STERIC MASS ACTION MODEL FOR LACTOFERRIN ADSORPTION IN CRYOGEL WITH IMMOBILIZED COPPER IONS

Parameters of equilibrium adsorption obtained from experiments using immobilized metal affinity chromatography (IMAC) were used to evaluate the applicability of the steric mass-action (SMA) model to describe the adsorption of lactoferrin to cryogel resin under different conditions. The adsorption of lactoferrin on continuous supermacroporous cryogel with immobilized Cu ions was evaluated in batch adsorption experiments at different pH (6-8) and temperature (293-313 K) values. Estimated values of the equilibrium constant (K) and characteristic number of binding sites (n) showed that these parameters decreased with increasing ionic strength, pH and temperature, while the nonlinear parameter, the steric factor (), increased with increasing ionic strength and temperature. Expressions correlating these parameters with pH, ionic strength and temperature were then derived.


INTRODUCTION
The recent requirements of high purity proteins (both natural and recombinant), and the need of reducing costs of downstream processes have stimulated the development of more efficient and cheaper separation techniques (Frerick et al., 2008).It has been shown that Immobilized Metal Affinity Chromatography (IMAC) meets these requirements (Carvalho et al., 2014;Wang et al., 2008;Cheung et al., 2012).This technology is based on the chemical affinity displayed by certain groups of amino acid residues present on the surface of proteins (e.g., the imidazole group of histidine, thiol group of cysteine and tryptophan's indole group) with the metal ions immobilized on chromatographic resins (Gupta et al., 2002;Çimen and Denizli, 2012).
IMAC has been reported as a promissing technology for purification of proteins with an "N-terminal metal biding tag" (e.g., histidine tail and NT1A) (Puri et al., 2010;Petzold et al., 2014;Cheung et al., 2012), including on a large scale (Gaberc-Porekar and Menart, 2005), due to its low cost and the high purity of the eluate, even in a single step process (Puri et al., 2010;Carvalho et al., 2014).However, when approaching the purification of natural pro-Brazilian Journal of Chemical Engineering teins, IMAC may present some challenges since the amount of histidine on the surface accounts for only 1% of the total number of amino acids (Ueda et al., 2003).Then, optimum conditions of the medium, such as temperature, salt concentration and pH, should be determined to improve the specific adsorption of the target protein.Over the years, acceptance of IMAC as a reliable technique for separation on a laboratory scale has increased.However, its use on an industrial scale has still been only slightly explored.
The main interaction in IMAC is the coordinate bond.However, other interactions, such as electrostatic and hydrophobic, may also occur due to the environmental conditions.Generally, these three types of interplay should be considered.Nonetheless, it is not always possible to determine the relative contribution of each of them.It is known that the prevalence of a particular type of interaction over the others is essentially governed by certain variables, such as the nature of the chelating agent, the composition of the protein's surface and the chemical environment where the interplay occurs, that is, the solution's ionic strength, pH and type of salts are also determinants of the driving forces (Bresolin et al., 2009).This makes IMAC less predictable and its optimization a difficult task.Projects for IMAC on a preparative scale require a deep understanding of all the fundamental mechanisms that govern the protein adsorption.The knowledge of these processes provides a rational basis to establish chromatographic conditions for purification and scale-up (Bornhorst and Falke, 2000;Ueda et al., 2003).
Although the adsorption process in IMAC is considerably different from conventional methods, previous studies have shown that the interaction between a protein molecule and immobilized metal ions may be explained based on the application of isotherm models of both affinity and ion exchange phenomena (Jiang and Hearn, 1996;Chen et al.. 2005).Nonetheless, the universal applicability of a model to elucidate the precise molecular mechanisms by which proteins are retained in resins with chelated metals still must be established.Brooks and Cramer (1992) presented a new model, steric mass action (SMA), for protein adsorption equilibrium in nonlinear ion exchange systems.This model combines the stoichiometric displacement model (Rounds and Regnier, 1984;Drager and Regnier, 1986) with the concept of steric shielding of macromolecules presented later by Velayudhan (1990).Mainly used in ion exchange chromatography, the model involves three parameters, the number of identical binding sites (n), the equilibrium constant (K) and the steric factor ().It is assumed that the adsorption is an exchange process between the free protein molecule and a certain number of ions bound to the resin, which considers explicitly the steric hindrance of the counter ions of the salt on the binding of proteins.Recent studies have used the SMA model to describe protein adsorption equilibrium and the results have shown its efficiency for predicting the non-linear adsorption behavior of proteins (Chen et al., 2006;Barz et al., 2010).
Given the high demand for purified proteins, the development of mechanistic models which both predict adsorption with accuracy and provide one with process information (e.g., pH, salt concentration, temperature) is needed to design purification plants.Langmuir and other adsorption models, for example, do not explain the process at the molecular level.Detailed models like the SMA can indicate more clearly the driving force for the adsorption.Thus, in the present study, the applicability of the SMA model and the parametric sensitivity that describes the adsorption equilibrium of bovine lactoferrin in cryogel resins with copper ions immobilized through iminodiacetic acid (IDA-Cu +2 -cryogel) was analyzed under different conditions (pH, salt concentration and temperature) as an approach to mechanistic modeling for further industrial process development applications.

