( ~ ~ $ 1 ~
(15)
(16)
These equations were applied to the experimental data in the following manner: Two series of solutions, a and 0, were prepared. The same salt was employed in both series. The hydrogen-ion concentration of each solution was determined. These values were plotted on a large-scale
896
A. C. BATCHELDER .4ND CARL L. A. SCHMIDT
graph against the square root of the ionic strength, and a smooth curve was drawn through the points. This graph is shown in figure 1. The hydrogen-ion concentration of both series at several values of the ionic strength was then obtained from the graph. Several pairs of values for CH+ a t equal values of the ionic strength were thus obtained. The values of the two constants a t each of these several values of the ionic strength were then calculated from the hydrogen-ion concentration by equations 15 and 16. The effects of potassium chloride and sodium chloride on the -log K: of aspartic acid are shown in figure 2. The points are experimental, and the curves have been drawn to fit the points.
i
2
Pro. 2. The effects of varying amounts of sodium chloride and potassium chloride on -log K: of aspartic acid. 0 = sodium chloride; 0 = potassium chloride.
No attempt has been made to calculate the theoretical curves for the effects of salts on the -log K : of aspartic acid. Because of the assumptions involved in its derivation, Icirkwood’s equation (see reference 19 of the preceding paper (1)) for the activity coefficients of zwitter ions is not so adaptable to aspartic acid as it is to alanine. If, as the simplest cme possible, the activity coefficient of aspartic acid is equal to unity, and the activity coefficient of the aspartic acid cation equals that of the hydrogen ion, the resultant theoretical curve will be a horizontal line whose origin on the ordinate corresponds with the origin of the experimental curve. Any decrease of yR+- from unity will give the curve a negative slope. Any departure from yR+ = yH+ will give a negative slope if yR+ > yH+ , and a positive slope if y R + < YH+ . The exact shape of the theoretically calculated curve would depend on the functions describing
897
DISSOCI.\TION O F AMINO ACIDS
the 7’s. The general shape of the curve is similar to those in figure 3 of the preceding paper (1). The theoretical equation has the form
+
+
+
-log K: = -log KI f(d j’’(&J Bpc (17) where the functions of the ionic strength and the square root of the ionic strength of ( p c ) and j’(&) represent the theoretical expressions for the activity coefficients, and Bp. is the “salting-out” term. This type of curve, if f(pc) = j’(&) = 0, will approximately fit the experimental > 0, equation 17 will describe the experimental data data. If j’(&) exactly.
FIG. 3. The effects of sodium chloride and potassium chloride on -log K ; of aspartic acid. 0 = sodium chloride; 0 = potassium chloride.
The effects of sodium chloride and potassium chloride on the -log Ki of aspartic acid are shown in figure 3. Equation 29 (reference 1) will describe the present curves. If YR+- is taken as equal to unity a t all concentrations, equation 12 (reference 1) is in>roduced for 7R-and yH+ , C = 0, and a’ in this equation is equal to 4.0 A., the following modification of equation 29 (reference 1) is obtained:
This semi-empirical equation provides a means to fit the experimental results mathematically. The curves in figure 3 were calculated by equation 18. The values of the constants B and -log KS were determined from the experimental points. B for the potassium chloride curve has a
898
A. C . BATCHELbRR .4h4 CARL L. A. SCHMIDT
value of 0.208 and B for the sodium chloride curve has a value of 0.168. -log K Zhas a value of 3.895. In its logarithmic form, K : of aspartic acid is defined by
It applies to the equilibrium: -OOCCHzCHNH:COO-
-OOCCHzCHNHzCOO-
+ H+
(20)
In making up the experimental solutions, approximately 1.5 moles of sodium hydroxide were added to each mole of aspartic acid. In considera-
L
K
I
I
I
05
10
15
FIQ.4. The effects of sodium chloride, potassium chloride, and barium chloride = potassium chloride; 0 = sodium chloride: on -log K ; of aspartic acid. 0 = barium chloride.
