Modelling Affinity Chromatography

Accurate retention time determination of co-eluting proteins in analytical chromatography by means of spectral data

Chromatography is the method of choice for the separation of proteins, at both analytical and preparative scale. Orthogonal purification strategies for industrial use can easily be implemented by combining different modes of adsorption. Nevertheless, with flexibility comes the freedom of choice and optimal conditions for consecutive steps need to be identified in a robust and reproducible fashion. One way to address this issue is the use of mathematical models that allow for an in silico process optimization. Although this has been shown to work, model parameter estimation for complex feedstocks becomes the bottleneck in process development. An integral part of parameter assessment is the accurate measurement of retention times in a series of isocratic or gradient elution experiments. As high-resolution analytics that can differentiate between proteins are often not readily available, pure protein is mandatory for parameter determination. In this work, we present an approach that has the potential to solve this problem. Based on the uniqueness of UV absorption spectra of proteins, we were able to accurately measure retention times in systems of up to four co-eluting compounds. The presented approach is calibration-free, meaning that prior knowledge of pure component absorption spectra is not required. Actually, pure protein spectra can be determined from co-eluting proteins as part of the methodology. The approach was tested for size-exclusion chromatograms of 38 mixtures of co-eluting proteins. Retention times were determined with an average error of 0.6 s (1.6% of average peak width), approximated and measured pure component spectra showed an average coefficient of correlation of 0.992.

Characterization of a peptide affinity support that binds selectively to staphylococcal enterotoxin B

The influences of mass transfer and adsorption-desorption kinetics on the binding of staphylococcal enterotoxin B (SEB) to an affinity resin with the peptide ligand, Tyr-Tyr-Trp-Leu-His-His (YYWLHH) have been studied. The bed and particle porosities, the axial dispersion coefficient and the pore diffusivity were measured using pulse experiments under unretained conditions. Adsorption isotherms for SEB on YYWLHH resins with peptide densities in the range from 6 to 220 micromol/g were measured and fitted to a bi-Langmuir equation. At peptide densities below 9 micromol/g and above 50 micromol/g, dissociation constants were lower (2 x 10(-3) to 7 x 10(-3) mol/m3), and binding capacities were larger (43-47 mg SEB/g). In the range from 9 to 50 micromol/g dissociation constants were larger (13 x 10(-3) to 24 x 10(-3) mol/m3) and capacities were lower (33-37 mg SEB/g). These observations are consistent with a transition from single point attachment of the protein to the ligand at low peptide densities to multipoint attachment at high peptide densities. The general rate (GR) model of chromatography was used to fit experimental breakthrough curves under retained conditions to determine the intrinsic rate constants for adsorption, which varied from 0.13 to 0.50 m3 mol(-1) s(-1), and exhibited no clear trend with increasing peptide density. An analysis of the number of transfer units for the various mass transfer steps in the column indicated that film mass transfer, pore diffusion (POR) and the kinetics of adsorption can all play an important role in the overall rate of adsorption, with the intrinsic adsorption step apparently being the rate determining step at peptide densities below 50 micromol/g.

Molecular dynamics simulation studies of the transport and adsorption of a charged macromolecule onto a charged adsorbent solid surface immersed in an electrolytic solution

Molecular dynamics simulations were performed in order to study the transport and adsorption of a charged macromolecule (desmopressin) onto a charged solid surface in an electrolytic solution. The strong Coulombic interaction from the charged solid surface represents the major force for accelerating, orienting, entrapping in the electrical double layer, and adsorbing the macromolecule onto the charged solid surface. The macromolecule is flattened as it approaches the charged surface, giving rise to a stronger surface exclusion effect that shields surface sites. When adsorbed, the macromolecule is restrained by a surface interaction more than one hundred times stronger than the thermal energy, of which 99.8% results from the strong dominant Coulombic interaction, and trapped by a hydration layer adjacent to the surface. This leads to zero lateral displacement of the adsorbed macromolecule and indicates that surface diffusion is a physically implausible mechanism in similar systems. Explicit solvent is required for realistic representation of the macromolecular structure and the surface interaction energy. The adsorbed macromolecule also decreased the electrostatic potential gradient perpendicular to the charged solid surface and introduced additional electrostatic potential gradients laterally. The results obtained from the molecular dynamics simulations confirm the importance of electrophoretic migration and support the physical mechanisms used in a macroscopic continuum model that predicts an overshoot in the concentration of a charged macromolecule in the adsorbed phase under certain conditions of pH and ionic strength.

