3.2.1 Calculation of the Hydrogen Positions The programs makes one first pass through the protein structure calculating a locus for each donor heavy atom. The positions of the hydrogens are taken from Momany, McGuire et al (1975) and the main-chain NH hydrogen from Pauling and Corey et al (1951). They are illustrated in figures 2 and 3, together with information on planarity and loci. The precise bond angles and lengths are listed in table III. Each donor heavy atom in an amino acid is classified according to the hybridization of its electron orbitals and how many hydrogens or heavy atoms it is covalently bound to. The hybridization may be sp2 (trigonal planar) or sp3 (tetrahedral). The numbers of bound atoms are listed as 1, 2 or 3 hydrogens and then 1 or 2 DDs. The method of calculation is described below. The hydrogens bound to "sp2" and "sp3" hybridised atoms have different geometries. An atom with sp2 hybridisation has three orbitals projecting at about 120 degrees to each other, all in the same plane. These orbitals may or may not be part of covalent bonds to other atoms. For instance, ARG NE covalently bonds to two Cs and an H. In an optimal conformation, the C-N-C angle would be 120 degrees and the H would be exactly along the bisector. An atom with sp3 hybridisation has four orbitals pointing towards the corners of an imaginary tetrahedron. In an ideal conformation, the angles between any two orbitals would be 109.5 degrees. For instance, SER OG has sp3 hybridisation and a tetrahedral conformation. It is only attached to two atoms - a C and an H - and the C-O-H angle is still 109.5 degrees. 3.2.1.1 Hydrogens Bound to sp2 Hybridised (Trigonal Planar) Donors sp2 1H, 2DDs This includes NH groups on the main chain or Arg, His and Trp side chains. The donor atom is known to be attached to two DD heavy atoms and to the hydrogen. The angle DD1-D-DD2 is bisected by finding the mean of the directions of the vectors DD1-D and DD2-D. For main-chain groups the hydrogen is rotated within the plane of the peptide bond towards the CA in accordance with Pauling, Corey et al (1951). The hydrogen is placed a set distance away from D (usually 1.00 Angstroms for N donors) Fig 2: sp2 Hybridised (trigonal planar) hydrogen positions sp2 1H 2DDs sp2 1H 1DD sp2 2H 1DD DDD1 DDD2 DDD1 DDD2 DDD1 DDD2 H \ / \ / \ / | DD DD DD D | or | | /:\ D D D DD1 : DD2 \ / / \ : H H H H Planarity ? Y Planarity ? Y Planarity ? Y Fixed hydrogen ? Y Fixed hydrogen ? N Fixed hydrogens ? Y The locus is composed eg NH on main-chains of the two alternative eg ARG NH, ASN ND2, GLN OE2 Arg, His and Trp conformations shown side-chains above eg TYR OH sp2 1H, 1DD Although there are no standard amino acid donors that fall into this category, the Tyr OH, which is a combination of sp2 and sp3 hybridisation, behaves in a geometrically similar fashion and is modelled with this part of the algorithm. The H, DD, and one of the donor's lone electron pairs form a planar trigonal arrangement around D. the hydrogen may take one of the two positions where H, DD, DDD1 and DDD2 are coplanar and the H-D-DD angle takes the angle given in table 2. This locus is determined by first calculating hydrogen positions in a local co-ordinate system, and then transforming and translating them onto the donor atom. sp2 2H, 1DD This includes Asn and Gln amide groups and ARG NE. These all have a donor bound to three atoms that lie in the same plane and all angles at D are 120 degrees. DD, DDD1 and DDD2 also lie in the same plane. The two hydrogen positions are calculated in a local co-ordinate system before being transformed and translated onto the donor atom. 3.2.1.2 Hydrogens Bound to sp3 Hybridised (Tetrahedral) Donors Irrespective of the number of hydrogens, if there is only one DD heavy atom attached to the donor, then they may rotate around the D-DD bond, forming a circular locus. Steric hindrance is known to favour three particular staggered H-D-DD-DDD torsion angles 120 degrees apart. It is not obvious whether the expected locu of an sp3 hydrogen should be a circle or three alternative staggered points. The algorithm makes it is the former for single sp3 hydrogens and the latter for triple sp3 hydrogens. sp3 1 H, 1 DD These include OH on Ser and Thr, and SH on Cyh. The centre of the circular locus is found by projecting the D-DD bond a distance that depends on the lengths and angles for the group in question. A default position, staggered relative to the D-DD line, is calculated in a local co-ordinate system, then transformed and translated. the circular locus that the hydrogen is allowed to move along is normal to the D-DD line. sp3 3 Hs, 1 DD The only example of this is LYS NZ, and terminal amino groups. the combined locus is made up of three alternative points, equally spaced and staggred relative to DDD, where DDD is one covalent bond beyond DD from D. The positions are calculated using a local co-ordinate system and relevant bond lengths and angles, and transformed and translated onto the donor. Fig 3: sp3 hybridised ( tetrahedral orientations ) hydrogen positions sp3 1H 1DD sp3 3Hs 1DD H -> (goes in a circle) *H H H Planarity ? N \ \|/ (although the H marked * is D D in the same plane as D, DD | | and DDD) DD DD \ \ Fixed Hydrogens ? Y DDD DDD Planarity ? N H Fixed Hydrogen ? N / *H-D -DDD <- DD is hidden by D The hydrogen may swivel round \ All three DD-D-H angles are the DD-D axis towards the H equal. acceptor. eg SER OG, THR OG1, CYH OG1 eg LYS NZ, terminyl amino groups =================================================================== TABLE III - DONOR GROUP GEOMETRIES FOR CALCULATED HYDROGENS Name of Donor Atom H Bonds Angles etc D-H ==================================================================== HIS ND1, HIS NE2 sp2 1H 2DD DD1-D-H = DD2-D-H 1.00 ARG NE , TRP NE1 -------------------------------------------------------------------- TYR OH sp2 1H 1DD DD-D-H = 110, 250 1.00 DD1,DD2,D,H are planar -------------------------------------------------------------------- ASN ND2, GLN NE2 sp2 2H 1DD DD-D-H = 120 1.00 ARG NH1, ARG NH2 DDD-DD-D-H = 0, 180 ==================================================================== CYH SG , CYS SG sp3 1H 1DD DD-D-H = 96 1.33 -------------------------------------------------------------------- SER OG , THR OG sp3 1H 1DD DD-D-H = 110 1.00 -------------------------------------------------------------------- LYS NZ, any amino sp3 3H 1DD DD-D-H = 110 1.01 terminus DDD-DD-D0H = 180 ==================================================================== Backbone N sp2 1H 2DD (C-N-H)-(CA-N-H) = 4 1.00 C, CA, N, H are planar ==================================================================== H hybridisation - sp2 (trigonal planar) or sp3 (tetrahedral) Bonds number of covalently attached hydrogens (H) and heavy atoms (DDs) Angles Angles and conditions used to precisely define hydrogen position D-H D-H distance for the calculated hydrogen in Angstroms ====================================================================