The protein-protein interaction plays a key role in many biological functions, such as drug design and functional analysis. Gaining insights of various binding abilities will deepen our understanding on interaction. Determination of binding sites is widely applied in molecular biology research. Therefore, many efficient methods [1, 2] have been developed for identifying binding sites.

Some existing approaches are based on analyzing differences between interface residues and non-interface residues, through machine learning methods or statistical methods. They analyze different features, such as sequence and structural properties or physical attributes. ProMate [3] creates interface or non-interface sphere around each residue. The histograms of many features are statistically obtained from spheres in training proteins. The probability for each sphere of a testing protein can be estimated to be on interface or not. The interface spheres are clustered to identify binding sites. PPI-Pred [4] uses several features to build an SVM model on interface prediction. It generates an interacting patch and a non-interacting patch for each training protein. Seven features are extracted from all interacting and noninteracting patches to predict if a testing patch is an interacting patch. Li et al. [5] divide protein residues into four different classes, which are distinguished by percentage of their neighboring interface residues. The core-SVM model is built over eight features and used to compute whether a residue is a core interface residue. In PINUP [6], an empirical scoring function consists of interface propensity and residue conservation score for predicting binding sites. PINUP takes top scoring patches and ranks residues based on their occurrences in these patches, clustered as predicted interface residues. Burgoyne et al. [7] analyze clefts on surface, that are likely to be binding sites. They can be ranked according to sequence conservation and physical properties. Meta-servers have also been constructed to combine strengths of some existing approaches. The program called meta-PPISP [8] combines three individual servers, namely cons-PPISP, ProMate and PINUP; another program called metaPPI [9] combines five prediction methods, namely PPI-Pred, PINUP, PPISP, ProMate, and Sppider.

In addition, several structural algorithms have also been used to identify binding sites, through analyzing surface structures. SiteEngine [10] recognizes surface regions of a testing protein that are similar to some known binding sites, using geometric hashing triangles. ProBiS [11] predicts interface residues by local surface structure alignment. It compares a testing protein to known binding sites, for detecting structurally similar residues. Ortuso et al. [12] define most relevant interaction areas, based on 3D maps. The GRID program is used to compute on known structural complexes.

Another kind of methods are to examine all possible poses of two protein subunits; that is, how subunits may dock. Docking methods based on fast Fourier transformation (FFT) [13], geometric surface matching [14], as well as intermolecular energy [15] have been proposed. ZRANK [16, 17] combines an atom-based potential (IFACE) with five residue-based potentials for ranking docked conformations. It provides fast and accurate re-scoring of ZDOCK models [18]. ClusPro [19] develops a fast algorithm for filtering docked conformations with good surface complementarity, and ranks them based on their properties. RosettaDock [20] constructs an energy function using van der Waals energies, orientation-dependent hydrogen bonding, implicit Gaussian solvation, side-chain rotamer probabilities and a low-weighted electrostatics energy. HADDOCK [21] makes use of biochemical and biophysical interaction data, such as chemical shift perturbation data resulting from NMR titration experiments. Fernandez-Recio et al. [22] apply docking simulations and analyze interaction energy landscapes to identify interface residues. They use a global docking method based on multi-start energy optimization, and predict low-energy regions as binding sites.

Identifying of protein-protein interface depends on many features, such as sequence, structure, as well as other physicochemical properties. Hydrogen bonds and salt bridges are known to be essential in identifying binding specificity [23]. Most of binding sites are hydrophobic and conserved polar residues at specific locations [24]. Secondary structure composition analysis shows that neither helices nor β-sheets are dominantly populated on interface [25]. Several geometrical features such as weighted atomic packing density, relative surface area burial and weighted hydrophobicity are most effective features for predicting interface residues [26]. Some features only describe properties of current interacting residues, but cannot represent real situation well, thus are insufficient to predict binding sites with high accuracy.

In this paper, we analyze structural neighboring property on protein-protein interface, through Voronoi diagram. Using 6,438 complexes, we study local biases of structural neighboring property on interface. We propose a novel statistical method based on structural neighboring property to extract interacting residues, and interacting patches can be clustered as predicted interface residues. In addition, structural neighboring property can be adopted to limit the search space, for discovering native-like poses. Here, we construct an energy function to evaluate docking solutions, which includes new statistical property as well as existing energy items [27]. Finally, we use trained SVM models to further select best poses for each pair of input proteins.

Experiments show that our method achieves better results than some state-of-theart methods. Here, we use CAPRI evaluation criteria, I _rmsd and F _nat . Comparing to existing methods for identifying binding sites, our approach improves overall F _nat value by at least 3%. On Benchmark v4.0, our method has average I _rmsd value of 3.31Å and overall F _nat value of 63%, which improves upon I _rmsd of 3.89Å and F _nat of 49% for ZRANK, and I _rmsd of 3.99 Å and F _nat of 46% for ClusPro. On CAPRI targets, our method has average I _rmsd value of 3.46 Å and overall F _nat value of 45%, which improves upon Irmsd of 4.18 Å and F _nat of 40% for ZRANK, and I _rmsd of Å and F _nat of 32% for ClusPro.

In this paper, we calculate structural neighboring property on protein-protein interface, through Voronoi diagram. We propose a novel statistical method to extract interacting residues, and interacting patches can be clustered as predicted interface residues. In addition, structural neighboring property can be adopted to construct an energy function to evaluate docking solutions, which includes new statistical property as well as existing energy items.

Structural neighboring property

Most of those features only describe current interacting residues, but cannot represent real situation well, thus are insufficient to predict binding sites with high accuracy. Here, we develop a method to calculate structural neighboring property on interface, using Voronoi diagram.

Site features

The physicochemical features are used to characterize potential interacting residues. The most interesting features are described as follows.

