Methods

The Dezymer algorithm uses a geometric description of the ligands around a metal, the three-dimensional structure of a protein, and a library of sidechain rotamers of amino acids (or atoms from the mainchain) to identify a set of potential binding sites (Hellinga &, Richards, 1991). In principle, this program can search for any coordination number, geometry and combination of amino acid ligands based on the appropriate positioning of amino acids. The identification of potential calcium-binding sites in natural calcium-binding proteins is divided into two major steps: Site-Search and Refinement.

In the Site-Search step of this study, the high-resolution X-ray structures of calmodulin (3cln) (Babu et al., 1988), parvalbumin (5cpv) (Swain et al., 1989) and calbindinD9k (4icb) (Svensson et al., 1992) are used. Calcium binding sites in all three proteins are removed by deleting all the heteroatoms in these structural files including water and calcium molecules. The first residue located in the calculation (called anchor) defines the position of the calcium atom in the protein frame and is used as a starting point to construct a calcium-binding site. Since both classical and pseudo EF-hand motifs use glutamate as a bidentate ligand, Glu residue was used as an anchor for the design of all calcium binding sites. A calcium atom is placed on the same plane of two sidechain oxygen atoms and the C 5 atom with a distance between the calcium and oxygen atoms of 2.4 A The angle of O-Ca-O and Ca-O-C 5 are set to 53.8o and 93.5o, mimicking the natural interaction between the bidentate glutamate and calcium. This anchor residue (Glu-Ca) shares the same rotamer library of the Glu sidechain with 24 configurations (Hellinga & Richards, 1991). After attaching the anchor residue to the backbone of the protein along the protein sequence, the calcium-binding geometry or positions of other ligands are then defined around the anchor (Fig. 2). The geometry of pentagonal bipyramidal, with five oxygen atoms on the same plane and the other two above or below the plane, was used to describe all calcium-binding sites in natural EF-hand proteins. The two oxygen atoms from the anchor residue Glu are placed on the plane. One position either above or below the plane is deliberately unoccupied to allow for the oxygen atom from water to be used as a ligand. The other four ligand-positions are further defined according to the relative position of each ligand residue to the anchor residue using oxygen atoms from the sidechain oxygens of Asp and Asn and the mainchain oxygen from the protein backbone. To define the relative position between the anchor and a ligand, a total of six atoms, three from the anchor residue (atom 1, 2 and 3) and three from the residues being tested (atom 4, 5 and 6), are used. Atoms 3 and 4 are the calcium atom attached to the anchor and the oxygen atom from the ligand residue, respectively (Fig. 2). The other four atoms are CS and C y in Glu-Ca and C y and C P in Asp or Asn. The position of one potential ligand is defined by the length of atom 3_4, the angles of atoms 2_3_4 and 3_4_5, and the dihedral angles of atoms 1_2_3_4 2_3_4_5 and 3_4_5_6. To define the position of the oxygen atom from a ligand residue in a calcium-binding site, the length of 3_4, angle of 2_3_4 and dihedral angles of 1_2_3_4 need to be described (Fig. 2). All of these parameters are given limited ranges. The other intra-residue parameters such as dihedral angles for atoms within the ligand residue are not constrained (-180o - 180°), but are restricted by the sidechain configurations of each residue type (rotamers) and the protein backbone. The complete construction of a potential site must meet two criteria. First, all the geometric definitions of the metal site must be fit. Secondly, the positions of potential ligand atoms should not overlap with the existing atoms such as the backbone of the protein or pre-located residues. If any configurations of the potential sites cannot satisfy the geometry definition or if there is clash with neighboring atoms, this potential site is rejected.

In the Refinement step, the accepted test configurations generated from the previous Site-Search step will be minimized using the Polak-Ribiere non-linear conjugate gradient algorithm (Press et al., 1988) with equation 1 (Hellinga & Richards, 1991).

U(P) = ^1(1/ a\j) (l„ - + con £(1 / (to,- Q/ + coeJ (1 / <*„) (G# - (1)

(bond lengths) (bond angles) (dihedral angles)

(shift constraints) (non-bonded contacts)

where Pi is the test configuration I, COl, ® © ro0 and ro vdw are weights for bond lengths 1.. .NL (Hellinga & Richards, 1991), bond angles 1 . . . Nn, position shift constraints of amino acid backbone atoms 1.. .Ns, and van der Waals' contact between all atom pairs 1.. .NAin the test configuration. ox are the standard deviations for parameter type X: lj and Lj are the measured and target jth bond lengths, respectively. Similar definitions are given for bond angle ro j and Qj, dihedrals 9 j and ro j, coordinates xj and Xj, and the distance djk between non-bonded atoms j and k with the atomic hard-sphere radii ri and rj, respectively (Hellinga & Richards, 199 1).

The first three items in equation 1 are the geometry deviation, such as the differences of oxygen-calcium-oxygen angle, oxygen-calcium distance and O-Ca-O-C 5 dihedral angle between the constructed site and the target site. For all of the studies here, a geometry of pentagonal bipyramidal is used to describe the target site. The distance between oxygen and calcium is 2.4 hi. 72o and 90o are used for the oxygen-calcium-oxygen angle between neighboring oxygen on the same plane, and that between oxygen atoms on the plane and off the plane, respectively. The target O-Ca-O-C5 for the oxygen on the same plane is 0o and for that off the plane is 90o. The positions of all the atoms from sidechain and backbone of ligand residues in a constructed site are also shifted to minimize the deviation pseudo-energy. The minimized pseudo-energy U(P) gives a quantitative evaluation of the deviation between the site and target site. All the minimized sites are further filtered using the computer program, CLEAN (Yang et al., unpublished results) to remove the degenerated sites. Sites with the lowest U(p) number in the degenerated sites will be further analyzed.

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