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Analysis of surface structures of hydrogen bonding in protein–ligand interactions using the alpha shape model
Chemical Physics Letters 545 (2012) 125–131
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Analysis of surface structures of hydrogen bonding in protein–ligand interactions using the alpha shape model Weiqiang Zhou a,⇑, Hong Yan a, Quan Hao b a b
Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong Department of Physiology, University of Hong Kong, Pokfulam, Hong Kong
a r t i c l e
i n f o
Article history: Received 21 May 2012 In final form 9 July 2012 Available online 20 July 2012
a b s t r a c t Hydrogen bonding provides useful information for the study of protein–ligand interactions. However, the physical role that a hydrogen bond plays and its 3D surface characteristics in protein–ligand interaction are still not well understood. We apply the 3D alpha shape model to reconstruct the interface of a protein–ligand structure and use solid angles at interface atoms to represent the surface geometric properties of a hydrogen bond. The result shows that 77.2% of the hydrogen bonds show complementary geometric patterns and 95.0% of the protein–ligand complexes contain at least one such hydrogen bond. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Interactions between a protein and another molecule such as another protein, DNA or a ligand take place in many biological processes. Among these interactions, protein–ligand interaction is of particular importance because it is related to the understanding of protein functions and drug development [1,2]. In protein–ligand interactions, hydrogen bonding plays a significant role [3,4]. Babine and Bender reported that hydrogen bonding contributed much to the stability in protein–ligand complexes [5]. Hydrogen bonding has already been used widely in the study of protein–ligand interactions. Gohlke et al. used hydrogen bonding to construct a scoring function for the prediction of protein–ligand interactions [6]. Luo et al. applied hydrogen bond matching to develop a fast protein–ligand docking algorithm [7]. Mancera developed a hydration penalty score for protein–ligand interactions using hydrogen bond formation [8]. Laurie and Jackson proposed to use the hydrogen bonding potential in the prediction of protein–ligand binding sites [9]. Although many studies show that surface properties play an important role in macromolecular interactions in general [10–14], few studies focus on the surface geometric properties of hydrogen bonding. The alpha shape model can be applied to the study of 3D surface properties of biomolecules. This model was first used to study molecular volume computation and cavity detection in proteins by Liang et al. [15,16]. Albou et al. used alpha shape to analyze the surface characteristics of proteins [17]. Recently, Zhou and Yan applied the alpha shape model to analyze the interface surface properties in protein-DNA and protein–protein interactions and achieved good results [10,18]. These studies demonstrate that ⇑ Corresponding author. E-mail address: [email protected] (W. Zhou). 0009-2614/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cplett.2012.07.016
the alpha shape model is an effective means for the study of geometric properties of the interface in molecular interactions. In this Letter, we apply the 3D alpha shape model to represent the interface of a protein–ligand structure and use the solid angles at interface atoms to study the geometric properties of hydrogen bonds in the structure. Complementary geometric surface patterns are found in these hydrogen bonds. 2. Materials and methods 2.1. Data selection The experimental data used in this Letter were obtained from the protein–ligand structures in CCDCnAstex (http://www.ccdc. cam.ac.uk/products/life_sciences/gold/validation/astex/) [19]. The CCDCnAstex test set consists of 305 protein–ligand complexes with various proteins from different families and diverse ligand structures. These structures are already preprocessed and the coordinates of hydrogen atoms in the structures are added using SYBYL. The hydrogen atom coordinates are calculated only from atom types and hybrid states without the intermolecular hydrogen bond information. We use the protein molecule and the original ligand molecule provided in the data set. Further filtering of the data is carried out using the following constraints: (a) the structure contains at least one hydrogen bond; (b) the acceptor atom and hydrogen atom of the hydrogen bond must be on the surface of the alpha shape. The 278 protein–ligand complexes selected are used for analysis of the surface geometric properties of hydrogen bonds. 2.2. Hydrogen bonding Early studies demonstrate the importance of hydrogen bonding for the structure and function of biomolecules [20]. For example,
