Linear optimization of predictors for secondary structure. Application to transbilayer segments of membrane proteins

Sliding-window averaging of amino acid properties is a standard method for predicting protein secondary structure. For example, transmembrane segments are predicted to occur near the peaks in a hydropathy plot of a membrane protein. Such a scheme (linear convolutional recognizer, LCR) assigns a number (weight) to each type of monomer, and then convolutes some window function with the sequence of weights. The window has commonly been rectangular, and the weights derived from singlet amino acid frequencies in proteins of known secondary structure or from physical properties of amino acids. The accuracy of the windows and weights have remained unknown. We use linear optimization theory to develop a general method for approximating the optimal window and weights for a LCR. The method assumes that one knows the sequences of one or more chains and the locations of their "features", regions having the secondary structure of interest. We present formulae for quantifying the accuracy of predictors. We show why the optimal LCR is more accurate than methods based on the differences between singlet monomer frequencies inside and outside features. The advantage of an optimal LCR is that its weights inherently include correlations between nearby monomer positions. The optimal predictor is not perfect though. We argue that its inaccuracy is an intrinsic limitation of linear predictors based on monomer weights. As a practical example, we study predictors for transbilayer segments of membrane proteins. We estimate the optimal weights and windows for the two bacterial photosynthetic reaction centers whose three-dimensional structures are known. The resultant LCR, which is more accurate than previous ones, is still inexact. We apply it to bacteriorhodopsin and halorhodopsin. Several non-linear generalizations are examined as possible improvements to the LCR method: non-linear combinations of linear predictors and windowed Fourier transforms of the weight sequences. The former do not significantly increase the accuracy, while the latter reveal a weak negative correlation between the segments and periodic variations of the weights.