Lumped parameter model for prediction of initial breakthrough profiles for the chromatographic capture of antibodies from a complex feedstock

A simple mathematical model to predict initial breakthrough profiles from preparative chromatographic separations of biological macromolecules has been developed. A lumped parameter approach was applied, employing Langmuirian adsorption kinetics to describe the rate of mass transfer (MT) from the bulk liquid in the column to the bound state. Equilibrium and kinetic adsorption data were determined for six different packed bed chromatographic adsorbents: two derivatised with rProtein A; and four functionalised with synthetic low molecular weight ligands. All adsorption isotherms were well described by the Langmuir model, whereas the data fitting to kinetic batch experiments showed that the model was inadequate after the first approximately 25 min of adsorption for four of the six adsorbents. The model underestimated the dynamic Ig breakthough on packed beds of rProtein A Sepharose FF, MabSelect, MBI HyperCel, and MabSorbent A1P, applying a feedstock of 20-100% (v/v) clarified rabbit antiserum. However, when employing a maximum adsorption capacity 25% greater than that determined in batch binding studies, excellent agreement was obtained at all antiserum strengths for most adsorbents. Useful insights into scale-up and process design can be obtained by applying the model, without determining tentative parameters specific for each adsorbent and target protein concentration. However, the model parameters are solvent dependent so a prerequisite for its true applicability is that binding is both Langmuirian and essentially independent of the ionic strength of the feedstock applied.     

Modeling linear and variable growth in phosphate limited suspension cultures of Opium poppy

In examining the growth kinetics of cell suspensions of opium poppy (Papaver somniferum), the increase in biomass with time was observed to be linear over the entire batch growth period of up to 20 days. Although batch growth profiles were reproducible utilizing the same inoculum, growth rates varied tremendously when experiments were inoculated with cells from different flasks. Both of these phenomena are difficult to explain with conventional batch growth models. In a series of a experiments, phosphate was determined to be the growth-rate-limiting substrate. By expressing growth rate in terms of the intracellular reserves of phosphorus, a growth model which expresses kinetics in terms of the intracellular phosphorus contents of the cells is shown to predict both linear growth character and inoculum dependent variability in growth. The stationary phase phosphate content of seven plant suspension cultures of different plant species was found to be comparable to phosphorus levels of phosphate-starved poppy cells, which suggests that phosphate limitation may be common for plant tissue culture. The applicability of this model to other biological systems which display similar batch growth patterns when subjected to inorganic nutrient deprivation is discussed.     

Growth Kinetics of Thiobacillus thiooxidans on the Surface of Elemental Sulfur

The growth kinetics of Thiobacillus thiooxidans on elemental sulfur in batch cultures at 30(deg)C and pH 1.5 was studied by measuring the time courses of the concentration of adsorbed cells on sulfur, the concentration of free cells suspended in liquid medium, and the amount of sulfur oxidized. As the elemental sulfur was oxidized to sulfate ions, the surface concentration of adsorbed cells per unit mass of sulfur approached a maximum value (maximum adsorption capacity of sulfur particles) whereas the concentration of free cells continued to increase with time. There was a close relationship between the concentrations of free and adsorbed cells during the microbial sulfur oxidation, and the two cell concentrations were well correlated by the Langmuir isotherm with adsorption equilibrium constant K(infA) and maximum adsorption capacity X(infAm) of 2.10 x 10(sup-9) ml per cell and 4.57 x 10(sup10) cells per g, respectively. The total concentration of free and adsorbed cells increased in parallel with the amount of sulfate formed. The total growth on elemental sulfur gave a characteristic growth curve in which a linear-growth phase followed the period of an initial exponential phase. The batch rate data collected under a wide variety of inoculum levels (about 10(sup5) to 10(sup8) cells per ml) were consistent with a kinetic model assuming that the growth rate of adsorbed bacteria is proportional to the product of the concentration, X(infA), of adsorbed cells and the fraction, (theta)(infV), of adsorption sites unoccupied by cells. The kinetic and stoichiometric parameters appearing in the model were estimated from the experimental data, and the specific growth rate, (mu)(infA), and growth yield, Y(infA), were 2.58 day(sup-1) and 2.05 x 10(sup11) cells per g, respectively. The proposed model and the parameter values allowed us to predict quantitatively the surface attachment of T. thiooxidans cells on elemental sulfur and the bacterial growth in both initial exponential and subsequent linear phases. The transition from exponential to linear growth was a result of two competing factors: an increase in the adsorbed-cell concentration, X(infA), permitted a decrease in the unoccupied-site fraction, (theta)(infV).     