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hydrogen bonding controls the mechanisms of binding specificity and stabilization of antibody-antigen and protease–inhibitor complexes in solution [21]. Atom types and spatial constraints restrict the formation of intermolecular hydrogen bonds. We define potential hydrogen bond sites using the rules discussed below. A hydrogen bond consists of three basic elements: donor atom (D), hydrogen atom (H) and acceptor atom (A). Not all the atoms can serve as a hydrogen bond donor or acceptor. For example, alpha carbon atoms, sulfur atoms and aromatic ring acceptors are relatively too weak to form hydrogen bonds. Therefore, we use rules similar to those from Meyer et al. [21] to identify donors and acceptors in proteins. Donors include main-chain N–H, His NE2, His ND1, Lys NZ, Asn ND2, Gln NE2, Arg NE, Arg NH1, Arg NH2, Ser OG, Thr OG1, Tyr OH, Trp NE1, and Asn OD1, and acceptors include main-chain C@O, Asp OD1, Asp OD2, Glu OE1, Glu OE2, Asn OD1, Gln OE1, Ser OG, Thr OG1, Tyr OH, His, ND1, Glu NE2, and Asn ND2. For ligands, we apply the same criteria used by Luo et al. [7], which define nitrogen atoms bonded with hydrogen and sp3 hybridized oxygen atoms as donors, and treat all other forms of oxygen atoms and nitrogen atoms as acceptors. In addition to the availability of proper donor and acceptor atoms, the formation of a hydrogen bond still requires the satisfaction of two spatial constraints: distance and angle. Here, we use the criteria proposed by Baker and Hubbard [22]. Consider a hydrogen bond structure D–H. . .A, the distance between H and A should be less than 2.5 Å while the distance between D and A should be less than 3.9 Å. For the angle constraint, \D–H. . .A must exceed 90°. 2.3. Alpha shape In this Letter, we use a weighted alpha shape model to represent the surface of the protein–ligand structure and use solid angles to characterize the surface geometric properties of hydrogen bonds in protein–ligand interactions. The alpha shape, as introduced by Edelsbrunner and Mücke, offers a formal mathematical definition of a shape that can be computed [23]. It has many applications to the study of molecular structures, such as surface area computation, volume calculation, cavities detection etc. [15,16,24,25]. There are two types of alpha shapes: the basic one and the weighted one. In a set of unweighted points S, we can compute the basic alpha shape based on the Delaunay triangulation. In the 3D space, the Delaunay triangulation uses tetrahedrons to represent the structure of an object. The alpha shape is a subset of the Delaunay triangulation, which is controlled by the value of a. For a particular value of a, the basic alpha shape contains all the simplices (including points, edges, facets and tetrahedrons), which have an empty circumscribing sphere with radius equal to or smalpffiffiffi ler than a. Here the term empty means that the open sphere does not contain any point in S. The definition of the weighted alpha shape is similar to that of the basic one. Two points with centers
at P1 and P2 and radii r1 and r2 are defined as orthogonal if P1 P22 ¼ r21 þ r22 , and they are defined as suborthogonal if P1 P22 < r21 þ r22 . For a given value of a, the weighted alpha shape contains all the simplices that meet the condition that there is a sphere orthogonal to the points in each simplex and suborthogonal to the other points. Detailed illustration of the alpha shape model can be found in a paper by Edelsbrunner and Mücke [23]. In the present study, the radii of the input atoms are set as the common VDW radii used to calculate the Connolly surface area. We use the CGAL library to compute the weighted alpha shape and apply an alpha value of 0, a probe sphere radius of 1.4 Å, which means that the vertices in the weighted alpha shape correspond to the solvent accessible atoms. The weighted alpha shape surface and the solvent accessible surface of protein ‘1a07’ are shown in Figure 1. The 3D objects displayed in Figure 1 is produced using UCSF Chimera [26]. 2.4. Solid angle We use interface curvature to characterize the surface geometric properties of hydrogen bonds in protein–ligand structures. The interface curvature is represented by the solid angle of an interface atom in the alpha shape model. The solid angle in a Delaunay triangulation is defined as follows (Figure 2). Let OABC be the vertices of a tetrahedron with its origin at O subtended by the triangular face ABC, and /ab, /bc, /ac be the dihedral angle between OAC and OBC, OAB and OAC, OAB and OBC, respectively. The solid angle can be presented as: X = /ab + /bc + /ac p. Let a, b and c be the vectors of vertices A, B and C with respect to the origin O, respectively. We can use the following equations to calculate /ab, /bc and /ac:
n1 ¼
ab bc ca ; n2 ¼ ; n3 ¼ ; ja bj jb cj jc aj
/ ab = p arccos (n1 n2), /bc = p arccos (n1 n3), /ac = p arccos (n2 n3). After obtaining the solid angle X = /ab + /bc + /ac - p, we use cosðX4 Þ to transform its value to the range of 1 to 1. 3. Results and discussions Potential hydrogen bonds are identified according to the atom types and spatial constraints. In order to evaluate the surface geometric properties of these bonds, we compute the alpha shapes of the protein and the ligand in each complex separately. After that, we search for the atoms of the hydrogen bonds in the alpha shape model to obtain the solid angles corresponding to the surface curvature of the atoms. In order to ensure the atoms on the surface of the alpha shape are solvent accessible, we set the alpha value to 0 and use a probe radius of 1.4 Å.
