Cation exchange equilibria of amino acids

Reactwe Polymers, 11 (1989) 261-277

261

Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

CATION EXCHANGE EQUILIBRIA OF AMINO ACIDS N.-H.L. WANG *, Q. YU and S.U. KIM

School of Chemical Engineering, Purdue University, West Lafayette, IN 47907 (U.S.A.) (Received November 17, 1988; accepted in revised form March 14, 1989)

Equilibrium ion exchange behavior of typical neutral, acidic, and basic amino acids has been examined In a p H range from 2 to 7, neutral and acidic amino acids undergo monovalent cation exchange. The amino acid in the form of a-NH3 + / a - C O O H has a high cation exchange affinity, whereas the a - N H J / a - C O 0 - form has a negligible affinity. At a p H near the p K a of a-COOH, both forms coexist," the average affinity changes significantly as p H approaches the p K , of a-COOH. Basic amino acids have two potential cation exchange sites, ot-NHJ and R(side chain)-NH3 +. The a-NH f / o~-COOH form binds at both sites, whereas the et-NH3 + / a - C O 0 - form binds only at the R - N H 3 +. As a result, the average valence of a basic amino acid can be a fractional number in the p H range from 2 to 7. As p H increases, the average valence decreases from 2 at low p H ( < pKa°) to unity at high p H ( > pKg,). At a given pH, the average valence and average separation factor of a basic amino acid against Na + can change with amino acid concentration, Na + concentration, total concentration, and exchanger capacity. A theory which accounts for the heterogeneous charge structures and multiple equilibria has been developed to explain the fundamental ion exchange behavior. The theory correctly predicts how pH, salt concentration, and composition affect the average valence and the average separation factor. The results on basic amino acids can explain why peptides and proteins exhibit fractional valences and their average affinities change with pH, salt concentration, and solution composition. Our results also indicate that an opposite charge within 5 from an ion exchange site of a biochemical can prevent its electrostatic interaction with an ion exchanger.

INTRODUCTION

Since most biochemicals such as amino acids, peptides, and proteins have unique charge distributions, ion exchange chromatography has been widely used in the analysis of complex mixtures of biochemicals. Ion * To whom correspondence should be directed. 0923-1137/89/$03.50

exchange is also a useful large-scale separation technique for the recovery of biochemicals because it requires nondenaturing processing conditions and is highly selective, energy efficient, and relatively inexpensive. Design and scale-up of such large-scale ion exchange processes require information on equilibrium parameters. Although numerous papers in the literature have reported the use

© 1989 Elsevier Science Publishers B.V.

262

of ion exchange for analytical or large-scale separations [1-4], there have been relatively few systematic studies of ion exchange equilibrium properties of amino acids [5]. Most literature studies focus on dilute systems in a narrow range of pH or salt concentration [6-10]. Some studies report retention times of amino acids under nonlinear or not well-defined pH or ionic strength gradients [11]. Other studies report amounts of adsorbed amino acids in the presence of two competing ions [12,13]. Such information is inadequate for design or scale-up of large-scale ion exchange processes. More important, there has been no quantitative theory which predicts how pH and salt concentration affect the equilibria of amino acids. Most biochemicals have complex and labile three-dimensional structures. The ion exchange behavior of biochemicals is much more complex than that of inorganic ions. Basic amino acids, peptides, and proteins usually have multiple charged groups, which are either weak acids or weak bases. Their charge distributions change with p H and are heterogeneous at a given pH. Moreover, because of steric hindrance, only a small fraction of the charged groups can bind cooperatively. Competition of the various bindings can lead to a complex dependence of the apparent affinity on concentration, pH, and salt concentration. For most proteins, neither the exact binding sites nor the number of binding sites are well understood; the number of binding sites of only a few systems have been analyzed recently [14-16]. For amino acids, there have been few studies confirming the ion exchange sites or the number of binding sites in a given system. The aims of this paper are (1) to identify ion exchange sites and understand the fundamental ion exchange behavior of amino acids, and (2) to develop a theory for correlating equilibrium data, which can be used for designing analytical or large-scale separation processes for amino acids.

Three neutral amino acids, two acidic amino acids, and three basic amino acids were studied in a pH range from 2 to 7. A strong-acid cation exchanger was chosen for this study because its charge density and capacity do not change with pH. A theory which accounts for the change of charge structures with pH and for heterogeneous binding was developed. The theory was in good agreement with our data from batch equilibrium experiments. It can also explain the pH dependence of retention times of amino acids reported in the literature. We found that ion exchange of basic amino acids involves multiple equilibria, which cannot be well described by a single mass-action law. The theory predicts well how the affinities and valences of amino acids are affected by pH, salt concentration, and surface coverage. These results also give valuable insight on ion exchange of peptides and proteins. THEORY

Structures of amino acids All amino acids have one a-amino group, one a-carboxyl group, and a side chain (R). According to their side-chain functional groups, amino acids have been classified into three types. Neutral amino acids, such as alanine, phenylalanine, and proline, have no charged group on the side chain. Acidic amino acids, aspartic acid and glutamic acid, have an acidic side chain at neutral pH. Basic amino acids, arginine, histidine, and lysine, have a basic side chain at neutral pH. The pK a values of the a and side-chain carboxyl groups are about 2 and 4, respectively. For the amino groups, the p K a values are about 9 or higher [17]. Within the p H range tested, the amino groups are always positively charged, whereas the degree of ionization of the carboxyl groups strongly depends on pH and is governed by the association-dissociation equilibria.

