J . Phys. Chem. 1984, 88, 1627-1630
1627
K1Intexp( K2 = [SH+-CI-] [SH'] [Cl-]
'
-6
-4
4
-2
log K r '
Figure 12. Relationship between k,'"' (e),k-l'"t (O), and intrinsic acidity constant Kaint:(1) present system, (2) TiOz (ref 1 l), (3) Fe203(ref lo), (4) Fe,O, (ref lo), and (5) a-zirconium phosphate (ref 12).
- [SH'-Cl-]
[SH'] [Cl-1,
k,, = kalintexp( f
k+2 = k + P t exp( f
2) 2)
(A-2)
2)
=
where e is the elementary charge, k is the Boltzmann constant, T i s the absolute temperature, and the subscripts s and p denote the surface and j3 plane defined by Davis and Leckie, re~pectively.~ Thus, the reciprocal fast and slow relaxation times are given byI4 Ti1
= k 2int(exp( "Y")([sH+] 2kT
+ [Cl-1) +
Kint exp(
conductivity due to the removal of usual electrostriction.
Appendix Taking into account the potentials created by the C1- and H+ adsorbed on the Sephadex A-25(C1), the rate and equilibrium constants for steps 1 and 2 in mechanism I1 are expressed on the basis of the Davis and Leckie's electrical double-layer model and the previous theoretical treatments:loJ3
exp(
$)
7,-1
-")) 2kT
k p F l (A-3)
+ [H+]) + [SH'] + KC1 intF = - klintF2 + k -1 3 [SH'] + [Cl-] + K2-l
= k,'"' exp( -'")([SI 2kT
k-lintexp
();:;
-
-1
(A-4)
For mechanism 11, the following relation was derived:
([SI + [SH+I)[Cl-l [SH+-Cl-] ( K1K2) -1 [H+]-l + K 2-1 = ( K 1intK2int ) -1 x
with Registry No. Cl-, 16887-00-6;Sephadex A-25, 9085-82-9. (13) Sasaki, M.; Moriya, M.; Yasunaga, T.; Asturnian, R. D. J . Phys. Chem. 1983, 87, 1449.
(14)
Bernasconi, C. F. "Relaxation Kinetics"; Academic Press: New York,
1976.
Ion-Exchange Kinetics on an Ion Exchanger Using the Pressure-Jump Technique. 2. Aspartic Acid Adsorption-Desorption on the Diethylaminoethyl Group of Sephadex A-25 (CI) Minoru Sasaki, Kazuaki Hachiya, Tetsuya Ikeda, and Tatsuya Yasunaga* Department of Chemistry, Faculty of Science, Hiroshima University, Hiroshima 730, Japan (Received: March 23, 1983; In Final Form: August 30, 1983)
In an aqueous suspension of Sephadex A-25(C1) containing aspartic acid, a single relaxation of the order of milliseconds was observed by using the pressure-jump technique with conductivity detection. The relaxation time decreases with the concentration of aspartic acid. The amount of aspartic acid adsorbed is larger than that of C1- released. From the static and kinetic results obtained, the relaxation was attributed to the adsorption-desorption of zwitterions of aspartic acid on the protonated diethylaminoethyl group of the Sephadex A-25(C1). The values of the adsorption and desorption rate constants were determined to be (1.6 f 0.4) X lo4mol-' dm3 s-' and (7 k 2) X 10 s-', respectively, at 25 'C. The equilibrium constant obtained kinetically was in good agreement with that obtained statically.
Introduction The ion exchangers have been used for chromatography in the separation of amino acids, proteins, enzymes, nucleic acids, and lipids.'-' For further development of ion-exchange chromatog0022-3654/84/2088-1627$01.50/0
raphy, kinetics on ion exchange of biochemical materials is important to obtain information on its elementary process. The (1) Peterson, E. A,; Sober, H.A. J . Am. Chem. SOC.1956, 78, 751, 756.
