<html> <head> <title> DIHEDRAL ANGLES phi, psi, omega, chi1, chi2, chi3, chi4, chi5, rotamers, dihedral angle, definitions, garlic, Damir Zucic </title> </head> <h1 align=center> DIHEDRAL ANGLES </h1> <hr size="3"> <font size="-1" color=RED> dihedral angles, phi, psi, omega, chi1, chi2, chi3, chi4, chi5, rotamers, dihedral angle, definitions, garlic, Damir Zucic. </font> <hr size="3"> <font color=#880000> <b> MAIN CHAIN DIHEDRAL ANGLES <br> </b> </font> The main chain dihedral angles are defined as follows: <br><br> (1) The phi angle is the angle of right-handed rotation around N-CA bond, the value being zero if CA-C bond is cis to C-N bond. Range: from -180 to 180 degrees. <br><br> (2) The psi angle is the angle of right-handed rotation around CA-C bond, the value being zero if C-N bond is cis to N-CA bond. Range: from -180 to 180 degrees. <br><br> (3) The omega angle is the angle of right-handed rotation about C-N bond, the value being zero if CA-C bond of the preceding residue is cis to N-CA bond. Most residues in a typical protein are involved in the formation of two peptide bonds. The peptide bond formed by the residues I and I + 1 is assigned to the residue I + 1. The same applies to the omega angle. For that reason no omega angle is assigned to the first residue. <br><br> Since version 1.2, garlic uses the following procedure to calculate the main chain dihedral angles: <br><br> (1) In the first attempt, the coordinates of the main chain atoms are used to calculate the dihedral angles phi and psi. The phi angle will be missing for the first residue in each chain. The psi angle will be missing for the last residue in each chain. <br><br> (2) In the second attempt, the missing phi angles will be calculated using the coordinates of H (hydrogen) atoms, if available. The missing psi angles will be calculated using the coordinates of O (oxygen) atoms. <br><br> <img src="phipsi.gif"> <br><br><br><br> <font color=#880000> <b> SIDE CHAIN DIHEDRAL ANGLES <br> </b> </font> For each side chain dihedral angle, the coordinates of four atoms are required. The table below contains the list of atoms and the range of values, for each side chain angle and for each residue. In garlic, the angle chi1 is not calculated for ALA and GLY. The angle chi2 is not calculated for ALA, CYS, GLY, SER, THR and VAL. The angle chi3 is calculated for ARG, GLN, GLU, LYS and MET, the angle chi4 is calculated for ARG and LYS and the angle CHI5 is calculated only for ARG. <br><br> <table border=2 width=700 cellspacing=2 cellpading=0> <td colspan=5 align="center" bgcolor="#FFE7DE"> CHI1 </td> <tr> <td align="center"> SIDE <br> CHAIN </td> <td align="center"> AXIS </td> <td align="center"> ATOMS USED TO <br> DEFINE ANGLE </td> <td align="center"> ZERO VALUE </td> <td align="center"> FORMAL RANGE </td> <tr> <td align="center"> ARG </td> <td align="center"> CA-CB </td> <td align="center"> N-CA-CB-CG </td> <td align="center"> CG cis to N </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> ASN </td> <td align="center"> CA-CB </td> <td align="center"> N-CA-CB-CG </td> <td align="center"> CG cis to N </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> ASP </td> <td align="center"> CA-CB </td> <td align="center"> N-CA-CB-CG </td> <td align="center"> CG cis to N </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> CYS </td> <td align="center"> CA-CB </td> <td align="center"> N-CA-CB-SG </td> <td align="center"> SG cis to N </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> GLN </td> <td align="center"> CA-CB </td> <td align="center"> N-CA-CB-CG </td> <td align="center"> CG cis to N </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> GLU </td> <td align="center"> CA-CB </td> <td align="center"> N-CA-CB-CG </td> <td align="center"> CG cis to N </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> HIS </td> <td align="center"> CA-CB </td> <td align="center"> N-CA-CB-CG </td> <td align="center"> CG cis to N </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> ILE </td> <td align="center"> CA-CB </td> <td align="center"> N-CA-CB-CG1 </td> <td align="center"> CG1 cis to N </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> LEU </td> <td align="center"> CA-CB </td> <td align="center"> N-CA-CB-CG </td> <td align="center"> CG cis to N </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> LYS </td> <td align="center"> CA-CB </td> <td align="center"> N-CA-CB-CG </td> <td align="center"> CG cis to N </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> MET </td> <td align="center"> CA-CB </td> <td align="center"> N-CA-CB-CG </td> <td align="center"> CG cis to N </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> PHE </td> <td align="center"> CA-CB </td> <td align="center"> N-CA-CB-CG </td> <td align="center"> CG cis to N </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> PRO </td> <td align="center"> CA-CB </td> <td align="center"> N-CA-CB-CG </td> <td align="center"> CG cis to N </td> <td align="center"> CA-CB is part of ring </td> <tr> <td align="center"> SER </td> <td align="center"> CA-CB </td> <td align="center"> N-CA-CB-OG </td> <td align="center"> OG cis to N </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> THR </td> <td align="center"> CA-CB </td> <td align="center"> N-CA-CB-OG1 </td> <td align="center"> OG1 cis to N </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> TRP </td> <td align="center"> CA-CB </td> <td align="center"> N-CA-CB-CG </td> <td align="center"> CG cis to N </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> TYR </td> <td align="center"> CA-CB </td> <td align="center"> N-CA-CB-CG </td> <td align="center"> CG cis to N </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> VAL </td> <td align="center"> CA-CB </td> <td align="center"> N-CA-CB-CG1 </td> <td align="center"> CG1 cis to N </td> <td align="center"> from -180 to +180 deg </td> <tr> <td colspan=5 align="center" bgcolor="#FFE7DE"> CHI2 </td> <tr> <td align="center"> ARG </td> <td align="center"> CB-CG </td> <td align="center"> CA-CB-CG-CD </td> <td align="center"> CD cis to CA </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> ASN </td> <td align="center"> CB-CG </td> <td align="center"> CA-CB-CG-OD1 </td> <td align="center"> OD1 cis to CA </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> ASP </td> <td align="center"> CB-CG </td> <td align="center"> CA-CB-CG-OD1 </td> <td align="center"> OD1 cis to CA </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> GLN </td> <td align="center"> CB-CG </td> <td align="center"> CA-CB-CG-CD </td> <td align="center"> CD cis to CA </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> GLU </td> <td align="center"> CB-CG </td> <td align="center"> CA-CB-CG-CD </td> <td align="center"> CD cis to CA </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> HIS </td> <td align="center"> CB-CG </td> <td align="center"> CA-CB-CG-ND1 </td> <td align="center"> ND1 cis to CA </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> ILE </td> <td align="center"> CB-CG1 </td> <td align="center"> CA-CB-CG1-CD </td> <td align="center"> CD cis to CA </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> LEU </td> <td align="center"> CB-CG </td> <td align="center"> CA-CB-CG-CD1 </td> <td align="center"> CD1 cis to CA </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> LYS </td> <td align="center"> CB-CG </td> <td align="center"> CA-CB-CG-CD </td> <td align="center"> CD cis to CA </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> MET </td> <td align="center"> CB-CG </td> <td align="center"> CA-CB-CG-SD </td> <td align="center"> SD cis to CA </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> PHE </td> <td align="center"> CB-CG </td> <td align="center"> CA-CB-CG-CD1 </td> <td align="center"> CD1 cis to CA </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> PRO </td> <td align="center"> CB-CG </td> <td align="center"> CA-CB-CG-CD </td> <td align="center"> CD cis to CA </td> <td align="center"> CB-CG is part of ring </td> <tr> <td align="center"> TRP </td> <td align="center"> CB-CG </td> <td align="center"> CA-CB-CG-CD1 </td> <td align="center"> CD1 cis to CA </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> TYR </td> <td align="center"> CB-CG </td> <td align="center"> CA-CB-CG-CD1 </td> <td align="center"> CD1 cis to CA </td> <td align="center"> from -180 to +180 deg </td> <tr> <td colspan=5 align="center" bgcolor="#FFE7DE"> CHI3 </td> <tr> <td align="center"> ARG </td> <td align="center"> CG-CD </td> <td align="center"> CB-CG-CD-NE </td> <td align="center"> NE cis to CB </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> GLN </td> <td align="center"> CG-CD </td> <td align="center"> CB-CG-CD-OE1 </td> <td align="center"> OE1 cis to CB </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> GLU </td> <td align="center"> CG-CD </td> <td align="center"> CB-CG-CD-OE1 </td> <td align="center"> OE1 cis to CB </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> LYS </td> <td align="center"> CG-CD </td> <td align="center"> CB-CG-CD-CE </td> <td align="center"> CE cis to CB </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> MET </td> <td align="center"> CG-SD </td> <td align="center"> CB-CG-SD-CE </td> <td align="center"> CE cis to CB </td> <td align="center"> from -180 to +180 deg </td> <tr> <td colspan=5 align="center" bgcolor="#FFE7DE"> CHI4 </td> <tr> <td align="center"> ARG </td> <td align="center"> CD-NE </td> <td align="center"> CG-CD-NE-CZ </td> <td align="center"> CZ cis to CG </td> <td align="center"> from -180 to +180 deg </td> <tr> <td align="center"> LYS </td> <td align="center"> CD-CE </td> <td align="center"> CG-CD-CE-NZ </td> <td align="center"> NZ cis to CG </td> <td align="center"> from -180 to +180 deg </td> <tr> <td colspan=5 align="center" bgcolor="#FFE7DE"> CHI5 </td> <tr> <td align="center"> ARG </td> <td align="center"> NE-CZ </td> <td align="center"> CD-NE-CZ-Nh1 </td> <td align="center"> Nh1 cis to CD </td> <td align="center"> from -180 to +180 deg </td> </table> <br><br> <img src="chi_angles.gif"> <br><br> <hr size="3"> </html>