263

Ion exchange equilibria of neutral amino acids At a given pH, the a-carboxyl group can be either protonated or deprotonated. The negative charge of a - C O O - appears to prevent ion exchange of the adjacent a-NH~group with a cation exchanger (see Results and Discussion). As a result, the a-COOH form has a high affinity, whereas the a - C O O form has a low affinity. Since the relative concentrations of the two forms vary with pH, the apparent affinity also varies with pH. The average equilibrium constant (Kt) or the average separation factor against N a + ( a t ) can be expressed as a function of pH as derived in our previous paper [18]. at = Kt

K1 + KZ10(PH-pK"~) =

] + 10 (pH-pKa~)

(1)

where Kao is the dissociation equilibrium constant of the a-COOH group, and K 1 and K 2 a r e the ion exchange equilibrium constants for protonated and deprotonated amino acid, respectively. We chose to correlate equilibrium data in the form of separation factors because (1) separation factors are dimensionless and represent the relative affinities of various amino acids against a common ion, and (2) more importantly, the calculations of multicomponent column dynamics are relatively easy for systems with constant separation factors [19]. Strictly speaking, the assumption of constant separation factors is valid only for monovalent exchange or Langmuir adsorption. Nevertheless, we found in our previous work that in many applications the separation factors do not vary significantly in the concentration range of interest. As a result, the effluent histories calculated based on the assumption of constant separation factors closely agree with experimental results [18]. For these two

reasons, equilibrium data here are correlated in terms of separation factors. Equation (1) is based on the assumption that the different ionic forms can have different affinities for the exchanger. Although the net charge is zero for deprotonated neutral amino acids, we did not a s s u m e K 2 is negligible for the following two reasons. First, large ions such as proteins can undergo ion exchange at pI. This indicates that local charge instead of net charge controls the binding [14,15]. Secondly, if nonionic adsorption is significant, the best-fit values of K 2 will not be zero, because nonionic adsorption has a similar concentration dependence as monovalent exchange. For these reasons, we retained the K 2 term here and estimated the values of K 2 from equilibrium data.

Ion exchange equilibria of acidic amino acids Both the a- and the side-chain (R) carboxyl groups of an acidic amino can be protonated or deprotonated. Therefore, at a given pH there are four different ionic forms: aC O O H / R - C O O H , a - C O O - / R - C O O H , aC O O H / R - C O O - , and a - C O O - / R - C O O - . Assuming each ionic form has an intrinsic equilibrium constant and following a similar derivation as for neutral amino acids, one can express and average equilibrium constant, K t , or an average separation factor, at, as in eqn. (2) below, where K 1 is the intrinsic equilibrium constant of a - C O O H / R - C O O H , K 2 of a - C O O - / R - C O O H , K 3 of a - C O O H / R - C O O - , and K 4 of a - C O O - / R - C O O - . The values of PKao and PKaR for acidic amino acids are known from the literature: PKa~ = 2.09 and pKaR = 3.86 for aspartic acid; PKao = 2.19 and PKa, = 4.25 for glutamic acid [17]. Since the difference between PKao and pKaR is about 2, the fraction of a-

K 1 + K210(PH-pKa~ ) + K310(PH--pKaR ) + K410(2pH--pKaa--PK"R ) at=Kt

=

1 + 10(PH-pKaa ) + 10(PH--PK"R ) + 10(2pH--pK"--PK"R )

(2)

264 1.0

a-COOH R-C00H

a-COOR-COOH

0.8 Z ~

0.6 0.4 0.2 0. 1

2

3

4 pH

5

6

7

Fig. 1. The fractions of various charge structures of glutamic acid as a function of pH.

C O O H / R - C O O - is very small (Fig. 1). The m a x i m u m fraction of this form is less than I% for both aspartic and glutamic acids; therefore the contribution of the K 3 term is small and eqn. (2) can be reduced to:

stants: K a for the a - C O O H form and monovalent binding at the a-NH~-; K 2 for the a - C O O H form and monovalent binding at the side chain amino group; K 3 for the aC O O H form and divalent binding at both amino groups, K 4 for the a - C O O - form and monovalent binding at the a-NH~- group, K 5 for the a - C O O - form and monovalent binding at the R-NH~- group, and K 6 for the a - C O O - form and divalent binding at both amino groups. The apparent valence (or n u m b e r of binding sites) is an average value weighted by the concentrations of the different forms. After some algebraic manipulations, we get the final expression of z t given in eqn. (4) below. The distribution coefficient of N a +, kNa, is defined as follows: CNa+ CTYNa + kNa = CNa+ -- CTXNa-"""" ~

(5)

K 1 + K210(PH-pK.~ ) + K410(ZpH--pKa~--PK"R) at=

1 + 10 (pH-pKa~) + 10 (2pH-pK-'-pK"R)

(3) Again, we did not assume K 2 and K 4 are negligible from net charge considerations. Instead, we estimated best-fit values of K 2 and K 4 from equilibrium data in order to see whether the local charge of a-NH~- or nonionic adsorption affects the binding.

