Chemical Engineering Thermodynamics and Protein Adsorption

Article pubs.acs.org/jced

Chemical Engineering Thermodynamics and Protein Adsorption Chromatography Jørgen M. Mollerup* PrepChrom Christiansholmsvej 26, Klampenborg 2930, Denmark S Supporting Information *

ABSTRACT: The process of chromatographic separation and purification of recombinant products is of singular importance to the biopharmaceutical industries because it is the only separation process that can deliver high-purity products. A prerequisite for the application of process simulation in the development of chromatographic separations is the quality of the thermodynamic models of adsorption equilibria. The first part of the paper outlines the general thermodynamic principles of protein adsorption equilibria using well-established thermodynamic concepts, theories, and models. In the second part of the paper we present four examples. The first example shows how oligomer formation will modify a chromatographic run. In the second example we explore the separation potential of oligomer formation in the design of a chromatographic purification step. The third example demonstrates how synergies in the thermodynamic model development can be obtained by combining disparate experiments, here, chromatographic experiments with solubility data. In the last example we analyze the general features of the interplay between salt and cosolvent in hydrophobic interaction chromatography and reversed phase chromatography using a model developed by Kirkwood.

1. INTRODUCTION In a series of papers, Prausnitz and co-workers1−5 have drawn our attention to the opportunities and challenges for chemical engineering thermodynamics in biotechnology by giving a variety of examples of new frontiers in the thermodynamics of protein solutions. Our paper is to a large extent inspired by the spirit and the enthusiasm conveyed in the publications of Prausnitz and co-workers and in fact, last but not least, by the opportunities they, in our opinion, have overlook. A prominent example is protein adsorption chromatography. The process of chromatographic separation and purification of biopharmaceutical products is of singular importance to the biopharmaceutical industries because it is the only separation process that can deliver high-purity products. The chromatographic steps provide a relatively efficient means to meet manufacturing goals, and they are easily scalable from a laboratory scale of a few milliliter to a production scale of several hundred liters or even into the cubic meter range. They are used from early on in the recovery of the product from the fermentation broth and throughout the process to the final polishing step. The aqueous broth leaving a bioreactor is a mixture of solids and solutes, and one of the first downstream process steps is a chromatographic step that captures the products and also some of the impurities in the broth, of course. The selectivity in the capture step may be moderate, but the water is removed. The following process steps include chemical modifications, protein refolding, and several chromatographic purification and polishing steps (the old insulin purification process is outlined in ref 6). Because of its generality, thermodynamics is applicable to all kinds of phase equilibrium calculations including the adsorption © 2013 American Chemical Society

equilibria in protein chromatography. The adsorption equilibrium entails a reversible association of some functional groups of the protein with the functional groups of the immobilized ligands.7 A major challenge in the equilibrium calculation is the modeling of the fluid phase properties of aqueous systems containing salts, cosolvents, and large, charged biological macromolecules. The pH dependence of the solution properties is of particular interest. The thermodynamics of adsorption equilibria can be used to attain some broad approximate results that can be reached relatively easily, but also to attain specific highly accurate results for the development, design, and optimization of a purification process as well as for the investigation of the design space as required by the Agencies. The first part of this paper is a brief introduction to the very basic principles of adsorption and various types of adsorption equilibria including the well-known Langmuir isotherm. An outline of the general thermodynamic principles of adsorption is deferred to the Supporting Information in order make the paper more readable to those who are not particular familiar with or interested in the thermodynamic subtleties. In the second part of the paper we present four examples. The first example shows how oligomer formation will modify the chromatographic run completely. The oligomer formation is brought about by adding a water-soluble calcium salt to the chromatographic liquids. The utilization of controlled oligomer formation in chromatography is a fairly unexplored research Special Issue: In Honor of Grant Wilson Received: August 15, 2013 Accepted: December 13, 2013 Published: December 20, 2013 991

dx.doi.org/10.1021/je400739j | J. Chem. Eng. Data 2014, 59, 991−998

Journal of Chemical & Engineering Data

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out of the pore volume of the adsorbent is by diffusion. In the equilibrium model we assume that the immobilized ligands are homogeneously distributed throughout the pore volume. The solute concentrations in the pore volume, ci, and the adsorbate concentrations, qi, are equilibrium concentrations. The overall molar concentration in the pore volume, c, is the sum of the molar concentration of solvents, salts, solutes, ligands, and adsorbates. The preparative chromatographic separation is a batch process including the process steps; column equilibration, load, wash to elute unbound impurities, elution, and column regeneration. The principles of simulation of preparative chromatographic processes are outlined in ref 11.

