Description

Calculation

The uploaded PDB files are calculated and stored by Voronoia in .vol files, a PDB file format that contains two kinds of information:
First, the atomic volume, a measure in cubic Angstroms that describes the available space assigned by the Voronoi Cell algorithm [2]. Second, cavities - locations where a water molecule with 1.4 Angstrom radius would fit are listed. From the .vol files, reports of atomic packing densities can be generated, that may also be compared to a set of reference packing density values for different atom types, using the z-score-rms. Due to almost all cavities having a spherical shape, their center points can be approximated by calculating the center of mass of all their neighbouring atoms. In the Voronoi Cell procedure, atomic volumes are numerically calculated using a cubic lattice. If more than one atom compartment is within one cube, the lattice will be refined locally. The minimal grid distance can be adjusted for greater precision by the user, the default being 0.2 Angstrom.

Packing

Generally, atomic packing analysis quantifies, how close an atom is located to all its neighbouring atoms. To weigh each neighbor atoms' contribution in a reasonable way, the atomic volumes are calculated. This can be done in various ways. Voronoia applies Voronoi Cell [2], an extension of the original Voronoi procedure, where hyperboloid interfaces are constructed between atoms, allocating the total space within a protein structure among all atoms (fig. 1 and fig. 2).

The atomic packing density is a measure that qualifies how well a certain protein is packed. To evaluate this, the Van-der-Waals Volume V(VdW) of an atom (the space inside the atom's Van-der-Waals radius) is extended by 1.4 Angstrom, a convened value for the radius of a solvent molecule. This latter volume is called Solvent Excluded Volume V(SE). Both, the atoms' Van-der-Waals Volume (fig. 1, dark colours) and the Solvent Excluded Volume (fig. 1, bright colours) are cut by the separating surfaces with atoms in very close proximity. Only, in a perfectly packed structure, the V(SE) would be occupied entirely by separating surfaces and the packing density value would be 1.0. To estimate the packing value calculated by Voronoia the user may compare it to reference values that were calculated from defined sets of proteins.

The atomic packing density is definded as: PD = V(VdW) / [V(VdW) + V(SE)]


Cavities

Protein cavities are regularly found in protein structures with more than 150 amino acids. These packing defects are defined to be large enough to enclose at least one water molecule. Cavities are totally buried locations, in which a 1.4 Angstrom virtual atom could be placed. This probe must not intersect any atoms' Van-der-Waals sphere and the cavity must not extend to the protein surface. Many of these cavities are occupied by water molecules in vivo, but often they remain undetected in crystal or NMR structures.

Voronoia uses regular PDB structure files as input, and creates modified PDB files containing packing densities for each atom. The positions of interior cavities, their neighbor atoms and protein surface atoms are listeded separately. Both cavities and their surroundings may be written as separate structure files. Textual reports that summarizes all this information and the deviation of packing from reference data are created for each structure. Voronoia is capable to create these reports for sets of structures in one go. This also generates average packing values, that may be used as a new reference set. Along with the program, reference data is provided for a current non-redundant set of structures based on SCOP superfamilies, and for a set of 66 transmembrane domains.


Download Reference Values

Dictionary Of Packing in Proteins

DOPP is a database that stores precalculated packing files in a data bank. The calculation of packing files at higher accuracy is a time consuming process that may last up to several minutes. To allow the user to quickly visualize the packing of a particular file, the packing of all biounits from the PDB 2007 release was calculated beforehand at high accuracy. For this purpose the PDB header was extracted and stored in a relational database to provide fast searching. On top of that a live search with a powerful query mechanism was implemented with Asynchronous JavaScript And XML (AJAX) and PHP. Furthermore, all biounit files where filtered for certain properties which do not allow the display of the results on a webpage. Thus, it is for example not possible to show large files with up to several hundred MB. In that case the user will be informed about the reason why a particular file is not available in our database.
The recent release of DOPP contains biounits. This database will be updated every six month by means of an automatic script. The next data drop will take place in February. Currently new biounit files are calculated.
To get an overview about the biountis in DOPP with resolution and methods see here.

Atomic radii

To apply the Voronoi Cell procedure, a Van-der-Waals radius has to be assigned to each atom. In total, 173 different amino acid/heavy atom name combinations occur in polypeptide chains, including oxidized and reduced cysteine. Clustering these types by chemical and numerical criteria resulted in 18 more concise atom types having similar packing properties [6]. These atom types were named by the scheme ExHyZ, in which E is the element, x the number of covalently linked atoms, y the number of hydrogens and Z is a letter distinguishing between big and small subtypes of a particular chemical type. A set of Van-der-Waals radii has been empirically determined from structures of small organic molecules, known as the Protor set [2]. Radii for non-protein atoms have been determined separately [7]. Because heavy atoms and their bonded hydrogen atoms are combined to a structural entity, the term 'atom group' is also used.

