Hydrophobic free energy eigenfunctions of pore, channel, and transporter proteins contain beta-burst patterns

Hydropathy plots are often used in place of missing physical data to model transmembrane proteins that are difficult to crystallize. The sequential maxima of their graphs approximate the number and locations of transmembrane segments, but potentially useful additional information about sequential hydrophobic variation is lost in this smoothing procedure. To explore a broader range of hydrophobic variations without loss of the transmembrane segment-relevant sequential maxima, we utilize a sequence of linear decompositions and transformations of the n-length hydrophobic free energy sequences, Hi, i = 1...n, of proteins. Constructions of hydrophobic free energy eigenfunctions, psil, from M-lagged, M x M autocovariance matrices, CM, were followed by their all-poles, maximum entropy power spectral, Somega(psil), and Mexican Hat wavelet, Wa,b(psil), transformations. These procedures yielded graphs indicative of inverse frequencies, omega-1, and sequence locations of hydrophobic modes suggestive of secondary and supersecondary protein structures. The graphs of these computations discriminated between Greek Key, Jelly Role, and Up and Down categories of antiparallel beta-barrel proteins. With these methods, examples of porins, connexins, hexose transporters, nuclear membrane proteins, and potassium but not sodium channels appear to belong to the Up and Down antiparallel beta-barrel variety.