topic. In the second example we explore the separation potential of oligomer formation to the design of a chromatographic purification step. The third example demonstrates how synergies in the thermodynamic model development were obtained by combining disparate experiments, here, chromatographic experiments with solubility data. Finally, in the last example, we take what Prausnitz called a bird’s-eye view to use a model developed by Kirkwood to analyze the features of the interplay between salt and cosolvent in hydrophobic chromatography, which includes hydrophobic interaction chromatography (HIC) and reversed phase chromatography (RPC). Obviously, the driving force in academic research shall be the scientific challenges, only, and not fiscal ones, but let us just in passing mention that pharmaceutical proteins purified by chromatographic methods represent annual sales of the order of magnitude of a $100 billion. Grant Wilson’s career covered an array of topics from experimental data to molecular theory. For this special issue, the Editors solicited papers covering the wide range of Dr. Wilson’s contributions to engineering thermodynamics. I initiated my professional career 46 years ago working with natural gas properties and other hydrocarbon related systems both experimentally and theoretically using many of Dr. Wilson’s data and concepts. However, some 15 years ago I included protein chromatography as part of my research capabilities looking for new opportunities for chemical engineering thermodynamics. It is my hope that the examples given here will encourage researchers in chemical engineering thermodynamics to utilize their talents with confidence to explore protein chromatography. It is a genuine chemical engineering discipline, but the subject is almost absent at PPEPPD, and at the chemical engineering thermodynamic conferences, at least in Europe. 1.1. Protein Adsorption. Protein adsorption is modeled as a reversible association of some functional groups of the protein with the functional groups of the immobilized ligands that are covalently bonded to the chromatographic adsorbent, because it provides a simple solution to a complex problem and allows for the application of well-established thermodynamic concepts, theories, and models.7−10 Depending on the functional groups of the ligands both electrostatic and hydrophobic interactions may take place. When the ligands carry charged groups, groups of the protein of opposite charge may associate with the charged groups of the ligands by displacing some or all of the small counterions associated with the charged groups of the ligands. When the ligands carry hydrophobic groups, the adsorption entails a reversible association of the hydrophobic moieties of the protein with the hydrophobic groups of the ligands to form a complex by hydrophobic interactions. Some ligands can display bimodal interactions if they carry both hydrophobic and ionic groups. If the ionic groups are weak acids or bases, the bimodal ligands will in some pH ranges operate as hydrophobic ligands only. 1.2. The Chromatographic Column and the Adsorbent. The chromatographic column is a cylinder with a solid packed bed of adsorbent. Flow takes place in the axial direction of the column. The adsorbent is composed of small, solid, and highly porous particles where the ligands are covalently bonded to the backbone of the adsorbent or to a soft gel in the macropores of the adsorbent. There are two fluid phases in the column, a mobile fluid phase in the interstices and a stationary fluid phase in the pores of the adsorbent. The transport in and

2. THE CLASSICAL ADSORPTION ISOTHERM The classical adsorption isotherm of the Langmuirian type has a negative curvature, that is, the second derivative of the adsorbate concentration, qi, with respect to the solute concentration, ci, is negative at all values of ci. The classical isotherm gives rise to an eluting chromatographic peak where the front is steeper then the rear of the peak.11 When increasing the load on the column an overlay of the eluting peaks shows that the rears of the peaks coincide, whereas the fronts move to the left as shown in Figure 1. Conformational changes of the

Figure 1. An overlay of experimental (pink) and simulated (black) elution profiles of an insulin intermediate on a reversed phase column. The classical isotherm gives rise to a peak where the front is steeper than the rear of the peak. When the load on the column is increased, the overlay shows that the rears of the peaks coincide, whereas the fronts move to the left.

protein do take place during adsorption, but the proteins do not self or cross associate. The model is derived in the Supporting Information, section A2.1 where the equilibrium scheme is given in eq A7. The model of the classical isotherm is ⎛ c ⎞νβi iσ ⎛ Λ ⎞νi ⎛ = K i Γi⎜ ⎟ ⎜ ⎟ ⎜⎜1 − ci ⎝ cS ⎠ ⎝ c ⎠ ⎝

qi

⎛ = Ai ⎜⎜1 − ⎝

m

∑ j=1

qj ⎞ ⎟ qjmax ⎟⎠

m

∑ j=1

νi qj ⎞ ⎟ qjmax ⎟⎠

νi

(1)

where ⎛ c ⎞νβi iσ ⎛ Λ ⎞νi Ai = K i Γi⎜ ⎟ ⎜ ⎟ ⎝ cS ⎠ ⎝ c ⎠ 992

(2)



