Radiotracer measurements of protein mass transfer: kinetics in ion exchange media

We describe a method to measure protein mass transfer kinetics in ion exchange adsorbents for preparative chromatography based on the use of radioactively labeled protein. The method was developed and evaluated using lysozyme as a test protein with the three commercial strong-acid cation exchangers SP-Sepharose-FF, SP-Sepharose-XL, and S-HyperD. Iodination with 125I was used to label the protein, which was added in trace amounts (approximately 0.1%) to an unlabeled protein solution. The solution was recirculated through a shallow bed of the adsorbent particles and the radioactivity accumulated in the bed measured with a gamma-counter as a function of time. Radiotracer-based kinetics measurements were found to be in good agreement with results obtained with a conventional shallow-bed technique, provided that freshly labeled protein solutions were used. The method has advantages in terms of simplicity, ability to deal with adsorption from complex mixtures, and the potential for measurements under tracer diffusion conditions. Kinetics results obtained for the three different stationary phases were generally consistent with previous studies. Protein mass transfer can be described by a pore diffusion model with a nearly salt-independent pore diffusivity for SP-Sepharose-FF and by a homogeneous diffusion model with a saltindependent adsorbed phase diffusivity for S-HyperD. However, it appears that a more complex model, accounting for parallel pore and surface diffusion, is needed to describe protein mass transfer in SP-Sepharose-XL. The modeling results were found to be correlated with the apparent pore sizes determined by inverse SEC.     

Adsorption of rutin with a novel β-cyclodextrin polymer adsorbent: Thermodynamic and kinetic study

The adsorption properties toward rutin of a cyclodextrin polymer adsorbent CroCD-TuC 3 have been studied. The adsorption capacity is reduced as temperature and pH of solution rises, but increases with the increase of solvent polarity. Compared with Sephadex? G-15 dextran gel beads, CroCD-TuC 3 shows dramatically higher isosteric enthalpy due to a significant contribution of rutin/β-cyclodextrin inclusion complex formation in CroCD-TuC 3 skeleton. A highlight in our study is that the pore diffusion model has been employed to describe the mass transfer inside the adsorbent pores. It reveals that the diffusion inside the pores is the rate-restricting step in the whole adsorption process. The effective pore diffusivity of rutin in CroCD-TuC 3 calculated is much lower than the diffusivity in diluted solution. The pore diffusion model is an available tool to investigate the profile of mass transfer inside the pores, and provides an effective method to describe adsorption kinetics.     

Modeling of preparative reversed-phase HPLC of insulin

The adsorption isotherms of three recombinant proteins, human insulin, porcine insulin, and Lispro, were measured by frontal analysis on a YMC-ODS C18 column with an aqueous solution at 31% acetonitrile (0.1% TFA) as the mobile phase. The retention behavior of insulin, its related molecular structure, its conformation, and its aggregation in this phase system are discussed. The experimental isotherm data were fitted to the Langmuir, the Langmuir-Freundlich, and the Toth models. The results allow for a quantitative comparison of the saturation capacities, the equilibrium constants, and the exponents that represent the heterogeneity of the stationary phase obtained for the different insulin variants studied. The Toth model provided the best fit of the experimental data. The overloaded band profiles were calculated using the lumped pore diffusion and the equilibrium-dispersive model of chromatography. An excellent agreement between calculated and experimental profiles was demonstrated.     

Apolipoprotein A-I(Milano) anion exchange chromatography: mass transfer and adsorption kinetics

The mass transfer and adsorption kinetics of self-associating apolipoprotein A-I(Milano) (apoA-I(M)) was investigated for the two anion exchangers Q-Sepharose-HP and Macro-Prep-HQ. At high salt where no protein binding occurs and without urea, mass transfer was controlled by hindered pore diffusion of multiple associated forms for both materials. Adding urea suppressed self-association, but resulted in higher viscosity and caused unfolding. As a consequence, the effective diffusivity decreased as urea was added and was greater for the larger pore Macro-Prep-HQ resin. At low salt, under strong binding conditions, the adsorption kinetics followed a more complex mechanism. In this case, the kinetics was very slow for both stationary phases up to 2 M urea. However, at higher urea concentrations, the adsorption kinetics for the smaller pore Q-Sepharose-HP matrix became much faster, suggesting a transition from pore- to surface-dominated diffusion. Microscopic observations confirmed that different transport mechanisms were in play below and above 2 M urea, which marked the approximate boundary above which self-association was suppressed and unfolding occurred. The net result was enhanced uptake kinetics at high urea concentrations (e.g., 4 M) where protein unfolding is thought to lead to a more flexible structure that can reptate along the pore surface. Although the observed enhancement was dependent on the pore size and, thus, the surface area of the resin, it was not limited to apoA-I(M). BSA showed a similar trend as a function of urea when its disulfide bonds were reduced.     