Growth models of cultures with two liquid phases. VI. Parameter estimation and statistical analysis

Parameter estimation studies have been conducted employing mathematical models developed previously by the investigators and experimental data collected by the last author. A batch fermentation process in which Candida lipolytica were cultured on n-hexadecane dissolved in dewaxed gas oil was employed to obtain the experimental data. The kinetic data from a number of batch experiments conducted at different initial substrate concentrations and different dispersed phase volume fractions were analyzed assuming that, the basic model parameters (maximum specific growth rate, saturation constant, substrate phase equilibrium constant, adsorption constant, desorption constant, etc.) did not change from experiment to experiment. The Gauss-Newton method with modification by Greenstadt, Eisenpress, Bard, and Carroll was used to minimize the conventional sum of squares criterion on the IBM 300/50 computer. The individual confidence intervals were obtained for each individual parameter. Tin- models were compared employing the F-test for equality of variances and an analysis of residuals. For the two best models, the estimated parameter values were compared with available experimental information. The results showed good agreement between the experimental data and the values predicted by the mathematical models. The results presented in this work did suggest that growth on small segregated drops may be more important than continuous phase growth on dissolved substrate.     

黑曲霉过氧化氢酶发酵过程的数学模型

研究了黑曲霉发酵生产过程氧化氢酶的分批发酵动力学,并建立了发酵过程菌体生长,基质消耗及酶合成的随时间变化的数学模型。Logistic方程,Luedekin-Piret方程及与Luedeking-Piret方程相似的基质消耗方程能够很好地分别描述黑曲霉细胞的生长,发酵产酶过程及葡萄糖的消耗,过氧化氢酶的发酵合成是生长耦联的,研究中还将3个动力学模型的预测值和实验值进行了比较。     

Enzyme adsorption in porous supports: local thermodynamic equilibrium model

Enzyme adsorption from a finite bath (batch adsorption) onto porous spherical supports is investigated both experimentally and theoretically using beta-galactosidase and Duolite ion-exchange resin as a model system. Efficient numerical techniques are presented that have been used in conjunction with a parameter estimation routine to evaluate adsorption isotherm constants. Results show that even for adsorption processes lasting almost 10 h, the majority of the enzyme is confined to the outer half of the support and, for high initial enzyme concentrations in the bath, this loading takes place as a slowly moving front. Information on the enzyme distribution has practical importance in the design of immobilized enzyme reactors that in previous works have almost always been analyzed assuming a uniform catalyst distribution.     

Kinetics of adsorption of proteins at interfaces: role of protein conformation in diffusional adsorption

To elucidate the role of protein conformation in the kinetics of adsorption at interfaces, seven structural intermediates of bovine serum albumin were prepared and their adsorption at the air/water interface was studied. Molecular area calculations indicated two distinct molecular processes, the first being the creation of an area, delta A1, for anchoring the molecule during the initial phase of adsorption and the second being the delta A2 cleared during subsequent reorientation and rearrangement of adsorbed molecules at the interface. The delta A1 values for all the albumin intermediates were the same, indicating that the initial work pi delta A1 needed to anchor the molecule at the interface was independent of solution conformation of the protein. Unlike delta A1, delta A2 exhibited a bell-shaped relationship with the extent of refolded state of the intermediates. Calculation of diffusion coefficients indicated that greater the unfolded state of the albumin intermediate, the greater was the diffusion coefficient. It is shown that the simple diffusion theory is inadequate to explain quantitatively the kinetics of protein adsorption. Specific, conformation-dependent, solute-solvent and solute-interface interactions also seem to influence the kinetics of adsorption of proteins.     

