Amino Acids Separations by Displacement Chromatography. Effects of

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Ind. Eng. Chem. Res. 2000, 39, 2468-2479

Amino Acids Separations by Displacement Chromatography. Effects of Homogeneous and Heterogeneous Equilibria on Separation Performances Amel Zammouri,* Laurence Muhr,†,‡ and Georges Grevillot†,§ Laboratoire des Sciences du Ge´ nie Chimique, CNRS, 1 rue Grandville, 54001 Nancy, France

In this paper we investigate displacement chromatography of amino acids on columns of strong anionic resins in the hydroxyl form. The displacer used here is carbon dioxide dissolved in water, but the theory is also valid to other types of displacers. A theoretical study of the effect of both dissociation equilibria in solution and ion-exchange equilibria is presented. It is shown that the separation quality depends not only on the selectivity coefficient but also on a term relative to homogeneous equilibria in the liquid phase. This factor is related to the ratio of the second amino acid deprotonation constants. Introduction Amino acids are of great importance in the food and pharmaceutical industries. Present separation processes of amino acids mixtures are based on their amphoteric nature and use ion-exchange resins. Several steps are needed, using anion- and cation-exchange resins combined with salts and acidic and basic buffers in order to fix the pH and ionic strength during sorption and elution. Solutions to reduce the amount of chemicals have been sought.1,2,4 We have shown in a recent paper5 that separations can be performed by a new type of displacement chromatography which takes advantage of reactions in solution, with carbon dioxide being the displacer. This method was proved experimentally and supported by simulations of a column model. In particular, it was shown that homogeneous and heterogeneous equilibria take place and both solution and ionexchange equilibria contribute to the separation feasibility. However, a general theoretical approach able to handle various cases depending on the nature of amino acids and the resin types was not developed yet. Thus, the objectives of this paper are to make an inventory of possible situations, to perform simulations in order to describe each behavior, to identify when a separation can be expected or not, and finally to bring out general rules in order to allow a better understanding of the contribution of the homogeneous and heterogeneous equilibria to the separation quality. All results are based on simulations through an equilibria model characterizing ion-exchange fixed beds. Three systems were chosen to carry out this study: phenylalanine-glycine, histidine-lysine, and phenylalanine-histidine. This choice is based on the fact that this set is representative of the behaviors of equimolar amino acid mixtures whose ionizations are (1) different, (2) very different, and (3) of the same order. * To whom correspondence should be addressed. Present address: ENIG, route de Medenine 6029, Gabe`s, Tunisia. E-mail: [email protected]. Telephone: (05) 282 100. Fax: (05) 275 190. † Telephone: (03) 83175231. Fax: (03) 83322975. ‡ E-mail: [email protected]. § E-mail: [email protected].

For each system, different values of the selectivity coefficient were attributed to amino acids in order to scan all of the possible cases. Dissociation Equilibria in Solution. Carbon dioxide dissolved in water gives rise to the following reactions: K1

CO2 + H2O 798 HCO3- + H+, pK1 ) 6.36 K2

HCO3- 798 CO32- + H+, pK2 ) 10.37

(1) (2)

In addition to carbonic acid dissociation in solution, the neutral amino acids Phe and Gly and the basic amino acids His and Lys dissociate to give the following products:

Phe+ T Phe( + H+, pK1Phe ) 1.83

(3)

Phe( T Phe- + H+, pK2Phe ) 9.13

(4)

Gly+ T Gly( + H+, pK1Gly ) 2.34

(5)

Gly( T Gly- + H+, pK2Gly ) 9.60

(6)

His2+ T His+ + H+, pK1His ) 1.82

(7)

His+ T His( + H+, pK2His ) 6.00

(8)

His( T His- + H+, pK3His ) 9.17

(9)

Lys2+ T Lys+ + H+, pK1Lys ) 2.18

(10)

Lys+ T Lys( + H+, pK2Lys ) 8.95

(11)

Lys( T Lys- + H+, pK3Lys ) 10.53

(12)

The total concentration of a neutral amino acid is given by

CAn ) CAn( + CAn+ + CAn-

10.1021/ie990810n CCC: $19.00 © 2000 American Chemical Society Published on Web 05/20/2000

(13)

Ind. Eng. Chem. Res., Vol. 39, No. 7, 2000 2469

The total concentration of a basic amino acid is given by

CAb ) CAb2+ + CAb( + CAb+ + CAb-

(14)

The negatively charged species concentrations are obtained as functions of their total concentrations and H+ concentration by rearranging eqs 1-12:

CAn- )

