Intrinsic Kinetic Constants Research Articles

Convection, diffusion and reaction in a surface-based biosensor: Modeling of cooperativity and binding site competition on the surface and in the hydrogel

We study theoretically the transport and kinetic processes underlying the operation of a biosensor (particularly the surface plasmon sensor “Biacore”) used to study the surface binding kinetics of biomolecules in solution to immobilized receptors. Unlike previous studies, we concentrate mainly on the modeling of system-specific phenomena rather than on the influence of mass transport limitations on the intrinsic kinetic rate constants determined from binding data. In the first problem, the case of two-site binding where each receptor unit on the surface can accommodate two analyte molecules on two different sites is considered. One analyte molecule always binds first to a specific site. Subsequently, the second analyte molecule can bind to the adjacent unoccupied site. In the second problem, two different analytes compete for one binding site on the same surface receptor. Finally, the third problem considers the case of positive cooperativity among bound molecules in the hydrogel using a simple mean-field approach. The transport in both the flow channel and the hydrogel phases of the biosensor is taken into account in this case (with few exceptions, most previous studies assume a simpler model in which the hydrogel is treated as a planar surface with the receptors). We consider simultaneously diffusion and convection through the flow channel together with diffusion and cooperativity binding on the surface and in the hydrogel. In each case, typical results for the concentration contours of the free and bound molecules in the flow channel and hydrogel regions are presented together with the time-dependent association/dissociation curves and reaction rates. For binding site competition, the analysis predicts overshoot phenomena.

A theoretical and experimental analysis of a membrane bioreactor performance in recycle configuration

The behavior of membrane bioreactors operating in recycle configuration is characterized from both a theoretical and an experimental point of view. The theoretical model is based on the unsteady-state balance equations governing momentum and mass transfer within the regions that can be identified in a membrane reactor with immobilized enzyme, coupled to the unsteady-state mass balance on the components in feed tank. The resulting system of non-linear partial differential equations has been numerically solved by Finite Elements Method (FEM), implemented by a commercial package called FEMLAB. The available CFD code allowed determining the time evolution of both velocity and concentration profiles without resorting to considerable simplification hypotheses. As far as the reaction term in the mass balance equations is concerned, reference has been made to lactose hydrolysis catalyzed by immobilized β-galactosidase, also carried out in the experimental part of this work. The chemical reaction is supposed to take place solely in the membrane dense and spongy layers where biocatalyst is actually confined and distributed according to its concentration ratio E 3/ E 2. A set of intrinsic kinetic constants, obtained from the literature, has been used to evaluate the actual reaction rate thus evaluating the effects of immobilization on enzyme activity. The contribution of the most significant transport mechanisms affecting reactor performance has been determined analyzing the dynamic evolution of three representative parameters, i.e. the effectiveness factor, the degree of conversion within the membrane and the bioreactor performance index, as functions of the operating conditions. The proposed transport model is very general as it may describe the behavior of different types of heterogeneous reacting systems by just adapting either the reaction rate expression or the set of intrinsic kinetic constants. An experimental analysis of system behavior has validated the theoretical predictions, showing a good agreement between experimental and theoretical results.

Optimizing the solar photo-Fenton process in the treatment of contaminated water. Determination of intrinsic kinetic constants for scale-up

The elimination of aromatic compounds present in surface water by photo-Fenton with sunlight as the source of radiation was studied. The concentrations of Fe 3+ and H 2O 2 are key factors for this process. A solar simulator and a prototype parabolic collector were used as laboratory-scale reactors to find the parameters of those key factors to be used in the CPC (compound parabolic collector) pilot plant reactor. The initial mineralization rate constant ( k obs) was determined and evaluated at different Fe 3+ and H 2O 2 concentrations to find the best values for maximum efficiency. In all the experiments the mineralization of an aqueous phenol solution was described by assuming a pseudo-first-order reaction. The intrinsic kinetic constants not dependent on the lighting conditions were also estimated for scale-up.

