Fractal kinetics of o-nitrophenylgalactopiranoside hydrolysis catalyzed by K. lactis Beta-Galactosidase confined in a Langmuir-Blodgett film

PEDRO D. CLOP; MARIA A. PERILLO

Angra dos Reis - Rio de Janeiro - Brasil

Workshop; Worksop in Mathematical Methods and Modeling of Biophysical Phenomena; 2006

Instituto de Matemática Pura y Aplicada

Previously we reported that the ortho-nitrophenylgalactopyranoside (8) hydrolysis catalyzed by beta-Gal turned into a cooperative phenomenon when this enzyme was in a bi-dimensional phospholipid film packed at lateral surface pressures pi >=35 mN/m (Langmuir-Blodgett (LB) film), prepared by the transference of Langmuir films (L) from the air-water interface to a hydrophobic solid surface. In the present work we measured reaction rates at different enzyme concentrations ([EJ). Kinetic data plotted in log-Iog plots let estimate the kinetic order with respect to 8 (gs=0.74) and the fractal Michaelis constant (Kf) which resulted an [E]-dependent value. A secondary plot (gs*Log(Kf) vs Log[EJ) let calculate the kinetic order with respect to enzyme, resulting a value ge=2.31 close to the fractal dimension of proteins surface. The value [3-ge]=0.69, representing the dimension of the actual space where the reaction takes place, was similar to gs. Detrended fluctuation analysis (DFA) on pi fluctuations during L transference showed an alpha=0.827 and autocorrelation lost at 38s (equivalent to 623 micrometers=mesoscopic level). DFA on height values taken from atomic force microscopic analysis of LB topology showed an alpha=0.87. Fractal kinetics seems to be coupled to a su rface , the fractality of which can be predicted by pi fluctuation during L transference.