A folded protein may be thought of as a 'three-dimensional jigsaw'. The folding of the polypeptide chain allows the van der Waals surfaces of atoms to fit together snugly, filling up most of the space in the interior. The packing efficiency is such that the interiors of proteins have a similar packing density to organic solids (Richards, 1974).
The packing density of a residue or moleculeis the ratio of the volume enclosed by the van der Waals surface to the volume occupied in the state in question (protein interior, crystal, liquid, etc).
The 'volume occupied' by an irregular-shaped residue or molecule can be determined by the use of Voronoi polyhedra (Richards, 1974). The entire volume of a molecule is divided by planes which delimit the polyhedra, each of which effectively correpsonds to one atom.
The packing density of organic solids is in the range of 0.68-0.80 (the range for crystals of organic solids is described as 0.70-0.78 by Richards, 1977); the value for organic liquids is about 15% lower. The ratio for amino acids was found to be 0.72-0.77 (Klapper, 1971). Note that the volume of amino acids in crystals has been found to be the same as the mean volume of the amino acid in protein interiors. The main-chain regions in the interior which hydrogen bond are denser than the side chains which associate by Van der Waals interactions (Kuntz and Crippen, 1979).
About 25% of the protein's volume is unoccupied, mostly consisting of very small cavities. Thermal fluctuations of surrounding atoms vary the cavities' sizes. This allows dynamic behaviour such as side-chain rotation. Solvent molecules do occur internally where a cavity is large enough to accommodate it. Protein-solvent interactions will be examined in a later section of the course.
Nonpolar, uncharged polar and charged atomic surface areas are all involved in packing. As well as van der Waals interactions between nonpolar atoms, polar and charged atoms take part in hydrogen bonds and salt bridges within the protein. Refer to the section on Non-bonded Interactions in Section 7.
Although, in globular, water-soluble proteins, there is certainly a tendency for hydrophobic residues to be located in the protein interior, and polar residues to be on the protein surface, this principle must be qualified; it must not be considered to mean that nonpolar surface is buried, and polar surface exposed on the protein exterior. Firstly, note that the side chains of certain amino acids are of mixed hydropathy (e.g. lysine, typtophan). Secondly, all amino acid residues have polar groups (carbonyl and imide) in the backbone. Therefore a large amount of polar surface is necessarily buried, considering that backbone hydrogen bonds are the basis of secondary structures. Also, approximately half of the surface of a protein that is water-soluble is nonpolar (Lee and Richards, 1971). 'Thus the "grease" is by no means all "buried" '.
Studies by Chothia (1976) showed that the surface buried within secondary structures is mostly polar, while that buried between secondary structures is mostly hydrophobic. Note that a -NH...OC- hydrogen bond still leaves an unsatisfied hydrogen bonding capacity on the carbonyl oxygen. Internal polar side-chains may hydrogen bond to each other or to main chain groups - by being brought into close contact by tertiary interactions - or to internal solvent molecules.
Many of the contacts within a protein are between atoms of residues close to each other sequentially or in the same piece of secondary structure (Crippen and Kuntz, 1978)
Protein Volume Evaluation, by Joan Pontius Unité de Conformation des Macromolécules Biologiques at Université libre de Bruxelles
Last updated 7th April '97