Equivalent models of indanol isomers adsorption on cellulose tribenzoate

The adsorption isotherm data of (R)- and (S)-1-indanol and of their racemic mixture on cellulose tribenzoate were measured by frontal analysis. The experimental data for each enantiomers were fitted to the single-component bilangmuir isotherm model. The competitive experimental data were fitted to the ideal adsorption solution model (IAS), the real adsorption solution model (RAS), and the bilangmuir thermodynamically consistent model (BTC). The mass transfer kinetic parameters were estimated from systematic comparisons between the experimental single-component band profiles and profiles calculated using the general rate model (GR) of chromatography coupled with the generalized Maxwell-Stefan equation (GMS). The validation of the isotherm model and of the mass transfer kinetic model was made by comparing the experimental band profiles obtained for solutions of the two enantiomers and those calculated with the competitive GR-GMS model. The excellent agreement observed proves that a combination of the BTC isotherm model and the GMS kinetic model, using the best values of the BTC and GMS parameters estimated from single component experiments, allows an excellent prediction of the binary isotherm and the binary mass transfer kinetics.     

Characterization of a continuous supermacroporous monolithic matrix for chromatographic separation of large bioparticles

A continuous supermacroporous monolithic chromatographic matrix has been characterized using a capillary model, experimental breakthrough curves, and pressure drop experiments. The model describes the convective flow and its dispersive mixing effects, mass transfer resistance, pore size distribution, and the adsorption behavior of the monolithic matrix. It is possible to determine an effective pore size distribution by fitting the capillary model to experimental breakthrough curves and pressure drop experiments. The model is able to describe the flow rate dependence of the experimental breakthrough curves. Mass transport resistance was due to: (i) dispersive mixing effects in the convective flow in the pores; and (ii) slow diffusion in the stagnant film covering the surface within each pore, under adsorption conditions. The monolithic matrix can be described by a very narrow pore size distribution, illustrating one of the advantages of the gel. A broader pore size distribution results in increased band broadening. This can be studied easily using the model developed in this investigation.     

A study of mass transfer kinetics in an enantiomeric separation system using a polymeric imprinted stationary phase

Chromatographic data pertaining to the enantioseparation of L- and D-phenylalanine anilide (PA) on a polymeric stationary phase imprinted with L-PA were studied from the viewpoints of phase equilibrium, mass transfer kinetics, and the thermodynamic properties of this enantiomeric separation system. The concentration dependence of the lumped mass transfer rate coefficient (k(m,L)) previously published was analyzed to obtain new information concerning the mass transfer characteristics in this chiral separation system. It was shown that intraparticle diffusion contributed much more to k(m,L) than adsorption/desorption. The positive concentration dependence of k(m,L) seemed to be interpreted by considering that of the surface diffusion coefficient, itself explained by the heterogeneous surface model. The characteristic features of the phase equilibrium, the mass transfer kinetics, and the thermodynamics of the enantiomeric separation system probably result from the adsorption energy distribution on the surface of the imprinted phase having an exponential decay.     

Adsorption kinetics and equilibria of bovine serum albumin on rigid ion-exchange and hydrophobic interaction chromatography matrices in a stirred cell

Rigid adsorbents have advantages over soft gel media for downstream processing of proteins. The adsorption of bovine serum albumin (BSA) has been investigated on a rigid adsorbent based on a wide-pore, hydrophilically coated, silica-gel matrix. The effects of surface chemistry (weak anion exchanger and hydrophobic interaction chromatography) and particle size have been studied on the physical properties of the adsorbent and on the adsorption equilibria and adsorption kinetics. The rates of adsorption of BSA have been measured in a stirred cell and are found to be satisfactorily described by a two-step theoretical model, in which the mass transfer involves a pore diffusion resistance and an extra-particle film resistance. On the anion exchanger, the effective pore diffusivity decreases substantially with increasing protein concentration, approximately halving as the initial concentration rises from 0.7 to 2g/l. In the hydrophobic interaction chromatography medium, the pore diffusivity is less sensitive to protein concentration and is also reduced by a factor of about 4 by aggregation of the protein. Effective pore diffusivities with the "wide-pore" silica adsorbents in anion-exchange form are 36-94 times lower than the diffusivity in free solution and are comparable with the lower of the wide range of values published for soft gels.     

