Fractal mechanisms for the allosteric effects of proteins and enzymes.

Investigations have been made on the reaction kinetics of proteins and enzymes by the statistical methods of random walks on fractal structures. From the point of view of networks of Trap (R) and Free (T) sites, the relationships between the Hill coefficients (h) and the fractal (df) as well as spectral (ds) dimensions of protein molecules are obtained. For example, h = (1 + 2/df) for the one-step conformational changes and hb = (2 + 2/ds) for the multistep conformational changes, respectively. In comparison with that of the literature, the theoretical value is reasonable, thus suggesting a new mechanism for the allosteric effects of proteins and enzymes.