• Hydrophobicity: a numerical hydrophobicity of an amino acid [29],

• Electrostatic potential: the number of electrostatic charge in an amino acid [30],

• Hydrogen bonds: the number of potential hydrogen bonds for all atoms in an amino acid [31].

We use Voronoi diagram to evaluate polygonal face area of each surface residue, and calculate structural neighboring property on these physicochemical features.

Polygonal face area

We use VLDP [32] for geometrically analyzing protein 3D structures, based on Voronoi Tessellation. Voronoi Tessellation is a partition of space into polyhedra, whereas Delaunay diagram builds a graph with vertices at atoms. These graphs define nearest neighbours for each atom of one protein. It calculates Delaunay diagram by using an optimized incremental algorithm. The weights can be interpreted as squared radius. The surface residues appear as a packing of polyhedra, that is necessary to have a reasonable Tessellation throughout entire system.

VLDP can be used to evaluate residue contacts and residue volumes, defined as polygonal face area and polyhedral volume for each atom. In particular, contact area of two residues is sum of atomic interface areas on pairs of atoms; surface area of one residue is sum of surface areas exposed to solvent in this residue; total area of one residue is sum of all areas in this residue. We calculate structural neighboring property, based on polygonal face area.

Property function

Given a protein, structural neighboring property of one surface residue x is defined as follow:

$p^{\prime }\left(x\right)=\frac{surface\left(x\right)}{total\left(x\right)}\times p\left(x\right)+{\displaystyle \sum _{contact\left(x;y\right)>0}}\frac{surface\left(y\right)}{total\left(y\right)}\times p\left(y\right)$

where p(x) is site feature of each residue, contact(x, y) >0 means that contact area between residues x and y is greater than zero, $\frac{surface\left(x\right)}{total\left(x\right)}$ shows surface area of residue x divided by its total area, as shown in Figure 1.

We use a normal distribution F (x) to estimate probability of structural neighboring property on one side of interface. We also use a bivariate normal distribution F (x1, x2) [33] to estimate probability of structural neighboring property on both sides of interface. Given a pair of proteins, effective free energy of interacting residue pair can be calculated as:

$S\left(x_1,x_2\right)=-k_{B}T{\displaystyle \sum _{\left(x_{{}_1},x_{{}_2}\right)\in R}}\mathsf{\text{ln}}\frac{F\left(x_1,x_2\right)}{F\left(x_1\right)\times F\left(x_2\right)}$

where R is a set of all residue pairs on interface.

In this section, we have done three kinds of experiments. First, we present statistical analysis of structural neighboring property on interface. Then, we compare our method to some existing methods, for identifying binding sites. The results show that our method performs better than other machine learning and statistical approaches. Finally, we examine docking solutions of our method on Benchmark v4.0 and CAPRI targets. Experiments show that our method outperforms some state-of-the-art methods.

Statistical property

The physicochemical features are used to characterize potential interacting residues. The most interesting features are described by three values, as shown in Table 1.

Amino Acid	Hydrophobicity	Electrostatic potential	Hydrogen bonds
Ala	1.8	0	2
Arg	-4.5	1	4
Asn	-3.5	0	4
Asp	-3.5	-1	4
Cys	2.5	0	2
Gln	-3.5	0	4
Glu	-3.5	-1	4
Gly	-0.4	0	2
His	-3.2	0	4
Ile	4.5	0	2
Leu	3.8	0	2
Lys	-3.9	1	2
Met	1.9	0	2
Phe	2.8	0	2
Pro	-1.6	0	2
Ser	-0.8	0	4
Thr	-0.7	0	4
Trp	0.9	0	3
Tyr	-1.3	0	3
Val	4.2	0	2

We present statistical analysis of structural neighboring property on interface. The statistics are carried out on 6,438 complexes. For each feature, we model a bivariate normal distribution. First, we represent an assessment for hydrophobicity on interface, as shown in Figure 2(a). The cluster centered at (1.89, 2.21) can be obtained. The groups of more hydrophobic amino acids often appear on interface. Second, local bias preferences of electrostatic potential on interface are shown in Figure 2b. We observe probability distribution centered at (0.12, −0.09). Many interfaces usually involve a lot of neutral amino acids. Third, we analyze hydrogen bonds on interface, as shown in Figure 2c. The data contains one cluster centered at (8.37, 7.96). The interface residues contain several potential hydrogen bonds, and the number of potential hydrogen bonds on each side of interface must be very similar.

We further investigate whether changing value of s _th help to improve interface prediction. Here, we calculate structural neighboring property on 100 interface residues and 100 non-interface residues, randomly extracted from Benchmark v4.0 [38]. The relationship between interface prediction and the value of s _th is shown in Table 2. We can observe that when increasing the value of s _th , the overall F _nat value of prediction is improved; however, the overall F _non−nat value of prediction also increases as well.

	F nat	F non−nat
s th = −100	38%	21%
s th = −50	62%	37%
s th = 0	65%	53%
s th = 50	68%	68%
s th = 100	69%	72%

In this paper, we calculate structural neighboring property on interface, through Voronoi diagram. We propose a novel statistical method to extract interacting residues, and interacting patches can be clustered as predicted interface residues. Experiments show that our method achieves better results than some state-of-the-art methods. Comparing to existing methods for binding sites prediction, our approach improves overall F _nat value by at least 3%.

In addition, structural neighboring property can be adopted to construct an energy function, for evaluating docking solutions. It includes new statistical property as well as existing energy items. On Benchmark v4.0, our method has average I _rmsd value of 3.31Å and overall F _nat value of 63%. On CAPRI targets, our method has average I _rmsd value of 3.46Å and overall F _nat value of 45%.