Quadratic minimization of predictors for protein secondary structure. Application to transmembrane alpha-helices.

Sliding-window averaging of amino acid properties is often used for predicting protein secondary structure. Such a scheme (linear convolutional recognizer, LCR) assigns a number (weight) to each type of monomer, and then convolutes a window function with the sequence of weights to yield a decision function. Features, regions having the property of interest, are predicted to occur where the decision function exceeds some threshold. A general method for approximating the best possible window and weights is presented. The needed data are the sequences of some chains and the locations of their features. The method is applied to transmembrane helices (TMH) of membrane proteins. Optimal weights and windows are calculated, using bacteriorhodopsin and photosynthetic reaction centers as the reference chains. The predictor is then tested on other proteins. No TMH are predicted in porin, whose transmembrane segments are beta-sheets. This shows that the predictor is specific for helical segments. Few segments are predicted for non-membrane globular proteins. The predictor thus correctly rejects their hydrophobic helices. Finally, the predictor is tested with some membrane proteins whose transmembrane topology is partially known. Among their TMH, the LCR is unable to resolve 6% which are closely spaced. Taking 17 as the minimum allowed length of a predicted TMH, 4% of the known ones are missed and 6% of the predicted ones are false. For a minimum length of 10, 0.5% are missed and 14% are false. The mean magnitude of the endpoint error is about four residues. Alternative prediction methods make more errors.