1.
A fractal-like kinetic equation to investigate temperature effect on cellulose hydrolysis by free and immobilized cellulase.
Zhang, Y, Xu, JL, Qi, W, Yuan, ZH, Zhuang, XS, Liu, Y, He, MC
Applied biochemistry and biotechnology. 2012;(1):144-53
Abstract
According to fractal-like theory in the heterogeneous system, a cellulase-catalyzed kinetic equation that contained two parameters (rate constant k and fractal dimension h) was deduced. The equation described directly the mathematical relationship between reducing sugar concentration and hydrolytic time, and accurately fitted the experimental data of free/immobilized cellulase at 37, 40, 44, 47, and 50 °C (R(2)>0.99). The fitted h value is estimated as a constant (0.6148) in these tested temperatures. The fitted k value increased with temperature increase, and the relationship agreed with Arrhenius equation (R(2)>0.98). The fractal-like equation could predict accurately the experimental data at low temperature 34 °C for free/immobilized cellulase and high temperature 53 °C for immobilized cellulase, but the prediction at 53 °C for free cellulase was not accurate enough due to its lower stability than immobilized cellulase. The application of fractal-like theory in cellulase kinetics is successful.
2.
Numerical determination of competitive adsorption isotherm of mandelic acid enantiomers on cellulose-based chiral stationary phase.
Zhang, Y, Rohani, S, Ray, AK
Journal of chromatography. A. 2008;(1):34-9
Abstract
The use of inverse method for the determination of competitive adsorption isotherm of mandelic acid enantiomers on cellulose tris(3,5-diethylphenyl carbamate) stationary phase is proposed in this work. Non-dominated sorting genetic algorithm with jumping genes (NSGA-II-JG) was applied to acquire the isotherm parameters by minimizing the sum of square deviations of the model predictions from the measured elution profiles. Three different competitive isotherm models, i.e., Langmuir, biLangmuir and Tóth, combined with transport-dispersive chromatographic model were used in predicting the elution profiles. Orthogonal collocation on finite element (OCFE) method was applied to obtain the calculated elution profiles. Results indicate that biLangmuir isotherm and Tóth isotherm give remarkably similar equilibrium isotherms within the investigated liquid concentration range. Band profiles calculated from both isotherm models are in good agreement with the experimental data. The validity of the determined parameters was verified by comparing the model predictions with experimental elution profiles at various experimental conditions.