Kinetic and equilibrium models for biosorption of Cr(VI) on chemically modified seaweed,Cystoseira indica

The biosorption data of hexavalent chromium by marine brown algae Cystoseira indica, which was chemically modified by crosslinking with epichlorohydrin (CB1, CB2), or oxidized by potassium permanganate (CB3), or only washed with distilled water (RB), has been used for kinetic studies based on fractional power, Elovich, pseudo-first order and pseudo-second order rate expressions. Five three parameter biosorption isotherm models, viz. Redlich–Peterson, Sips, Khan, Radke–Prausnitz and Toth are tested for their applicability apart from 6 two-parameter models. Non-linear curve fitting procedure was adopted for fitting the kinetic as well as equilibrium data in the kinetic and isotherm models and for the determination of parameters. The time-dependent Cr(VI) biosorption data were well-described by pseudo-second-order kinetic model. The intraparticle diffusion study revealed that film diffusion might be involved in Cr(VI) biosorption in the present case. Among the two-parameter models, the Langmuir model produces the best fit, while, among the three-parameter models, the best fit is produced by the Khan model, for the biosorption of Cr(VI) on all the four biosorbents studied.     

Equilibrium and kinetics studies of heavy metal ions biosorption on green algae waste biomass

The biosorption of Pb(II), Cd(II), and Co(II), respectively, from aqueous solution on green algae waste biomass was investigated. The green algae waste biomass was obtained from marine green algae after extraction of oil, and was used as low-cost biosorbent. Batch shaking experiments were performed to examine the effects of initial solution pH, contact time and temperature. The equilibrium biosorption data were analyzed using two isotherm models (Langmuir and Freundlich) and two kinetics models (pseudo-first order and pseudo-second order). The results indicate that Langmuir model provide best correlation of experimental data, and the pseudo-second order kinetic equation could best describe the biosorption kinetics of considered heavy metals.     

Diagnosis of enzyme inhibition based on the degree of inhibition

In this work, a method for the diagnosis of kinetic inhibition, based on the dependence of the degree of inhibition (epsilon(i)) on the inhibitor concentration [I] and on the substrate concentration [S], is presented. Because the degree of inhibition is a ratio between rates, kinetic data are normalized by the introduction of an internal control-the rate of the uninhibited reaction. Therefore, the error associated with the kinetic measurements decreases and less experimental measurements are necessary to achieve the diagnosis. The process described, which uses graphical and/or non-linear fitting procedures, allows distinguishing between 20 different kinds of inhibition, including not only linear and hyperbolic, but also parabolic and rational 2,2 inhibitions. Rational 2,2 indicates a new type of inhibition corresponding to an incomplete parabolic inhibition, i.e. mechanistically it corresponds to an inhibitor that binds to two inhibition sites producing enzymatic complexes that are still active. In spite of its comprehensiveness, the diagnosis process is greatly facilitated by the division of the diagnosis of the inhibition in a step-by-step procedure, where only two rival models are evaluated in each step. In the non-linear fittings, the choice between rival models uses a test based on information statistics theory, the Akaike information criterion test, in order to penalize complex models that tend to be favoured in fittings. Finally, equations that allow the determination of inhibition kinetic constants were also deduced. The formalism presented was tested by examining inhibition of acid phosphatase by phosphate (a linear competitive inhibitor).     

A generalization of the clonal survival models: Equations for the families of curves obtained with fractionated irradiation

Summary The survival curves obtained when cellular recovery follows various first radiation dose deliveriesDI seem, when semi-logarithmically plotted, to be translated from the part of the curve corresponding to an unfractionated irradiation beyond a doseDR. A possible assumption consistent with such experimental observations is proposed which allows the generalization of any survival modelS = f(D). The derived equationS = f(DR + D - DI)f(DI)/f(DR) is convenient for the whole family of experimental survival curves involving cellular damage repairs when the first radiation doses vary. All the parameters of the family equation can be simultaneously fitted so that their reliability is increased. The generalized equations are given for the four following models: two-hits targets, Chadwick and Leenhouts, Green and Burki, Wideröe. As an example, the Chadwick and Leenhouts generalized model parameters are fitted to a family of experimental survival curves concerningChlorella cells exposed to fractionated and continuous gamma irradiation. The fittings are presented with their confidence limits and are briefly discussed.     