Macro kinetic studies for photocatalytic degradation of benzoic acid in immobilized systems

Semiconductor photocatalytic process has been studied extensively in recent years due to its intriguing advantages in environmental remediation. In this study, a two-phase swirl-flow monolithic-type reactor is used to study the kinetics of photocatalytic degradation of benzoic acid in immobilized systems. Transport contributions into the observed degradation rates were determined when catalyst is immobilized. Intrinsic kinetic rate constants and its dependence on light intensity and catalyst layer thickness, values of adsorption equilibrium constant, internal as well as external mass transfer parameters were determined. The simultaneous effect of catalyst loading and light intensity and optimum catalyst layer thickness were also determined experimentally. Reaction rate constants and overall observed degradation rates were compared with slurry systems.

Enzymatic membrane reactor for the kinetic resolution of racemic ibuprofen ester: modeling and experimental studies

The production of (S)-ibuprofen acid was studied in a hollow fiber membrane reactor, with the aim to develop a clean and ecofriendly technology. The modeling and simulation of enzymatic membrane reactor was studied for lipase-catalyzed hydrolysis of racemic ibuprofen ester in hollow fiber membrane reactor. Mathematical model was developed to simulate the behavior of enzymatic reaction in the membrane matrix region. The model equation was derived considering reaction over immobilized enzyme in the membrane porous support with the substrate flowing along the shell side. The model was simulated on the basis of experimental operating conditions, physical and hollow fiber geometrical parameters. The model equation was a nonlinear second-order differential equation and solved numerically using Matlab. The parameters studied were Thiele Modulus ( Φ 2 ) , Bodenstein number ( B 0 ) , transmembrane pressure (TMP) and intrinsic enzyme kinetic constants ( V max and K m ). Simulation results showed that a satisfactory product separation was achieved with 60% conversion of (S)-ester, enantiomeric excess of substrate, ee s in the range 35–43%, enantiomeric excess of product, ee p in the range 80–85%, and enantiomeric ratio ( E value) of 11.2–15.3 at 4.34 < B 0 < 13.89 and Φ 2 < 1 . The simulated results agreed with the experimental data within an error of ± 7.5 % . The reaction–separation functionality of EMR system has shown the potential of membrane reactor application for kinetic resolution of racemic compounds especially in overcoming the difficulties associated with conventional technology particularly in downstream separation and enzyme recovery.

Adsorption, Diffusion, and Reaction Phenomena on FCC Catalysts in the CREC Riser Simulator

Two typical FCC catalysts with similar acidities and structural properties and different crystallite sizes, CAT-SC (0.4 μm) and CAT-LC (0.9 μm), are studied in a novel CREC riser simulator using 1,3,5-triisopropylbenzene. Catalytic and thermal runs allow for the development of a heterogeneous kinetic model and the assessment of intrinsic kinetic constants and adsorption and diffusional parameters. Analysis of 1,3,5-triisopropylbenzene conversions and product distribution helps establish the influence of intracrystallite diffusion as the controlling step at lower reaction temperatures (350−450 °C). Moreover, product distribution and selectivity differences between the CAT-SC and CAT-LC catalysts provide evidence of cracking reactions affected by hindered diffusion of the reactant and products.

Multiplicative dependence of the first order rate constant and its impact on clinical pharmacokinetics and bioequivalence.

The purpose of the study was to investigate the factors upon which the first order rate constant depends in order to assess the impact on the body-drug concentration when it changes throughout a treatment. A reasoning for linking the first order rate constants with several factors in a multiplicative way was proposed out taking into account kinetic and thermodynamic aspects. A multi-compartment model for drug disposition was analyzed and compartment mean drug concentrations at steady state were obtained as a function of the model kinetic constants. At the moment, only four factors were identified as responsible for the actual rate constant value. Apart from an intrinsic kinetic constant, they are the inverse of compartment volume, the transfer surface area, the fraction of mass able to be transferred, and the fraction of mass that effectively can be transferred. In clinical practice some of these factors might change throughout time (because of chronophysiological rhythms or drug availability at the action sites) and consequently, an inconstant extra-plasma/plasma drug concentration ratio could be obtained. In conclusion, therapeutic response prediction for a treatment does not upon plasma drug concentration monitoring. Equivalence in plasma drug exposure should not mean therapeutic equivalence, because differences in the rate and in the extent between test and reference products may induce a change in the action site/plasma drug concentration ratio.