Novel general expressions that describe the behavior of the height equivalent of a theoretical plate in chromatographic systems involving electrically-driven and pressure-driven flows

Novel general expressions are constructed and presented that describe the behavior of the height equivalent of a theoretical plate (plate height), H, as a function of the linear velocity, Vx, along the axis, x, of the column and the kinetic parameters that characterize the mass transfer and adsorption mechanisms in chromatographic columns. Open tube capillaries as well as columns packed with either non-porous or porous particles are studied. The porous particles could have unimodal or bimodal pore-size distributions and intraparticle convective fluid flow and pore diffusion are considered. The expressions for the plate height, H, presented in this work could be applicable to high-performance liquid chromatography (HPLC) and capillary electrochromatography (CEC) systems, and could be used together with experimental plate height, H, versus linear velocity, Vx, data to determine the values of the parameters that characterize intraparticle convective fluid flow and pore diffusion. Furthermore, chromatographic systems under unretained as well as under retained conditions are examined. The experimental values of the plate height, H, versus the linear velocity, Vx, for a CEC system involving charged porous silica C8 particles and an uncharged analyte are compared with the theoretical results for the plate height, H, obtained from the expressions presented in this work. The agreement between theory and experiment is good, and the results indicate that the magnitude of the intraparticle electroosmotic flow (EOF) in the pores of the particles is substantial while the pore diffusion coefficient was of small magnitude. But the overall intraparticle mass transfer resistance in these particles was low because of the significant contribution of the intraparticle EOF. Simulation results are also presented (i) for a hybrid HPLC-CEC system, and (ii) for different CEC systems involving open capillaries as well as packed columns having non-porous or porous particles. The analysis of the results indicates (a) the reasons for the superior performance exhibited by the hybrid HPLC-CEC system over the performance obtained when the system is operated only in the HPLC mode, and (b) the operational configuration and the properties that the structure of the porous particles would have to have in CEC systems involving uncharged or charged analytes under unretained or retained conditions in order to obtain high CEC efficiency (low values of the plate height, H).

Analysis of diffusion models for protein adsorption to porous anion-exchange adsorbent

The ion-exchange adsorption kinetics of bovine serum albumin (BSA) and gamma-globulin to an anion exchanger, DEAE Spherodex M, has been studied by batch adsorption experiments. Various diffusion models, that is, pore diffusion, surface diffusion, homogeneous diffusion and parallel diffusion models, are analyzed for their suitabilities to depict the adsorption kinetics. Protein diffusivities are estimated by matching the models with the experimental data. The dependence of the diffusivities on initial protein concentration is observed and discussed. The adsorption isotherm of BSA is nearly rectangular, so there is little surface diffusion. As a result, the surface and homogeneous diffusion models do not fit to the kinetic data of BSA adsorption. The adsorption isotherm of gamma-globulin is less favorable, and the surface diffusion contributes greatly to the mass transport. Consequently, both the surface and homogeneous diffusion models fit to the kinetic data of gamma-globulin well. The adsorption kinetics of BSA and gamma-globulin can be very well fitted by parallel diffusion model, because the model reflects correctly the intraparticle mass transfer mechanism. In addition, for both the favorably bound proteins, the pore diffusion model fits the adsorption kinetics reasonably well. The results here indicate that the pore diffusion model can be used as a good approximate to depict protein adsorption kinetics for protein adsorption systems from rectangular to linear isotherms.

The Interplay of Diffusional and Electrophoretic Transport Mechanisms of Charged Solutes in the Liquid Film Surrounding Charged Nonporous Adsorbent Particles Employed in Finite Bath Adsorption Systems