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where qi is the concentration of protein of species i associated with νi immobilized ligands, ci is the concentration of solute protein of species i, cS is the concentration of the counterion, S, and c is the overall molar concentration in the pore volume. Ki is the thermodynamic equilibrium constant, and Γi is the corresponding equilibrium excess energy of species i. The excess potentials are calculable from activity coefficient models, electrostatic models, or equations of state. m is the number of adsorbed species. νiβi is the fraction of ligands where the counterions are displaced, βi = 0 corresponds to pure hydrophobic interactions, and βi = 1 corresponds to ionic interactions, that is, ion-exchange. σ = ZL/ZS where zL is the charge number of the ligand and zS is the charge number of the counterion. If the ligands do not carry any charged groups σ = 0. Λ is the ligand density and qmax is the maximum available i capacity of species i. Ai is the thermodynamic retention factor. Equation 1 is not identical with the Langmuir isotherm but there are many similarities. In the following section, we will compare the two models. 2.1. The Langmuir Isotherm. The Langmuir model involves an interaction between the adsorbate and a single site on the adsorbent; that is, the stoichiometric coefficients are unity. In section 4.1.2 in ref 11, the model is derived from a kinetic approach. The eventual result is qi q

max

ka , i c kd , i i

= 1+

m ka , j ∑ j = 1 k cj d ,j

=

bici m 1 + ∑ j = 1 bjcj

pH, ionic strength, the chemical composition of the salt, and the presence of suitable ligands. High temperature may disperse aggregates and complexes.12,13 In chromatographic separations proteins are present at high concentrations in the pore volume of the adsorbent. We must therefore expect oligomer formation to play a major role in protein purification. The classical isotherm displays a negative curvature at all protein concentrations. When oligomer formation takes place the isotherm will display an inflection point. It will display a positive curvature at low protein concentration, and as the protein concentration increases the curvature will change from positive to negative. This type of isotherm is often denoted as an anti-Langmuirian isotherm. The presence of oligomers can be observed by inspecting the shape of the eluting peak. If it displays fronting it is an indication of the presence of oligomers.11 The oligomer formations can take place in the fluid phase as well as in the immobilized state. The thermodynamic principles of modeling of oligomer formation in adsorption chromatography is analyzed in the Supporting Information in sections A2.3 and A2.4. Minor changes in the protein structure can change the shape of the isotherm from a classical form to an anti-Langmuirian type of isotherm, that is, a sigmoid isotherm. Perhaps the most well-known example is β-lactoglobulin A and B. The A form displays strong anti-Langmuirian behavior,14,15 whereas the B form displays normal behavior.

4. THE EQUILIBRIUM EXCESS In electrolyte solutions, the equilibrium excess energy, Γ, is a function of the inverse Debye length, κ. However, in some cases one can disregard the modeling of the equilibrium excess energy in ion-exchange chromatography (IEC). It turns out that Γ is not very sensitive to variations of the salt concentration, at least when halide salts are used. This may not be the case if salts that are commonly used as salting-out agents are utilized in the eluant in IEC.21 There is a very simple test that one can carry out to observe whether the excess potentials neutralize or not. We normally utilize isocratic elution data at analytical load to determine the thermodynamic retention parameter, Ai, and analyze the data by preparing a double logarithmic plot of Ai versus the salt concentration. Taking the logarithm of eq 2 gives the following equation

(3)

where bi is the ratio of the rate constant of adsorption, ka,i, over the rate constant of desorption, kd,i, of species i. A limitation of the Langmuir model is that the stoichiometric coefficients are unity and identical column saturation capacities for all species are assumed. When the stoichiometric coefficient, νi, in the association scheme, eq A7, is unity, eq 1 shows that ⎛ = Ai ⎜⎜1 − ci ⎝

qi

m

∑ j=1

qj ⎞ ⎟ qjmax ⎟⎠

(4)

This equation can be expressed in a form similar to eq 3. The result is qi =

ln Ai = ln K i + ln Γi[κ ] − νσ i ln cS + νi(σ − 1) ln c

Ai ci m

Aj

1 + ∑ j = 1 q max cj j

+ νi ln Λ

(5)

(6)

This relationship shows that, essentially, a log−log plot of Ai versus the counterion concentration, cS, shall be a straight-line plot provided Γi is independent of the salt concentration. An example is shown in Figure 2 in ref 20. The slope of the straight-line is −νσ. For halide salts, σ is unity. When ethanol is used as a cosolvent in IEC it, of course, modulates Γ. The corresponding equation in the HIC and RPC mode is

Equation 5 shows that there is some similarity between the Langmuir model and the model derived from association theory; but eq 5 is more convenient to use that eq 3 because Ai accounts for the solution nonideality as shown in eq 2. However, the classical model in eq 1 is preferable because it is not limited to a stoichiometric coefficient of unity.

ln Ai = ln K i + ln Γi[κ ] − νi ln c + νi ln Λ

3. NONCLASSICAL ISOTHERMS Most proteins, particular at high concentrations, tend to form aggregates and clusters in solution having both ordered oligomeric structure and random nonspecific forms. Small molecules or ions might serve as bridges between agreeable side chains or neighboring molecules. Asp and Glu residues are effective chelators of certain metal ions and Cys residues form complexes of varying degree of stability with a variety of metal ions. Aggregation is a function of concentration, temperature,

(7)

The dependence of Ai on the solution properties is therefore solely due to the variation of Γi with the solution properties, that is, salt concentration, type of salt, pH, solvent permittivity, and temperature. A model for Γ is analyzed in section 5.3.

