Mechanism and mathematical modeling of electro-enzymatic denitrification

In this study, a novel nitrate reduction method using an electro-enzymatic system was investigated to treat an aqueous solution containing high concentrations of nitrate. This system was comprised of working electrodes and their counter electrodes, where enzymes for nitrate removal were located inside the microorganisms. A nitrate reduction mechanism for the electro-enzymatic system was proposed and a mathematical model was developed. The modeling results were compared to the experimental results and all the experimental results fit well with the model; thus, the derived mathematical model can be used for reactor control and effluent prediction.     

Prediction of a protein band profile in preparative reversed-phase gradient elution chromatography

The overloaded band profiles of lysozyme in reversedphase preparative chromatography were recorded on a C18 chemically bonded silica column, with acetonitrile/water as the mobile phase. These experiments were carried out under isocratic conditions at 31.6, 31.9, and 32.2% acetonitrile (ACN) for loading factors up to 43% of the column saturation capacity and under linear-solvent-strength gradientelution with gradient slopes of 0.5 and 1% ACN/min, for loading factors up to 11.3%. The adsorption isotherms of lysozyme were measured for the same solvent compositions and found to be accurately accounted for by a bi-Langmuir isotherm model.With the use of a Craig model implementation of the equilibrium-dispersive model of chromatography, the band profiles of lysozyme were calculated. An excellent agreement was observed between these calculated profiles and the experimental profiles recorded at loading factors below 5%. By contrast, band profiles calculated using a Langmuir isotherm failed to describe the experimental bands. At column loadings exceeding 8%, a slight but systematic deviation takes place between calculated and experimental profiles. It is most probably explained by the considerable concentration effect of the gradient, making the band experience phase equilibrium in a concentration range that exceeds largely the one where the isotherm data have been measured.     

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.     

On-line monitoring of breakthrough curves within an expanded bed adsorber

By abstracting samples of the liquid phase from various positions along the height of an expanded bed, it has been possible to monitor the breakthrough profiles of adsorbing components during the application of feedstock. Similarly, the concentration profiles of the subsequent washing and elution procedures were also followed. The procedure involves the abstraction of liquid samples from the voids of the expanded bed using a specially modified column and assaying the levels of proteins in the withdrawn stream by on-line rapid chromatographic monitoring. Studies of the residence time distribution showed that the modifications to the expanded bed did not cause additional mixing and dispersion. Breakthrough profiles have been measured in a simple single component system and in a complex feedstock in which the adsorption of lysozyme from skimmed cows' milk was monitored. The system shows promise for the on-line control and monitoring of expanded bed adsorption separations, together with providing additional insight into the hydrodynamic and adsorption/desorption processes that occur during bioseparations using expanded bed adsorption.     

Biospecific adsorption in fixed and periodic countercurrent beds

A mathematical model that describes the adsorption and wash stages of biospecific adsorption (affinity chromatography) in a packed column is presented. The model expressions account for film and pre diffusion mass transfer as well as for different mechanisms of interaction between the adsorbate(s) and the ligand. The model equations may be applicable to single and multi-component biospecific adsorption systems involving both monovalent and multivalent adsorbates.The results obtained from model simulations show that the breakthrough time of the adsorbate is significantly influenced by the rate of the interaction step between the adsorbate and the ligand. The results indicate that when short beds are employed, then the choice of ligand with respect to its rate of interaction with the adsorbate may be of paramount importance. In certain systems involving bivalent adsorbates, the adsorbate may be displaced from the one-site complex, reenter the flowing fluid stream, and increase the effluent adsorbate concentration above its inlet value. It is also shown that when a single column is divided into two beds operating in a periodic counter current mode, the ligand utilization can be almost four times higher than that obtained in a column of the same length operating in the fixed bed mode.The studies on the wash stage indicate that the reduction of the concentration of the contaminant to a specified low level may be accomplished for certain systems in a shorter time, if the direction of flow in the wash stage is opposite to that used in the adsorption stage. However, a larger amount of product will be lost, in general, when the direction of flow of the washing medium is opposite to that employed during the adsorption stage.     

A new kinetic model of protein adsorption on suspended anion-exchange resin particles.

