Use of conditional probabilities for determining relationships between amino acid sequence and protein secondary structure

The conditional probability, P(sigma/x), is a statement of the probability that the value of sigma will be found given the prior information that a value of x has been observed. Here sigma represents any one of the secondary structure types, alpha, beta, tau, and rho for helix, sheet, turn, and random, respectively, and x represents a sequence attribute, including, but not limited to: (1) hydropathy; (2) hydrophobic moments assuming helix and sheet; (3) Richardson and Richardson helical N-cap and C-cap values; (4) Chou-Fasman conformational parameters for helix, P alpha, for sheet, P beta, and for turn, P tau; and (5) Garnier, Osguthorpe, and Robson (GOR) information values for helix, I alpha, for sheet, I beta, for turn, I tau, and for random structure, I rho. Plots of P(sigma/x) vs. x are demonstrated to provide information about the correlation between structure and attribute, sigma and x. The separations between different P(sigma/x) vs. x curves indicate the capacity of a given attribute to discriminate between different secondary structural types and permit comparison of different attributes. P(alpha/x), P(beta/x), P(tau/x) and P(rho/x) vs. x plots show that the most useful attributes for discriminating helix are, in order: hydrophobic moment assuming helix greater than P alpha much greater than N-cap greater than C-cap approximately I alpha approximately I tau. The information value for turns, I tau, was found to discriminate helix better than turns. Discrimination for sheet was found to be in the following order: I beta much greater than P beta approximately hydropathy greater than I rho approximately hydrophobic moment assuming sheet. Three attributes, at their low values, were found to give significant discrimination for the absence of helix: I alpha approximately P alpha approximately hydrophobic moment assuming helix. Also, three other attributes were found to indicate the absence of sheet: P beta much greater than I rho approximately hydropathy. Indications of the absence of sigma could be as useful for some applications as the indication of the presence of sigma.