Synthesis of IDA-Cu 2+ Cryogel Adsorbent Resin
The synthesis of IDA-Cu 2+ -cryogel resin was carried out according to Kumar et al. (2006), as described by Carvalho et al. (2013).The cryo-copoly-Brazilian Journal of Chemical Engineering Vol. 33, No. 01, pp. 215 -223, January -March, 2016 merization reaction of solution containing AAm, MBAAm, AGE, TEMED and APS was performed.IDA was used as chelating agent to load copper within the matrix.All experiments were performed in triplicate.

Obtaining Adsorption Isotherms
Adsorption isotherm data were obtained by batch experiments, as described by Carvalho et al. (2013).3 mg of dried cryogel matrix were weighed in eppendorf tubes.Initially, the resin was equilibrated with 400 μL of equilibration buffer (20 mmol.L -1 HEPES containing 200 mmol.L -1 NaCl, pH 7.0).The tubes were left under mild stirring for a period of two hours to condition the resin.After this period, the equilibration buffer was removed and different volumes (0 to 300 μL) of a 10 mg.mL -1 solution of lactoferrin were added.Adsorption buffer (20 mmol.L -1 HEPES containing 400 mmol.L -1 , different pHs) was then added to make the volume up to 1200 L.The final protein concentrations in the tubes were 0, 0.1, 0.2, 0.3, 0.4, 0.6, 0.9, 1.2, 1.5, 1.8 and 2.2 mg.mL -1 .The tubes were kept under constant agitation for 24 hours under controlled temperature (101M Mod BOD/3 Eletrolab ®, Brazil), to achieve the equilibrium state.Subsequently, the resin was removed from the eppendorf tubes and the concentration of protein contained in the supernatant was determined spectrophotometrically at 280 nm (Thermo Scientific Model BIOMATE 3).The protein concentration in the solid phase was determined according to Equation (1): where q (mg.g -1 ) is the concentration of protein in the solid phase, V (mL) the volume of the liquid phase, M (g) is the mass of the solid phase, C 0 (mg.mL - ) is the initial concentration of protein in the liquid phase and (mg.mL -1 ) C is the final protein concentration in the liquid phase after the equilibrium state has been established.The experiment was conducted using a factorial design with three temperatures (20, 30 and 40 °C), three different pHs (6.0, 7.0 and 8.0) and a salt concentration of 400 mmol.L -1 .

