Fractal Dimension Of Biomacromolecules And Fractal Reaction Kinetics Of Enzymes

Biomacromolecules as the main parts of life system not only have the biologic functions but also have the complex structures. Fractal theory as an important branch of non-linear science is widely used to study the irregular and complicated systems.In this paper, the degree of the irregularity for the complex biomacromolecules was described by fractal dimension, which is a mathematical index of fractal theory from microcosmic level, and as a mathematical language, fractal was also used to simulate the enzymatic reactions by modified M-M equation. The researches were carried out from following aspects by combining theories and experiments:1.The dimensions of proteins or enzymes were calculated by box dimension simulation, and they were also measured by small angle X-light scattering and static light scattering. By comparing the results the method was established for characterizing the relationship between structure and function of biomacromolecules.2.The processes of enzymatic hydrolysis of hetero-polysaccharides were analyzed under restrictive dimension, and the influence of anomalous diffusion to the reaction kinetics was also explained. On the one hand, the Michaelis-Menten equation was modified by integrating spectral dimension into traditional kinetic equation. On the other hand, the spectral dimension was combined with the reactor dimension to analyze the influence of reactor structure to reaction behavior.3.In order to elaborate the anomalous phenomena of reactions, Monte Carlo was applied to simulate the process of enzymatic hydrolysis of polysaccharides under 2-D, which was beneficial to the preparation of fuel ethanol.This paper showed that the aim of the research was to explore the relationship between structure and function of biomacromolecules by fractal theory, and used the mathematical fractal index to explain the biomacromolecules and its enzymatic reactions.