FRACTAL STRUCTURE AND CONFORMATIONAL ENTROPY OF PROTEIN CHAIN

The structures of 25 proteins arbitrarily chosen are investigated by fractal geometry, and their fractal dimensions (Df) and conformational entropies S(N0) are calculated by Havlin-Ben Avraham and Monte Carlo method, respectively. Comparison of the Df and S(N0) gives the relation: Df = 1.532 - 3.00 × 10-4 S(N0). The entropy data obtained by Monte Carlo method for the chain of random self-avoiding walks confirm the prediction of renormalization group: S(N0) = 1.544N0 + 0.1667 In N0 + 0.1570 where N0 is the number of residues in a protein chain. Both the Df and S(N0) reflect the conformational properties of a protein molecular chain. The idea resulting from the present communication suggests that the thermodynamic behaviours of proteins may be related to multifractals. © 1990.