CAn

CAb CH+ CH+2 CH+3 1+ + + K3b K2bK3b K1bK2bK3b

1+

CH2CO3 C H+ CH+2 1+ + K2H2CO3 K1H2CO3K2H2CO3

-

i

+ COH- + CHCO3- + 2CCO32- )

∑i CA

+

i

+ CH+ (17)

Once CH+ is determined, ionic fractions in solution are calculated by

Xi )

Ci-

∑k Ck

-

(18)

+ COH-

Ion-Exchange Equilibria. The binary exchange of neutral or basic amino acid with an anionic resin in the hydroxyl form can be written as

R-OH + A- T R-A + OH-

(19)

This equilibrium can be described by the selectivity coefficient:

SA-,OH- )

SHCO3-,OH-

Vs (L)

0.01

0.01

0.1

2

0.5

Table 2. Characteristics of the Column Used for Simulations packed bed length (m) column diameter (m) bed porosity bed ion exchange capacity (mequiv)

SA,B )

qA/CA qA-/CB ) qB/CB qB-/CA

(22)

YA-XOHYOH-XA-

Z ) z/L

T ) tu/L

The mass balance for an amino acid Ai may be written as

(20)

2 1 - ∂qAi- ∂CAi 1 ∂ CAi + + )0 ∂T ∂T ∂Z Pe ∂Z2

∂CAi

(24)

The mass balance for carbonic acid is

YA- ) qA-/Q The selectivity coefficient of an amino acid A relative to an amino acid B is given by

qA-CB- YA-XB) qB-CA- YB-XA-

(23)

The selectivity coefficient expresses the mass action law and thus defines the real affinity of the resin with respect to anions A- and B-. By analogy, the global separation factor will define an apparent affinity of the resin for the species A and B. This factor is the product of a term relative to heterogeneous equilibria and of a term depending only on homogeneous equilibria. (i) Mathematical Modeling of the Column. The dynamic behavior of the fixed bed used for the separation of amino acids is described by means of differential equations of mass balance. The following assumptions are used: (1) Local dissociation equilibria in solution are established. (2) Kinetic mass-transfer effects are neglected; that is, local equilibrium between liquid and solid phase is attained. (3) Co-ions are excluded from the resin by the Donnan effect. (4) Selectivity coefficients are constants. (5) The system is isothermal. (6) The undissociated species are not sorbed by the ion-exchange resin. By using the dimensionless variables:

Where YA- is the ionic fraction in the resin:

SA-,B- )

0.12 0.016 0.4 22

CA-/CB SA,B ) SA-,BCB-/CA

(16)

These relations are inserted into the electroneutrality constraint to get H+ concentration:

∑i CA

CH2CO3 (mol/L)

Because only anions are fixed, qA ) qA-. The relation between the global separation factor and the selectivity coefficient is given by

K2H2CO3 CH+ + K1H2CO3 C H+ CCO32- )

CB (mol/L)

(15)

CH2CO3

CHCO3- )

CA (mol/L)

This coefficient is a function of the concentration of the negatively charged species. A global separation factor SA,B can be defined, in terms of total amino acid concentrations. This factor can be written as

CH+ CH+2 1+ + K2n K1nK2n CAb- )

Table 1. Numerical Data Used for Simulations

(21)

∂CH2CO3 ∂T

+

1 - ∂qHCO3- ∂CH2CO3 1 ∂CH2CO3 )0 + ∂T ∂Z Pe ∂Z2 (25)

where the following apply: (1) CAi is the total amino acid i concentration in the liquid phase. (2) CH2CO3 is

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Ind. Eng. Chem. Res., Vol. 39, No. 7, 2000

Figure 1. Displacement of a phenylalanine-glycine mixture. SPhe-,OH- ) 1, and SGly-,OH- ) 1.

Figure 2. Lines of a constant separation factor for the mixture phenylalanine-glycine. SPhe-,OH- ) 1, and SGly-,OH- ) 1.

the total carbonic acid concentration in the liquid phase. In the entire pH range used here, the ionic fraction of carbonate ions was negligible and so was its fixation. (3) is the bed porosity. (4) Pe is the column Peclet number, Pe ) uL/Da, where Da is the axial dispersion coefficient. The boundary conditions are the following:

Z)0 Z)L

Ci ) CFi ∂Ci/∂Z ) 0

CF is the feed concentration.