A model that describes the diffusive and electrophoretic mass transport of the cation and anion species of a buffer electrolyte and of a charged adsorbate in the liquid film surrounding nonporous adsorbent particles in a finite bath adsorption system, in which adsorption of the charged adsorbate onto the charged surface of the nonporous particles occurs, is constructed and solved. The dynamic behavior of the mechanisms of this model explicitly demonstrates (a) the interplay between the diffusive and electrophoretic molar fluxes of the charged adsorbate and of the species of the buffer electrolyte in the liquid film surrounding the nonporous adsorbent particles, (b) the significant effect that the functioning of the electrical double layer has on the transport of the charged species and on the adsorption of the charged adsorbate, and (c) the substantial effect that the dynamic behavior of the surface charge density has on the functioning of the electrical double layer. It is found that at equilibrium, the value of the concentration of the charged adsorbate in the fluid layer adjacent to the surface of the adsorbent particles is significantly greater than the value of the concentration of the adsorbate in the finite bath, while, of course, the net molar flux of the charged adsorbate in the liquid film is equal to zero at equilibrium. This result is very different than that obtained from the conventional model that is currently used to describe the transport of a charged adsorbate in the liquid film for systems involving the adsorption of a charged adsorbate onto the charged surface of nonporous adsorbent particles; the conventional model (i) does not consider the existence of an electrical double layer, (ii) assumes that the transport of the charged adsorbate occurs only by diffusion in the liquid film, and (iii) causes at equilibrium the value of the charged adsorbate in the liquid layer adjacent to the surface of the particles to become equal to the value of the concentration of the charged adsorbate in the liquid of the finite bath. Furthermore, it was found that a maximum can occur in the dynamic behavior of the concentration of the adsorbate in the adsorbed phase when the value of the free molecular diffusion coefficient of the adsorbate is relatively large, because the increased magnitude of the synergistic interplay between the diffusive and electrophoretic molar fluxes of the adsorbate in the liquid film allows the adsorbate to accumulate (to be entrapped) in the liquid layer adjacent to the surface of the adsorbent particles faster than the concentrations of the electrolyte species, whose net molar fluxes are significantly hindered due to their opposing diffusive and electrophoretic molar fluxes, can adjust to account for the change in the surface charge density of the particles that arises from the adsorption of the charged adsorbate. The results presented in this work also have significant implications in finite bath adsorption systems involving the adsorption of a charged adsorbate onto the surface of the pores of charged porous adsorbent particles, because the diffusion and the electrophoretic migration of the charged solutes (cations, anions, and charged adsorbate) in the pores of the adsorbent particles will depend on the dynamic concentration profiles of the charged solutes in the liquid film surrounding the charged porous adsorbent particles. The results of the present work are also used to illustrate how the functioning of the electrical double layer could contribute to the development of inner radial humps (concentration rings) in the concentration of the adsorbate in the adsorbed phase of charged porous adsorbent particles.

Mathematical analysis of frontal affinity chromatography in particle and membrane configurations

The scaleup and optimization of large-scale affinity-chromatographic operations in the recovery, separation and purification of biochemical components is of major industrial importance. The development of mathematical models to describe affinity-chromatographic processes, and the use of these models in computer programs to predict column performance is an engineering approach that can help to attain these bioprocess engineering tasks successfully. Most affinity-chromatographic separations are operated in the frontal mode, using fixed-bed columns. Purely diffusive and perfusion particles and membrane-based affinity chromatography are among the main commercially available technologies for these separations. For a particular application, a basic understanding of the main similarities and differences between particle and membrane frontal affinity chromatography and how these characteristics are reflected in the transport models is of fundamental relevance. This review presents the basic theoretical considerations used in the development of particle and membrane affinity chromatography models that can be applied in the design and operation of large-scale affinity separations in fixed-bed columns. A transport model for column affinity chromatography that considers column dispersion, particle internal convection, external film resistance, finite kinetic rate, plus macropore and micropore resistances is analyzed as a framework for exploring further the mathematical analysis. Such models provide a general realistic description of almost all practical systems. Specific mathematical models that take into account geometric considerations and transport effects have been developed for both particle and membrane affinity chromatography systems. Some of the most common simplified models, based on linear driving-force (LDF) and equilibrium assumptions, are emphasized. Analytical solutions of the corresponding simplified dimensionless affinity models are presented. Particular methods for estimating the parameters that characterize the mass-transfer and adsorption mechanisms in affinity systems are described.

Modeling and analysis of the dynamic behavior of mechanisms that result in the development of inner radial humps in the concentration of a single adsorbate in the adsorbed phase of porous adsorbent particles observed in confocal scanning laser microscopy experiments: diffusional mass transfer and adsorption in the presence of an electrical double layer

A theoretical model for adsorption of a single charged adsorbate that accounts for the presence of an electrical double layer in the pores of adsorbent particles is constructed and solved. The dynamic behavior of the mechanisms of the model can result in the development of inner radial humps (concentration rings) in the concentration of a single charged analyte (adsorbate) in the adsorbed phase of porous adsorbent particles. The results of the present work demonstrate the implication of the concept regarding the effect of the presence of an electrical double layer in the pores of adsorbent particles and the induced interactions between the electrostatic potential distribution and the mechanisms of mass transport of the species by diffusion, electrophoretic migration, and adsorption. Furthermore, the mechanisms of the model could explain qualitatively the development of the concentration ring (hump) observed in confocal scanning laser microscopy experiments.

