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FOLDING THE SHEETS: USING COMPUTATIONAL METHODS TO PREDICT THE STRUCTURE OF PROTEINS 265 secondary structure as a guide to approximate tertiary structure. A complete description of these combinatorial algorithms can be found in a recent review (Cohen and Kuntz, 1989). If the hierarchical approach to protein structure prediction is to succeed, secondary structure prediction must improve (to at least the 80 percent accuracy level), the combinatorial methods must be further refined, and the radius of convergence of existing potential functions must be extended to allow optimization of the final structure (Wilson and Doniach, 1989; Sippl, 1990; Troyer and Cohen, 1991). PREDICTING MYOGLOBIN STRUCTURE:AN EXCURSION Myoglobin, a 153-residue oxygen-carrying protein, was the first protein structure to be determined by X-ray crystallography. It is composed of six long α-helices and two other smaller helices that do not contribute to the protein's hydrophobic core. In the 1970s we showed that it is possible to construct three-dimensional models of myoglobin by the successive addition of helices to an initial helix using the putative hydrophobic interfaces, while respecting the geometric preferences of helix-helix interactions. From the work of Pauling (1967), we know the conformation and hence the atomic coordinates of the backbone of an α-helix. To begin, we are free to place helix A (residues 3 through 18) so that its axis is coincident with the x-axis with its centroid at the origin. Residue 10 is the center of a potential helix-helix interaction site and creates a sticky patch on the surface of helix A. One possible pairing of helices would join A and B (20 through 35) through sticky patches centered at residues 10 and 28. A line segment perpendicular to the axis of helix A that passes through the Cα of residue 10 with a length of 8.5 à can be used to place helix B such that the segment passes through the Cα of residue 28, is normal to the axis of helix B, and terminates at this axis. Helix E could be placed via its interaction with helix B, and so on. While the packing of helices B and E will be sensible, nothing in this procedure prevents helices A and E from colliding. For the six helices of myoglobin, there are 14 likely helix-helix interaction sites and 3.4 à 108 possible structures.