5. FOUR EXAMPLES 5.1. Oligomer Formation of an Insulin Intermediate by Divalent Cations. In neutral solutions positively charged 993



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the concentration of the Ca2+ ions. KFAA is the equilibrium constant, and ΓFAA is the corresponding equilibrium excess energy. The adsorption equilibrium relation for the monomer insulin intermediate is

molecules may combine with negatively charged insulin. The presence of Ca2+ and Zn2+ ions have been observed to diminish the solubility, and the addition of basic proteins or peptides or small amounts of cationic detergents will also decrease the solubility. A decrease in the solubility indicates oligomer formation.16 It has also been observed that the admixture of calcium chloride to the solvents modulates the chromatographic behavior of insulins to a great extent due to oligomer formation. Figure 1 shows an overlay of experimental (pink) and simulated (black) chromatograms of an insulin intermediate eluting at isocratic conditions on a silica-based reversed phase adsorbent with C18-ligands. The solvents are at neutral pH and contain ethanol.17 The shapes of the peaks show that the isotherm is a classical one having a negative curvature. When the load on the column is increased the overlay shows that the rears of the peaks coincide, whereas the fronts move to the left. However, if a little calcium chloride is added to the solvents the shapes of the eluting peaks change as shown in Figure 2. The

νA qA ⎛ c ⎞ KA ΓA = ⎜⎜ ⎟⎟ cA ⎝ qL ⎠

(9)

where qA is the concentration of the monomer adsorbate, qL is the concentration of the vacant ligands, and νA is the stoichiometric coefficient. KA is the equilibrium constant, and ΓA is the corresponding equilibrium excess energy. The adsorption equilibrium relation for the dimer is I Γ IAA KAA

νA qAA ⎛ c ⎞ ⎜ ⎟ = cAA ⎜⎝ qL ⎟⎠

(10)

KIAA

where qAA is the concentrations of the dimer adsorbate. is I the equilibrium constant, and ΓAA is the corresponding equilibrium excess energy. The material balance is Λ = qL + νAζAqA + νAζAAqAA

(11)

where ζA and ζAA are steric hindrance factors. Details are given in the Supporting Information, section A.2.3. The shapes of the corresponding isotherms are shown in Figure 3. The complex formation modifies the isotherm giving

Figure 2. An overlay of experimental (red) and simulated (black) elution profiles of an insulin intermediate on a reversed phase column after the admixture of calcium chloride to the solvents. The insulin intermediate forms a complex with the divalent calcium ion, and that changes the shape of the chromatographic peak as compared to that in Figure 1.

change is a result of a complex formation of the insulin intermediate with the divalent calcium ion. A comparison of the chromatograms in Figures 1 and 2 shows that the main peak is separated better from the weaker bound impurity, eluting before the main peak, when calcium chloride is added to the solvents. Furthermore, the pool concentration is higher using the solvents containing calcium chloride. The simulation shown in Figure 1 includes the species A and LvAA where A is the insulin intermediate, L is the C18-ligand, and νA is the stoichiometric coefficient. The complex formation is modeled as a dimer formation in the fluid phase. The impurities do not form dimers. The simulation shown in Figure 2 includes the species, A, LvAA, A2Ca2+, and LvAA2Ca2+. The equilibrium relation for the dimer formation in the fluid phase is cAA ⎛ c ⎞2 ⎛ c 2 + ⎞ F = KAA Γ FAA⎜ A ⎟ ⎜ Ca ⎟ ⎝c⎠⎝ c ⎠ c

Figure 3. The isotherms used in the simulation of the elution profiles in Figures 1 and 2, respectively. The dashed line (pink) is the classical isotherm of the insulin intermediate, and the full line (red) is the isotherm after the admixture of calcium chloride to the solvents. The insulin intermediate forms a complex with the divalent calcium ion, and that changes the shape of the isotherm.

rise to a sigmoid shape. This is best observed when looking at the slopes of the two isotherms shown in Figure 4. The slope of the classical isotherm decreases at all concentrations, whereas the slope of the isotherm including the dimer starts to increase, goes through a maximum at the inflection point and then decreases. Bogsnes18 have also demonstrated that the presence of Ca2+ ions in the solution modulates the retention of insulin, a principle that can be utilized in industrial separations.19 In reversed phase chromatography the chromatographic behavior is modulated by a water-soluble organic solvent in the eluant. In the example we used ethanol. The solution behavior

(8)

where cAA is the concentration of the dimer insulin complex, cA is the concentration of the corresponding monomer insulin intermediate, c is the overall molar concentration, and cca2+ is 994



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Figure 5. Isocratic elution profiles of the monomers at 75 mM salt on an anion-exchange column. The full line (red) is the API, the dasheddotted line (green) is impurity A, the dashed line (blue) is impurity B, and the dashed-double-dotted line (black) is the salt profile. The load was 5·10−3 mol API/liter of CV and the equivalent amount of the impurities A and B.

