Fractal Reactions on Enzyme Surfaces

This paper reports the of effects of fractal geometry on the enzymatic reactions. The computer aimulations have ben used to explore the fractal scaling relationships to model surface phenomena which occur during catalysis. Modelling immobilised enzyme as a fractal object in the form of a DLA cluster and each enzyme molecule as another fractal object in the form of a percolation cluster, we find the active site probability distribution of enzyme surface is D_AS（a,M） ∝exp（A/lnM）a-a₀（M）² and the fractal dimension is given by D_R 1n（b-θ）（b-θ+1）/2十2θ/1nb where M is the localized cluster mass of enzymes, a₀（M） = BlnM, and A, B are constants, b is the radius of gyration, θ is the number of "empty layers" of enzyme cluster. It is found that the "poison" time T_p is dependent on the size （L） and the perimeter fractal dimension （D_p） of enzyme, namely T_p∝L^zD_p^β where ^z = 1. 96 ±0.02, ^β = 1.5. The product formation as a function of time and the rate of reaction as function of substrate concentration are discussed.