Figure 1. The alpha shape (A) and solvent accessible surface (B) of protein ‘1a07’ from the PDB.
W. Zhou et al. / Chemical Physics Letters 545 (2012) 125–131
Figure 2. Illustration for the calculation of the solid angle for point O in tetrahedron OABC.
There are 1072 hydrogen bonds extracted from the experimental data. We first classify the hydrogen bonds into two groups according to the hydrogen bond donor: Group I for (protein donor) – (hydrogen atom) – (ligand acceptor) and Group II for (ligand donor) – (hydrogen atom) – (protein acceptor). Group I and Group II contain 631 and 441 hydrogen bonds, respectively. The data selection process ensures that both H and A are on the surface of the
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alpha shape. Therefore, there should be two situations: (a) H is on the surface of the alpha shape but D is not; (b) both D and H are on the surface of the alpha shape. Finally, we can classify the hydrogen bonds into four types (Figure 3) for further analysis: DPHSALS DPSHSALS, DLHSAPS, and DLSHSAPS, where D, H and A stand for donor, hydrogen and acceptor atoms respectively, subscripts P and L represent protein and ligand respectively, and subscript S indicates that the atom is on the surface of the alpha shape. According to the definition, solid angle values ranging from 1 to 0 represent a convex shape on the surface while values ranging from 0 to 1 represent a concave shape. The distributions of the solid angle values for the four types of hydrogen bonds are shown in Figure 4. Geometrically, the two atoms match well in the interface if they have opposite solid angle values. Figure 4A and C show that there are spatial matches between hydrogen atoms and acceptor atoms in DPHSALS and DLHSAPS hydrogen bonds. Similarly, Figure 4B and D indicate spatial matches between donor atoms and acceptor atoms in DPSHSALS and DLSHSAPS hydrogen bonds. However, we notice that each ligand is a small molecule and its atoms that are in contact with a protein surface usually have small solid angles, which result in high positive solid angle values. In the present study, we use the following basic condition to check for a potential spatial match: the solid angles of the two atoms involved in the matching should have opposite signs. We have examined two patterns: H-A matching pair and D-A matching pair. In the following discussions, if the solid angles of the two atoms (H–A or D–A) have opposite signs, we call the hydrogen bond a spatially matched one. Otherwise, we call it a spatially unmatched one.
Figure 3. Different types of hydrogen bonds. Donor, hydrogen and acceptor atoms are shown in blue, white and red respectively. (A) DPHSALS hydrogen bond. (B) DPSHSALS hydrogen bond. (C) DLHSAPS hydrogen bond. (D) DLSHSAPS hydrogen bond. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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W. Zhou et al. / Chemical Physics Letters 545 (2012) 125–131 D H A
D
P S LS
B
1
1
0.8
0.6
0.6
0.4
0.4
0.2 0 −0.2
0.2 0 −0.2
−0.4
−0.4
−0.6
−0.6 −0.8
−0.8
−1
−1 Hydrogen
Donor
Acceptor
D H A
L S PS
1
D1
0.8
0.8
0.6
0.6
0.4
0.4 Solid angle
Solid angle
C
H A
PS S LS
0.8
Solid angle
Solid angle
A
0.2 0
Hydrogen
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DLSHSAPS
0.2 0 −0.2
−0.2
−0.4
−0.4
−0.6 −0.8
−0.6
−1 Hydrogen
Acceptor
Donor
Hydrogen
Acceptor
Figure 4. Distribution of solid angles of different types of hydrogen bonds: (A) DPHSALS, (B) DLHSAPS, (C) DPSHSALS and (D) DLSHSAPS.