The initial condition is the following:

T ) 0; 0 < Z < 1; Ci ) 0 The axial dispersion term is included mainly to stabilize numerically the equation. The solution for a plug flow is obtained by giving high values to the Peclet number Pe ) 104. The assumption of instantaneous equilibria allows expression of the derivatives of the solid-phase concentration as a function of the derivatives of the liquid-




phase concentrations:

∂qi

)

∂T

∂qi ∂Ck

∑k ∂C

k

i, k ) 1, m

(26)

∂T

where qi is the concentration in the resin phase calculated by

qi ) Q 1+

Si,OH-Xi

∑k (Sk,OH

-

i, k ) 1, m (27) - 1)Xk

To obtain a numerical solution, spatial derivatives were replaced by a first-order backward difference for the convective term and a second-order central difference for the dispersion term. The set of algebraic differential equations thus obtained was solved by using the DASSL solver.3 Simulations Conditions and Data. All of the results presented here have been obtained with simulations based on the model described above. In each case, two steps were included in the simulation: (1) The column (which was initially in the OH- form) is first partially saturated by feeding it with the amino

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Figure 6. Displacement of a phenylalanine-lycine mixture. SPhe-,OH- ) 1, and SGly-,OH- ) 8.

acid mixture A-B. The concentration of these amino acids A and B as well as the volume of the solution Vs percolated are given in Table 1. (2) An elution step is then carried out by feeding the column with a solution of carbon dioxide dissolved in water. The concentration of carbon dioxide used for the simulations, CH2CO3 ) 0.1 mol/L, corresponds to an absorption performed at a pressure close to 3 bar that is 3 × 105 Pa (T = 20 °C). The selectivity coefficient SHCO3-,OH- used is close to the mean value obtained in the case of the strong base resin Amberlite IRA458.

The numerical data and the characteristics of the column used for the simulations are summed up in Tables 1 and 2. Three pairs of amino acids have been chosen with their real acid-base properties. These properties are kept constant. The selectivity coefficients have been varied in the simulations in order to scan all of the possible situations. This could correspond to different types of actual or future resins. The selectivity HCO3-/ OH- is considered to be constant.


Figure 7. Displacement of histidine-lysine mixture. SHis-,OH- ) 1, and SLys-,OH- ) 1.

Figure 8. Lines of a constant separation factor for the mixture histidine-lysine. S

Results and Discussion System Phenylalanine-Glycine. Case 1: SPhe-,OH) 1; SGly-,OH- ) 1. Let us consider the displacement of a mixture of Phe and Gly whose selectivity coefficients with respective to OH- are both equal to unity. This means that Phe- and Gly- ions have the same affinity for the resin. Concentration profiles in the column effluent are shown in Figure 1. A Gly band followed by a Phe one is obtained. A slight interference between bands is noted, but amino acids are well separated. In

His-,OH-

) 1, and SLys-,OH- ) 1.

this case the global separation factor of Phe related to Gly can be written as

SPhe,Gly )

CPhe-CGly S CGly-CPhe Phe-,Gly-

(28)

Because SPhe-,Gly- equals unity, the global separation factor is determined only by the dissociation equilibria in solution. By using eq 15 for these two neutral amino

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Figure 9. Lines of a constant separation factor for the mixture histidine-lysine. SHis-,OH- ) 1, and SLys-,OH- ) 4.

Figure 10. Displacement of a histidine-lysine mixture. SHis-,OH- ) 1, and SLys-,OH- ) 4.

acids, we obtain

SPhe,Gly )

by

CH+2 CH + + 1+ K2Gly K1GlyK2Gly CH + CH+2 1+ + K2Phe K1PheK2Phe

C An

CAi+ ) (29)

SPhe,Gly is therefore a function of the pH of the solution. To get pH values, the electroneutrality equation is used, and CAi- is replaced by its value and CAi+

1+

K2n CH+

+

K1nK2n CH+2

So, from eq 17 the following relation is obtained:

f (H+) CA + g(H+) CB + h(H+) ) 0 where f, g, and h are algebraic (polynomial) expressions.


Figure 11. Displacement of a histidine-lysine mixture. SHis-,OH- ) 1, and SLys-,OH- ) 10.

Figure 12. Lines of a constant separation factor for the mixture histidine-lysine. S

Iso-pH curves are thus straight lines in the plane of coordinates CPhe and CGly. From eq 28, to each pH value corresponds a SPhe,Gly value. Iso-pH lines are thus also lines of constant separation factor. This is represented in Figure 2. It can be noted that the range of variation of the solution pH is narrow. It is near PIPhe = 5.51 when glycine is in trace relative to phenylalanine and near PIGly = 6.00 when phenylalanine is in trace compared to glycine (values are indicated by arrows on Figure 2 and calculated for CPhe ) 0.1 M and CGly ) 0.1 M). The global separation factor also undergoes very small changes and stays close to 2.95. Its value is near 2.95.

His-,OH-

) 1, and SLys-,OH- ) 10.

