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The flexibility of amino acid side chain is important for flexible protein docking algorithms. These information can be purchased by scoring the different conformations of a side chain by using energy functions or statistical analysis of side chain changes. For energy calculations, amino acid side chain conformation are generated by rotating the side chain around its torsion angles 1-4. To score these conformations the potential energy of the protein is calculated. The potential energy is calculated by using the AMBER  force field. The calculated minima are compared to the results of the statistical approach.
We have analysed 33.330 residues not counting glycine, alanine and proline from 220 PDB- Entries . The resultion was 2 Å or better. The software to perform these calculations was implemented using the BALL library . The distribution of the angles show significant featuers. Both approaches show that the 1 torsion angle all residue types show three peaks.
Looking at the results for the 2 angle the residues can be divided up into two groups. The residues asparagine, aspartic acid, histidine and phenylalanine build up the first groups showing two rotamers at g- and g+ position. The other amino acids (arginine, glutamic acid, glutamine, lysine, leucine, isoleucine, methionine and tryptophan) have three rotamers.
We have also analysed the torsion angles 3 and 4. The results for the 3 show that the residues also can be splitted up into the two groups mentioned above.
The two graphics above show the distribution of the 1 for arginine residues. On the left side, the frequency for a special 1 angle from a testset of PDB structures is shown. On the right, the distrubution of the calculated energy minimas for each arginine residue of the testset is plotted. Comparing the two graphics it can be seen that the found rotamers in the PDB structures correspond to the maxima of the energy distribution.
To gain a measurement for flexibility, protein structures of complexed and unbound proteins are taken to investigate angle differences and rotamer changes. The rotamers are choosen according to Dunbrack  and dependencies are calculated with Bayes statistics. The angle differences vary according to amino acid type and location of the amino acid. Long and polar side chains show greater flexibility than unpolar ones, ecspecially in the active site . The flexibility measure will be used for pruning the search tree of the Docking Algorithm .