Kinetics,Isotherms, and Thermodynamics of Hg(II) Biosorption onto Carica papaya

Carica papaya, a novel sorbent, was evaluated for sorption of Hg(II) from synthetic aqueous solutions using various pseudo-second order kinetic models as well as equilibrium sorption models. Batch kinetic and equilibrium experiments were carried out for the sorption of Hg(II) onto C. papaya at pH 6.5 and solid to liquid ratio (s/l) 1.0 g L^?1. The kinetic data were fitted to second order models of Sobkowsk and Czerwinski, Ritchie, Blanchard, Ho and McKay, whereas Langmuir, Freundlich, and Redlich-Peterson models were used for the equilibrium data. A comparative study on both linear and nonlinear regression showed that the Sobkowsk and Czerwinski and Ritchie's second order model were the same. Ho and McKay's pseudo-second order model fitted well to the experimental data when compared with the other second order kinetic expressions. Langmuir isotherm parameters obtained from the four Langmuir linear equations by using linear method were dissimilar, but were the same when nonlinear method was used. Additionally, various thermodynamic parameters, such as ΔG ⁰, ΔH ⁰, and ΔS ⁰, were calculated. The negative values of Gibbs free energy (ΔG ⁰) and ΔH ⁰ confirmed the intrinsic nature of biosorption process and exothermic, respectively. The negative value of ΔS ⁰ showed the decreased randomness at the solid-solution interface during biosorption.     

Kinetics and mechanism of peptide synthesis in solution

The kinetics of the reaction of Boc-Xaa fluorophenyl esters (where Xaa = Ala, Val, Phe, Ser, Leu, Gly, Met, Pro, or Ile) with leucinamide was studied measuring changes in the fluorescence emission at 375 nm of the fluorophenyl chromophore accompanying the reaction. It was found that the experimental kinetic data couldn't be described by a simple scheme of the second order reaction. The measurements of the kinetic parameters of the reaction at various initial concentrations of reagents indicated that the reaction rate can be expressed as: v = kCNaCAEb, where k is the reaction rate constant, CN is the concentration of leucinamide, and LeuNH2, CAE is the concentration of fluorophenyl ester. The a and b reaction orders were close to 1/2 and 3/2 for Xaa = Ala, Val, Phe, Ser, or Leu, 1/2 and 1 for Gly, Met, or Pro, and 1 and 2 for Ile. The experimental equations for the reaction rate can theoretically be derived from a single scheme of chain reactions with various deactivation ways for active intermediates. The English version of the paper.     

Biosorption of a textile dye (Acid Blue 40) by cone biomass of Thuja orientalis: estimation of equilibrium, thermodynamic and kinetic parameters

Biosorption of Acid Blue 40 (AB40) onto cone biomass of Thuja orientalis was studied with variation in the parameters of pH, contact time, biosorbent and dye concentration and temperature to estimate the equilibrium, thermodynamic and kinetic parameters. The AB40 biosorption was fast and the equilibrium was attained within 50 min. Equilibrium data fitted well to the Langmuir isotherm model in the studied concentration range of AB40 and at various temperatures. Maximum biosorption capacity (q(max)) for AB40 was 2.05 x 10(-4)mol g(-1) or 97.06 mg g(-1) at 20 degrees C. The changes of Gibbs free energy, enthalpy and entropy of biosorption were also evaluated for the biosorption of AB40 onto T. orientalis. The results indicate that the biosorption was spontaneous and exothermic. Kinetics of biosorption of AB40 was analyzed and rate constants were also derived and the results show that the pseudo-second-order kinetic model agrees very well with the experimental data.     