Table 1 Analysis of spatial properties of the hydrogen bonds. H–bond type
H–A matching pairs
D–A matching pairs
Total number of Hbonds
H–A distance (Å)
D–A distance (Å)
D–H– A angle (°)
DPHSALS DPSHSALS DLHSAPS DLSHSAPS
255 96 45 238
278 250
287 344 71 370
1.98 2.02 2.08 2.02
2.89 2.89 3.00 2.86
154.66 149.44 155.87 145.16
A statistical analysis is shown in Table 1. Out of a total of 287 DPHSALS H–A pairs, 255 H–A pairs meet the basic condition. This result indicates that 88.8% of the DPHSALS hydrogen bonds form potential matches between their hydrogen atoms and acceptor atoms. For DLHSAPS hydrogen bonds, 45 H–A pairs out of 71 H–A pairs are matched. Compared to the high percentage of spatial matches of H–A pairs in DPHSALS, the percentage of that in DLHSAPS is low. In order to find out why DLHSAPS hydrogen bonds show a low H–A spatial match, we calculate the average H–A distance and D–A distance for DPHSALS and DLHSAPS hydrogen bonds, respectively. As it is shown in Table 1, we can see that the average H–A distances for DPHSALS and DLHSAPS hydrogen bonds are 1.98 and 2.08 Å, respectively. The average D–A distances for the two types of bonds are 2.89 and 3.00 Å, respectively. The standard deviation for the H–A and D–A distances of both types of hydrogen bonds are 0.22 and 0.21 Å, respectively. This implies the variance of the distance values is very small. The differences between the average H–A distance and the average D–A distance for two types of bonds are 0.1 and 0.11 Å, which are 45% and 52% of the standard
deviation. From this comparison, we can see that DLHSAPS hydrogen bonds have larger H–A and D–A distances. This means that they are formed in places with larger distances between the protein and ligand molecules. On the contrary, DPHSALS hydrogen bonds are formed in places with small distances between two molecules. At the same time, smaller H–A and D–A distances correspond to stronger hydrogen bond strength. This shows why more spatially matched H–A pairs appear in DPHSALS hydrogen bonds. We have examined both H–A and D–A matching pairs in DPSHSALS and DLSHSAPS hydrogen bonds. The result shows that H– A matching pairs are only a minor part in DPSHSALS hydrogen bonds, while D–A matching pairs are a majority part. Comparing the average H–A distances, D–A distances and D–H–A angles of DPSHSALS and DPHSALS hydrogen bonds shown in Table 1, we can see that DPSHSALS hydrogen bonds show a larger H–A distance, a medium D–A distance and a smaller D–H–A angle. This result indicates that the acceptor atom is bending towards the donor atom side, which means a spatial match is required for the acceptor and donor atoms. The situation is different in DLSHSAPS hydrogen bonds, where there are both H–A and D–A matching pairs. The distribution of the solid angle values for DLSHSAPS hydrogen bonds show that both donor and hydrogen atoms have mainly positive values while acceptor atoms have negative values. This is the reason why there are spatial matches for both H–A and D–A pairs. An analysis is carried out to study the average D–H–A angles of the H– A and D–A matching pairs and spatially unmatched hydrogen bonds. The result shows that their values are 155.16°, 147.24° and 148.72°, respectively. We can see that H–A matched hydrogen bonds have a significantly larger average D–H–A angle than D–A matched ones and unmatched ones. The reason is that H-A matched hydrogen bonds come from DPHSALS and DLHSAPS types.
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W. Zhou et al. / Chemical Physics Letters 545 (2012) 125–131 Table 2 Association energy (kcal/mol) of different hydrogen bond types. Donor
O.3 N.3 N.am N.pl3
Acceptor O.2
O.3
O.co2
N.2
3.69 20.64 3.02 3.40
2.69 15.61 3.99 4.13
16.02 N/Aa 21.72 22.58
4.62 25.32 4.45 6.17
a Liu et al. [29] report that the energy does not reflect the formation of this type of hydrogen bonds.