Modeling the Equilibrium Data -The SMA Model
The applicability of the Zhang and Sun (2002) SMA model to describe the adsorption of LF onto IDA-Cu +2 -cryogel was evaluated in this work.In this model, the protein (Lactoferrin) would interact with ligands (immobilized Cu 2+ ions), present at a density L t (mmol.L -1 ), according to a "characteristic number of binding sites", n i .Further, during the protein adsorption, there may be a number of copper ions blocked by the 3D structure of the molecule, which prevents that other proteins coordinate to the ions.The number (average) of shielded cooper ions is given by the steric factor,  i .The following interaction balance can be written for each protein of the mixture (i): where C i and Q i represent, respectively, the concentrations of protein free in solution and bound to metal ions immobilized in the cryogel, and v L is the amount of immobilized copper free and unblocked to bind to molecules of LF.The equilibrium constant K i for the metal affinity process is given by: v 1,2, ...,N Because many ligands may be blocked by bound LF molecules, the equilibrium constant is redefined as: 1 ( ) where the term 1 ( )  is a mass balance for the copper ions and is equal to the density of metal available for protein binding.In this study, the equilibrium adsorption of lactoferrin onto IDA-Cu 2+cryogel was studied to examine the usefulness of the SMA model in describing such process.For this system, Equation (4) may be reduced to: In a dilute protein solution, the isotherm can be written as:    As shown in Table 2, for the majority of the cases studied, the steric factor value decreases with increasing temperature and, in some cases, it passes through a minimum at a temperature equal to 303 K. Indeed, as seen in Figure 2, the temperature increase leads to an increase of adsorption capacity of lactoferrin on IDA-Cu +2 -cryogel.When the temperature rise occurs in the adsorption process, there is a decrease in the energy of protein-water interaction, which results in increasing interactions between protein-copper ion.Thus, the increase of temperature is sufficient to break down the diffuse region of the electrical double layer, and thus the protein molecules interact more strongly with the resin, favoring the adsorptive phenomenon.Regarding the behavior of the steric factor values with respect to ionic strength and pH, it was observed that the steric factor decreased with increasing ionic strength, except for the conditions of pH 8, 293 K and 303 K.With regard to the pH, it is noted that, in some cases, the steric factor decreased with increasing pH, except at pH 7.0, where there was a peak in its value.Reasons for such behavior may be due to the fact that, in IMAC, the adsorption capacity and selectivity depend not only on the metal chelates immobilized on the chromatographic matrix, but also on the composition of the mobile phase.The protein retention in IMAC adsorbents occurs due to the contribution of various physico-chemical interactions, which may be enhanced or minimized depending on the composition of the mobile phase.When IMAC is operated at high salt concentration (0.5 to 1.0 mol.L -1 NaCl, for example), the predominant interaction is the coordinate bond between the immobilized metal ions and amino acid residues accessible on the surface proteins, while the electrostatic interactions occur with a lesser intensity.The electrostatic effects are more intense when employing a mobile phase with low ionic strength.These effects occur between charged proteins and the positive charges of the metal ions or negative charges remaining on the surface of the matrix (unreacted functional groups remaining from the activation and coupling of the chelator, or residual carboxylic groups of chelating agents due to incomplete chelation of metal ions) (Winzerling et al., 1992;Guitiérrez et al., 2007).
In IMAC, regarding the pH, coordinate bonds are favored when ionizable groups of electron donors amino acid residues present in biomolecules are partially deprotonated, i.e., when the pH of the solution is above the pKa of the ionizable groups (Bresolin et al. 2009).Moreover, since the coordinate bonds with the immobilized metal ions may occur simultaneously with electrostatic interactions, protein adsorption on IMAC is pH dependent.However, the effects of each interaction on the protein adsorption are difficult parameters to be determined.
On the one hand, high ionic strength leads to strong binding of salt ions to the IDA-Cu 2+ -cryogel resin, reducing the number of accessible binding sites for the protein (Wrzosek et al., 2009).On the other hand, there is a greater selectivity of coordinate binding, which is favored by high salt concentrations.The decreased resin adsorption capacity is a direct result of the binding of salt ions to metal ligands.It is shown in the SMA model as an apparent increase in σ.
Figure 2 shows a comparison between the simulations of the SMA model and equilibrium affinity data for the lactoferrin-IDA-Cu 2+ -cryogel complex at 400 mmol.L -1 NaCl, temperatures equal to 293 K, 303 K and 313 K, and pH 6.0, 7.0 and 8.0.It was found that the predicted adsorption capacities had higher values than the corresponding experimental ones, in most of the analyzed cases.At pHs near the lactoferrin isoelectric point, the accuracy of the model decreased further.It is known that the net charge and threedimensional structure of proteins are influenced by the pH of the buffer solution.Because lactoferrin has nine histidine residues (responsible for protein retention on the IDA-Cu 2+ -cryogel complex) having pKa = 6.5, in conditions above this value the medium is deprotonated, favoring other types of binding, not only the affinity.Thus, under these conditions, the SMA model failed to predict the change in behavior.
Figure 3 shows a comparison between experimental and predicted protein concentration values.As can be seen, there was a reasonable agreement between predicted concentrations of lactoferrin and those measured experimentally through variation of ionic strength, pH and temperature.Osberghaus et al. (2012) have determined parameters for the steric mass action model through two methods; approach I was based on frontal and gradient experiments, while approach II relied on the "application of an inverse method for parameter estimation".The SMA parameter obtained from this last method led to the best accuracy of "a mechanistic model" developed for column Fig tio liz sor mm tem Th 6.0 0.9 0.9 0.9