Effects of Fulvic Acid on TNT Adsorption in Soil

In order to study the effect of fulvic acids (FA) on the migration of TNT in soil, batch experiments in which 2%, 5%, and 10% (w/w) of FA were added to soils were conducted. Adsorption kinetics and adsorption-desorption isotherms of TNT in soils were investigated, with results of the kinetics tests showing that the adsorption process could be divided into a fast and a slow stage and that FA could extend the adsorption time. Kinetic data were fit to pseudo first-order, pseudo second-order, Elovich, and intra-particle diffusion kinetic models. The fitting results showed that a pseudo second-order kinetic model best described the adsorption process, while Elovich and intra-particle diffusion kinetic models could accurately predict the adsorption at higher FA content. The adsorption-desorption isotherms were predicted using Linear, Freundlich, and Langmuir isotherm models. Results showed that the Freundlich model best described the adsorption-desorption process, and that FA increased adsorption capacity and enhanced the adsorption affinity. The hysteresis index suggested that FA could reduce the desorption of TNT in soil.     

Propionic acid production by whole cells of Propionibacterium freudenreichii

The microbial production of propionic acid by Propionibacterium freudenreichii NCIM 2111, has been studied in this communication. Shake-flask studies were carried out to determine the optimum combination of various process parameters like stab age, inoculum age, inoculum level, medium constituents, temperature, and the initial pH for maximizing the production of propionic acid by using central composite design method. The system was found to exhibit product inhibition and hence the product inhibition kinetics was studied. A two parameter kinetic model, taking into account of the product inhibition, was proposed. Leudeking and Piret model was used to describe the production kinetics. The result from the shake-flask studies were compared with that obtained from mechanically stirred batch bioreactor and total recycle batch bioreactor.     

Kinetics of thermophilic,anaerobic oxidation of straight and branched chain butyrate and valerate

The degradation kinetics of normal and branched chain butyrate and valerate are important in protein-fed anaerobic systems, as a number of amino acids degrade to these organic acids. Including activated and primary wastewater sludge digesters, the majority of full-scale systems digest feeds with a significant or major fraction of COD as protein. This study assesses the validity of using a common kinetic parameter set and biological catalyst to represent butyrate, n-valerate, and i-valerate degradation in dynamic models. The i-valerate degradation stoichiometry in a continuous, mixed population system is also addressed, extending previous pure-culture and batch studies. A previously published mathematical model was modified to allow competitive uptake of i-valerate, and used to model a thermophilic manure digester operated over 180 days. The digester was periodically pulsed with straight and branched chain butyrate and valerate. Parameters were separately optimized to describe butyrate, i-valerate, and n-valerate degradation, as well as a lumped set optimized for all three substrates, and nonlinear, correlated parameter spaces estimated using an F distribution in the objective function (J). Each parameter set occupied mutually exclusive parameter spaces, indicating that all were statistically different from each other. However, qualitatively, the influence on model outputs was similar, and the lumped set would be reasonable for mixed acid digestion. The main characteristic not represented by Monod kinetics was a delay in i-valerate uptake, and was compensated for by a decreased maximum uptake rate (k(m)). Therefore, the kinetics need modification if fed predominantly i-valerate. Butyrate (i- and n-) and n-valerate could be modeled using stoichiometry consistent with beta-oxidation degradation pathways. However, i-valerate produced acetate only, supporting the stoichiometry of a reaction determined by other researchers in pure culture. Therefore, lumping i-valerate stoichiometry with that of n-valerate will not allow good system representation, especially when the feed consists of proteins high in leucine (which produces i-valerate), and the modified model structure and stoichiometry as proposed here should be used. This requires no additional kinetic parameters and one additional dynamic concentration state variable (i-valerate) in addition to the variables in the base model.     

Manganese adsorption by sediment in Wadi Tafna,Algeria

The removal of manganese from aqueous solution by sediment in Wadi Tafna, north-western Algeria, was investigated under batch conditions in 2003. Kinetic data equilibrium removal isotherms were measured at 20 °C. The influence of different experimental parameters, such as contact time, manganese concentration and sediment mass on the removal kinetics of manganese was studied. The content of carbonate in sediment increased the adsorption rate, indicating the active phase towards manganese cations. The process followed pseudo-second-order kinetics. Manganese uptake by sediment was quantitatively evaluated using sorption isotherms. In order to describe the adsorption isotherm mathematically, the experimental data of the removal equilibrium were analysed with Langmuir and Freundlich models revealing that the equilibrium data were perfectly represented using both isotherms.     