Pervaporation Aided Esterification of Carboxylic Acids with Ethanol Catalyzed by Porcine pancreatic Lipase

The results of pervaporation-coupled esterification of various carboxylic acids with ethanol catalyzed by Porcine pancreatic lipase are reported. The effect of lipase and substrate concentrations has been studied and the advantage of pervaporation on the equilibrium conversion has been deduced. The kinetics of reaction were analyzed with a three-parameter model which coupled the effect of pervaporation. The intrinsic kinetic constants for all the reactions were estimated and correlated with the carbon number, an indicator of hydrophobicity of the acids. It was found that the rate constant increases with decrease in carbon number. The experimental concentration profiles were simulated from the model for all the reactions and the model prediction was found to be reasonably good. The water permeability was also correlated well with acid hydrophobicity. The pervaporation coupled reaction efficiency, as represented by the reaction time for equilibrium conversion, was found to bear a profound relation to membrane surface area per unit volume of the reaction mixture (A/V). The time for equilibrium conversion was found to decrease with an increase in A/V value, reaching a minimum and then increasing with a further increase of A/V. A probable explanation has been postulated for such an observation.

Molecular Competition of C 7 and C 9n-Alkanes in Vapor- and Liquid-Phase Hydroconversion over Bifunctional Pt–USY Zeolite Catalysts

Molecular competition effects in the hydroconversion of an equimolar heptane/nonane mixture were studied in liquid-phase reaction conditions in a fixed-bed reactor filled with a Pt–ultrastable-Y (USY) catalyst. Liquid-phase conditions were attained by feeding the hydrocarbon mixture with hydrogen dissolved in it at 100 bar and 230°C. Comparative vapor-phase experiments were run at 230°C, a pressure of 4.5 bar, and a hydrogen-to-hydrocarbon ratio of 13. Whereas catalytic experiments in the vapor-phase showed a marked referential conversion of nonane over heptane, in liquid-phase the differences in conversion rate between nonane and heptane were much less pronounced. Adsorption-reaction models were used to explain the difference. For this purpose, intrinsic kinetic constants for heptane and nonane were derived from experimental data from vapor-phase conversions of the n-alkanes individually, using an adsorption-reaction model with independently determined adsorption equilibria, and assuming the classic bifunctional reaction scheme. The liquid-phase conversion of the heptane/nonane mixture was predicted very well using these intrinsic reaction kinetics derived from the vapor-phase experiments and assuming no adsorption preference between heptane and nonane. In contrast to this, the conversion of the heptane/nonane mixture in the vapor phase could only be appropriately described by a model involving adsorption according to a Langmuir-with-interaction model, favoring adsorption of the heaviest compound. In liquid-phase reaction conditions and at saturation of the Pt–USY zeolite pores with n-alkanes, there is no such selective adsorption of the heaviest compound. In liquid-phase, the conversion of the mixture reflects the intrinsic reaction kinetics of the individual compounds.

Application of an optimization algorithm for estimating intrinsic kinetic parameters of immobilized enzymes

A simple optimization methodology is applied to estimate the intrinsic kinetic parameters for both reversible and irreversible unireactant immobilized enzyme systems that follow the Michaelis-Menten mechanism. The method utilizes a direct-search optimization algorithm along with the numerical solution of the governing differential equations. The usefulness and validity of the method is demonstrated by comparing the predicted values of the intrinsic kinetic constants using the proposed method with a series of experimental values reported in the literature for different immobilized enzyme systems with irreversible and reversible reactions.

Application of an Optimization Algorithm for Estimating Intrinsic Kinetic Parameters of Immobilized Enzymes

A simple optimization methodology is applied to estimate the intrinsic kinetic parameters for both reversible and irreversible unireactant immobilized enzyme systems that follow the Michaelis-Menten mechanism. The method utilizes a direct-search optimization algorithm along with the numerical solution of the governing differential equations. The usefulness and validity of the method is demonstrated by comparing the predicted values of the intrinsic kinetic constants using the proposed method with a series of experimental values reported in the literature for different immobilized enzyme systems with irreversible and reversible reactions.