1on exchange equilibria of basic amino acids Basic amino acids also have two ionic forms: a - C O O H or a - C O O - . For each form, there can be three types of binding to a cation exchanger, binding at the a-NH~- group, binding at the R-NH~- group, or binding at both groups. Thus, we can define a total of six intrinsic ion exchange equilibrium con-

where (~T is the total molar concentration of bound species, C T is the total molar concentration in solution, yNa + is the mole fraction of N a + in the resin phase, and XNa÷ is the mole fraction of Na + in the solution phase. The apparent separation factor is also a function of both p H and kNa. The final form is shown in eqn. (6). In deriving eqns. (4) and (6), we assume that the basic amino acids in the form of a - C O O - / R - N H 2 have negligible affinity for the cation exchanger. This assumption is justified because our results (see Table 2) show that the form with a - C O O - / R - N H ~ only binds at the R-NH~- with a low affinity and its a-NH~- does not bind. Therefore the form with a - C O O - / R - N H 2 is expected to have negligible affinity. At a salt concentra-

K 1 + K z + 2K3kNa + 10(PH-pK..)(K 4 + K 5 + 2K6kNa) Zt=

K1+

K 2+

K3kNa

+ 10(PH-pK..)(K 4 +

K 1 + K 2 + K3kNa + I0(PH--pKa.)(K4 + K 5 + K6kNa ) at~

] + ]0(PH--pKa. )

(4)

K 5 + K6kNa ) (6)

265 tion much higher than 0.2 N, hydrophobic adsorption in addition to ion exchange can be important. Under such conditions, eqns. (4) and (6) must be modified to include nonionic adsorption.

EXPERIMENTAL

Materials The ion exchanger used is AG50W-X8, a strong-acid cation exchange resin (gel type) from Bio-Rad Laboratories (Richmond, CA 94804). Its charge density and capacity do not change with pH. The resin has a particle size distribution from 200 to 400 mesh and a capacity of 5.1 m e q / ( g dry H÷-form) or 1.7 meq./(ml packed volume). It was received in H ÷ form and converted into Na ÷ form with 1 N NaOH. All of the amino acids were purchased from Chemical Dynamics Corporation (South Plainfield, NJ 07080) and used as received. The buffer solution was sodium citrate. Solutions of 1 N HC1 were used to adjust the buffer pH. The total ionic concentration was kept at 0.2 N.

Methods of assay The Na + concentration was determined by atomic absorption spectrophotometry (Perkin Elmer 2380) and the pH values were measured with an Orion pH meter. Primary amino acids were analyzed with an HPLC precolumn derivatization technique reported in the literature [20]. Amino acids were first derivatized with o-phthalaldehyde at pH 10 and room temperature for one minute to yield strongly fluorescent isoindoles, which were then detected with a fluorescence detector (excitation at 360 nm and emission at 455 nm). The derivatization was carried out automatically with an autosampler (Varian

9090LC) and a Krato's HPLC system was used in this analysis. Secondary amino acids, such as proline, cannot be analyzed by the aforementioned HPLC technique. In this study, proline and some primary amino acids were analyzed with a ninhydrin derivatization technique [21]. Amino acids were derivatized with ninhydrin at pH 5 and 100°C for one hour to yield Ruhmann's purples, which were then analyzed with a UV-Vis spectrophotometer (Perkin Elmer Lambda 3A) at 570 nm for primary amino acids and 440 nm for proline. Phenylalanine was analyzed directly with UV spectrophotometry at 254 nm. Detailed assay procedures for sodium ions and amino acids have been reported elsewhere [22].

Batch equilibrium experiments The pre-treated resin in Na + form was rinsed with deionized water and filtered-dry in a Buchner funnel. Resin samples of 1.6 g, which contained about 1 g dry resin, were weighed into separate vials. Two or three of the resin samples were dried in a vacuum oven at 100°C for 24 hours in order to determine an average moisture content. A 10 ml sodium citrate buffer solution was added to each of the other vials. The total concentration of the solution was kept constant at 0.2 N, whereas pH and the amount of amino acid in the solution were varied. After static equilibration and intermittent shaking for 24 hours, the equilibrium pH values, Na ÷ concentrations, and amino acid concentrations of the solution phases were determined. The amino acid and sodium concentrations of the resin phases were then calculated from the total resin capacities and the initial and final pH values and concentrations of the solution phases. Separation factors of amino acids against Na + were calculated from the concentrations of amino acids and Na + in the two phases.