This indicates a higher apparent affinity of the resin for Phe respectively to Gly, making thus the separation possible. Case 2: SPhe-,OH- ) 1; SGly-,OH- ) 2. When Gly selectivity is doubled, the global separation factor becomes near 1.47. Phe is always preferred by the resin, but competition between the two amino acids is more important and Phe front is less sharp. The separation becomes difficult (Figure 3). Case 3: SPhe-,OH- ) 1; SGly-,OH- ) 3. The global separation factor is near 0.98. Phe and Gly have comparable affinities. Phe is slightly less preferred than

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Figure 13. Displacement of a phenylalanine-histidine mixture. SPhe-,OH- ) 1, and SHis-,OH- ) 1.

Figure 14. Lines of a constant separation factor for the mixture phenylalanine-histidine: SPhe-,OH- ) 1, and SHis-,OH- ) 1.

Gly. This explains the inversion of breakthrough order of the two amino acids. This mixture behaves as if it was composed of only one amino acid and the two amino acids are not separated at all (Figure 4). Case 4: SPhe-,OH- ) 1; SGly-,OH- ) 4. SPhe,Gly ) 0.75 and SGly,Phe ) 1.35. This case is comparable to the one obtained in Figure 3 with an inversion of Phe and Gly (Figure 5). Case 5: SPhe-,OH- ) 1; SGly-,OH- ) 8. SGly,Phe ) 2.71. Gly becomes preferred enough relative to Phe to displace it with a sharp front (Figure 6). System Histidine-Lysine. Case 1: SHis-,OH- ) 1; SLys-,OH- ) 1. Displacement profiles are given in Figure

7 and show a good separation of the two amino acids. On Figure 8 where lines of the constant separation factor are represented, it is noted that the global separation factor varies with His and Lys concentrations. For the same His concentration, SHis,Lys decreases when the Lys concentration increases. However, His remains always very preferred over Lys even when it Hisf0 ) 6.5. is in trace: SHis,Lys Case 2: SHis-,OH- ) 1; SLys-,OH- ) 4. The global separation factor is divided by 4 (Figure 9). Displacement profiles are comparable to Figure 7; however, it can be observed that the two amino acids interference




is slightly more important. His front tail is in fact less Hisf0 sharp. This may be explained by the fact that SHis,Lys becomes 1.6 instead of 6.5. This relatively small value is then not sufficient to eliminate His from the Lys band (Figure 10). Case 3: SHis-,OH- ) 1; SLys-,OH- ) 10. In this case displacement profiles have a particular shape: a pure His band is obtained, but its width is smaller than that found previously. However, the Lys band is not pure anymore; it is mixed with His (Figure 11). To understand this behavior, Figure 12 is used. It can be noted that, for small values of the His concentration, the global

separation factor decreases when the Lys concentration increases. The remarkable fact is that SHis,Lys becomes equal to unity for a concentration ratio CLys/CHis ) 5 and that, when this ratio becomes larger than 5, there is an affinity inversion: SHis,Lys becomes smaller than Hisf0 unity (SHis,Lys ) 0.65). For high histidine concentrations, Lys is always less Lysf0 preferred, SHis,Lys ) 52. This enables the recovery of a pure fraction of His. System Phenylalanine-Histidine. Case 1: SPhe-,OH- ) 1; SHis-,OH- ) 1. Displacement profiles are

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Figure 17. Lines of a constant separation factor for the mixture phenylalanine-histidine: SPhe-,OH- ) 1, and SHis-,OH- ) 2.

Figure 18. Variation of the concentration of ionic species of amino acids with pH: (1) Phe, (2) Gly, (3) His, (4) Lys.

shown in Figure 13. It is noted that the two amino acids are not separated. SPhe,His is almost constant (Figure 14). Except for the concentration zone where CPhe/CHis > 10, its mean value is 1.13. Phe and His coexist at close concentrations. Case 2: SPhe-,OH- ) 2; SHis-,OH- ) 1. In this case, two well-separated amino acid bands are obtained. The mean value of SPhe,His is 2.3. Phe is preferred enough

relative to His to displace it with a sharp front (Figure 15). Case 3: SPhe-,OH- ) 1; SHis-,OH- ) 2. If His selectivity is doubled, the His band obtained is purer than the Phe band, but His front is not sharp (Figure 16). In this case SHis,Phe is superior to unity. Its value decreases very slightly when the His concentration decreases and the Phe concentration increases. When His becomes in trace

Ind. Eng. Chem. Res., Vol. 39, No. 7, 2000 2479 Table 3. Determinant Parameters of the Global Separation Factor SA,B for SA-,B- ) 1 system A-B Phe-Gly His-Lys Phe-His