Software sensor design considering oscillating conditions as present in industrial scale fed‐batch cultivations

Investigations of inhomogeneous dynamics in industrial‐scale bioreactors can be realized in laboratory simulators. Such studies will be improved by on line observation of the growth of microorganisms and their product synthesis at oscillating substrate availability which represents the conditions in industrial‐scale fed‐batch cultivations. A method for the kinetic monitoring of such processes, supported by on line measurements accessible in industrial practice, is proposed. It consists of a software sensor (SS) system composed of a cascade structure. Process kinetics are simulated in models with a structure including time‐varying yield coefficients. SSs for measured variable kinetics have classical structures. The SS design of unmeasured variables is realized after a linear transformation using a logarithmic function. For these software sensors, a tuning procedure is proposed, at which an arbitrary choice of one tuning parameter value that guarantees stability of the monitoring system allows the calculation of the optimal values of six parameters. The effectiveness of the proposed monitoring approach is demonstrated with experimental data from a glucose‐limited fed‐batch process of Bacillus subtilis in a laboratory two‐compartment scale down reactor which tries to mimic the conditions present in industrial scale nutrient‐limited fed‐batch cultivations. Biotechnol. Bioeng. 2013; 110: 1945–1955. © 2013 Wiley Periodicals, Inc.     

Analysis of the statistical thermodynamic model for nonlinear binary protein adsorption equilibria

The statistical thermodynamic (ST) model was used to study nonlinear binary protein adsorption equilibria on an anion exchanger. Single-component and binary protein adsorption isotherms of bovine hemoglobin (Hb) and bovine serum albumin (BSA) on DEAE Spherodex M were determined by batch adsorption experiments in 10 mM Tris-HCl buffer containing a specific NaCl concentration (0.05, 0.10, and 0.15 M) at pH 7.40. The ST model was found to depict the effect of ionic strength on the single-component equilibria well, with model parameters depending on ionic strength. Moreover, the ST model gave acceptable fitting to the binary adsorption data with the fitted single-component model parameters, leading to the estimation of the binary ST model parameter. The effects of ionic strength on the model parameters are reasonably interpreted by the electrostatic and thermodynamic theories. The effective charge of protein in adsorption phase can be separately calculated from the two categories of the model parameters, and the values obtained from the two methods are consistent. The results demonstrate the utility of the ST model for describing nonlinear binary protein adsorption equilibria.     

Use of the weighted jackknife method to calculate the variance in cellular-specific protein secretion rate: application to monoclonal antibody secretion rate kinetics in response to osmotic stress

The specific secretion rate (q, mug protein secreted/viable cell-h) and its variance are very useful to compare the capability of cell lines for protein secretion. An assessment of specific secretion rate variability is also beneficial and important when the specific secretion rate is to be used as an on-line process parameter to monitor culture production behavior or for in-process decisionmaking. Experimental errors in mammalian cell culture (e.g., protein concentration measurement and cell counting) and estimation error in the method of calculating q contribute to the total variance of the specific secretion rate. Although the variance of q is essential for comparing the differences between cell lines and the response of the same cell line to different nutrient or environmental conditions, few methods for calculating the variance of the specific secretion rate have been reported. As a model system, we have used the weighted jackknife method and the delta method to calculate the variance in the specific secretion rate of a murine monoclonal antibody (q(mAb)) determined by a differential method. These methods were applied to calculate q(mAb) and its standard deviation to determine the change in q(mAb) kinetics during batch culture of the 9.2.27 hybridoma in response to growth in hyperosmotic media or osmotic stress. Without osmotic stress, during exponential growth in DMEM + 5% FBS spinner culture, the estimate of q(mAb) decreases at least threefold. Results indicate that the 9.2.27 hybridoma responds to hyperosmotic media (400 mOsm, 470 mOsm) by significantly reducing the degree of q(mAb) decrease in the exponential phase, thus maintaining a higher q(mAb) through the stationary phase. The trend of q(mAb) during the batch cultures studied is further confirmed by t-test. Osmotic stress is statistically shown to be able to alter significantly the hybridoma-specific mAb secretion kinetics during batch culture. Determination of the variance of specific secretion rate using the weighted jackknife method offers a powerful approach for establishing the confidence limits of specific protein secretion rate between cell cultures in different nutritional or osmotic environments. (c) 1996 John Wiley & Sons, Inc.     