266

Regression analysis The best fit values of the intrinsic equilibrium constants of eqns. (1), (3) and (6) were obtained from regression analysis of the apparent separation factors at various pH and k~qa. The regression routine used was based on Powell's Conjugate Direction Method [23,24]. The objective function to be minimized was the sum of squares of relative errors, which are the fractional differences between experimentally determined separation factors and the best-fit separation factors. The optimization was carried out until a preset error criterion was satisfied.

RESULTS AND DISCUSSION

Equilibria of neutral amino acids For neutral amino acids, the a-amino group is the only positively charged site that can undergo cation exchange. The valence therefore should be unity if nonionic adsorption is insignificant. This is verified by the results shown in Fig. 2. In this figure, the fraction of

0.6

~2~

0.5

~'~

0.4

O

ALANINE

o

PHENYLALANINE r~o~B

o

j

amino acid bound, ACA/qM , is plotted against the fraction of Na + displaced, -ACNa+/q M. The amount of amino acid bound was determined from the H P L C analysis or ninhydrin analysis. The amount of Na + ions displaced was determined independently by atomic absorption spectrophotometry. The diagonal line in this figure corresponds to monovalent exchange. As shown in this figure, all three neutral amino acids undergo monovalent ion exchange and nonionic adsorption is insignificant under the experimental conditions. Although the data were obtained at different pH values, the valences were found to be independent of pH. As expected, if ion exchange is the only mechanism of uptake, pH affects only the average affinity but not the valence of a neutral amino acid. The average separation factors of three neutral amino acids against Na + were analyzed with the theory developed. Figure 3 shows the average separation factor of alanine against Na + as a function of pH. Similar results for phenylalanine and proline were reported previously [18]. The solid line in Fig. 3 is the best-fit curve obtained from regression according to eqn. (1). The two best-fit values of intrinsic equilibrium c o n s t a n t s g 1 and K 2 are listed in Table 1. The values of

~

2.0

THEORY

o 0

0.3

o

EXPERIMENT

1.5

z ~

0.2

Z o

1.0

0.1 0,00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.5

SODIUM Fig. 2. The fraction of neutral amino acid adsorbed, ACA_/qM, versus the fraction of Na + displaced, - ACNa+/qM, for alanine (O), phenylalanine (rn), and proline (~). The diagonal line corresponds to monovalent exchange.

0.0

~

2

3

4

-"~

5

3

i

6

pH Fig. 3. The separation factor of alanine against Na + as a function of pH.

267 TABLE 1

0.20

/

Ala K1

Kz K 4

pKa, PKa, (fitted) pKaR pKaR (fitted) N a S.D. b

Phe

1.86 0.00 2.34 c

1.83 2.11

1.62 0.02 1.99 c

11 0.13

26 0.27

21 0.36

--

8.06 0.10

Pro

-

Asp

ASPABTIC ACID

0

Best-fit K~ values for neutral and acidic amino acids

/

-

Glu

1.97 0.04 0.03 2.09 2.15 3.86 4.30

1.77 0.04 0.00 2.19 2.40 4.25 4.86

18 0.28

18 0.22

a N: no. of data points in the regression analysis. b S.O,: standard deviation; S.D. - { o [ ( a - ath]2/(N1)} 1/2 (ath: best-fit value of a). c Insufficient data for fitting p K a ,

K 2 are all smaller than the standard deviations. This clearly shows that when an acarboxyl group is negatively charged, the adjacent a-amino group does not undergo cation exchange. The average distance between two - S O 3- ~roups in the resin is estimated to be about 6A, which is greater than the distance between a - C O O - and a - N H f (less than 5A). Apparently, the a - C O O - prevents the electrostatic interaction between a-NH~- and - S O 3 in the resin. Moreover, the small K z values also support the conclusion from Fig. 2 that nonionic adsorption is relatively insignificant under the experimental conditions.

0.I0

0.05

00 0.0

0.i0

0,05

0.20

0.15

SODIUM Fig. 4. The fraction of acidic amino acid adsorbed, ACA/qM, versus the fraction of Na + displaced, - ACNa+/qM, for aspartic acid ( O ) and glutamic acid

(D). or a - C O O - / R - C O O H does not bind to the exchanger through cation or nonionic adsorption. Therefore the apparent separation factors of acidic amino acids have a pH dependence similar to that of neutral amino acids. Although aspartic acid has a slightly higher K 1 value than glutamic acid, it has a lower PKao. In the pH range from 2 to 3.8, glutamic acid has a slightly higher apparent affinity than aspartic acid. This result is in agreement with that of Moore et al. [6], who reported that at pH 3.25 glutamic acid has a higher affinity than aspartic acid. 2,0

Equilibria of acidic amino acids O

An acidic amino acid has only one cation exchange site. The results in Fig. 4 indicate that aspartic acid and glutamic acid undergo monovalent cation exchange. The average separation factors of acidic amino acids against Na + ions are plotted against p H in Fig. 5. The solid line and the dashed line represent the best-fit curves according to eqn. (3). The best-fit values of K1, K 2 and K 4 a r e listed in Table 1. The values of K 2 and K 4 are negligible. This indicates that an acidic amino acid in the form of a - C O O - / R - C O O -

-

~

1.5

Z

1.0

0,5

- -

0

ASPARTIC ACID

.....