0 1984 American Chemical Society
1628
The Journal of Physical Chemistry, Vol. 88, No. 8, 1984
Sasaki et al.
T
4
-
m
N
-
0
I
I
I
I
I
I
I
I
b2
I
Figure 1. Typical relaxation curve in the suspensions of Sephadex A25(C1) containing aspartic acid observed by the pressure-jump technique with conductivity detection at C, = 3 g dm-3 and 25 OC; sweep 2 ms/ division.
ion-exchange mechanism has been discussed only statically since the reaction is too fast to be observed by the ordinary methods.8 In part 1,9 the dynamic properties of the diethylaminoethyl group of Sephadex A-25(Cl), which is one of the anion exchangers, was clarified by using a pressure-jump technique. This success promotes the application of the relaxation methods to ion exchange of the biochemical materials on the ion exchangers. The purpose of the present study is to clarify kinetically the ion-exchange mechanism of aspartic acid on the diethylaminoethyl group (DEAE) of Sephadex A-25(Cl) by using the pressure-jump technique.
0
I
I
1
2
added Asp, 10Zrnol dm3
Figure 2. Dependence of T-’ on the concentration of aspartic acid added into the suspension of Sephadex A-25(C1) at C, = 3 g dmT3and 25 O C .
Experimental Section The preparation of the Sephadex A-25(C1) used was described previo~sly.~The aspartic acid (Wako reagent grade; Wako Chemical Co.) was used without further purification. All measurements were performed at a particle concentration of C, = 3 g dm-3 a t 25 OC. The amount of aspartic acid adsorbed was determined indirectly from the concentration change in the supernatant solution by means of colorimetric analysis with ninhydrin at a wavelength of 570 nm.lo
Results and Discussion Kinetic measurements were carried out in an aqueous suspension of Sephadex A-25(C1) containing various amino acids such as aspartic acid and glutamic acids (acidic amino acid), glycine (neutral amino acid), and lysine (basic amino acid) by using the pressure-jump technique with conductivity and turbidity detections. In the suspensions of Sephadex A-25(C1) containing the acidic amino acids aspartic acid and glutamic acid, single relaxation was observed in the pH range of 3.0-3.2 as shown in Figure 1, where the direction of the relaxation signal indicates a decrease in conductivity of the suspension. However, no turbidity change was detected on the same time scale as the relaxation. Furthermore, no relaxation was observed in the supernatant solution of the suspensions, in the aqueous solutions of acidic amino acids, and the aqueous suspensions of Sephadex A-25(Cl) containing glycine and lysine. Also, in aqueous acidic amino acid suspensions of Sephadex G-25 in which the DEAE does not exist on the surface, no relaxation was observed. These facts indicate that the relaxation observed is due to the interaction between the acidic amino acids and the DEAE group on the surface of the Sephadex A25(C1). In the present p H condition (pH 3.0-3.2), it has been (2) Bendich, A.; Pahl, H. B.; Korngold, G. C.; Rosenkranz, H. S.; Fresco, J. R. J . Am. Chem. SOC.1958.80, 3949. ( 3 ) Peterson, E. A. In “Laboratory Techniques in Biochemistry and Molecular Biology”; Work, T. S., Work, E., Eds.; North-Holland Publishing Co.: Amsterdam, 1970. (4) Cannan, K. K. J . Biol. Chem. 1944, 152,401. (5) Consden, R.; Cordon, A. H.; Martin, A. J. P. Biochem. J . 1948, 42, 443. (6) Hirs, C. H. W.; Moore, S.; Stein, W. H. J . Am. Chem. SOC.1954, 76, 6063. (7) Wilcox, P. E.; Cohen, E.; Tan, W. J. Biol. Chem. 1957, 228, 999. (8) Boardman, N. K.; Partridge, S. M. Nature (London) 1953, 171, 208; Biochem. J . 1955, 59, 543. (9) Hachiya, K.; Sasaki, M.; Nabeshima, Y.; Mikami, N.; Yasunaga, T.