Mass transfer effects on the reaction rate for heterogeneously distributed immobilized yeast cells

Here we examine the efficiency of different immobilized cell gradients applied to immobilized Saccharomyces cerevisiae fermenting glucose to ethanol. We developed a simulation model to fully study the competing effects of mass transfer hindrance and kinetics. It is based on a diffusion-reaction model and can be used to analyze the different cell concentration profiles inside an immobilized gel bead, in terms of effectiveness factors, productivity, and mass flux. The internal diffusion coefficient, which varies with the local cell concentration, as well as the external mass transfer, is taken into account when describing the efficiency. Although the diffusion hindrance is greater at higher cell concentrations, high cell concentration is still advantageous in the present case because the increase in reaction rate outweighs the diffusion hindrance. Thus, high cell concentrations contribute to increased productivity. The influence of the cell concentration gradient on the efficiency of the beads is negligible. Within the range of cell profiles studied it has been established that the location of the cells within the bead is of lesser importance. However, a steep cell gradient increases the importance of the external mass transfer.     

An Efficient Wavelet Analysis Method to Film–Pore Diffusion Model Arising in Mathematical Chemistry

In this paper, we have established an efficient Legendre wavelet based approximation method to solve film–pore diffusion model arising in engineering. Film–pore diffusion model is widely used to determine study the kinetics of adsorption systems. The use of Legendre wavelet based approximation method is found to be accurate, simple, fast, flexible, convenient, and computationally attractive. It is shown that film–pore diffusion model satisfactorily describe kinetics of methylene blue adsorption onto the three low-cost adsorbents, Guava, teak and gulmohar plant leaf powders, used in this study.     

Influence of mass transfer limitations on the enzymatic synthesis of β-lactam antibiotics catalyzed by penicillin G acylase immobilized on glioxil-agarose

Mass transfer effects were investigated for the synthesis of ampicillin and amoxicillin, at pH 6.5 and 25 degrees C, catalyzed by penicillin G acylase immobilized on agarose. The influence of external mass transfer was analysed using different stirring rates, ranging form 200 to 800 rpm. Above 400 rpm, the film resistance may be neglected. Intra-particle diffusion limitation was investigated using biocatalysts prepared with different enzyme loads and agarose with different mean pore diameters. When agarose with 6, 8 and 10% of crosslinking were used, for the same enzyme load, substrates and products concentration profiles presented no expressive differences, suggesting pore diameter is not important parameter. An increase on enzyme load showed that when more than 90 IU of enzyme activity were used per mL of support, the system was influenced by intra-particle mass transfer. A reactive-diffusive model was used to estimate effective diffusivities of substrates and products.     

Pore network modelling of affinity chromatography: determination of the dynamic profiles of the pore diffusivity of beta-galactosidase and its effect on column performance as the loading of beta-galactosidase onto anti-beta-galactosidase varies with time.

