Kinetics of the enzymatic decomposition of macromolecules with a fractal structure

Abstract

Mechanisms of enzymatic decomposition of an organic substance consisting of fractal macromolecules of different sizes are studied. A kinetic decomposition equation in which the reaction rate coefficient depends on the characteristic of the fractal structure is formulated. The solution for a fraction of macromolecules of the same size and for a mixture of macromolecules of different sizes is analyzed. It is shown that the decomposition kinetics depends on the fractal structure of the macromolecules and the type of their initial distribution by size. Conditions under which the decrease in the concentration of the organic substance obeys the power law are found. The theoretical relations are used for analyzing the literature data on the decomposition kinetics of organic matter in sea sediments in the time interval from several hours to about one million years. It is shown that in this whole interval the concentration decreases with time according to the universal power law with a 0.14 exponent. The kinetics of enzymatic decomposition of lignin (product of the natural decomposition of plant remains or byproduct of wood processing) is also discussed. It is found that the exponent accounting for the concentration decrease is equal to 0.4 to 0.5 for the decomposition of industrial lignin in bulk water and 1 to 2 for its decomposition in the water with bottom sediments.