Figure 4. The slopes of the isotherms shown in Figure 3. The dashed line (pink) is the slope of the classical isotherm, and the full line (red) is the slope of the isotherm after the admixture of calcium chloride to the solvents. A maximum in the slope corresponds to an inflection point on the isotherm.

is strongly nonideal, and a challenge is the modeling of the equilibrium excess energies. This challange was ignored in the simulations shown in Figures 1 and 2 because the experiments were carried out at isocratic conditions, i.e., at constant solvent composition, wherefore the equilibrium excess energies are constant. The example in section 5.3 includes the modeling of Γ. 5.2. The Separation Potential of Oligomer Formation. The classical isotherm is prevailing in much chromatographic equilibria. At low column load, the separation is easy but the productivity is low, and in order to increase the productivity the load on the column is increased but, because of the peak compression, the separation becomes more challenging as the load on the column is increased.11 The optimal load to the column and the eluting conditions are determined as a compromise between purity, productivity, and recovery. However, as shown in Figure 2, if one can induce the formation of an oligomer the picture can be reversed and the separation becomes easier when the load is increased because the oligomer acts as a displacer of the impurities. The anionexchange parameters used in this example were from ref 20, and the results of the simulations are shown in Figures 5 to 7. The concentrations of the proteins in the solution loaded onto the column were as follows: impurity A, 0.0295 mM, the active pharmaceutical ingredient (API), 0.50 mM, and impurity B, 0.060 mM. The API formed an oligomer in the presence of a divalent cation but the impurities A and B did not. Details of the modeling are given in ref 10. Figure 5 shows an elution profile without oligomer formation, which indicates that it was difficult to purify the API. The elution profile was simulated using the classical adsorption model given in eqs 1 and 2. The load was 5·10−3 mol API/liter of CV plus the equivalent amount of impurities. When we induced oligomer formation, it became possible to purify the API at high column load because the impurities A and B did not form oligomers. In this example, the oligomer formation was modeled as a dimer formation formed in the adsorbed state. To illustrate that the separation became more feasible when the load was increased we show the elution profiles at three different column loads, namely (5·10−5, 5·10−4, and 5·10−3) mol API/liter of CV plus the equivalent amount of

Figure 6. Isocratic elution profiles at 75 mM salt on an anion-exchange column when the API forms a dimer. The load was (5·10−5 and 5· 10−4) mole API/liter of CV and the equivalent amount of the impurities A and B. The full lines (red) are the API, the dashed-dotted lines (green) are impurity A, and the dashed lines (blue) are impurity B. The salt profiles are not shown.

impurities. The results of the simulations are shown in Figures 6 and 7. Figure 6 shows the elution profiles at column loads of (5·10−5 and 5·10−4) mol API/liter of CV plus impurities. It is observed that the amount of impurities was so low that their isotherms must be linear because the peaks of the two impurities are symmetric. The peaks of the dimer display a behavior that is the mirror image of what is shown in Figure 1. The fronts of the peaks coincide, whereas the rears move to the right when the load increases. The difference is due to the different curvatures of the isotherms. The classical Langmuirian isotherm has a negative curvature, whereas the isotherm, when the dimer is formed, has a positive curvature at low load. The result of the simulation, when we increase the load of the API to 5·10−3 mol API/liter of CV plus the equivalent amount of impurities, is shown in Figure 7. It is the same load as we applied in the simulation shown in Figure 5. The shapes of the peaks of the impurities are still symmetric but the shape of the peak of the API has changed. To understand the difference between the shapes of the peaks of the API shown in Figures 6 and 7, we must remember that the isotherm displays an inflection point. The isotherm has a positive curvature at 995



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static theory in which the solvent was idealized as a structureless dielectric continuum characterized by its relative permittivity alone. The electrostatic interactions between the ion dipole of the macro-ion and the charges of small ions in an electrolyte solution give rise to a “salting-in” excess potential (KW) as well as a “salting-out” excess potential (kw) of the macro-ion. The model of the thermodynamic retention, Ai (see eq 7) becomes22 ln Ai = ln K i + νi ln(Λ /c) + ln Γi[κ ] = ln A 0[Λ , ε , νi] + μiKW [κ , τ , η]/RT + μi kw [κ , τ ]/RT

