Optimization of hydrophobic interaction chromatography using a mathematical model of elution curves of a protein mixture

Abstract

This paper describes a methodology for optimizing performance of hydrophobic interaction chromatography (HIC) for protein mixtures in which Rate Model simulations and evaluation of cost function are used. The system under study was HIC of a two-protein mixture (alpha-chymotrypsin and alpha-amylase), carried out with different conditions (gradient steepness, salt, concentration, volume of sample, pH, type of matrix, and flow rates). Parameters in the rate model were obtained from different sources. Mass transfer parameters (Reynolds, Peclet, and Biot numbers) were calculated using empirical correlations. Under the experimental conditions Re number was small (0.23) and axial dispersion negligible (PeL>300). Mass transfer was controlled by intraparticle diffusion (Bi>50). The model assumes that equilibrium constant (b) in the Langmuir isotherm was salt concentration (I) dependent [b(I)]. Parameters in the relationship for b(I) were estimated from experimental single protein elution curves and used to simulate protein mixtures. Rate model simulations showed that if protein sample load to the column was below 1 mg, displacement effects were negligible; in other cases protein interactions would limit the proposed mathematical description of HIC. The calibrated Rate Model successfully predicted elution curves of the protein mixture with deviations lower than 6x10(-4) absorbance units. The model was also able to predict that the Butyl Sepharose--NaCl 4 M system allowed to obtain the highest resolution (>1) for the two-protein mixture evaluated. The cost function built for optimizing the performance of HIC considers yield, purity, concentration, and the time needed to accomplish the separation. This function contains two types of parameters that have to be determined. The ones dependent on the HIC system and process conditions were obtained from simulations of elution curves of the two-protein mixture, by the calibrated Rate Model. The other parameters are dependent on characteristic and quality of the protein product; these were assumed for illustration purpose. Minimization of the cost function allows determination of flow rate, gradient steepness, and the fraction of eluted peak that has to be collected. Novelty of the present work is in showing how parameters in the fundamentally based Rate Model for HIC can be calibrated and how simulations can be used for the optimization of process conditions for the separation of a protein mixture.

Elution relationships to model affinity chromatography using a general rate model

“…Several papers can be found in the literature that present models to simulate protein elution curves of different types of chromatography (Yamamoto et al, 1983;Gallant et al, 1996;Li et al, 1998;Gu and Zheng, 1999;Gu et al, 2003;Shene et al, 2006;Lienqueo et al, 2009;Orellana et al, 2009). In particular, for affinity chromatography, there is work from Gu and coworkers (2003) who use a general rate model with a second-order kinetic binding reaction including size exclusion factors.…”

Mathematical Modeling of Protein Chromatograms

“…The relationship proposed by Melander et al [50] that relates the retention factor k′ and the concentration of the displacer has been used in the simulation of HIC [71], AC [72], and IEX [77]: log 10 k′ a′ À b log 10 C N1 cC N1 (14) where b and c are the electrostatic and hydrophobic interaction parameters, respectively, and a′ is a constant involving characteristic system parameters. These three parameters have to be determined experimentally for each protein.…”

“…(15), the term fC ∞ was lumped into a parameter a (= a′log 10 (fC ∞ )). In the HIC simulation b was set to zero [71] because the process is driven by the hydrophobic interaction effect while for IEX c was set to zero [73].…”

“…McCue et al [87] used this isotherm to solve the GRM for simulating isocratic curves of a monomer and aggregate protein mixture. Lienqueo et al [71] included the multicomponent Langmuir isotherm in the GRM to describe and simulate elution curves of protein mixtures in HIC as well as to optimize their separation using salt gradient elution.…”

Characterization and modeling of nonlinear hydrophobic interaction chromatographic systems

“…Recently, a new thermodynamic isotherm has been proposed that describes adsorption in terms of water displacement, protein and ligand density and distinguishes the effects of ligand densities and types [29][30]. Furthermore, Lienqueo et al [31] have recently developed a methodology for optimizing performance of protein mixtures in HIC systems using simple rate model. The general rate model of chromatography is the most comprehensive of all the transport models and has been used to describe both linear [32,33] and nonlinear [34][35][36] chromatographic systems.…”