In these two types of hydrogen bonds, the donor atoms are not on the surface of the molecule while the hydrogen atoms and acceptor atoms are spatially matched (Figure 3A and C). Under this configuration, the donor has more freedom to move to a position so that it can become collinear with the hydrogen and acceptor atom as much as possible. This results in a larger D–H–A angle. The D–A matched hydrogen bonds come from DPSHSALS and DLSHSAPS hydrogen bonds, in which both the donor atom and hydrogen atom are on the surface of the molecule (Figure 3B and D). Because the hydrogen bonds are formed in the interface between the protein and ligand molecules, the three atoms (D, H, A) are less likely to become collinear since all of them are on the molecular surface. From the analysis above, we can conclude that hydrogen bonds show two spatial patterns. The hydrogen and the acceptor atoms are spatially matched in DPHSALS and DLHSAPS hydrogen bonds with larger D–H–A angles. Donor and acceptor atoms are spatially matched in DPSHSALS and DLSHSAPS hydrogen bonds with smaller D–H–A angles. Various studies show that hydrogen bond strength can be estimated from the donor and acceptor atom types [27–29]. In this Letter, we assign the association energy to each hydrogen bond according to their donor and acceptor atom types. The association energy data in Table 2 are obtained from Liu et al. [29], which were calculated from the hydrogen bonds in the protein–ligand interface using quantum mechanics method. Here, we consider four types of donor atoms including O.3 (sp3 oxygen atom in a hydroxyl group), N.3 (sp3 nitrogen atom in an amine group), N.am (nitrogen atom in an amide group) and N.pl3 (sp3 or sp2 nitrogen atom with a
triangular geometry). For acceptor atoms, we consider O.2 (sp2 oxygen atom), O.3 (sp3 oxygen atom in a hydroxyl group), O.co2 (sp3 oxygen atom in a carboxylic group) and N.2 (sp2 nitrogen atom). The result shows that the spatially matched hydrogen bonds have average association energy of 10.65 kcal/mol while the unmatched ones 9.97 kcal/mol. We can see that the spatially matched hydrogen bonds require larger energy in the association process than the unmatched ones. In other words, the spatially matched hydrogen bonds have stronger bonding strength, which indicates they play a more important role than other hydrogen bonds in protein–ligand interactions. In order to reveal the importance of the hydrogen bonds with spatial match during protein–ligand interactions, we analyze the number of these hydrogen bonds in each structure. As discussed above, we define a hydrogen bond as a spatially matched one if the solid angle of the hydrogen atom or donor atom is of opposite sign with that of the acceptor atom. Figure 5 shows the total number of hydrogen bonds and the number of spatially matched ones in each protein–ligand complex. We can calculate from the diagram that 77.2% of the hydrogen bonds from all structures have either an H–A or a D-A matching pair. At least half of the hydrogen bonds show spatial match in 87.7% of the structures. Only 5% of the structures contain no spatially matched hydrogen bond. Out of all the hydrogen bonds in each structure, the average percentage of spatially matched ones is 77.5%. This analysis demonstrates that the spatially matched hydrogen bonds play a significant role in protein–ligand interactions. Comparing the four types of hydrogen bonds, we find that DPHSALS shows the largest percentage (88.8%) of H–A matching pairs and the smallest value of average H–A distance (1.98 Å). These properties imply that DPHSALS may show stronger bonding strength than the other three types of hydrogen bonds. This signifies its importance in protein–ligand interactions. In order to reveal the relation between these types of hydrogen bonds and their protein structure, we study the residue type of the donor atom. Here, we focus on the (protein donor) – (hydrogen atom) – (ligand acceptor) hydrogen bonds. The distribution of the residue type for DPHSALS and DPSHSALS donor atom is shown in Figure 6. We can see that the DPHSALS type of hydrogen bond appears with a high percentage in Phe, Glu, Cys, Met, Ala, Val, Leu and Asp residues.
Distribution of spatially matched hydrogen bonds in each protein−ligand structure 18 Number of spatially matched hydrogen bonds Total number of hydrogen bonds
16
Number of hydrogen bonds
14
12
10
8
6
4
2
0
0
50
100 150 Index of protein−ligand complex
200
Figure 5. Distribution of spatially matched hydrogen bonds in each protein–ligand structure.
250
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W. Zhou et al. / Chemical Physics Letters 545 (2012) 125–131 Distribution of residue type for donor atom 200 180
Number of DPHSALS hydrogen bonds Number of DPSHSALS hydrogen bonds
Number of hydrogen bonds
160 140 120 100 80 60 40 20 0
PHE GLU CYS MET ALA
ILE
TRP VAL HIS LEU GLN ASP THR LYS SER ASN TYR GLY ARG
Figure 6. Distribution of the residue type for DPHSALS and DPSHSALS donor atom.