Catalytic properties in deNO x and SO 2–SO 3 reactions

SCR-deNO x reaction and SO 2–SO 3 oxidation tests were carried out by different research groups over fresh and used EUROCAT oxide samples in order to characterize the reactivity of the catalysts and to compare data obtained in several laboratories (Politecnico of Milan, Università of Salerno, ENEL of Milan, Boreskov Insitute of Catalysis). Data are presented which indicate that the used EUROCAT catalyst is slightly more active both in the deNO x reaction and SO 2–SO 3 oxidation than the fresh sample. An analyses of data collected over honeycomb catalysts by means of a 2D, single-channel model of the SCR monolith reactor has been performed to evaluate the intrinsic kinetic constant of the deNO x reaction; a satisfactory comparison has been obtained between estimation of the intrinsic kinetic constant and estimation of the intrinsic catalyst activity from data collected over powdered catalysts. A good agreement has been found in the experimental results collected in the different labs, both for the deNO x reaction and SO 2–SO 3 oxidation.

Competitive physisorption effects in hydroisomerisation of n-alkane mixtures on Pt/Y and Pt/USY zeolite catalysts

Physisorption isotherms and separation factors of n-C6–n-C12 alkanes on zeolite Y with Si/Al of 2.7 and on ultrastable Y (USY) zeolites with Si/Al ratios of 13 and 30 were determined using perturbation chromatography, at 506 K and for the hydrocarbon pressure range relevant to hydroisomerisation catalysis with platinum loaded versions of these zeolites. For the n-alkane pressure range from 0.3 to 0.9 bar, a refined Langmuir model with an interaction factor accounting for adsorbate–adsorbate interactions and surface heterogeneity gave the best agreement with the experimental single component adsorption data. Expressions for multicomponent adsorption equilibria among the n-alkanes, their isomers and cracked products, and expressions with interaction factors for the single components into multicomponent expressions were obtained. Separation factors among the n-alkanes and their variation with adsorbent loading derived from these multicomponent expressions are in agreement with experimental separation factors. The expressions for the adsorption equilibria were used to extract intrinsic kinetic constants of individual n-alkanes from experimental catalytic conversion data of pure compounds. It is demonstrated that the conversion of the individual components of a four component n-alkane mixture can be accurately predicted by a model combining intrinsic reaction constants for the individual components with the multicomponent adsorption isotherms. The approach was equally successful with the H-Y zeolite as with the strongly dealuminated USY zeolites exhibiting strongly different acidity, catalytic activity and adsorption behaviour.

The normalized pressure dependence method for the evaluation of kinetic rates of metal hydride formation/decomposition

An assumption is put forward, here, that the main reason for the large discrepancies between results derived from kinetic measurements, carried out by various investigators, is the fact that the pressure dependence of the overall kinetic flow rates has been given a different interpretation by various investigators. The new approach presented here, the normalized pressure dependence method (NPDM), for the interpretation of the overall kinetic flow rates consists of several main elements: (1) the pressure dependence function, has the general form of F(P)=|Peq-P|/Peq where, P and Peq are the system and equilibrium pressure, respectively. The function F(P) changes continuously with time. (2) F(P) is to be inserted, as a factor, into an integrated rate equation as follows: Ri(α)=−ktF(P) where, α is the reacted fraction and i refers to a particular mechanism or process order. (3) By plotting, for an isothermal experiment, Ri(α)/F(P) vs t an intrinsic kinetic rate constant, k, which depends on temperature only, is derived. (4) From each experimental run, the reacted fraction for a decomposition experiment into vacuum, αv(t), can be calculated, without running an experiment with P=0. It is shown that for a decomposition experiment F(P) changes within the inherent limits, 0<F(P)≤1. Thus F(P) serves as a normalizing factor. Utilizing the NPDM kinetic measurements carried out under different pressure conditions can be compared. The NPDM is considered here, for brittle metal hydrides such as the intermetallics AB5 (LaNi5), AB (TiFe) and pseudo AB2, of Laves phases structure, for concentrations in the two-phase region, α+β. During the so termed, `second activation step', associated with the disintegration of the bulk into powder, the thermodynamic and kinetic parameters of the reaction change and reach, at the end, stable values. The mean particle diameter, Dm, has been shown to reduce sharply at the beginning of a cycling process and to reduce at a slowing down rate with an increasing number of cycles. An important empirical fact is that, upon cyclic hydrogenation, brittle MH materials asymptotically reach a minimal particle size (or rather a size distribution), but do not atomize. Adopting a fracture behavior approach applied to an isotropic, brittle, crystalline material, in the absence of plastic deformation, the qualitative approximation δVVmin∼ΔA(Γ/Ev) was received. Where Vmin is the smallest particle volume, δV is the volume misfit and ΔA the area of the newly formed surface. Γ is the surface energy per unit surface, and Ev is an elastic strain energy, per unit volume associated with the M↔MH phase transformation. The ratio (Γ/Ev) has the dimension of length. Combining these results with the empirical finding of the existence of a minimal particle size, Dm,min, it can be concluded that a particle of a volume smaller than Vmin would not be able to produce a crack by forming two new surfaces. Thus, further fractionating is prevented and the atomizing of the material is excluded. The effectiveness of the NPDM for the determination of kinetic rates is demonstrated for LANi5 at 10°C and for the alloy Ti0.95Zr0.05Mn1.48V0.43Fe0.08Al0.01, labeled C5, at 20°C, assuming a first-order reaction in both cases.