酿酒酵母吸附重金属离子的研究进展

重金属污染成为当今最重要的环境问题之一。生物吸附法是处理大体积低浓度重金属废水的一种理想方法,近年来有关的研究报道不断增多,但尚未实现工业化应用。酿酒酵母(Saccharomyces cerevisiae)不仅是具有实用潜力的生物吸附剂,也是研究重金属生物吸附机理的良好材料。结合自己的研究成果,总结了酿酒酵母作为生物吸附材料的优点、研究中的表现形式和吸附性能,重点讨论了酿酒酵母生物吸附机理,介绍了等温吸附平衡模型和动力学模型在酵母生物吸附中的应用情况。最后提出生物吸附进一步的研究方向。     

Kinetic analysis of enzyme reactions with slow-binding inhibition.

In this paper we present a general kinetic study of slow-binding inhibition processes, i.e. enzyme reactions that do not respond instantly to the presence of a competitive inhibitor. The analysis that we present is based on the equation that describes the formation of products with time in each case on the experimental progress curve. It is carried out under the condition of limiting enzyme concentration and allows the discrimination between the different cases of slow-binding inhibition. The mechanism in which the formation of complex enzyme-inhibitor is a single or two slow steps or follow a rapid equilibrium, has been considered. The corresponding explicit equations of each case have been obtained and checked by numerical integration. A kinetic data analysis to evaluate the corresponding kinetic parameters is suggested. We illustrate the method, numerically by computer simulation, of the reaction and present some numerical examples that demonstrate the applicability of our procedure.     

A new kinetic model of recombinant beta-galactosidase from Kluyveromyces lactis for both hydrolysis and transgalactosylation reactions

Previous models based on the Michaelis-Menten kinetic equation, that glucose was not used as an acceptor, did not explain our experimental data for lactose conversion by a recombinant beta-galactosidase from Kluyeromyces lactis. In order to create a new kinetic model based on the data, the effects of galactose and glucose on beta-galactosidase activity were investigated. Galactose acted as an inhibitor at low concentrations of galactose and lactose, but did not inhibit the activity of beta-galactosidase at high concentrations of galactose (above 50mM) and lactose (above 100mM). The addition of glucose at concentrations below 50mM resulted in an increased reaction rate. A new model of K. lactis beta-galactosidase for both hydrolysis and transgalactosylation reactions with glucose and lactose as acceptors was proposed. The proposed model was fitted well to the experimental data of the time-course reactions for lactose conversion by K. lactis beta-galactosidase at various concentrations of substrate.     

Removal of Acid Blue25 from aqueous solutions using Bengal gram fruit shell (BGFS) biomass

The feasibility for the removal of Acid Blue25 (AB25) by Bengal gram fruit shell (BGFS), an agricultural by-product, has been investigated as an alternative for high-cost adsorbents. The impact of various experimental parameters such as dose, different dye concentration, solution pH, and temperature on the removal of Acid Blue25 (AB25) has been studied under the batch mode of operation. pH is a significant impact on the sorption of AB25 onto BGFS. The maximum removal of AB25 was achieved at a pH of 2 (83.84%). The optimum dose of biosorbent was selected as 200 mg for the removal of AB25 onto BGFS. Kinetic studies reveal that equilibrium reached within 180 minutes. Biosorption kinetics has been described by Lagergren equation and biosorption isotherms by classical Langmuir and Freundlich models. Equilibrium data were found to fit well with the Langmuir and Freundlich models, and the maximum monolayer biosorption capacity was 29.41 mg g^?1 of AB25 onto BGFS. The kinetic studies indicated that the pseudo-second-order (PSO) model fitted the experimental data well. In addition, thermodynamic parameters have been calculated. The biosorption process was spontaneous and exothermic in nature with negative values of ΔG° (?1.6031 to ?0.1089 kJ mol^?1) and ΔH° (?16.7920 kJ mol^?1). The negative ΔG° indicates the feasibility of physical biosorption process. The results indicate that BGFS could be used as an eco-friendly and cost-effective biosorbent for the removal of AB25 from aqueous solution.     

The use of steady-state rate equations to analyse progress curve data.