According to the definition of the donor atom type, the donor atoms from these residues are all main chain nitrogen atoms. The donor atoms of the DPHSALS hydrogen bonds in these types of residues are not accessible by solvent. In these residues, the hydrogen atoms usually show a negative solid angle, which means they are concave spots on the protein surface. The acceptor atoms from the ligand are mostly on the convex spots on the ligand surface. Therefore, geometric complementarity is necessary for hydrogen bonding in these residues. In Figure 6, we can also see that a large number of donor atoms come from Arg. In the structure of arginine, besides the main chain nitrogen atom, there are three side-chain nitrogen atoms serving as donor atoms for hydrogen bonding. The three nitrogen atoms come from a guanidine in the side chain, which is a plane-like structure in the 3D space. Due to the planar structure, the nitrogen atoms from guanidine are likely to be on the surface of the protein structure. Therefore, arginine dominates the residue type in hydrogen bonding. Surface characteristics are important in molecular interactions, as demonstrated in our previous studies [10,18,30,31]. The result in this Letter indicates that geometric surface matching is a requirement in protein–ligand interactions. In these interactions, hydrogen bonds play the most significant role in the stability of the structure, and there is a higher probability for a hydrogen bond to be formed in places with a better geometric match. This property provides us with a deeper insight into the physical nature of hydrogen bonding. The findings in this Letter are useful for the study of protein–ligand interactions such as structure-based drug design. Two essential issues in structure-based drug design are docking and scoring. The aim of the docking process is to find the best binding site and the binding pose between a protein and a drug molecule. A number of docking methods have been proposed but most of them are computational expensive. Recently, researchers have applied hydrogen bonding to the docking process, which can reduce the computational complexity substantially [7,32]. According to the finding in this Letter, we can see that geometric complementary is an important element for the formation of hydrogen bonds in protein–ligand interactions. Therefore, we can apply this criterion in a docking method by considering spatially matched hydrogen bonds rather than all hydrogen bonds. This approach may further improve the accuracy and speed of the docking method. At the same time, hydrogen bonding is widely
used in the scoring process of structure-based drug design [33–36]. In this Letter, we have demonstrated that the spatially matched hydrogen bonds show stronger bonding strength than unmatched ones. This result can be applied to the scoring process by assigning the hydrogen bonds with different weights according to their spatially matching property, which increase the influence of the spatially matched hydrogen bonds in the scoring function. 4. Conclusions In this Letter, we apply 3D alpha shape modeling to the study of the surface geometric properties of hydrogen bonding in protein– ligand complexes. The hydrogen bonds are classified into four types according their surface geometric properties. We use solid angles to evaluate the spatial match within the H–A and D–A pairs. The result demonstrates that hydrogen bonds show spatially matching patterns protein–ligand complexes. Our study here indicates that surface match play an important role in hydrogen bond formation in protein–ligand interactions, which contributes to the stability of a protein–ligand structure. As the key element during protein–ligand interaction, hydrogen bonding requires not only charge complementarity but also geometric complementarity. Acknowledgement This work is supported by the Hong Kong Research Grant Council (Project CityU 123809). References [1] L.M. Amzel, Curr. Opin. Biotechnol. 9 (1998) 366. [2] C. DeWeese-Scott, J. Moult, Proteins 55 (2004) 942. [3] A.D. Buckingham, J.E. Del Bene, S.A.C. McDowell, Chem. Phys. Lett. 463 (2008) 1. [4] Y. Harano, R. Roth, Y. Sugita, M. Ikeguchi, M. Kinoshita, Chem. Phys. Lett. 437 (2007) 112. [5] R.E. Babine, S.L. Bender, Chem. Rev. 97 (1997) 1359. [6] H. Gohlke, M. Hendlich, G. Klebe, J. Mol. Biol. 295 (2000) 337. [7] W. Luo, J. Pei, Y. Zhu, J. Mol. Model. 16 (2010) 903. [8] R.L. Mancera, Chem. Phys. Lett. 399 (2004) 271. [9] A.T.R. Laurie, R.M. Jackson, Bioinformatics 21 (2005) 1908. [10] W. Zhou, H. Yan, Bioinformatics 26 (2010) 2541. [11] T.W. Siggers, A. Silkov, B. Honig, J. Mol. Biol. 345 (2005) 1027.
