Wavelet transformation of protein hydrophobicity sequences suggests their memberships in structural families

The amino acids of representative proteins were transformed into sequences of hydrophobic free energies per residue, the values derived from equilibrium partitions between aqueous and hydrocarbon phases of a binary solvent. The distributions of the amplitudes of the sequential fluctuations in hydrophobic free energy were then examined with respect to location and scale using Morlet wavelet transformations. Graphs of the wavelet coefficientsʹ imaginary parts discriminated among proteins whose tertiary structures are dominated by helices, sheets or their combination, using protein X-ray structures and X-ray fractal dimensions as reference criteria.