Analysis of progress curves for enzyme-catalyzed reactions has been made by using a procedure that does not require the derivation of complex integrated rate equations. The method involves conversion of progress curve data to reaction velocities that are then fitted to the appropriate differential rate equation. Application of the procedure to data obtained for the reaction catalyzed by aspartate aminotransferase (L-aspartate:2-oxoglutarate aminotransferase, EC 2.6.1.1), showed that the resulting values for the kinetic parameters agreed well with those obtained by conventional progress curve analysis (Duggleby, R.G. and Morrison, J.F. (1978) Biochim. Biophys. Acta 526, 398--409).     

Bioremediation potential of a widespread industrial biowaste as renewable and sustainable biosorbent for synthetic dye pollution

In this study, a model synthetic azo dye (Basic red 46) bioremoval by Carpinus betulus sawdust as inexpensive, eco-friendly, and sustainable biosorbent from aqueous solution was examined in a batch biosorption system. The effective environmental parameters on the biosorption process, such as the value of pH, amount of biosorbent, initial dye concentration and contact time were optimized using classical test design. The possible dye-biosorbent interaction was determined by Fourier Transform Infrared Spectroscopy (FTIR) and Scanning Electron Microscopy (SEM). The equilibrium, thermodynamic, and kinetic studies for the biosorption of Basic red 46 onto the sawdust biomass were performed. In addition, a single-stage batch dye biosorption system was also designed. The dye biosorption yield of biosorbent was significantly influenced by the change of operating variables. The experimental data were best described by the Freundlich isotherm model and both the pseudo-first-order kinetic and the pseudo-second-order kinetic models. Thermodynamic research indicated that the biosorption of dye was feasible and spontaneous. Based on the Langmuir isotherm model, the biosorbent was found to have a maximum biosorption potential higher than many other biosorbents in the literature (264.915?mg g^?1). Thus, this investigation presents a novel green option for the assessment of waste sawdust biomass as a cheap and effective biosorbent material.     

An explicit solution for progress curve analysis in systems characterized by endogenous substrate production

The Lambert W function was used to explicitly relate substrate concentration S, to time t, and the kinetic parameters V (m), K (m), and R in the modified Michaelis-Menten equation that accounts for endogenous substrate production. The applicability of this explicit formulation for kinetic parameter estimation by progress curve analysis was demonstrated using a combination of synthetic and experimental substrate depletion data. Synthetic substrate depletion data were generated using S (0) values of 1, 2, and 3 μM and V (m), K (m), and R values of 1.0 μM h(-1), 1.0 μM, and 0.1 μM h(-1), respectively, and contained 5% normally distributed error. Experimental data were obtained from two previously published studies on hydrogen depletion in four experimental systems. In all instances, experimental data were well described by the explicit solution presented in this study. Differential equation solution and iterative S estimation are eliminated with the explicit solution approach, thereby simplifying progress curve analysis in systems characterized by endogenous substrate production.     

Biosorption behavior of heavy metals in bioleaching process of MSWI fly ash by Aspergillus niger

In this study, it was considered that the biosorption of heavy metals by biomass might occur during the bioleaching of fly ash. This work is focused on the biosorption behavior of Al, Fe, Pb and Zn by Aspergillus niger during the bioleaching process. The fungal biomass was contacted with heavy metals solution which extracted from fly ash by using gluconic acid as leaching agent. The equilibrium time for biosorption was about 120 min. The biosorption experiment data at initial pH 6.5 was used to fit the biosorption kinetics and isotherm models. The results indicated that the biosorption of Al, Fe and Zn by A. niger biomass were well described by the pseudo-first order kinetic model. The pseudo-second order kinetic model was more suitable for that of Pb. The Langmuir isotherm model could well describe the biosorption of Fe, Pb and Zn while the Freundlich model could well describe the biosorption of Al. Furthermore, the biosorption of metal ions decreased evidently in the presence of fly ash as compared to that in the absence of fly ash. This research showed that although the biomass sorption occurred during the bioleaching process, it did not inhibit the removal of Al, Fe, Pb and Zn evidently from fly ash.     