The kinetics of adsorption of bovine serum albumin on an anion-exchange resin were measured in a batch system using a flow cell and ultraviolet absorbance, as a function of initial liquid-phase protein concentration and solid-to-liquid phase ratio. A new mathematical model for adsorption kinetics is presented that fits the experimental data to give a highly linear relationship with time, following a short transient period. Numerical integration of the differential form of the new composite nonlinear (CNL) kinetic model, containing three independent parameters, is shown to describe the dynamics of batch adsorption much better than alternative lumped parameter models. Although the new model is phenomenological rather than mechanistic, its principal parameter is shown to be a direct linear function of a physically measurable quantity. This study demonstrates that the model can accurately simulate protein concentration-time profiles using parameter estimates derived from correlations over a wide range of initial protein concentrations and phase ratios. The new CNL model is shown to be considerably superior to the Langmuir and solid-film linear kinetic models in this regard, having the additional advantage that an equilibrium isotherm for the system is not required.     

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.     

FRACTIONATION OF SUSPENSIONS OF MOUSE SPLEEN CELLS BY COUNTER CURRENT DISTRIBUTION

Suspensions of mouse spleen cells were fractionated by means of counter current distribution in an aqueous two-phase polymer system composed of 5% (w/w) dextran and 4% (w/w) polyethylene glycol. Counter current distribution in this combination of polymers was not toxic for hemopoietic colony-forming units (CFU) and yielded a partial separation of CFU, granulocytes and antibody-producing cells. The results obtained indicate that counter current distribution is a useful means for the separation of populations of intact, viable hemopoietic cells.     

Long-term in vivo experience of an electrochemical sensor using the potential step technique for measurement of mixed venous oxygen pressure

An implantable amperometric blood oxygen sensor was developed to improve rate adaptation of heart pacemakers. Two different working electrode materials in direct contact with the blood were tested, smooth glassy carbon and gold. Reference electrodes of Ag/AgCl and porous pyrolytic carbon were evaluated. A counter electrode being the titanium housing of the pulse generator was partly coated with carbon. An implantable pacemaker system with chronocoulometric oxygen detection was developed. Heart synchronous potential steps were periodically applied to the 7.5 mm² working electrode in the atrium. Both single and double potential step techniques were evaluated. The oxygen diffusion limited current was used to calculate the stimulation rate. Bench tests and studies on 31 animals were performed to evaluate long-term stability and biocompatibility. In five dogs, the AV node was destroyed by RF ablation to create a realistic animal model of a pacemaker patient. Sensor stability and response to exercise was followed up to a maximum implantation time of 4 years. Post-mortem examinations of the electrode surfaces and tissue response were performed. The results show that a gold electrode is more stable than glassy carbon. The Ag/AgCl reference was found not to be biocompatible, but activated carbon was stable enough for use as reference for the potentiostat. Double potential steps stabilize the sensor response in comparison to single steps. Blood protein adsorption on the gold surface decreased the oxygen transport but not the reaction efficacy. No adverse tissue reactions were observed.     

Long-term in vivo experience of an electrochemical sensor using the potential step technique for measurement of mixed venous oxygen pressure

An implantable amperometric blood oxygen sensor was developed to improve rate adaptation of heart pacemakers. Two different working electrode materials in direct contact with the blood were tested, smooth glassy carbon and gold. Reference electrodes of Ag/AgCl and porous pyrolytic carbon were evaluated. A counter electrode being the titanium housing of the pulse generator was partly coated with carbon. An implantable pacemaker system with chronocoulometric oxygen detection was developed. Heart synchronous potential steps were periodically applied to the 7.5 mm² working electrode in the atrium. Both single and double potential step techniques were evaluated. The oxygen diffusion limited current was used to calculate the stimulation rate. Bench tests and studies on 31 animals were performed to evaluate long-term stability and biocompatibility. In five dogs, the AV node was destroyed by RF ablation to create a realistic animal model of a pacemaker patient. Sensor stability and response to exercise was followed up to a maximum implantation time of 4 years. Post-mortem examinations of the electrode surfaces and tissue response were performed. The results show that a gold electrode is more stable than glassy carbon. The Ag/AgCl reference was found not to be biocompatible, but activated carbon was stable enough for use as reference for the potentiostat. Double potential steps stabilize the sensor response in comparison to single steps. Blood protein adsorption on the gold surface decreased the oxygen transport but not the reaction efficacy. No adverse tissue reactions were observed.     

