The volume of atoms on the protein surface: calculated from simulation, using Voronoi polyhedra

We analyze the volume of atoms on the protein surface during a molecular-dynamics simulation of a small protein (pancreatic trypsin inhibitor). To calculate volumes, we use a particular geometric construction, called Voronoi polyhedra, that divides the total volume of the simulation box amongst the atoms, rendering them relatively larger or smaller depending on how tightly they are packed. We find that most of the atoms on the protein surface are larger than those buried in the core (by approximately 6%), except for the charged atoms, which decrease in size, presumably due to electroconstriction. We also find that water molecules are larger near apolar atoms on the protein surface and smaller near charged atoms, in comparison to "bulk" water molecules far from the protein. Taken together, these findings necessarily imply that apolar atoms on the protein surface and their associated water molecules are less tightly packed (than corresponding atoms in the protein core and bulk water) and the opposite is the case for charged atoms. This looser apolar packing and tighter charged packing fundamentally reflects protein-water distances that are larger or smaller than those expected from van der Waals radii. In addition to the calculation of mean volumes, simulations allow us to investigate the volume fluctuations and hence compressibilities of the protein and solvent atoms. The relatively large volume fluctuations of atoms at the protein-water interface indicates that they have a more variable packing than corresponding atoms in the protein core or in bulk water. We try to adhere to traditional conventions throughout our calculations. Nevertheless, we are aware of and discuss three complexities that significantly qualify our calculations: the positioning of the dividing plane between atoms, the problem of vertex error, and the choice of atom radii. In particular, our results highlight how poor a "compromise" the commonly accepted value of 1.4 A is for the radius of a water molecule.