A Fractal-Like Kinetic Equation to Investigate Temperature Effect on Cellulose Hydrolysis by Free and Immobilized Cellulase

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 (R2 > 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 (R2 > 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.