Kinetic Modeling of n-Hexane Oxyfunctionalization over Titanium Silicalites: Effects of Titanium Content

The kinetics of n-hexane oxyfunctionalization over a series of titanium silicalites (TS-1) has been investigated using aqueous hydrogen peroxide (30 wt %). The oxyfunctionalization reaction has been modeled using results from a batch reactor. All catalysts were also characterized using analytical techniques such as XRD, UV−vis, and FT IR spectroscopies. The intrinsic kinetic constants were found to be proportional to the fraction of T atoms substituted with titanium in the TS-1 framework. This kinetic analysis indicates a substitutional limit of 1.9% T atoms, in full agreement with previous literature data obtained by analytical techniques. The effects of temperature and extra-framework titanium are also discussed.

Denitrification kinetics in a rotating disk biofilm reactor

Abstract Denitrification kinetics of a synthetic substrate containing molasses, sodium nitrate, Na2HPO4 · 12H2O, KH2PO4 and tap water treated with Na2SO3 was studied in a rotating disk biofilm reactor (RDBR). Experiments were performed at various conditions: biofilm thickness in the range 100−1100 μm and nitrate concentration in the feed of 5 to 50 mg N1−1. Biofilm density decreases with increasing biofilm thickness. Most experiments were in the kinetic controlled regime or fully penetrated biofilms. The intrinsic zero-order kinetic constant was found to be ko = 7.96 × 10−6 kg NO3-N*kg biofilm−1 s−1 (at 25 °C). Some runs were in the diffusion controlled regime or partially penetrated biofilms; the effective diffusivity of nitrate in the biofilm which fitted experimental results was Db= 1.5 × 10−9 m2s−1. The efficiency of the RDBR, considered as a CSTR, predicted by a model based on a zero-order reaction and diffusion inside the biofilm, reasonably agrees with experimental data.

Kinetic analysis of a protein antigen-antibody interaction limited by mass transport on an optical biosensor

Using BIAcore™ technology, we determined the rate constants for a protein antigen-antibody interaction that was mass transport limited on the optical biosensor. The antigen consisted of a soluble form of the human T-cell receptor CD4 (two amino terminal domains, D1D2) and the antibody was an anti-CD4 monoclonal from monkey engineered with the constant domains from human IgG1. High quality response data were obtained for this interaction by orienting the attachment of the antibody on the sensor surface and correcting for instrument artifacts with control experiments. Using numerical integration and global fitting, we demonstrate that a mass transport limited reaction was the only model of those tested that described well D1D2 binding to three different surface densities of the antibody. Statistical profiling techniques showed that the error space and correlation for the parameters in the non-linear model were essentially linear, but only when the model was simultaneously fitted to data from multiple surface densities. The “on” and “off” rate constants (1.2 × 10 −6 M −1 s −1 and 2.9 × 10 −4 s −1) determined from the kinetic analysis predict an equilibrium dissociation constant ( K D = 0.24 ± 0.01 nM) that agrees with the value measured in solution by titration calorimetry ( K D = 0.2 ± 0.1 nM). The results indicate that, although the D1D2-antibody reaction is partially controlled by mass transport on the optical biosensor, by optimizing the experimental design and analyzing data from multiple surface densities it is possible to determine accurate estimates of the intrinsic equilibrium and kinetic rate constants.