A three-dimensional pore network model for diffusion in porous adsorbent particles was employed in a dynamic adsorption model that simulates the adsorption of a solute in porous particles packed in a chromatographic column. The solution of the combined model yielded the dynamic profiles of the pore diffusion coefficient of beta-galactosidase along the radius of porous adsorbent particles and along the length of the column as the loading of beta-galactosidase onto anti-beta-galactosidase immobilized on the surface of the pores of the particles occurred, and, the dynamic adsorptive capacity of the chromatographic column as a function of the design and operational parameters of the chromatographic system. It was found that for a given column length the dynamic profiles of the pore diffusion coefficient were influenced by (a) the superficial fluid velocity in the column, (b) the diameter of the adsorbent particles, and (c) the pore connectivity of the porous structure of the adsorbent particles. The effect of the magnitude of the pore connectivity on the dynamic profiles of the pore diffusion coefficient of beta-galactosidase increased as the diameter of the adsorbent particles and the superficial fluid velocity in the column increased. The dynamic adsorptive capacity of the column increased as (i) the particle diameter and the superficial fluid velocity in the column decreased, and (ii) the column length and the pore connectivity increased. In preparative affinity chromatography, it is desirable to obtain high throughputs within acceptable pressure gradients, and this may require the employment of larger diameter adsorbent particles. In such a case, longer column lengths satisfying acceptable pressure gradients with adsorbent particles having higher pore connectivity values could provide high dynamic adsorptive capacities. An alternative chromatographic system could be comprised of a long column packed with large particles which have fractal pores (fractal particles) that have high pore connectivities and which allow high intraparticle diffusional and convective flow mass transfer rates providing high throughputs and high dynamic adsorptive capacities. If large scale monoliths could be made to be reproducible and operationally stable, they could also offer an alternative mode of operation that could provide high throughputs and high dynamic adsorptive capacities.     

Mass transfer limitations in diffusion-limited isotropic hollow fiber bioreactors

Diffusional mass transfer limitations in hollow fiber bioreactors – with densely packed whole cells in its extracapillary space to perform biotransformation reactions – have been studied theoretically using a steady-state diffusion and reaction model. Simple analytical expressions have been derived to calculate the radial and axial concentration profiles for zero- and first-order kinetics, as well as to plot effectiveness factor versus Thiele modulus plots for first-order kinetics. The influence of the magnitude of the effective diffusion coefficients, the thickness of the isotropic membrane as well as the size of the annular cell region have been assessed to optimise the reactor performance.     

Rate-limiting mass transfer in immunosorbents: characterisation of the adsorption of paraquat-protein conjugates to anti-paraquat Sepharose 4B

A series of paraquat-protein conjugates of different molecular size has been prepared by the coupling of paraquat hexanoate to the proteins lysozyme, ovalbumin, bovine serum albumin. The characteristics of the adsorption of these conjugates to an immunosorbent consisting of monoclonal anti-paraquat antibodies covalently immobilised to Sepharose 4B have been determined. Equilibrium adsorption isotherms were found to obey the Langmuir equation and indicated that 80% or more of the antibody binding sites were accessible to the conjugates. The rates of mass transfer of the conjugates to their adsorption sites on the immobilised antibodies was well described by a model in which mass transfer is controlled by transfer across the external film and diffusion within the porous adsorbent bead. The effective diffusivities of the conjugates within the immunosorbent were measured and has allowed the effect of the size of the adsorbing molecule on the rate of adsorption to be considered. The amount of paraquat that could be adsorbed and the rates of adsorption decreased as the size of the protein to which it is conjugated increased. The diffusivity of the conjugates within the pores of the adsorbent is reduced between two and five times compared to their diffusivities in free solution. The reduction is greater for the larger proteins and the variations of the effective diffusivities and the pore diffusivities with the molecular weight of the conjugate can be well described with simple correlations.     

Insulin adsorption into porous charged membranes: Effect of the electrostatic interaction

Insulin adsorption into a series of porous charged membranes was investigated by batch adsorption experiments, and the experimental results were analyzed by the homogeneous diffusion model. The membranes used in this study were prepared by pore‐surface modification of porous poly(acrylonitrile) (PAN) membranes by grafting with weak acidic and basic functional groups. The amount of insulin adsorbed into the membrane was determined from the material balance of insulin. The insulin partition coefficient K between the membrane and solution was estimated from the equilibrium adsorption amount, and the effective diffusion coefficient D was estimated by matching the model with the experimental data as a fitting parameter. The dependence of K and D on the charge properties of the insulin and membrane is observed and discussed. The partition coefficient K increased when the insulin and the membrane carried opposite charges, on the other hand, the effective diffusion coefficient D was reduced. These results indicate that the electrostatic interaction between the insulin and the membranes played an important role in the insulin adsorption. © 2009 American Institute of Chemical Engineers Biotechnol. Prog. 2009     

Identification of the mass transfer mechanisms involved in the transport of human immunoglobulin-G in N,N,N',N'-ethylenediaminetetramethylenephosphonic acid-modified zirconia