(12)

where A0 reflects the adsorbate−adsorbent interaction and it depends mainly on the standard state potentials, the ligand density, the permittivity of the solvent, and the stoichiometric coefficient. κ is the inverse Debye length, τ depends on the permittivity of the solvent and two size parameters, the radius of the cavity of low permittivity created by the macro-ion and the distance of closest approach between the macro-ion and the small ions of the salt. η depends on the two size parameters of the macro-ion and its dipole moment. Figure 8 shows correlated and experimental thermodynamic retention factors of lysozyme at linear conditions with

Figure 7. Isocratic elution profiles at 75 mM salt on an anion-exchange column when the API forms a dimer. The load was the same as the load used in the simulation in Figure 5, i.e., 5·10−3 mol API/liter of CV and the equivalent amount of the impurities A and B. The full line (red) is the API, the dashed-dotted line (green) is impurity A, the dashed line (blue) is impurity B, and the dashed-double-dotted line (black) is the salt profile.

concentrations below the inflection point and a negative curvature above this point. A negative curvature of the isotherm gives rise to a shock wave at increasing concentration and a diffuse wave when the concentration decreases and vice versa when the curvature is positive. The shape of the upper part of the peak of the API in Figure 7 is thus determined by the negative curvature above the inflection point and the shape of the lower part is determined by the positive curvature below the inflection point. The shapes of the API peaks in Figure 6 are determined by the positive curvature below the inflection point of the isotherm alone. A comparison of Figures 5 and 7 shows that it is possible to separate components having coeluting peaks if we can make the API form an oligomer, because it will change the front of the API peak from a shock wave to a defuse wave at low concentration giving rise to a very low initial slope of the front. The elution volume at the baseline where the fronts of the API peaks start, approximately 1.9 CV, are independent of the load because it is determined by the initial slope of the isotherm alone. Much research is needed toward a better knowledge of how to induce, control, and utilize oligomer formation in chromatographic separations. Its separation potential is unexplored. 5.3. Hydrophobic Interaction Chromatography and Protein Solubility. The chromatographic retention in hydrophobic interaction chromatography (HIC) and the solubility of proteins display some common features. The chromatographic retention, as well as the solubility, is modulated by the thermodynamic properties of the solute in the fluid phase. The retention measurements at linear conditions provide information of the solution properties of the protein at infinite dilution, and the solubility measurements produce the supporting information about the solution properties at the saturation limit. This provides a useful approach to a simultaneous correlation of the chromatographic retention and the solubility data.22 We applied Kirkwood’s theory of solutions of molecules containing widely separated charges to develop a model of the electrostatic chemical potentials of zwitterions in electrolyte solutions.22−24 The model was derived from classical electro-

Figure 8. Correlated thermodynamic retention factors of lysozyme with ammonium sulfate in the aqueous eluant at pH 7 on adsorbents with butyl, phenyl, and ether ligands, respectively. The symbols represent the experimental data, and the lines are the correlations. The figure also shows the effect of adding 7.5 vol % of ethanol to the eluant. B denotes the butyl adsorbent, E is the ether adsorbent, and 7.5 % denotes the volume % of ethanol.

ammonium sulfate in the aqueous eluant at pH 7 on absorbents with butyl, phenyl, and ether ligands, respectively. The open symbols represent the experimental data and the dashed and dashed-dotted lines were the result of the correlation. The curvature of the modeled retention parameter, Ai, is determined by the two Kirkwood potentials and it is therefore independent of the adsorbent. The only difference of the modeled retention data is the value of the A0 parameter. The figure also shows the effect of adding 7.5 vol % of ethanol to the eluant. The filled symbols represent the experimental data, and the full lines show the model calculations. The model parameters of lysozyme were unchanged. The admixture of ethanol to the eluant diminished the thermodynamic retention factor of lysozyme on the two adsorbents by equal amounts. That is, the change in A0, that is, 996



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the cosolvent and the salt. We will not be concerned with details but look at gross, overall properties. We pretend that the parameters in the Kirkwood potentials, estimated for lysozyme, can be used to calculate a qualitatively correct result. In the experiments analyzed in section 5.3 we observed that the thermodynamic retention factor in HIC was diminished when ethanol was added to the eluant, mainly because A0 decreased, but we also observed that the retention factor curve was revolved a little clockwise. This means that the salting-in region was increased while the salting-out region was decreased. Increasing the ethanol concentration will enhance this rotation. The ethanol concentration applied in RPC is typically from (30 to 50) vol %. When we increased the ethanol concentration to what is commonly used in RPC the model calculation predicted that salting-in will predominate in RPC while salting-out is predominating in HIC. The increase in the ethanol concentration diminishes the solubility of the salt and this will further limit the salting-out region and at high ethanol concentrations the salting-out region will disappear. The result is shown in Figure 10.