D

GLUTAMIC ACID

o',

f~ 0.0

- ~

2

3

4

r,

5

6

7

pH Fig. 5. The separation factors of acidic amino acids against N a + for aspartic acid ( © ) and glutamic acid

(D).

268

The results on cation exchange of neutral and acidic amino acid suggest that a-NH~should prevent anion exchange of a-COO-. Therefore neutral and basic amino acids should have very low affinities for anion exchangers in the p H range from 2 to 7. Acidic amino acids, on the other hand, can bind at the R - C O O - and they should have high affinities at pH >/PKaR. The results of Katz and Burtis confirmed this speculation [11]. At pH 4.4 acidic amino acids were found to have orders of magnitude higher affinities than basic and neutral amino acids.

The equilibrium pH within a charged gel phase can be quite different from the bulk solution p H [25,26]. This pH difference is especially pronounced at a low ionic strength. For a cation exchanger, because the H + ion concentration near a negatively charged surface is much higher than that in the bulk, the local p H is expected to be much lower than the bulk pH. In order to test this effect, the data for neutral amino acids were regressed according to eqn. (1) for best-fit values of PKa, , K 1 and K 2. The data for acidic amino acids were also regressed according to

0,

m

ACA

o. 6

qM O-

0.~

,<. '2.,.

o

q

q

-ACNa + ':t°

qM

.,aqo

Fig. 6. The fraction of basic amino acids adsorbed, ACA/qM, versus pH and the fraction of Na + displaced, - ACNa+/q M, at 0.2 N for arginine. The data ( * ) are projected onto the plane of ACA/qM versus -- ACNa+/q M.

269

eqn. (3) for best-fit values of pKao, pKa,, K a, and K 4. The best-fit K~ values were close to the values estimated when literature pK a values were used in the regression. The best-fit values of pKa, and pKaR are shown in Table 1. They are slightly higher than, but not significantly different from, the pK~ values in bulk solution. This evidence suggests that at a total concentration of 0.2 N, bulk pH and pK a values can be used in eqns. (1) and (3) for data correlation. Whether the local pH near a bound amino acid is similar to the bulk pH remains to be studied.

K 2

Equilibria of basic amino acids A basic amino acid has two amino groups that can undergo cation exchange. I_n Fig. 6, the fraction of arginine bound, ACA/qM , is plotted against_pH and the fraction of Na + displaced, --ACNa+/qM. The data are projected onto the plane of ACA/q M versus -ACNa+/q M. The projections show that the average valence approaches 2 for data at a low pH and approaches unity for data at a high pH. Similar results were obtained for lysine and histidine. These results indicate that when the a-carboxyl groups are protonated, both amino groups undergo cation exchange, whereas the a-carboxyl groups are deprotonated, only the side-chain amino groups undergo cation exchange. This conclusion is further supported by comparing the experimental z values with the z values which were calculated from the regression of apparent separation factors according to eqn. (6). The best-fit Ki values are reported in Table 2. The only significant terms a r e K 3 and K 4 + K 5. Since K 1 and K 2 are insignificant, K 4 must also be negligible. Therefore, the only two significant terms are K 3 for divalent binding at both amino groups of the a-COOH form, and K 5 for monovalent binding at R-NH~- of the a - C O O - form. Apparently, a - C O O - does not interfere with binding at the R-NH~- group. The equations

of z t and a t therefore can be simplified to the following: 2K3kNa + 10(PH-pKao)K5 Zt = +

10(PH-pK°°)K5

K3kNa +

10(PH-pK.o)K5

g3kNa

=

(7)

(8)

1 + 10 (pH-pK"-)

According to eqn. (7), the average valence of a basic amino acid is a function of both pH and kNa. In Fig. 7, the experimentally determined z t values for lysine are compared with the predicted values of z t, which were calculated from the best-fit K i values and literature values of Kao. In this figure, the deviations are shown by bars which connect the data and the predicted values at the same pH and kNa. As shown in the figure, the data for lysine are in good agreement with the theoretical predictions. Similar results were also obtained for histidine and arginine. The valence in eqn. (7) is a weighted average of divalent binding and monovalent binding. The weighting factors include k N a , K 3 , K 5, and 10 (pH-pKa-), which is the concentration of the deprotonated form relative to that of the protonated form. At a low pH, because the a-COOH form dominates, basic amino acids undergo divalent exchange and z t approaches 2. At a high pH, because the aC O O - form dominates, basic amino acids undergo monovalent ion exchange at the R-NH~- and z t approaches unity. The results shown in Fig. 7 are therefore consistent with

TABLE 2 Best-fit K i values for basic a m i n o acids Lys K1+ K 2 Ks (K4) + K 5 K6 N S.D.