J . Phys. Chem., preceding article in this issue. (10) Yamagishi, M.; Yoshida, T. J . Pharm. SOC.Jpn. 1953, 73, 675.
added Asp,
l d Z m o l dm-3
Figure 3. Adsorption isotherm of the aspartic acid and the amount of CI- released as a function of the concentration of aspartic acid added into the suspension of Sephadex A-25(C1) at C, = 3 g dm-’ and 25 OC.
reported in part 1 that the slow relaxation of the order of seconds was observed in the Sephadex A-25(C1) and was attributed to the protonation-deprotonation of the DEAE group of the Sephadex A-25(C1).9 However, the slow relaxation could not be observed in the present system. In the present investigation, kinetic measurements were performed in the suspension of Sephadex A-25(Cl) containing only aspartic acid because an amplitude of the relaxation observed in the suspension of Sephadex A-25(Cl) containing glutamic acid was too small. The dependence of the reciprocal relaxation time, T - ~ ,on the concentration of aspartic acid is shown in Figure 2. As can be seen from this figure, 7-l increases with the concentration of aspartic acid. The adsorption isotherm of aspartic acid on the DEAE group of Sephadex A-25(Cl) is shown in Figure 3. The amount of C1released, [Cl-I,,, which is caused by the adsorption of aspartic acid, is also shown in this figure. As can be seen from this figure, the amount of aspartic acid adsorbed, [Asp],,, is larger than that of C1- released. This fact suggests that the adsorption of aspartic acid is not due to a simple ion-exchange reaction. It is also noted that the concentration of zwitterions of aspartic acid, Asp’, is 1 order of magnitude larger than the concentration of monovalent anions of aspartic acid, Asp-, unmder the present pH conditions (pH 3.0-3.2). In part 1? the following mechanism was proposed for the Sephadex A-25(Cl) suspension: S
‘ I SH+ ’ 7 SH+-CICI
H+ Kl
with
-
K2
(1)
The Journal of Physical Chemistry, Vol. 88, No. 8, 1984 1629
Ion-Exchange Mechanism of Aspartic Acid on DEAE
with [SH-Asp-] [Cl-]
K=
[SH+-Cl-] [Asp-]
(d) Adsorption-desorption of Asp' involving C1- release: where S and SH+ are the DEAE group and the protonated DEAE group, respectively, K is the equilibrium constant, the superscript "int" denotes intrinsic, e is the elementary charge, k is the Boltzmann constant, T i s the absolute temperature, and 9,, and 9,are the potentials created by the adsorbed H+ and C1-, respe~tively.~J' In bulk phase, the protonation-deprotonation reaction of aspartic acid also exists as
s
. c 'G' SH+
H+
CI-
Kl
S H + - A ~ ~ ?(VI)
SH+-CICI-
Asp'
K2
K
with
K=
[SH+-Cl-] [Asp*]
(e) Electrostatic binding of Asp- on the protonated DEAE group: S
with
SH+- CI-
As mentioned in part 1, the adsorption and desorption processes of H + and C1- are affected by 9,and \ka In the present system, the adsorption and desorption processes of Asp- may also be affected by \kP. In order to obtain these electrostatic potentials, the (potential was measured, and the results are shown in Figure 4. According to the theoretical treatment reported in part 1: the values of \k, and 9,were estimated by using those of 3; and the apparent acidity constant reported in part 1 and are also shown in Figure 4. As can be seen from this figure, the values of 9, increase with the concentration of aspartic acid, while those of 9,are approximately constant. This result indicates that K 1 decreases with the concentration of aspartic acid, but K2 and the rate constants of adsorption and desorption processes of Asp- and Asp* are constants. Taking into account the fact that the aspartic acid is adsorbed on some sites of the Sephadex A-25(Cl) described in mechanism I and the C1- releases from the Sephadex A-25(Cl), the possible mechanisms are expressed as follows. (a) Adsorption-desorption of Asp- on the DEAE group: SH+-CI-
SH+
.*
7 S . S-AspH+
CI-
Kz-l
(111)
with
(b) Adsorption-desorption of Asp' on the DEAE group: S
't S * A s p '
(Iv)
CI
H+
K2-l
Asp'
K1-'
K
with
K=
[S*Asp*]
[SI [ASP*] (c) Ion-exchange of Asp- for Cl-:
s
SH+
k t .
