If it is assumed that the primary sequence determines the three-dimensional folded structure of a protein, then the regular folding patterns, such as alpha-helix, beta-sheet, and other ordered patterns in the three-dimensional structure must correspond to the periodic distribution of the physical properties of the amino acids along the primary sequence. An AutoRegressive Moving Average (ARMA) model method of spectral analysis is applied to analyze protein sequences represented by the hydrophobicity of their amino acids. The results for several membrane proteins of known structures indicate that the periodic distribution of hydrophobicity of the primary sequence is closely related to the regular folding patterns in a protein's three-dimensional structure. We also applied the method to the transmembrane regions of acetylcholine receptor alpha subunit and Shaker potassium channel for which no atomic resolution structure is available. This work is an extension of our analysis of globular proteins by a similar method.