Atomic volumes

An atomic volume is the space assigned to a particular atom, delimited by its neighbors. To calculate it, Voronoi polyhedra with hyperboloid surfaces are constructed around each atom. The Voronoi Cell procedure described in [2] uses a cubic lattice in order to assign the exact values. Different atom radii are taken into account. The procedure distinguishes between the volume inside the atoms' Van-der-Waals radius - the VdW volume V(VdW) - , and a layer of max. 1.4 Angstrom around it - the Solvent Excluded volume V(SE).

Atomic packing densities

The packing density of an atom is calculated as

PD = V(VdW) / [V(VdW) + V(SE)],

where V(VdW) and V(SE) are the Van-der-Waals and Solvent Excluded volumes of this atom. Thus, the maximum packing density of an atom is 1.0 (none of the Solvent Excluded volume remains, which never occurs for real-world data). The minimum is 0.0 (a larger atom fully contains a smaller), which neither occurs.

Cavities (packing defects)

Buried positions, large enough to include a virtual water probe (1.4 Angstrom radius). Cavities occupied by water molecules or other hetero atoms are labeled as filled, or partially filled if there is space for additional water molecules. Cavities are detected analytically by calculating the loci that are accessible for a virtual water molecule. These loci are parts of shapes touching one, two or three atoms simultaneously. Clustering of these shapes with common edge gives the accessible outer surface of the protein on one side, and non-accessible closed cavities on the other side. All atoms being in touch with an interior cavity are considered neighbors of that cavity. Due to almost all cavities having a spherical shape, their center points can be approximated by calculating the center of mass of all their neighbor atoms.

Surface and buried atoms

The packing of atoms at the surface is determined by rolling a virtual water molecule (of 1.4 Angstrom radius) over the protein. All atoms touched by the probe are assigned to the surface. The packing value of these atoms is therefore not directly comparable with those of buried atoms, where the computation of the packing is based on real atomic contacts.

z-Score-Rms

A statistical measure that is applied here to compare the packing of a distinct protein with precalculated reference values. It is calculated for each atom i of type k by the formula:


The resulting Z-Score-RMS is typically between 0.8 and 1.3 for buried atoms in protein structures complying to the reference values.

Voronoi Cell ( according to [Goede 1997] ):

The Voronoi Cell procedure assigns portions of space to each heavy atom. To do this, hyperboloid interfaces (see fig 2) are constructed between the atoms. The position of the interface depends on the atomic radii. The resulting compartment defined by the interfaces - the Voronoi Cell - thus consists of a mixture of convex and concave surfaces. More precisely, each of its points are from the atoms i and j exactly radius(i) + d and radius(j) + d apart. The procedure distinguishes between volume inside the atoms Van-der-Waals radius (VdW Volume) and that beyond (Solvent Excluded Volume). For atoms close to the protein surface, the compartment ends 1.4 Angstrom from the Van-der-Waals sphere. These two volumes are used to calculate the local packing density of an atom.

[1]	Pontius, J., J. Richelle, and S. J. Wodak. 1996. Deviations from standard atomic volumes as a quality measure for protein crystal structures. J Mol Biol 264, 9, 121-136. read more ...
[2]	Goede, A., R. Preissner, and C. Frömmel. 1997. Voronoi Cell: New Method for Allocation of Space among Atoms: Elimination of Avoidable Errors in computation of Atomic Volume and Density.Bioinformatics 18, 42, 985-995. read more ...
[3]	Tsai, J. and M. Gerstein. 2002. computations of protein volumes: sensitivity analysis and parameter database. Bioinformatics 18, 42, 985-995. read more ...
[4]	Rother, K., R. Preissner, A. Goede, and C. Frömmel. 2003. Inhomogeneous molecular density: reference packing densities and distribution of cavities within proteins. Bioinformatics 19, 5, 2112-2121. read more ...
[5]	Hildebrand, P. W., K. Rother, A. Goede, R. Preissner, and C. Frömmel. 2005. Molecular packing and packing defects in helical membrane proteins. Biophys J 88, 49, 1970-1977. read more ...
[6]	J. Tsai, N. Voss, and M. Gerstein. 2001. Determining the minimum number of types necessary to represent the sizes of protein atoms. Bioinformatics 17, 10, 949–956. read more ...
[7]	P. F. W. Stouten, C. Frömmel, H. Nakamura, and C. Sander. 1993. An effective solvation term based on atomic occupancies for use in protein. Mol Simul, 10, 97–120. read more ...
[8]	Rother K, Hildebrand PW, Goede A, Gruening B, Preissner R. 2009. Voronoia: analyzing packing in protein structures. Nucleic Acids Res. (Database issue), 37, D393-5. read more ...