A protein is a macromolecule consisting of the permutation of 20 different kinds of amino acids. Amino acids are linearly connected to one another via peptide bonds to form chains. When a protein consists of two chains, it is called a dimer as shown in Fig. 1(a). Shown in Fig. 1(b) and (c) are examples of a trimer (three chains) and a tetramer (four chains), respectively. Since interaction among chains is critical for protein functions, understanding the interaction is getting more important and the geometric properties of the interactions are getting more attention.

Fig. 1  Protein examples: (a) a dimer, (b) a trimer, and (c) a tetramer.

The interaction interface IIF is defined in this paper as follows. Let A = {a1, a2, ..., am}, B = {b1, b2,..., bn} be two chains in a protein, where ai and bj are atoms with appropriate centers and radii. The interaction interface between two chains A and B is defined as IF_∞(A,B) = { p | dist(p,A) = dist(p,B) }, where dist(p,A) denotes the minimum Euclidean distance from p to the surfaces of all van der Waals atoms in the set A. Then, IF_∞(A,B) is a subset of Voronoi faces in VD(A∪B). Hence, IF_∞(A,B) can be easily located by simply checking each Voronoi face with its generating atom types. Note that IF_∞(A,B) expands to infinity.

Fig. 2  A dimer (PDB ID: 1bh8): (a) van der Waals model, and (b) IIF(A,B),

  The infinite Voronoi faces in IF_∞(A,B) are biologically less significant since proteins, as well as IF_∞(A,B), are usually hydrated. Hence, we define a trimmed interaction interface IF_∞(A,B) against a probe of a water molecule. Fig. 2(a) and (b) illstrate the van der Waals atoms of a dimer 1bh8 downloaded from PDB and the corresponding IIF(A,B), respectively. Once an interaction interface is computed, various analyses can be done on the interaction behavior between chains in the protein polymer.