Aerobic biodegradation and microbial population of a synthetic wastewater in a channel with suspended and attached biomass

A well mixed indoor recirculating channel was adopted to investigate aerobic heterotrophic biodegradation kinetics and microbial communities in drainage systems with suspended and attached biomass. Experiments were run with synthetic substrate. The biofilm function was distinguished from the suspended biomass by using the Biological Oxygen Monitor (BOM) to measure suspended biomass activity. The microbial community was overall dominated by filaments (mainly Sphaerotilus natans) due to the selection pressure of the soluble organic substrate; the biofilm was surface film-dominated because of the low flow velocity and shear stress. The channel processes were dominated by the biofilm function. However, it was found that the intrinsic Monod kinetic constants were μmax=2.8 d−1, Ks=1.8 mg/l for the suspended biomass, 1.4 d−1, 2.7 mg/l for the biofilm biomass, both at 28°C; and 0.76 d−1, 2.5 mg/l, 0.52 d−1 and 2.9 mg/l respectively for the two types of biomass, both at 200°C. The specific activity of suspended biomass was 50-100% higher than the biofilm biomass, but no significant difference was found between surface and base film biomass. Biofilm oxygen uptake rates (BUR) were around 25 gO2/m2.d at 28°C, 18 gO2/m2.d at 20°C, and velocity dependent. The observed oxygen consumption coefficient of biofilm Yo/s (gO2/ggluc) decreased from 50 to 10% when biofilm surface loading increased from 50 to 300 ggluc/m2.d. The relationship between the biomass population, intrinsic kinetics and biofilm performance is discussed.

The role of the triplet state in the photosensitization of cationic polymerizations by anthracene

AbstractThe photosensitization mechanism for cationic polymerizations initiated by diaryliodonium salts photosensitized by anthracene was investigated using fluorescence and phosphorescence spectroscopy. In situ photosensitizer fluorescence measurements confirmed that the photosensitization reaction proceeds by an electron transfer process. Transient phosphorescence studies demonstrated that electron transfer occurred from the triplet excited state of anthracene to the initiator, with an intrinsic kinetic rate constant of 2 × 108 L/mol s. Further evidence for the role of the triplet state was provided by an observed seven‐fold decrease in the polymerization rate upon addition of a triplet state quencher. Finally, numerical solution of the photophysical kinetic equations indicated that the triplet state concentration was approximately three orders of magnitude higher than that of the singlet state, and that 94‐96% of the active cationic centers are produced by reaction of the initiator with the triplet state. These results indicate that the electron transfer occurs primarily from the triplet state of anthracene, with the singlet state providing only a minor contribution to the photosensitization reaction. © 1995 John Wiley &amp; Sons, Inc.

Aerobic biodegradation and microbial population of a synthetic wastewater in a channel with suspended and attached biomass

A well mixed indoor reciirculating channel was adopted to investigate aerobic heterotrophic biodegradation kinetics and microbial communities in drainage systems with suspended and attached biomass. Experiments were run with synthetic substrate. The biofilm function was distinguished from the suspended biomass by using the Biological Oxygen Monitor (BOM) to measure suspended biomass activity. The microbial community was overall dominated by filaments (mainly Sphaerotilus natans) due to the selection pressure of the soluble organic substrate; the biofilm was surface film-dominated because of the low flow velocity and shear stress. The channel processes were dominated by the biofilm function. However, it was found that the intrinsic Monod kinetic constants were μmax=2.8 d-1, KS=1.8 mg/l for the suspended biomass, 1.4 d-1, 2.7 mgA for the biofilm biomass, both at 28°C; and 0.76 d-1, 2.5 mg/l, 0.52 d-1 and 2.9 mgA respectively for the two types of biomass, both at 200°C. The specific activity of suspended biomass was 50-100% higher than the biofilm biomass. but no significant difference was found between surface and base film biomass. Biofilm oxygen uptake rates (BUR) were around 25 gO2/m2d at 28°C, 18 go2/m2d at 20°C, and velocity dependent. The observed oxygen consumption coefficient of biofdm Yo/s (gO2/ggluc) decreased from 50 to 10% when biofilm surface loading increased from 50 to 300 ggluc/m2d. The relationship between the biomass population, intrinsic kinetics and biofiilm performance is discussed.