Packing of protein interior: Structure and distribution of packing density

The classical definition of packing density determines the packing as a unitless ratio of the volume of the van der Waals spheres of all the atom to the total volume of the molecule. It is believed that packing density plays important role in the stabilization of the native state of the protein molecules. The average packing density of the molecule is approximately 0.7. However, within the volume of molecule, packing is irregularly distributed with the variations of values ranging from 0.4 to 0.9. Analysis of the distribution of the packing density within the volume of the molecule and as statistical analysis of packing was major goal of this dissertation. We developed two different algorithms for calculating the packing density from crystallographic data. First algorithm is based on the well known approach of molecular volume partitioning using the Voronoi procedure. Second algorithm determines the continuous packing density as a function of coordinates in the volume. We analyzed the number of proteins and found that the regions of high packing correlate with the location of the folding intermediates. Also the residues with the higher packing densities of cytochrome c tend to be the ones with higher evolutionary stability. We also considered a statistical distribution (frequencies of occurrence) of packing density values. The distribution revealed the two preferable values for packing density in form of two peak distribution. One peak with the maximum corresponding to density value 0.7 and the other corresponding to value 0.3-0.4. We can attribute this form of distribution to be a specific feature of protein structure which contains a combination of rigid highly packed framework filled and surrounded by relatively loose and flexible padding. Finally, we made an attempt to roughly estimate the van der Waals contribution to the energy of stabilization of the protein stability integrating the packing density function over the volume of the molecule. This simplified approach lays down the foundation for more precise determination of van der Waals contribution to protein stability.