Theory on the power-law distribution of the Michaelis-Menten enzyme kinetic parameters

We show on the biophysical basis that the observed enzyme kinetic parameters related to the substrate binding, product turnover and catalytic efficiency follow power-law type density functions. These finding are validated with the available datasets on various enzymes across different substrates. The product turnover rates and catalytic efficiencies seems to follow a bimodal type density functions in line with the single molecule experiments on enzyme catalysis which can be explained by a sum of two different power-law type density functions. The curve geometry of the density functions is decided by the underlying biophysical factors and the location of the peak is dictated by the natural selection pressure.