tion of this fact and the electrical neutrality of the solution, the ratio in equation 19 may be evaluated by = CB
- CT -
COH-
CR- = 2cr
- CB -
CQH-
cR--
(21)
where cB is the added concentration of sodium hydroxide, CT is the total concentration of aspartic acid, and the remaining c’s refer to the concentration of the species denoted by the subscript. -log cH+in each of the solutions was calculated by means of equation 3 (reference 1). QH- was evaluated in the manner described in the preceding paper (1). The experimental results are shown graphically in figure 4. By reasoning that is identical with that followed in obtaining equa-
DISSOCIATION O F AMINO ACIDS
899
tions 17 and 27 (preceding paper ( l ) ) , the following relation between -log K: and -log KI of aspartic acid is obtained: -log K: = -log Ka
+ log YR-- + log YE+ - log YR- + Bpc
(22)
The “salting-out” term has been added. If equation 12 (reference 1) is intr2duced for the activity coefficients, letting a’ for R- and R-- equal 4.8 A,, and a‘ for H+ equal 3.0 A., equation 22 will not fit the data even approximately. The limiting slope calculated in this manner is considerably greater than that indicated by the experimental data. Simms (10) suggested a modification of the Debye-Huckel equation to apply to the case of divalent ions with widely separated charges of like sign. For the present case, his equation may be written
where 2 is an empirically determined constant, the value,of which lies between 1.0 and 2.0. Introduction of equations 12 (reference 1) and 23 into equation 22, and inclusion of the values for a’, gives -log K:
=
-log Ks
- 0.504(T)d p :
+1.5746 - 0.5046 0’5046+ Bpc 1 + 0 . 9 8 4 6 4- 1 + 1.574dp0
1
(24)
Curves I and I1 in figure 4 were calculated with the aid of equation 24. The constants were determined from the experimental data. The following values were obtained: -log R: ,9.842; 5, 1.23. For curve I, B = 0.220 and for curve 11, B = 0.185. The displacement of curve I11 may be explained by the formation of complexes of the type noted by Cannan and Kibrick (2). Their equation (equation 4, page 2316, bottom of first column) has been applied to the present case. Using their values for CI and CZfor succinic acid, the correction to be applied to curve I11 for complex formation is calculated to be 0.46 unit a t p c = 1.5. This correction superimposes curve I11 on curve I a t this concentration. If it is assumed, in agreement with Cannan and Kibrick, that addition of potaasium chloride to the solution of aspartic acid does not result in the formation of complexes, the calculated correction for complex formation in the present case is of the correct magnitude. B. Arginine The effects of sodium chloride and lithium chloride on -log K: and -log K: of arginine have been determined. -log K: is defined by
900
A. C. BATCHELDER A N D CARL L. A. SCHMIDT
The equation applies to the equilibrium:
NH:C(=NH)NH(CH~)
s
~
~
NH:C(=NH)NH(CH2)3CHNH:COO-
~
~
+ Hf
(26)
+ H+
(28)
-log K: is defined by
It applies to the equilibrium:
NH:C(=NH)
NH (CH 2) ,CHNH:COO-
e NH:C(=NH)NH(CH2),CHNHzCOO-
As in the case of aspartic acid, the spatial location of the charges in the chemical formulas on any group is a matter of convenience only. It does not imply the non-existence of other isomeric forms in the solution. Arginine monohydrochloride was used in the present experiments. The ratio in equation 25 was evaluated by
where CB and CA are, respectively, the added concentrations of sodium hydroxide and hydrochloric acid, and the other symbols have their previous significance. A separate series of solutions was used for each constant. Equations 29 and 30 and the values for -log c H + that were obtained from equation 3 (reference 1) provided all the values necessary for the evaluation of equations 25 and 27. COH- was evaluated in the manner previously described. The results of these experiments are shown graphically in figures 5 and 6. In order to evaluate the ionic strength of the first three solutions of the series for -log K: , it was necessary to know the hydrogen-ion concentration. This, in turn, could not be evaluated without knowledge of the value of the ionic strength. A rough value of the hydrogen-ion concentration was therefore calculated, employing the assumption that cR++ = CA . With this approximatc valuc of the hydrogen-ion concentration, it was
901
DISSOCIATION O F A M I N O ACIDS
F
05
10
15
FIG.5 . The effects of sodium chloride and lithiunl chloride on -log h': of :irginin('. 0 = sodium chloride: 0 = lithium chloride.
