Validation of the detergent micelle classification for membrane protein crystals and explanation of the Matthews Graph for soluble proteins.

Protein crystals are of wide-spread interest because many of them allow structure analyses at atomic resolution. For soluble proteins, the packing density of such crystals is distributed according to the Matthews Graph. For integral membrane proteins, the respective graph is similar but at lower density and much broader. By visualizing the relative positions and orientations of membrane proteins in crystals, it has been suggested that the detergent micelles surrounding these proteins form sheets, filaments, or remain isolated in the crystal giving rise to three distinct packing density distributions that superimpose to form the observed broad distribution. This classification was indirect because detergent is not visible in X-ray crystallography. Given the extensive work involved in analyzing detergent structure directly by neutron diffraction, it seems unlikely that a statistically relevant number of them will be established in the near future. Therefore, the proposed classification is here scrutinized by a simulation in which an average detergent-carrying membrane protein was randomly packed to form crystals. The analysis reproduced the three types of detergent structures together with their packing density distributions and relative frequencies, which validates the previous classification. The simulation program was also run for crystals from soluble proteins using ellipsoids as reference shapes and defining a shape factor that quantifies the deviation from the nearest ellipsoid. This series reproduced and thus explained the Matthews Graph.