Bacteriophage adsorption efficiency and its effect on amplification

Existing models for bacteriophage adsorption are modified with the addition of a new term, adsorption efficiency, and applied to a T4–Escherichia coli system. The adsorption efficiency is the fraction of phage that adsorbs irreversibly to the host. Adsorption kinetics were modeled using the adsorption rate constant (k) and the adsorption efficiency (ε). Experimental data demonstrated that the adsorption rate constant depends strongly on the condition of the host while the adsorption efficiency is a property of the bacteriophage population. The adsorption efficiency exhibited a marked dependence on the concentration of l-tryptophan. The system was used to study the effect of adsorption kinetics on bacteriophage amplification. Increasing adsorption efficiency had an effect similar to increasing the initial multiplicity of infection; the number of phages produced during amplification decreased. Optimizing the adsorption efficiency by manipulating the l-tryptophan concentration yielded a 14-fold increase in the number of phages produced.     

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.     

Kinetic studies of enzymatic hydrolysis of insoluble cellulose: analysis of the initial rates

A study was conducted on the kinetics of enzymatic hydrolysis of pure insoluble cellulose using unpurified culture filtrate Trichoderma reesei, with the emphasis on the initial reaction period. The initial hydrolysis rate and extent of enzyme (soluble protein)adsorption, either apparent or initial, were evaluated under various experimental conditions. It has been found that the various mass-transfer steps do not control the overall hydrolysis rate and that the hydrolysis rate is mainly controlled by the surface reaction step promoted by the adsorbed enzyme. It has also been found that the initial hydrolysis rate strongly depends on the initial extent of soluble protein adsorption and the effectiveness of the adsorbed soluble protein to promote the hydrolysis. The initial extent of soluble protein adsorption, in turn, is related to the initial cellulose concentration, enzyme concentration, and specific surface area of cellulose, whereas the effectiveness of the initially adsorbed soluble protein to promote the derived to interrelate these parameters without resorting to the Michaelis-Menten kinetics. The present result appear to imply that the role of enzyme-substrate complex formation should not be ignored in deriving a mechanistic kinetic model for enzymatic hydrolysis of cellulose.     

Screening anion-exchange chromatographic matrices for isolation of onco-retroviral vectors

The adsorption kinetics of retroviral vectors to several chromatographic media, DEAE FF, Streamlinetrade mark Q XL and CHTtrade mark Ceramic Hydroxyapatite, in batch mode was investigated. The effects of buffer type, pH and operational temperature were studied. A mathematical model describing viral adsorption kinetics that considers viral degradation in solution was developed. The best results, either in terms of speed and extent of adsorbed infectious particles, were obtained with DEAE FF and Streamlinetrade mark Q XL. Fixed-bed chromatography was further investigated using DEAE FF, Q XL and Q FF, for validation of the batch adsorption process. Fixed-bed DEAE FF and Q XL proved to be good candidates for purification of MoMLV derived vectors due to resulting high yields, 53+/-13% and 51+/-7%, respectively, while removing more than 99% of protein and 90% of the DNA contaminants.     

Removal of organic pollutants from aqueous solutions by adsorbents prepared from an agroalimentary by-product

Two series of crosslinked starch polymers were tested for their ability to adsorb organic pollutants in aqueous solutions. The polymers were prepared by a crosslinking reaction of starch-enriched flour using epichlorohydrin as the crosslinking agent, without and in the presence of NH(4)OH. These polymers were used as sorbent materials for the removal of phenolic derivatives from wastewater. The influence of several parameters (kinetics, pH and polymer structure) on the sorption capacity was evaluated using the batch and the open column methods. Results of adsorption experiments showed that the starch-based materials exhibited high sorption capacities toward phenolic derivatives. The study of the kinetics of pollutant uptake revealed that the adsorbents presented a relatively fast rate of adsorption. The experimental data were examined using the Langmuir and Freundlich models and it was found that the Freundlich model appeared to fit the isotherm data better than the Langmuir model.