W0196

Generating Symmetry: Observed Macromolecular Crystal Contacts Explain Space Group Frequencies. Jennifer E. Padilla, Todd O. Yeates, Chemistry & Biochemistry, Univ. of California, Los Angeles, Box 951569, Los Angeles, CA 90095-1569 USA.

Here we present a study of the number of unique contacts found within crystals reported in the PDB. Biological macromolecules have been crystallized in all of the 65 biological space groups, however, these 65 space group symmetries are unevenly represented. An entropic model has been invoked to explain the observed space group frequencies [1]. According to this model, favored space groups, such as P2₁2₁2₁, allow more rigid body degrees of freedom, found in the number of independent unit cell parameters, and the number of meaningful ways to orient and position a molecule in the unit cell. Conversely, degrees of freedom are lost for each unique contact that is required in order to achieve connectivity in the crystal.

The minimum number of contacts required ranges from 2 to 5, depending on the space group. Where the minimum does not occur, degrees of freedom have been sacrificed for other gains, such as closer packing within the crystal, or overcoming geometric hindrances to making certain contacts. We find that minimal sets of unique contacts do not make up the majority of generating sets in real crystals. Sometimes, the generating set that is used is larger than the minimum, but still does not contain unnecessary elements. However, there are still are large number of cases in which nonessential crystal contacts are present. We are reinterpreting the observed space group frequencies in light of this new information on the actual number of unique contacts found to generate each space group. This study reveals the interplay between the degrees of freedom available in the nucleation of a crystal versus the advantage of achieving close packing within the crystal.