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Analysis of surface structures of hydrogen bonding in protein–ligand interactions using the alpha shape model Weiqiang Zhou a,⇑, Hong Yan a, Quan Hao b a b
Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong Department of Physiology, University of Hong Kong, Pokfulam, Hong Kong
a r t i c l e
i n f o
Article history: Received 21 May 2012 In final form 9 July 2012 Available online 20 July 2012
a b s t r a c t Hydrogen bonding provides useful information for the study of protein–ligand interactions. However, the physical role that a hydrogen bond plays and its 3D surface characteristics in protein–ligand interaction are still not well understood. We apply the 3D alpha shape model to reconstruct the interface of a protein–ligand structure and use solid angles at interface atoms to represent the surface geometric properties of a hydrogen bond. The result shows that 77.2% of the hydrogen bonds show complementary geometric patterns and 95.0% of the protein–ligand complexes contain at least one such hydrogen bond. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Interactions between a protein and another molecule such as another protein, DNA or a ligand take place in many biological processes. Among these interactions, protein–ligand interaction is of particular importance because it is related to the understanding of protein functions and drug development [1,2]. In protein–ligand interactions, hydrogen bonding plays a significant role [3,4]. Babine and Bender reported that hydrogen bonding contributed much to the stability in protein–ligand complexes [5]. Hydrogen bonding has already been used widely in the study of protein–ligand interactions. Gohlke et al. used hydrogen bonding to construct a scoring function for the prediction of protein–ligand interactions [6]. Luo et al. applied hydrogen bond matching to develop a fast protein–ligand docking algorithm [7]. Mancera developed a hydration penalty score for protein–ligand interactions using hydrogen bond formation [8]. Laurie and Jackson proposed to use the hydrogen bonding potential in the prediction of protein–ligand binding sites [9]. Although many studies show that surface properties play an important role in macromolecular interactions in general [10–14], few studies focus on the surface geometric properties of hydrogen bonding. The alpha shape model can be applied to the study of 3D surface properties of biomolecules. This model was first used to study molecular volume computation and cavity detection in proteins by Liang et al. [15,16]. Albou et al. used alpha shape to analyze the surface characteristics of proteins [17]. Recently, Zhou and Yan applied the alpha shape model to analyze the interface surface properties in protein-DNA and protein–protein interactions and achieved good results [10,18]. These studies demonstrate that ⇑ Corresponding author. E-mail address: [email protected] (W. Zhou). 0009-2614/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cplett.2012.07.016
the alpha shape model is an effective means for the study of geometric properties of the interface in molecular interactions. In this Letter, we apply the 3D alpha shape model to represent the interface of a protein–ligand structure and use the solid angles at interface atoms to study the geometric properties of hydrogen bonds in the structure. Complementary geometric surface patterns are found in these hydrogen bonds. 2. Materials and methods 2.1. Data selection The experimental data used in this Letter were obtained from the protein–ligand structures in CCDCnAstex (http://www.ccdc. cam.ac.uk/products/life_sciences/gold/validation/astex/) [19]. The CCDCnAstex test set consists of 305 protein–ligand complexes with various proteins from different families and diverse ligand structures. These structures are already preprocessed and the coordinates of hydrogen atoms in the structures are added using SYBYL. The hydrogen atom coordinates are calculated only from atom types and hybrid states without the intermolecular hydrogen bond information. We use the protein molecule and the original ligand molecule provided in the data set. Further filtering of the data is carried out using the following constraints: (a) the structure contains at least one hydrogen bond; (b) the acceptor atom and hydrogen atom of the hydrogen bond must be on the surface of the alpha shape. The 278 protein–ligand complexes selected are used for analysis of the surface geometric properties of hydrogen bonds. 2.2. Hydrogen bonding Early studies demonstrate the importance of hydrogen bonding for the structure and function of biomolecules [20]. For example,