His

Arg

0.00 9.19 0.66 0.00

0.00 7.12 1.69 0.00

0.00 41.21 2.93 0.00

46 0.18

22 0.34

33 0.23

270

O

1

%.,

Z O

%,°

,7,.

..x

Fig. 7. The average valence of basic amino acids z t versus p H and kNa for lysine. The theoretical predictions according to eqn. (7) and the K i values in Table 2 are shown as solid curves. The deviations between data ( * ) and predicted values are shown as bars.

those in Fig. 6. In Fig. 7 the smooth transition from divalent binding at a low pH to monovalent binding at a high pH is shown by the S-shaped curves at a given kN~. The inflection point for a given curve corresponds to z t = 1.5. If shifts toward a higher pH as the weighting factor for divalent binding, K3kNa , becomes larger. At pH = pK~o, z t = (2K3kr~ ~ + gs)//(K3kNa + Ks). Therefore, the inflection point coincides with pK~. only if k N a = K s / K 3. According to eqn. (8), the apparent separation factor of a basic amino acid against

Na ÷ is also a function of both pH and kNa. In Fig. 8, the separation factors of lysine determined experimentally are compared with the theoretical values calculated according to eqn. (8) from the best-fit K~s and literature values of Kao. The deviations between data and theoretical predictions are shown by bars and appear to be small. Similar results were also obtained for histidine and arginine. The apparent separation factor of a basic amino acid against Na ÷ is a weighted average of the two equilibrium constants, K 3 and K 5. The weighting factors include the relative

271

concentration 10 (pH-pKaa) a n d kNa for divalent binding. A high value of C.r/C. r or a low amino acid concentration results in a high a t because kNa is high. At a given kNa, a t decreases with increasing p H as the fraction with a - C O O - increases. The smooth transition from a high a t to a low a t is shown by the S-shaped curves in Fig. 8. The inflection point corresponds to a t = (K3kNa + K5)/2 and coincides with P K a . The K 1 values of monovalent binding at a - N H ; for neutral and acidic amino acids (Table 1) are similar in magnitude as the K 5 values for monovalent binding of basic amino acids at the side chain. The K 3 values for divalent binding of basic amino acids are

about an order of magnitude higher than those for monovalent binding. The average separation factor of a basic amino acid at a low p H can be two orders of magnitude higher than Ks, because the weighting factor for K 3 can be greater than 10 (Fig. 8). The competition of divalent binding against monovalent binding of lysine as a function of dimensionless lysine concentration x A is shown in Fig. 9. The best fit values of g i for lysine (Table 2) were used to calculate (1) 01, the fraction of sites occupied by monovalent binding, (2) 02 , that occupied by divalent binding, and (3) 0-r, that occupied by lysine ( 0 T = 01 "[- 0 2 ) . The N a + concentration is 0.15 M.

o°

q,.

._x

Fig. 8. The average separation factors of basic amino acids a t versus pH and kNa for lysine. The theoretical predictions according to eqn. (8) and the K i values in Table 2 are shown as solid curves. The deviations between data (*) and predicted values are shown as bars.

272

At a low pH, the fraction of lysine with a-COOH is high; lysine is mostly bound at both amino groups and the affinity of this divalent binding is high (see the K 3 values in Table 2). Therefore, O T is high and 02 dominates (Fig. 9a). As the pH increases, the fraction with a-COO- increases. Lysine with a-COO- binds only at the side-chain amino group and the affinity of this monovalent binding is low (see the K 5 values in Table 2). Therefore, both 0 T and 82 decrease with increasing pH. Eventually, at pH >1 5.0 (Fig. 9d), 91 (monovalent binding) dominates and 0 T is low. As shown in Fig. 9, 8 2 at pH 4.5 is slightly higher than 01 at a low lysine concentration

1.0

(x A < 0.28), but 02 becomes lower than 01 at a higher lysine concentration. This is because the partition coefficient for divalent binding is proportional to k2a whereas that for monovalent binding is proportional to kN,. As the lysine concentration increases, kN, decreases. This decrease in kN, affects the divalent binding more than the monovalent binding. For this reason, both the average valence and the average separation factor of lysine decrease with increasing lysine concentrations (Figs. 10 and 11). According to eqn. (7), the average valence of a basic amino acid should decrease with increasing Na ÷ concentration, because the weighting factor for divalent binding K3kNa

1.0

(a) pH 3.0

(b) pH 4.0

er 0.8

0.8

f

0.6

0.4

0.2

~

0.0

0.0

0.1

9T

0.6

92

0.4

0.2

I 0.2

I 0.3

I 0.4

I 0.5

0.0

0.0

0.6

0.1

0.2

0.3

0.4

0.5

0.6

X~

X~ 1.0

1.0 (d) p n

(¢) pH 4.5 0.8

0.8

0.6

0.6

~i.0

0.4

0.4

Ox

gt 0.2

0.2

@s

92 0.0 0.0

0.1

0.2

0.3

x,

0.4

0.5

0.6

0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

x~

Fig. 9. Fractions of resin sites occupied by lysine in different binding forms as a function of lysine concentration in solution at pH 3.0 (a), 4.0 (b), 4.5 (c), and 5.0 (d). The concentration of Na ÷ is 0.15 M.