in the adsorbate−adsorbent interaction parameter, is identical for the two adsorbents because it depends mainly on the change in the relative permittivity of the solvent, which also changed the slope of the A-curves a little. This is best observed by comparing the modeled phenyl data with the modeled B 7.5 % data. B stands for the adsorbent with butyl ligands and 7.5 denotes the volume % of ethanol of the solvent. Details are given in ref 22. To correlate solubility data of lysozyme in an aqueous solution of ammonium sulfate the Kirkwood potential model was extended to account for the nonelectrostatic interactions that became important when the lysozyme concentration got closer to the saturation limit.22 To determine the parameters in the nonelectrostatic part of the model, the solubility model was fitted to the experimental solubility data at pH 4. The result of the correlation is depicted in Figure 9. The dashed line is a prediction of the solubility at pH 8.

Figure 9. Experimental and correlated solubility data of lysozyme in an aqueous solution of ammonium sulfate at pH 4 (△) and pH 8 (◇). The symbols represent the experimental data. The full line resulted from a fit of the model to the solubility data at pH 4. The dashed line was a prediction of the solubility at pH 8.

Figure 10. The performance of the Kirkwood potentials, lnΓ[κ] in eq 12, for lysozyme in an aqueous solution of ethanol and ammonium sulfate at ethanol concentrations of (0, 10, 20, 30, 40, and 50) vol %. The symbols represent the calculated values.

The Kirkwood potentials have also been applied to correlate light scattering data of lysozyme in an aqueous solution of sodium acetate.25 5.4. From Salting-Out in HIC to Salting-In in RPC Application of Kirkwood’s Theory. There are two types of hydrophobic adsorbents, HIC and RPC adsorbents, respectively. The HIC adsorbents are much less hydrophobic than the RPC adsorbents. In HIC the eluant is an aqueous solution of a salt and the chromatographic performance is modulated by adjusting the salt concentration. Binding of proteins to the HIC adsorbent is usually done by increasing the salt concentration in the mobile phase and vice versa when the protein is eluted. In RPC the modulator is a water-soluble organic solvent, most often an alcohol. The salt concentration is moderate and the main purpose of adding a salt to the chromatographic liquids is to increase the solubility and to stabilize the protein. Binding of proteins to the RPC adsorbent is done by decreasing the concentration of the cosolvent in the mobile phase and vice versa when eluting the protein. If the admixture of a salt, at constant ethanol concentration, increases the solubility, that is salt-in, it must decrease the chromatographic retention. Let us take a bird’s-eye view to analyze the main features of HIC and RPC, or more precisely, analyze the interplay between

The model calculation confirms that one shall expect saltingout to predominate in HIC and salting-in to predominate in RPC. Preliminary experimental results, using some small biopharmaceutical molecules, were presented at the AIChE 2013 Annual Meeting.26 The experimental results showed that salting-out was observed at ethanol concentrations at (0 to 10) vol % on butyl and phenyl HIC adsorbents similar to the one used in ref 22. Salting-in was observed on the RPC adsorbents at ethanol concentrations from (30 to 40) vol %.

6. CONCLUSION The examples shown here illustrate how chemical engineering thermodynamics provides some very useful tools for interpretation and modeling of protein chromatography. The examples were all about exploring some of the challenges in protein chromatography, and one of the examples, in addition, also showed how one can integrate protein chromatography and solubility data when developing thermodynamic models of biological macromolecules. The Supporting Information provides the general outline for modeling the adsorption behavior in protein chromatography no matter how complex it may seem. The general framework of 997



Article

(20) Mollerup, J. M.; Hansen, T. B.; Kidal, S.; Sejergaard, L.; Hansen, E.; Staby, A. Use of Quality by the Design for the Modelling of Chromatographic Separations. J. Liq. Chromatgr. Relat. Technol. 2009, 32, 1577−1597. (21) Al-Jibbouri, S. The Influence of Salt Type on Retention of Bovine Serum Albumin in Ion-Exchange Chromatography. J. Chromatgr. A 2007, 1139, 57−62. (22) Mollerup, J. M.; Breil, M. P.; Vogelpohl, C.; Sadowski, G. Simultaneous Correlation of Hydrophobic Interactions in HIC and Protein Solubility in Aqueous Salt Solutions and Mixed Solvents. Fluid Phase Equilib. 2011, 301, 163−170. (23) Kirkwood, J. G. Theory of Solutions of Molecules Containing Widely Separated Charges with Special Application to Zwitterions. J. Chem. Phys. 1934, 2, 351−361. (24) Kirkwood, J. G. In Protein, Amino Acids and Peptides as Ions and Dipolar Ions, American Chemical Society Monograph Series; Cohn, E. J., Edsall, J. T., Eds.; Reinhold Publishing Corporation: New York, 1943; Chapter 12. (25) Breil, M. P.; Mollerup, J. M. Modelling of Molecular Light Scattering. Fluid Phase Equilib. 2011, 310, 120−128. (26) Johansson, K.; Frederiksen, S. S.; Degeman, M.; Breil, M. P.; Mollerup, J.; Nilsson, B. Modeling the synergies of saline and organic modifiers on RPC separation. Abstract No. 332992. Presented at the 2013 AIChE Annual Meeting, November 3−8, San Francisco, USA.