FIG.6. The effects of sodium chloride and lithium chloride on 0 = sodium chloride; 0 = lithium chloride.
--log
S.: of argininc.
then possible to evaluate cR++ with sufficient accuracy to obtain a truc value of the ionic strength. This true value was employed for the calculation of the actual hydrogen-ion concentration. In the remaining mem-
902
A. C. BATCHELDER A N D CARL L. A. SCHMIDT
bers of this series, the salt contributes such a large portion of the ionic strength that this approximation wag unnecessary. The relation between -log K: and -log K1 is given by the equation -log K: = -log K1
+ lOgyR+ + lOgyH+ - logy,++
(31)
where K I is the thermodynamic equilibrium constant for equation 26. Upon introduction of equation 12 (reference 1) into equation 31, and letting a’ equal 4.0 A. in all cases, the following equation is obtained: -1ogKi = -logK1+
l.008&
1
+1.3126
The curve given in figure 5 was calculated by this equation, using a value of 1.807 for -log K , . If Simms’ equation is employed, the limiting slope will be decreased. The experimental accuracy of the present experiments has been limited by the magnitude of the term cH+ in equation 29. It is not believed that the accuracy of the experimental data warrants this additional refinement of the theoretical calculations. The curves shown in figure 6 have been drawn to fit the experimental data. It was not considered feasible to investigate the effects of salts on -log K: of arginine. The high alkalinity of the solutions increases the effects of experimental deviations to such an extent that the experiments lose all significance.
C. Ornithine Ornithine ionizes according to the following equations:
+ H+ NHg(CH2)&HNH:COO+ H+ F-! NH2(CH2),CHNH2COO- + H+
?;H:(CH2)&HNH$COOH
F? XH:(CH2),CHXH:COO-
NH:(CH,) &HNH:COO-
$
NH2(CH2),CHNH:COO-
The apparent constants for these equilibria are defined by -log K: = -log
CH+
- log CRf
-log K ; = -log
CH+
CR- log CR+__
CR++
Schmidt, Kirk, and Schmidt (8, 5) found that the values for -log K: and -log K: are 8.65 and 10.77, respectively. The difference between the two values is 2.12. Simms (9) has shown that for malonic acid, whose
DISSOCIATION O F h M I N O ACIDS
903
constahts differ by 2.59 units, the true constants may be taken as identical with the “titration constants.” He has also shown that in the case of succinic acid, whose constants differ by 1.42 units, the titration constants and the true constants differ by 0.02 unit. Ornithine is, therefore, a borderline case: In the present calculations it is assumed that no correction need be applied for L‘overlapping,’lLe., that the constants rbtained by the following method of calculation are the true constants. The following equations were used to evaluate the ratios in equations 36, 37, and 38: CR+f
= CT
- CB -
CRf
= CB
+ cH+
CR+ CR+CR-
CR+-
CHf
(39)
- CB = CB - CT = CB - QH- - 2cT = 3cT - CB f = 2cT
(40) (41)
where the symbols have their previous significance. The equations are obtained upon consideration of the electrical neutrality of the solutions and the fact that ornithine dihydrochloride was employed in the experiments. The solutions used for determining the changes in -log K: , -log K: , and -log K,’, respectively, were prepared by adding 0.5, 1.5, and 2.5 moles of sodium hydroxide to each mole of ornithine dihydrochloride. -log CH+ in equations 36, 37, and 38 w&s obtained from equation 3 (reference 1). Q ~ was evaluated in the manner previously described. The effects of sodium chloride on the three constants are shown in figure 7. The curves have been moved to a common point of origin by addition or subtraction of the amount stated in the caption. The relation between -log K: and -log K 1 of ornithine is given by equation 31. Curve I in figure 7 was calculated with the aid of the following equation :
which was obtained by the addition of the term Bpc to equation 32. B = 0.0564 and -log Kl = 1.705. Curve I1 of figure 7 was calculated according to the empirical equation -log K: = -log Ke
+ Bpc
(43)
where B = 0.235. Considerations similar to those that were discussed in connection with the theoretical calculation of the effects of salts on -log K : of aspartic acid apply to the present case.