273 2.0

2.0

~. . . . . . . . . 0. . . . . . . . .

= 2.0

pH

Z

Z

3.0

1.5

1.5

4.0

4.5 5.0

1,0 0.0

I

I 0.i

I

0.2

I

1.O

0.4

0.3

0.5

0

1

2

3

4

5

CN.. (M)

C, (M) Fig. 10. Average valence of lysine as a function of lysine concentration at pH = 2.0, 3.0, 4.0, 4.5, and 5. The concentration of Na ÷ is 0.15 M. At a given pH, the average valence decreases with increasing lysine concentration.

Fig. 12. Average valence of lysine as a function of sodium ion concentration at pH = 2.0, 3.0, 4.0 and 5.0. At a given pH, the average valence decreases with increasing sodium ion concentration. - - : CA=1 mM; . . . . . . : CA = 5 0 m M .

decreases as kNa decreases. Figure 12 shows the average valence of lysine as a function of N a + concentration. The lysine c o n c e n t r a t i o n is 1 m M (solid lines) a n d 50 m M (dashed lines), respectively. The average valence of lysine is calculated f r o m the best-fit values of g 3 a n d K s (Table 2) according to eqn. (7). At a given p H a n d Cya+, the average valence of

lysine at I m M lysine c o n c e n t r a t i o n is slightly higher t h a n that at 50 m M lysine concentration, because divalent b i n d i n g is more competitive t h a n m o n o v a l e n t b i n d i n g at a lower lysine concentration.

20

o

i0

<

pH

-- 2.0

3.0 4.0

0 0.0

I 0.1

~,0 I 0.2

] 0.3

I 0.4

0.5

C, (M) Fig. 11. Average separation factor of lysine as a function of lysine concentration at pH = 2.0, 3.0, 4.0,and 5.0. The concentration of Na + is 0.15 M. At a given pH, the average separation factor decreases with increasing lysine concentration.

Analysis of literature data A c c o r d i n g to the K, values reported in Table 2, lysine should have a higher affinity t h a n histidine at a low pH, b u t a lower affinity at a high pH. M o o r e et al. reported that the elution sequence at p H 5.28 is lysine, histidine, a n d arginine [6]. At this p H , a t approaches K 5. F r o m the K 5 values in Table 2, the affinity sequence agrees with that rep o r t e d by M o o r e et al. The theory developed is also applied to literature d a t a of dilute systems for analytical applications [10]. C a p a c i t y factors of various a m i n o acids on a silica-based ion exchanger in s o d i u m citrate buffer were reported as a function of eluent pH. The silica-based cation exchanger has a p p r o x i m a t e l y 50% of the capacity of the organic resin used in this study. The capacity factor k ' is defined as t R = to(1 + k ' ) , where t R is the retention time

274

and t o is the retention time of an inert species [27]. The separation factor of an amino acid against Na ÷ ions is the ratio of the capacity factor of the amino acid to that of Na ÷. The capacity factor therefore should have the same pH dependence as the separation factor. In Fig. 13, the reported capacity factors are compared with the best-fit curves according to eqns. (1), (3), and (8). The pH dependence of the capacity factors appear to be well described by these equations.

lrnpfications on ion exchange of peptides and proteins Peptides and proteins usually have numerous weak-acid and weak-base groups distributed on their surfaces. The interactions between positive and negative charges significantly affect the tertiary and quaternary structures of proteins, enzymatic activities, thermal stabilities, and denaturation owing to acidic or basic conditions [28,29]. For a given tertiary structure, the charge distributions at a given pH can be heterogeneous. As shown in the case of acidic amino acids, ionization of the two weak acid groups results in four

~o~,~"i~u , ~

4

Arg

2 His Lys

1

Phe

2

3

4

5

different charge structures; the fractions of the four different forms change with pH. The different charge structures have different affinities and multiple equilibria of independent bindings can result. Therefore the average affinity of a protein can have a complex dependence on pH. Furthermore, proteins with numerous charged groups of the same sign can bind cooperatively. As shown in the case of basic amino acids, which have two potential cation exchange sites, the combination of independent bindings and cooperative bindings can result in a complex average affinity and a fractional valence, which can vary with ion exchanger capacity, total ionic concentration, composition, salt concentration, and pH. Other researchers have reported that many proteins appear to have fractional valences ranging between 1 and 5 for common ion exchange systems [14-16]. The apparent affinity of cytochrome C for a cation exchanger was reported to decrease with increasing Na ÷ concentration [30]. These findings are consistent with our results for basic amino acids. Other features of proteins and weak exchangers can further complicate their ion exchange behavior: adsorbed protein molecules appear to block many unused sites and prevent other molecules from undergoing ion exchange [16]; the protein tertiary structures themselves can change with p H and salt concentration; the conformation of adsorbed proteins can change slowly with time [31]; for exchangers that have weak-acid or weak-base functional groups, surface charge densities and capacities can change with pH. All these factors can contribute to an even more complex ion exchange behavior of peptides and proteins.