thermodynamics allows us to reduce seemingly complex problems to a set of equations easily solvable by the computer. The be-all and end-all is the modeling of the fluid phase properties of aqueous systems containing salts, cosolvents, and large, charged biological macromolecules.

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ASSOCIATED CONTENT

S Supporting Information *

General outline for modeling the adsorption behavior in protein chromatography. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: + 45 39 64 19 46. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Prausnitz, J. M. Biotechnology: A New Frontier for Molecular Thermodynamics. Fluid Phase Equilib. 1989, 53, 439−451. (2) Prausnitz, J. M. Some New Frontiers in Chemical Engineering Thermodynamics. Fluid Phase Equilib. 1995, 104, 1−20. (3) Prausnitz, J. M. Molecular thermodynamics for some applications in biotechnology. Pure Appl. Chem. 2003, 75, 859−873. (4) Prausnitz, J. M.; Foose, L. Three Frontiers in the Thermodynamics of Protein Solutions. Pure Appl. Chem. 2007, 79, 1435−1444. (5) Dey, S. S.; Prausnitz, J. M. Opportunities for Chemical Engineering Thermodynamics in Biotechnology: Some Examples. Ind. Eng. Chem. Res. 2011, 50, 3−15. (6) Mollerup, I.; Jensen, S. W.; Larsen, P.; Schou, O.; Snel, L. In Encyclopaedia of Bioprocess Technology, Fermentation, Biocatalysis, and Bioseparation; Flickinger, M. C., Drew, S. W., Eds.; John Wiley & Sons: New York, 1999; pp 1491−1498. (7) Melander, W.; Horváth, C. Salt Effects on Hydrophobic Interactions in Precipitation and Chromatography: An Interpretation of the Lyotropic Series. Arch. Biochem. Biophys. 1977, 183, 200−215. (8) Brooks, C. A.; Cramer, S. M. Steric Mass-Action Ion Exchange: Displacement Profiles and Induced Salt Gradients. AIChE J. 1992, 38, 1969−1978. (9) Mollerup, J. M. Applied Thermodynamics: A New Frontier for Biotechnology. Fluid Phase Equilib. 2006, 241, 205−215. (10) Mollerup, J. M. Modelling Oligomer Formation in Chromatographic Separations. J. Chromatgr. A 2011, 1218, 8869−8873. (11) Guiochon, G.; Felinger, A.; Shirazi, D. G.; Katti, A. M. Fundamentals of Preparative and Nonlinear Chromatography, 2nd ed.; Academic Press: San Diego, CA, 2006. (12) Creighton, T. Proteins Structures and Molecular Properties, 2nd ed.; W. H. Freeman: New York, 1993. (13) McPherson, A. Crystallization of Biological Macromolecules; Cold Spring Harbor Laboratory Press: New York, 1999. (14) Jen, S.-C. D.; Pinto, N G. Nonlinear Chromatography of βLactoglobulins A and B: Non-Langmuirian Behaviour. Ind. Eng. Chem. Res. 1995, 34, 2685−2691. (15) Mollerup, J. M. The Thermodynamic Principles of Ligand Binding in Chromatography and Biology. J. Biotechnol. 2007, 132, 187−195. (16) Brange, J. Galenics of Insulin; Springer-Verlag: Berlin, 1989. (17) Frederiksen, S. S.; Breil, M. P.; Mollerup, J. M. Modelling Reversed-Phase ChromatographyPart II. Poster presented at Recovery of Biological Products XV; 2012, 29 July−2 August, Stowe Mountain Lodge, Stowe, Vermont; USA. (18) Bogsnes, A. Eluents in preparative RP-HPLC purifications of insulin, Oral presentation at 5th HIC/RPC Bioseparation Conference; 2007, March 20−23; Interlaken; Switzerland. (19) Novo Nordisk A/S. Process for the separation of proteins using a Ca++ containing eluant. Patent US 6180757. 998


Chemical Engineering Thermodynamics and Protein Adsorption

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