Photoperiodic time measurement in the spider mite Tetranychus urticae: A novel concept

To explain photoperiodic induction of diapause in the spider mite Tetranychus urticae a new theoretical model was developed which took into account both the hourglass and rhythmic elements shown to be present in the photoperiodic reaction of these mites. It is emphasized that photoperiodic induction is the result of time measurement as well as the summation and integration of a number of successive photoperiodic cycles: the model, therefore, consists of separate ‘clock’ and ‘counter’ mechanisms. In current views involvement of the circadian system in photoperiodism is interpreted in terms of the hypothesis that the photoperiodic clock itself is based on one or more circadian oscillators. Here a different approach has been chosen as regards the role of the circadian system in photoperiodism: the possibility, previously put forward by other authors, that some aspect of the photoperiodic induction mechanism other than the clock is controlled by the circadian system was investigated by assuming a circadian influence on the photoperiodic counter mechanism. The derivation of this ‘hourglass timer oscillator counter’ model of photoperiodic induction in T. urticae is described and its operation demonstrated on the basis of a number of diel and nondiel photoperiods, with and without light interruptions.     

Biospecific adsorption of lysozyme onto monoclonal antibody ligand immobilized on nonporous silica particles

It is very important to understand the equilibrium and dynamic characteristics of biospecific adsorption (affinity chromatography) for both scientific and application purposes. Experimental equilibrium and dynamic column data are presented on the adsorption of lysozyme onto antibody immobilized on nonporous silica particles. The Langmuir model is found to represent the equilibrium experimental data satisfactorily, and the equilibrium association constants and heats of adsorption have been estimated for two systems with different ligand densities. The effects of nonspecific interactions are more pronounced in the system with low-density ligand. The dynamic interaction kinetic parameters are estimated by matching the predictions of a fixed-bed model with the experimental breakthrough curves. The agreement between theory and experiment is good for the initial phases of breakthrough, where the mechanism of biospecific adsorption is dominant. In the later phase (saturation neighborhood) of breakthrough, the effects of nonspecific interactions appear to be greater in the low-density ligand system. The kinetics of the nonspecific interactions were estimated from the data of the later phase of breakthrough and were found to be considerably slower than those attributed to biospecific adsorption.     

A new process combining adsorption and enzyme reaction for producing higher-fructose syrup

A process for producing a higher-fructose syrup containing more than 50% fructose was developed that involves a new system combining selective adsorption of fructose and an immobilized glucose isomerase reaction. Continuous countercurrent contact of the liquid stream with the solid adsorbent is simulated by advancing adsorption columns against the fixed inlets and outlet of liquid streams without actual movement of the solid adsorbent, while the immobilized enzyme reactors are stationary. Two mathematical models, an intermittent moving-bed and a continuous moving-bed model, are presented for calculation the concentration profiles of glucose and fructose in the system. The validity of the models is experimentally confirmed, and a criterion for good production in the system is presented. This system requires less desorbent than a process using a fixed-bed adsorber and a simulated moving-bed process to produce the syrup with 45-65% fructose content, the level desired in food manufacture.     

Prediction of band profiles of mixtures of bradykinin and kallidin from data acquired by competitive frontal analysis

The competitive adsorption isotherms of two closely related peptides, bradykinin and kallidin, were measured by frontal analysis on a Zorbax SB-C18 microbore column. An aqueous soluton at 20% acetonitrile (0.1% TFA) was used as the mobile phase. The competitive isotherm data were fitted to four different models: Langmuir, Bilangmuir, Langmuir-Freundlich, and Toth. These data fitted best to a Bilangmuir isotherm model. The influence of the pressure on the retention factors of the two peptides was found to be small and was not investigated in detail. The band profiles of large samples of the single components and of their mixtures were recorded. The overloaded profiles calculated using either the equilibrium-dispersive or POR model are in excellent agreement with the experimental profiles in all cases. Our results confirm that the competitive isotherm data derived from mixtures may suffice for a reasonably accurate prediction of the band profiles of all mixtures of the two components, provided their composition is close to 1/1.     