6

pH OF ELUENT Fig. 13. The capacity factors of amino acids on a silica-based cation exchanger as a function of eluent pH. Data were taken from Engelhardt [I0]. Solid lines are best-fit curves according to eqns. (1), (3), and (8).

CONCLUSIONS We have developed a theory which can explain the cation exchange equilibria of neu-

275 tral, acidic, and basic amino acids. The theory correlates well the equilibrium data of alanine, phenylalanine, proline, aspartic acid, glutamic acid, lysine, histidine, and arginine at various pH values and amino acid concentrations. In addition, this theory also explains the pH dependence of retention times of amino acids reported in the literature. The charge structures of amino acids are heterogeneous at a given pH; a fraction exists as a-COOH and the rest as a-COO-. The a-COOH form has a high affinity for cation exchangers whereas the a-COO- form has a negligible affinity. Because the concentrations of these two forms vary with pH, the average affinity of an amino acid is a strong function of pH. The results suggest that a-COO- prevents a-NH~- from undergoing cation exchange and a-NH~- prevents a-COO- from undergoing anion exchange. It appears that an opposite charge within 5 ~, from the binding group can prevent ion exchange. At a total concentration of 0.2 N, neutral and acidic amino acids undergo monovalent ion exchange at a pH < 7. Basic amino acids in the a-COO- form undergo monovalent ion exchange with the side-chain amino group and those in the a-COOH form undergo divalent ion exchange. As a result, the average

valence of a basic amino acid decreases from 2 at a low pH to unity at a high pH. At a given pH, the average valence decreases with increasing Na ÷ concentration or amino acid concentration. Ion exchange equilibria of basic amino acids are characterized by heterogeneous charge structures and multiple equilibria. In general, the overall equilibria of basic amino acids cannot be well described by a single mass-action law. Peptides and proteins have even more complex three-dimensional structures and charge distributions, which can vary with pH and salt concentrations. The results on basic amino acids explain why the affinities and valences of peptides and proteins are expected to change with pH, salt concentration, and solution composition.

ACKNOWLEDGEMENT This research is supported by a fellowship for S.U. Kim from Korea Explosives Company and NSF grants CBT-8412013, CBT8604906, CBT-8620221, and ECE 8613167. The assistance of J. Koepke, S. Dodd, and D. Lee in collecting the equilibrium data is also acknowledged.

LIST OF SYMBOLS CT

CA C+

CNa+ CNa+

K1 K2

total molar concentration of ions in solution molar concentration of amino acid in solution molar concentration of amino acid bound to the resin phase (on the basis of per unit volume of packed resin) total molar concentration of bound species (on the basis of per unit volume of packed resin) molar concentration of sodium ion in solution molar concentration of sodium ion in the resin phase (on the basis of per unit volume of packed resin) intrinsic mass action equilibrium constant for protonated amino acids bound at the a-NH~-, eqns. (1), (3) and (6). intrinsic equilibrium constant for deprotonated neutral and acidic amino acid bound at the a-NH~-, eqns. (1), (3), or for protonated basic amino acid bound at the side chain NH~-, eqn. (6).

276

intrinsic equilibrium constant for a - C O O H / R - C O O - form of an acidic amino acid, eqn. (2), or for a-COOH form of a basic amino acid bound at both amino groups, eqn. (6). intrinsic equilibrium constant for a - C O O - / R - C O O - form of an acidic amino acid, eqn. (3), or for a - C O O - form of a basic amino acid bound at the a-NH~-, eqn. (5). intrinsic equihbrium constant of a - C O O - form of a basic amino acid bound at the K5 R-NH~-, eqn. (6). intrinsic equilibrium constant of a - C O O - form of a basic amino acid bound at both K6 amino groups, eqn. (6). average equilibrium constant, eqns. (1) and (2). g t distribution coefficient of Na +, eqn. (5) kNa capacity factor of a species, t R = t0(1 + k ' ) k' dissociation constant of the a-carboxyl group of amino acid ga. dissociation constant of the side chain carboxyl group of an acidic amino acid gaa p K . characteristic constant, - log K a number of data points in regression analysis N total resin capacity, equivalents per unit packed volume qM S.D. standard deviation retention time of a nonadsorbing species to retention time of species i tR XNa + mole fraction of Na + in solution mole fraction of amino acid in solution XA YNa + mole fraction of Na + bound in resin phase Z valence (number of binding sites) average valence of an amino acid Zt K3

Greek letters a a t

61

0T

separation factor of an amino acid against Na + average separation factor against Na+; eqn. (1) for neutral amino acid; eqn. (3) for acidic amino acid; eqn. (6) for basic amino acid fraction of sites occupied by basic amino acid bound at the side chain amino group fraction of sites occupied by basic amino acid bound at both amino groups. total fraction of sites occupied by basic amino acid, 01- = 01 + 02

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