904
A. C. BATCHELDER AND CARL L. A. SCHMIDT
The relation between -log K : and -log Ka of ornithine is given by -log: K: = -log Ka
+ log
YH+
+ log
YR-
- log YR+-
(44)
Curve I11 of figure 7 has been calculated by the semi-empirical equation
which is obtained by introducing equation 12 (referencz 1) into equation 44,adding the “salting-out” term, letting a’ equal 4.0 A,, and employing
94
-
-
9.2
8.4-
I I.o
I
05
I I.5
FIQ. 7. The effects of sodium chloride on the ionization of ornithine. 0 = -log K : . 6.985 units have been added t o all values. 0 = -log K: = -log K: . 2.065 units have been subtracted from all values. Note: the curves are calculated.
.
the approximation that YR+- = 1.0. The values of 0.302 and 10.755have been obtained for B and -log K: , respectively. DISCUSSION
The effects of salts on the ionization of amino acids have been explained in the same manner as the effects of salts on the ionization or activity coefficients of other electrolytes. At low salt concentrations, the form of the curves showing the changes in the values of the apparent dissociation constants has been correctly predicted on the basis of the theory of interionic attraction. Because the activity coefficient of the electrically neutral portion of the amino acid and the “salting-out” term are proportional to the first power of the ionic strength, the chief factors that determine the shape of the curves a t low salt concentrations are the activity
905
DISSOCIATION OF AMINO ACIDS
coefficients of the other ionic species that are involved in the ionization equilibrium. In common with certain other electrolytes, it has been necessary to use a “salting-out” constant to obtain agreement between the experimental and the calculated values a t higher salt concentrations. At higher values of the ionic strength, the activity coefficient of the zwitterionic portion of the amino acid plays a relatively more important part in determining the course of the theoretical curve. However, the theoretical uncertainties a t these higher salt concentrations and the introduction of the “salting-out” term make accurate evaluation of the constants in Kirkwood’s equation difficult. In solvents of low dielectric constant, the effects of the electrostatic forces are increased and the effects of the non-electrostatic forces tend to disappear. In order to estimate the relative importance of these forces in determining the effects of salts on the ionization of amino acids, it would be of interest to determine the effects of salts in solvents with lower dielectric constants than that of water. On the assumption that none but electrostatic forces determine the effects of salts on the ionization of proteins as well as amino acids, the following method may be employed to obtain a limiting equation relating the pH of an ampholyte solution to the salt concentration. Each of the steps in the ionization of proteins and amino acids can be represented by the following general equation :
AH:
e AH:
+ H+
(46)
where A represents the isoelectric ampholyte. The value of n is greater than that of m by unity. The thermodynamic equilibrium constant is given by
=AH+AQIH+ =
K
CAH+ CH+
A
AH;
.
- TAH;TH+
(47)
TAH;
CAB:
Under the restriction that the value of the ratio
CAH+ 2
is constant, and
CAHt
incorporating its value with that of K , -log
C H + ~ H +=
-log
CYH+ =
-log K
- log YAH;
+ log
YAHL
(48)
0.5