Modelling adsorption and biological degradation of nutrients on peat

A dynamic mathematical and numerical model of adsorption and biological degradation of nutrients in an organic perfusion column with recycle has been developed. This model has applicability to industrial applications of biodegradation of nutrients in wastewater such as biofilters and biotrickling filters where concentrations are dilute and solid surface coverage is low. It successfully predicts that adsorption has the effect of masking a ‘true' rate of biological degradation behind an ‘observed' rate of degradation in the liquid phase. This is due to the adsorptive capacity of peat which provides a buffer for surges in loading and makes peat a useful carrier for engineered biological systems. Four dimensionless parameters were identified to totally describe the physical system without biological activity and a further two were identified for the system with biological activity. Analytical solutions to simplifications of the model were justified by showing that the assumption of a negligible concentration gradient in the column was valid after an initial perturbation in nutrient concentration had passed.     

Removal of MS-2 and PRD-1 bacteriophages from an ultrapure water system

Viruses must be removed from the ultrapure water environment, as they have the potential to deposit on microelectronic devices and generate killer defects. Controlled and well-defined challenges by MS-2 and PRD-1 bacteriophages were treated in a pilot-scale ultrapure water system using ultraviolet radiation (UV), ozone, mixed bed ion exchange adsorption, and reverse osmosis filtration technologies typical of those used in industrial systems. Applying a first order kinetic model to the data generated rate constants for MS-2 removal by UV-185, 50 mg L⁻¹ ozone, mixed bed ion exchange or reverse osmosis filtration of 15.5, 12.9, 3.9, and 10.4 min⁻¹, respectively, and PRD-1 removal of 13.8, 15.5, 8.2, and 11.9 min⁻¹, respectively. In all cases, removal of viruses by oxidative mechanisms such as ozone and UV were far superior to adsorption and filtration mechanisms. A theoretical viral population balance was generated to model the removal of the bacteriophages by these unit operations. This model relates the inlet time-dependent profile of viruses to the output, destruction, and accumulation profiles; it also relates these profiles to the unit operation’s treatment mechanisms including oxidation, adsorption, and filtration. This model is the first step in generating a site-independent theoretical model to project the persistence of viruses in ultrapure water systems. Received 19 October 1998/ Accepted in revised form 29 May 1999     

Efficient removal of both cationic and anionic dyes from aqueous solutions using a novel amphoteric straw-based adsorbent

In the current paper, a novel amphoteric straw-based adsorbent was prepared and applied to adsorb various dyes from aqueous solutions. The amphoteric adsorbent was proven effective in eliminating both cationic and anionic dyes (methylene blue and acid green 25), especially at corresponding favored pH conditions. The fundamental adsorption behavior of the adsorbent on removing various dyes was also investigated at different temperatures. The adsorption isotherms were all best-fitted by the Langmuir equation, whereas the adsorption kinetics was well-described by both the pseudo-second order model and the Elovich model. The experimental result revealed that the adsorption mechanism followed the monolayer chemical adsorption with an ion-exchange process.     

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.     

Characterization of Cation Exchange Resins as to Separation of Glucose and Fructose Using the Moment Analysis Technique

Chromatographic separation of glucose and fructose using columns of cation exchange resins in the Ca²⁺ form was analyzed with a dispersion model neglecting the adsorption process. Pulse response experiments were carried out with analysis by the moment method. Elution profiles of the sugars were successfully predicted by numerical inversion of the concentration calculated in the Laplace domain. The predicted elution profiles could be used for estimation of the column efficiency defined as the recovery of the separated sugar per unit time and per unit length of the column.     

Light-break experiments and photoperiodic time measurement in the spider mite Tetranychus urticae

To explain photoperiodic induction of diapause in the spider mite Tetranychus urticae (Acarina: Tetranychidae) a theoretical model was developed, consisting of two components, viz. a “clock” and a photoperiodic “counter” mechanism. The clock executes photoperiodic time measurement according to hourglass kinetics; the counter accumulates the photoperiodic information contained in a number of successive $\text{light}\text{dark}$ cycles by adding up the number of “long” and “short” nights experienced by the developmental stages of the mites sensitive to the photoperiod. The influence of the circadian system on photoperiodic induction is interpreted as an inhibitory effect exerted on the expression of the photoperiodic response; this effect is encountered only in certain photoperiodic regimes, where the circadian system and the photoperiod are out of “resonance” with each other. This “hourglass timer oscillator counter model”, devised to give a theoretical explanation of photoperiodic time measurement, the summation of photoperiodic information, and the influence of the circadian system on photoperiodic induction, proved to be consistent with experimental results obtained with T. urticae in both symmetrical and asymmetrical “skeleton” photoperiods, the latter based on diel as well as non-diel $\text{light}\text{dark}$ cycles.