Zirconia particles modified with N,N,N',N'-ethylenediaminetetramethylenephosphonic acid (EDTPA), further referred to as r_PEZ, were studied as a support material for use in chromatography. Our previous studies have demonstrated the utility of r_PEZ in the separation of immunoglobulins from biological fluids. In the present study we sought to understand the underlying factors and identify the rate-limiting mechanisms that govern the transport of biomolecules in r_PEZ. Pulse injection techniques were used to elucidate the individual mass transfer parameters. Elution profiles obtained under retained and unretained conditions were approximated by the Gaussian equation and the corresponding HETP contributions were estimated. The dependence of the HETP values on incremental salt concentration in the mobile phase was determined. Resulting data in conjunction with the equations outlined in literature were used to estimate the theoretical number of transfer units for the chromatographic separation process. Our results indicate that surface diffusion probably plays a minor role; however pore diffusion was established to be the rate limiting mechanism for immunoglobulin G adsorption to r_PEZ. The HETP based methodology may be used to estimate the rate limiting mechanisms of mass transfer for any given chromatographic system under appropriate conditions.     

Engineered Biofilms for Metal Ion Removal

Firstly, biofilm and biosorbents are defined. Mechanisms of interactions between metal ions and biofilm are discussed in terms of diffusion, mass transfer and sorption. In a second step, different processes using biofilm to remove heavy metal in aqueous solutions are presented. The continuously stirred processes are described for metal ion removal in wastewater by biofilm coating particles. In this case, the equilibrium data obtained with isotherm curves show a good adsorption of several metal ions onto biofilm. Examples of adsorption capacities for a large number of microorganisms and heavy metal ions are presented. The fixed bed reactors packed with grains coated with a biofilm are efficient to get a sorption (adsorption or ion exchange) of cations. The pressure drop is calculated with classical equations. Some values such as adsorption capacities and breakthrough times are got from the breakthrough curves. Several models (Adams-Bohart, mass transfer, and homogeneous surface diffusion models) are applied to get design data. A new approach using neural network to model breakthrough curves is proposed and discussed.     

Solute exclusion from cellulose in packed columns: process modeling and analysis

In this investigation, process modeling and analysis were used to explore the behavior of solute exclusion from cellulose in packed columns. The study focused on modeling the effects of dispersion, mass transport, and pore diffusion. Three mathematical models were used to predict the behavior of the columns: an equilibrium model, a mass transfer model, and a combined mass transfer and pore diffusion model. Computer implementations of these models were tested against experimental conditions where cellulose particle size and solution velocity were used to either amplify or minimize dispersion or skewness in the elution curves. For small cellulose particles (200-300 mesh), all three models accurately predicted the shape of the elution curve and the particle porosity. For larger particles (45-60 mesh), the mass transfer model and the combined mass and pore diffusion model best represented the behavior of the column. At high solution velocities (0.63 cm(3) min(-1)) and large particles, only the combined mass transfer and pore diffusion model accurately represent the column behavior. Sensitivity analysis revealed that the mass transfer coefficient had little effect on the elution curves for the range of values (10(-6)-10(-3) cm s(-1)) calculated from the experimental data. The combined mass transfer and pore diffusion model presented in this article can be used to design solute exclusion measurement experiments for the larger cellulose particles found in a commercial cellulose-to-ethanol plant.     

Removal of lead from aqueous solutions by agricultural waste maize bran

Maize bran is a low cost biosorbent that has been used for the removal of lead(II) from an aqueous solution. The effects of various parameters such as contact time, adsorbate concentration, pH of the medium and temperature were examined. Optimum removal at 20 degrees C was found to be 98.4% at pH 6.5, with an initial Pb(II) concentration of 100 mg l(-1). Dynamics of the sorption process and mass transfer of Pb(II) to maize bran were investigated and the values of rate constant of adsorption, rate constant of intraparticle diffusion and the mass transfer coefficients were calculated. Different thermodynamic parameters viz., changes in standard free energy, enthalpy and entropy were evaluated and it was found that the reaction was spontaneous and exothermic in nature. The adsorption data fitted the Langmuir isotherm. A generalized empirical model was proposed for the kinetics at different initial concentrations. The data were subjected to multiple regression analysis and a model was developed to predict the removal of Pb(II) from an aqueous solution.