CA(/CA K2A/K2B CB(/CB 2.951 22.9 1.09

|

pH)pIA

0.99/0.99 0.95/0.041 0.99/0.24

CA(/CA CB(/CB

|

pH)pHx

0.99/0.99 pHx ) 5.8 0.84/0.23 pHx ) 8.43 0.99/0.9 pHx ) 7

CA(/CA CB(/CB

|

pH)pIB

0.99/0.99 0.21/0.75 0.97/0.95

relative to Phe, SHis,Phe becomes smaller than unity Hisf0 ) 0.45). However, this inversion happens at (SHis,Phe very small His concentrations (Figure 17). Discussion about the Role of Dissociation Equilibria in Solution. The behavior of the chromatograms of an amino acid mixture can be deduced by analyzing the evolution of the global separation factor. This evolution is the consequence of the contribution of two effects: (1) ion-exchange equilibria and (2) dissociation equilibria in solution. By multiplying the denominator and the numerator of the second term of eq 22 by CA( and CB(, we get

SA,B ) SA-,B-

CA-CB( CA(/CA CB-CA( CB(/CB

CA-CB(/CB-CA( is the constants ratio K2A/K2B, where K2A is the equilibrium constant corresponding to the reaction

A( T A- + H+ The global separation factor can thus be written as

SA,B ) SA-,B-

K2A CA(/CA K2B CB(/CB

When SA-,B- ) 1, SA,B depends only on the ratio (CA(/ CA)/(CB(/CB). When Figure 18 was analyzed and the ratio (CA(/CA)/ (CB(/CB) was calculated for three pH values ranging between pIA and pIB, Table 3 was established. From this table, the following are noted: (i) SPhe,Gly is almost constant in the entire concentration range; its value depends only on the ratio K2Phe/K2Gly. SHis,Lys is variable in the entire concentration range; its value is very high depending on the ratio K2His/K2Lys. SPhe,His is variable in a small concentration range (CPhe/CHis > 10) but constant in the entire remaining range; its value is near the ratio K2Phe/K2His. Conclusion The separation of the two amino acids A and B depends on a global separation factor SA,B, which is the product of the selectivity coefficient of A relative to B,

SA-,B-, and of a term which depends on the dissociation equilibria of A and B in solution. In the cases where SA-,B- ) 1, it has been noticed that the term relative to dissociation equilibria depends mainly on the ratio K2A/K2B. SA,B varies in the amino acid concentration range but very weakly or very strongly depending on the nature of the amino acids. When SA-,B- is different from unity, displacement behaviors depend also on this coefficient. Generally when K2A/K2B . 1, as is the case for the system histidine-lysine, better separations are obtained. These kinds of systems have a tendency to attain rapidly a coherent state; therefore, shorter columns could be used for their separation. A new displacer, an aqueous solution of carbon dioxide under pressure, was used in this paper as an example, but the significance of the discussion and of the conclusions is more general. Nomenclature Ci ) concentration in solution (mol/L) Ki ) equilibrium dissociation constant of component i L ) packed bed length (m) m ) component number Pe ) Peclet number Q ) ion-exchange capacity of the resin (equiv/L) qi ) concentration in resin (mol/L) Si,j ) separation factor T ) dimensionless time t ) time (s) V ) solution volume (m3) Vp ) porous volume in the column (m3) Xi ) ionic fraction in the solution Yi ) ionic fraction in the resin zi ) anionic valence of i Greek Letter ) bed porosity

Literature Cited (1) Carta, G.; Saunders, M. S.; DeCarli, J. P., II. Dynamics of Fixed Bed Separations of Amino Acids by Ion Exchange. AIChE Symp. Ser. 1988, 164, 54. (2) DeCarli, J. P., II; Carta, G.; Byers, C. H. Displacement Separations by Continuous Annular Chromatography. AIChE J. 1990, 36, 1220. (3) Petzold, L. R. DASSL: A Differential/Algebraic System Solver; Lawrence Livermore National Laboratory: Livermore, CA, 1982. (4) Saunders, M. S.; Vierow, J. B.; Carta, G. Uptake of Phenylalanine and Tyrosine by a Strong Acid Cation Exchanger. AIChE J. 1989, 35, 53. (5) Zammouri, A.; Chanel, S.; Muhr, L.; Grevillot, G. Displacement Chromatography of Amino Acids by Carbon Dioxide Dissolved in Water. Ind. Eng. Chem. Res. 1999, 38, 4860.

Received for review November 5, 1999 Revised manuscript received March 20, 2000 Accepted April 3, 2000 IE990810N

Amino Acids Separations by Displacement Chromatography. Effects of

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