H+ Kl
y CI
-
K2
SH+-CI-
.&
S H + - A ~ ~ - (v) CI-
Asp-
K
(1 1) Davis, J. A,; James, R. 0.; Leckie, J. 0.J . Colloid Interface Sci. 1978, 63, 480.
SH+- ASP-
(VII)
AspK
with
(f) Adsorption-desorption of Asp* on the protonated DEAE group: S K I P
SH+-CI-
SH+
1-
-
.* H+
SH+-A~~'
CI
Asp+
Kz-'
K
(VIII)
with
K =
K
SH+
CI
.+
Kz-
Asp-
K1-I
SH+- CI-
TSH+
[SH+-Asp*]
[SH+I[ASP'] where k is the rate constant. As reported in part 1, two steps in mechanism I are slow under the present experimental conditions. Furthermore, the protonation-deprotonation reaction of aspartic acid in mechanism I1 should be very fast because usual protonation-deprotonation reactions in homogeneous systems are extremely fast. Taking into consideration these conditions, the equations of the reciprocal relaxation times for mechanism IIIVI11 are derived in the Appendix. For mechanism 111-V, the values of kb obtained were negative, which physically has no meaning. For mechanism VI, the value of the equilibrium constant obtained kinetically did not agree with that obtained statically. Therefore, these mechanisms were excluded. Both mechanisms VI1 and VIII, meanwhile, could interpret qualitatively the static and kinetic results obtained. As mentioned above, the concentration of Asp- is 1 order of magnitude smaller than that of Asp* under the present pH conditions. This fact suggests that mechanism VI11 may be reasonable rather than mechanism VII. At higher pH conditions (pH 2.9,where the concentration of Asp* can be neglected compared with that of Asp-, it is expected that the amplitude of relaxation for mechanism VI1 is larger but that for mechanism VI11 is negligibly small. In order to examine these mechanisms, the relaxation experiment was performed under the conditions of pH 5 . However, no relaxation was observed. This fact contradicts the prediction for mechanism VII.
1630 The Journal of Physical Chemistry, Vol, 88, No. 8, 1984 I
Sasaki et al. Taking into account the relatively strong adsorption of zwitterions of aspartic acid on the Sephadex A-25(Cl), the most reasonable adsorbed state of the zwitterions is presented as
I
Y
yH3+
(IX)
SH+--OOC-C-CH,COOH
I H
Further systematic investigation using the pressure-jump technique is an aqueous suspension of ion exchangers containing biochemical materials will lead to a quantitative clarification of the dynamic aspects of ion-exchange reactions on ion exchangers.
2
1
3
added A s p , I O 2 mol drn-3
Appendix Taking into account the \k8 potential, the equations of the reciprocal relaxation time can be given by the following equations.g8I2-l4 mechanism 111:
Figure 4. Dependence of q0( O ) , \E, ( O ) , and { potential ( 0 ) in the suspension of Sephadex A-25(CI) containing aspartic acid at Cp = 3 g dm-3 and 25 OC.
= -
,-II
kfintexp( 52 k) T ([S]F,
+ [Asp-]) + k P t exp (A-1)
with Fl
+ KAsp
=
+ iH+l + KAsp
mechanism IV: 7-l
= kf([S]F2 + [ASP*])
+ kb
(A-2)
with F 2
0
I
2
[SH*lF,+CAs