Protein adsorption equilibria and kinetics to a poly(vinyl alcohol)-based magnetic affinity support

A poly(vinyl alcohol)-based magnetic gel entrapping Fe3O4 colloids has been prepared by an emulsification-crosslinking method. The gel was modified with Cibacron blue 3GA, and thus a magnetic affinity support was produced. The adsorption equilibrium studies showed that the adsorption isotherm of lysozyme was nearly rectangular, with a capacity of 254 mg/ml, while the adsorption isotherm of bovine serum albumin obeyed the Henry's law. Uptake kinetics of the two proteins was investigated and analyzed with a pore diffusion model and a homogeneous diffusion model. Experimental results showed that the magnetic affinity gel had magnetic responsiveness and favorable properties in protein adsorption, and was mechanically and chemically stable.

Modeling and simulation of the dynamic behavior of monoliths. Effects of pore structure from pore network model analysis and comparison with columns packed with porous spherical particles

A mathematical model is presented that could be used to describe the dynamic behavior, scale-up, and design of monoliths involving the adsorption of a solute of interest. The value of the pore diffusivity of the solute in the pores of the skeletons of the monolith is determined in an a priori manner by employing the pore network modeling theory of Meyers and Liapis [J. Chromatogr. A, 827 (1998) 197 and 852 (1999) 3]. The results clearly show that the pore diffusion coefficient, Dmp, of the solute depends on both the pore size distribution and the pore connectivity, nT, of the pores in the skeletons. It is shown that, for a given type of monolith, the film mass transfer coefficient, Kf, of the solute in the monolith could be determined from experiments based on Eq. (3) which was derived by Liapis [Math. Modelling Sci. Comput., 1 (1993) 397] from the fundamental physics. The mathematical model presented in this work is numerically solved in order to study the dynamic behavior of the adsorption of bovine serum albumin (BSA) in a monolith having skeletons of radius r(o) = 0.75x10(-6) m and through-pores having diameters of 1.5x10(-6)-1.8x10(-6) m [H. Minakuchi et al., J. Chromatogr. A, 762 (1997) 135]. The breakthrough curves of the BSA obtained from the monolith were steeper than those from columns packed with porous spherical particles whose radii ranged from 2.50x10(-6) m to 15.00x10(-6) m. Furthermore, and most importantly, the dynamic adsorptive capacity of the monolith was always greater than that of the packed beds for all values of the superficial fluid velocity, Vtp. The results of this work indicate that since in monoliths the size of through-pores could be controlled independently from the size of the skeletons, then if one could construct monolith structures having (a) relatively large through-pores with high through-pore connectivity that can provide high flow-rates at low pressure drops and (b) small-sized skeletons with mesopores having an appropriate pore size distribution (mesopores having diameters that are relatively large when compared with the diameter of the diffusing solute) and high pore connectivity, nT, the following positive results, which are necessary for obtaining efficient separations, could be realized: (i) the value of the pore diffusion coefficient, Dmp, of the solute would be large, (ii) the diffusion path length in the skeletons would be short, (iii) the diffusion velocity, vD, would be high, and (iv) the diffusional response time, t(drt), would be small. Monoliths with such pore structures could provide more efficient separations with respect to (a) dynamic adsorptive capacity and (b) required pressure drop for a given flow-rate, than columns packed with porous particles.

Frontal chromatography of proteins. Effect of axial dispersion on column performance

A mathematical model describing the dynamic adsorption of proteins in columns packed with spherical porous adsorbent particles is used to study the effect of axial dispersion on the performance of chromatographic systems. The values of the axial dispersion coefficient, DL, are estimated from a correlation based on a model describing axial dispersion in packed beds that provides satisfactory results when compared with experiment. Simulations of frontal chromatography in systems including axial dispersion and in systems without axial dispersion are made and compared to determine the effect of axial dispersion on the efficiency of the adsorption process; also, the system parameters that influence axial dispersion are examined. It is found that the reduction in the efficiency of the adsorption process due to axial dispersion is small (< 1%) for columns of length 10 cm or greater. However, for short columns, this efficiency reduction can be as large as 10%. Increasing the adsorbent particle diameter, dp, increases the magnitude of the reduction in efficiency due to axial dispersion; the effect of increasing the adsorbent particle diameter, dp, is much more pronounced in a short column than in a long column.