Velocity of Ellman's reaction and its implication for kinetic studies in the millisecond time range

A detailed study of the velocity of the reaction between Ellman's reagent and thiocholine was undertaken, in order to test the possibilities of this reaction as a detection method for the earlier stages of cholinesterases reactions. Experiments were carried out on a stopped-flow apparatus with a built-in spectrophotometer. The obtained experimental data were analyzed by fitting the data to theoretical kinetic equations derived for the reaction. In this way, a complete kinetic characterization of the reaction was obtained. An important practical result derived from our investigations is the finding that, under most experimental conditions, the Ellman's reactions is more than sufficiently rapid as a detection method. However, in the case of reactions in the time scale of 200 milliseconds or less, this being 5 times the half life of Ellman's reaction at standard conditions, one has to consider the interference of this reaction with the enzyme reaction itself.     

An ecofriendly approach for bioremediation of contaminated water environment: Potential contribution of a coastal seaweed community to environmental improvement

High levels of heavy metals like copper ions in many industrial based effluents lead to serious environmental and health problems. Biosorption is a potential environmental biotechnology approach for biotreatment of aquatic sites polluted with heavy metal ions. Seaweeds have received great attention for their high bioremediation potential in recent years. However, the co-application of marine macroalgae for removal of heavy metals from wastewater is very limited. Thus, for the first time in literature, a coastal seaweed community composed of Chaetomorpha sp., Polysiphonia sp., Ulva sp. and Cystoseira sp. species was applied to remove copper ions from synthetic aqueous medium in this study. The biosorption experiments in batch mode were conducted to examine the effects of operating variables including pH, biosorbent amount, metal ion concentration and contact time on the biosorption process. The biosorption behavior of biosorbent was described by various equilibrium, kinetic and thermodynamic models. The biosorption of copper ions was strongly influenced by the operating parameters. The results indicated that the equilibrium data of biosorption were best modeled by Sips isotherm model. The values of mean free energy of biosorption computed from Dubinin-Radushkevich isotherm model and the standard Gibbs free energy change indicated a feasible, spontaneous and physical biotreatment system. The pseudo-second-order rate equation successfully defined the kinetic behavior of copper biosorption. The pore diffusion also played role in the control of biosorption process. The maximum copper uptake capacity of biosorbent was found to be greater than those of many other biosorbents. The obtained results revealed that this novel biosorbent could be a promising material for copper ion bioremediation implementations.     

The monod equation: A revisit and a generalization to product inhibition situations

This paper shows how to treat the substrate-limiting Monod equation in a straight forward manner for different types of fermentors (plug-flow, batch, and mixed-flow) using the general language of chemical reaction engineering. Straight-line plots are developed for directly finding the kinetic constants of the equation, and an example using Monod's original data illustrates the procedure. The Monod equation is then generalized to account for the effects of both substrate and inhibitory toxic wastes. Finally, for pure product inhibition performance, expressions are derived for various reactor types, and correlation graphs are developed for finding the kinetic constants of the reaction. An example from the recent literature shows that this equation form fits the data extremely well.     

Progress curve analysis for enzyme and microbial kinetic reactions using explicit solutions based on the Lambert W function

We present a simple method for estimating kinetic parameters from progress curve analysis of biologically catalyzed reactions that reduce to forms analogous to the Michaelis-Menten equation. Specifically, the Lambert W function is used to obtain explicit, closed-form solutions to differential rate expressions that describe the dynamics of substrate depletion. The explicit nature of the new solutions greatly simplifies nonlinear estimation of the kinetic parameters since numerical techniques such as the Runge-Kutta and Newton-Raphson methods used to solve the differential and integral forms of the kinetic equations, respectively, are replaced with a simple algebraic expression. The applicability of this approach for estimating Vmax and Km in the Michaelis-Menten equation was verified using a combination of simulated and experimental progress curve data. For simulated data, final estimates of Vmax and Km were close to the actual values of 1 microM/h and 1 microM, respectively, while the standard errors for these parameter estimates were proportional to the error level in the simulated data sets. The method was also applied to hydrogen depletion experiments by mixed cultures of bacteria in activated sludge resulting in Vmax and Km estimates of 6.531 microM/h and 2.136 microM, respectively. The algebraic nature of this solution, coupled with its relatively high accuracy, makes it an attractive candidate for kinetic parameter estimation from progress curve data.