Matching Protein-Sheet Partners by Feedforward and Recurrent Neural Networks
Predicting the secondary structure ( -helices, sheets, coils) of proteins is an important step towards understanding their three dimensional conformations. Unlike -helices that are built up from one contiguous region of the polypeptide chain, -sheets are more complex resulting from a combination of two or more disjoint regions. The exact nature of these long distance interactions remains unclear. Here we introduce two neural-network based methods for the prediction of amino acid partners in parallel as well as antiparallel -sheets. The neural architectures predict whether two residues located at the center of two distant windows are paired or not in a -sheet structure. Variations on these architecture, including also pro les and ensembles, are trained and tested via ve-fold cross validation using a large corpus of curated data. Prediction on both coupled and non-coupled residues currently approaches 84% accuracy, better than any previously reported method. Introduction Predicting the secondary structure ( -helices, -sheets, coils) of proteins is an important step towards understanding their three dimensional conformations. Unlike -helices that are built up from one contiguous region of the polypeptide chain, -sheets are built up from a combination of several disjoint regions. Such regions, or strands are typically 5-10 residues long. In the and Department of Biological Chemistry, College of Medicine, University of California, Irvine. To whom all correspondence should be addressed. folded protein, these strands are aligned adjacent to each other in parallel or anti-parallel fashion. Hydrogen bonds can form between C'O groups of one strand and NH groups on the adjacent strand and vice versa with C atoms successively a little above or below the plane of the sheet. Hydrogen bonds between parallel and anti-parallel strands have distinctive patterns, but the exact nature and behavior of -sheet long-ranged interactions is not clear. While the majority of sheets seems to consist of either parallel or antiparallel strands, mixed sheets are not uncommon. A -strand can have 1 or 2 partner strands, and an individual amino acid can have 0,1 or 2 hydrogen bonds with one or two residues in a partner strand. Sometimes one or several partner-less residues are found in a strand, giving rise to the so-called bulges. Finally, -strand partners are often located on a di erent protein chain. How amino acids located far apart in the sequence nd one another to form -sheets is still poorly understood, as is the degree of speci city between side-chain/side-chain interactions between residues on neighboring strands, which seems to be very weak (Wouters & Curmi, 1995). The presence of a turn between strands is also an essential ingredient. Partly as a result of the exponentially growing amount of available 3D data, machine learning methods have in general been among the most successful in secondary structure prediction (Baldi & Brunak, 1998). The best existing methods for predicting protein secondary structure, i.e. for classifying amino acids in a chain in one of the three classes, achieve prediction accuracy in the 75-77% range (Baldi et al., 1999; Cu & Barton, 1999; Jones, 1999). Not surprisingly, -sheet is almost invariably the weakest category in terms of correct percentages, and it is never the highest scoring in terms of correlation coe cients. Therefore any improvement in -sheet prediction is signi cant as a stand-alone result, but also in relation to secondary and tertiary structure prediction methods in general. Here we design and train a neural network architecture for the prediction of amino acid partners in sheets (see also (Hubbard, 1994; Zhu & Braun, 1999; Street & Mayo, 1999)). Data Preparation Selecting the Data As always the case in machine learning approaches, the starting point is the construction of a well-curated data set. The data set used here consists of 826 protein chains from the PDB select list of June 1998 (Hobohm & Sander, 1994) (several chains were removed since DSSP could not run on them). All the selected chains have less than 25% sequence identity using the Abagyan-function (Abagyan & Batalov, 1997). The selection has been performed by applying the all against all Huang-Miller sequence alignment using the "sim" algorithm (Huang & Miller, 1991), where the chains had been sorted according to their quality (i.e. resolution plus R-factor/20 for X-ray and 99 for NMR). Assigning -sheet Partners The -sheets are assigned using Kabsch and Sander's DSSP program (Kabsch & Sander, 1983), which species where the extended -sheets are situated and how they are connected. This is based on the intra-backbone H-bonds forming the sheet according to the Pauling pairing rules (Pauling & Corey, 1951). An H-bond is assigned if the Coulomb binding energy is below 0:5 kcal/mol. In wildtype proteins there are many deviations from Paulings ideal binding pattern, so Kabsch and Sander have implemented the following rules: a sheet ('E') amino acid is de ned when it forms two Hbonds in the sheet or is surrounded by two H-bonds in the sheet. The minimal sheet is two amino acids long; if only one amino acid ful lls the criteria, then it is called -bridge ('B'). Bulges in sheets are also assigned 'E' if they are surrounded by normal sheet residues of the same type (parallel or anti-parallel) and comprise at most 4 and 1 residue(s) in the two backbone partner segments, respectively. A standard example of how the partner assignments are made is shown in Figure 1. In the case of -bridges the same rules are followed, while in the special case of -bulge residues then no partner is assigned. Statistical Analysis This large curated data set allows us to compute a number of -sheet and -strand statistics, including rst and second order composition statistics and various length statistics. Furthermore these statistics can be computed for parallel strands, antiparalllel strands, side versus internal strands, and -bulges. Here we give a few examples. The complete statistics will be reported elsewhere. First Order Statistics The rst order statistics associated with the frequency of occurrence of each amino acid in the data in general, and speci cally within -sheets are displayed in Figures 2 and 3. To enhance the similarities and di erences, the ratio of the frequencies in -sheets over data are given in Figure 4. Second Order Statistics Second order statistics are associated with pairings of amino acids in -sheets. The frequency of pairings can be normalized in di erent ways. In each row of Figure 6, we have plotted the conditional probabilities P (X jY ) of observing a X knowing that the partner is Y in a sheet. Length Distribution Interval distances between paired -strands, measured in residue positions along the chain, are given in Figure 8. A small number of pairs have large distances above 200 amino acids and are not represented. Distances could also be measured circularly but this would not alter the fundamental features of the plot. Arti cial Neural Network Architecture A number of di erent arti cial neural network (ANN) approaches can be considered. Because of the longranged interactions involved in beta-sheets, neural architectures must have either very large input windows or distant shorter windows. Very large input windows lead to architectures with many parameters which are potentially prone to over tting, especially with sparse amino acid input encoding. Over tting, however, is not necessarily the main obstacle because data is becoming abundant and techniques, such as weight sharing, can be used to mitigate the risk. Perhaps the main obstacle associated with large input windows is that they tend to dilute sparse information present in the input that is really relevant for the prediction (Lund et al., 1997). Here we have used a basic two-windows approach. Since the distance between the windows plays a key role in the prediction, one can either provide the distance information as a third input to the system or one can train a di erent architecture for each distance type. Here, we use the rst strategy with the neural network architecture depicted in Figure 9 (see also (Riis & Krogh, 1996)). The architecture has two input windows of length W corresponding to two amino acid substrings in a given chain. The goal of the architecture is to output a probability re ecting whether the two amino acids located at the center of each window are partners or not. The sequence separation between the windows, measured by the number D of amino acids, is essential for the prediction and is also given as an input