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hydrogen bonding controls the mechanisms of binding specificity and stabilization of antibody-antigen and protease–inhibitor complexes in solution [21]. Atom types and spatial constraints restrict the formation of intermolecular hydrogen bonds. We define potential hydrogen bond sites using the rules discussed below. A hydrogen bond consists of three basic elements: donor atom (D), hydrogen atom (H) and acceptor atom (A). Not all the atoms can serve as a hydrogen bond donor or acceptor. For example, alpha carbon atoms, sulfur atoms and aromatic ring acceptors are relatively too weak to form hydrogen bonds. Therefore, we use rules similar to those from Meyer et al. [21] to identify donors and acceptors in proteins. Donors include main-chain N–H, His NE2, His ND1, Lys NZ, Asn ND2, Gln NE2, Arg NE, Arg NH1, Arg NH2, Ser OG, Thr OG1, Tyr OH, Trp NE1, and Asn OD1, and acceptors include main-chain C@O, Asp OD1, Asp OD2, Glu OE1, Glu OE2, Asn OD1, Gln OE1, Ser OG, Thr OG1, Tyr OH, His, ND1, Glu NE2, and Asn ND2. For ligands, we apply the same criteria used by Luo et al. [7], which define nitrogen atoms bonded with hydrogen and sp3 hybridized oxygen atoms as donors, and treat all other forms of oxygen atoms and nitrogen atoms as acceptors. In addition to the availability of proper donor and acceptor atoms, the formation of a hydrogen bond still requires the satisfaction of two spatial constraints: distance and angle. Here, we use the criteria proposed by Baker and Hubbard [22]. Consider a hydrogen bond structure D–H. . .A, the distance between H and A should be less than 2.5 Å while the distance between D and A should be less than 3.9 Å. For the angle constraint, \D–H. . .A must exceed 90°. 2.3. Alpha shape In this Letter, we use a weighted alpha shape model to represent the surface of the protein–ligand structure and use solid angles to characterize the surface geometric properties of hydrogen bonds in protein–ligand interactions. The alpha shape, as introduced by Edelsbrunner and Mücke, offers a formal mathematical definition of a shape that can be computed [23]. It has many applications to the study of molecular structures, such as surface area computation, volume calculation, cavities detection etc. [15,16,24,25]. There are two types of alpha shapes: the basic one and the weighted one. In a set of unweighted points S, we can compute the basic alpha shape based on the Delaunay triangulation. In the 3D space, the Delaunay triangulation uses tetrahedrons to represent the structure of an object. The alpha shape is a subset of the Delaunay triangulation, which is controlled by the value of a. For a particular value of a, the basic alpha shape contains all the simplices (including points, edges, facets and tetrahedrons), which have an empty circumscribing sphere with radius equal to or smalpffiffiffi ler than a. Here the term empty means that the open sphere does not contain any point in S. The definition of the weighted alpha shape is similar to that of the basic one. Two points with centers
at P1 and P2 and radii r1 and r2 are defined as orthogonal if P1 P22 ¼ r21 þ r22 , and they are defined as suborthogonal if P1 P22 < r21 þ r22 . For a given value of a, the weighted alpha shape contains all the simplices that meet the condition that there is a sphere orthogonal to the points in each simplex and suborthogonal to the other points. Detailed illustration of the alpha shape model can be found in a paper by Edelsbrunner and Mücke [23]. In the present study, the radii of the input atoms are set as the common VDW radii used to calculate the Connolly surface area. We use the CGAL library to compute the weighted alpha shape and apply an alpha value of 0, a probe sphere radius of 1.4 Å, which means that the vertices in the weighted alpha shape correspond to the solvent accessible atoms. The weighted alpha shape surface and the solvent accessible surface of protein ‘1a07’ are shown in Figure 1. The 3D objects displayed in Figure 1 is produced using UCSF Chimera [26]. 2.4. Solid angle We use interface curvature to characterize the surface geometric properties of hydrogen bonds in protein–ligand structures. The interface curvature is represented by the solid angle of an interface atom in the alpha shape model. The solid angle in a Delaunay triangulation is defined as follows (Figure 2). Let OABC be the vertices of a tetrahedron with its origin at O subtended by the triangular face ABC, and /ab, /bc, /ac be the dihedral angle between OAC and OBC, OAB and OAC, OAB and OBC, respectively. The solid angle can be presented as: X = /ab + /bc + /ac p. Let a, b and c be the vectors of vertices A, B and C with respect to the origin O, respectively. We can use the following equations to calculate /ab, /bc and /ac:
n1 ¼
ab bc ca ; n2 ¼ ; n3 ¼ ; ja bj jb cj jc aj
/ ab = p arccos (n1 n2), /bc = p arccos (n1 n3), /ac = p arccos (n2 n3). After obtaining the solid angle X = /ab + /bc + /ac - p, we use cosðX4 Þ to transform its value to the range of 1 to 1. 3. Results and discussions Potential hydrogen bonds are identified according to the atom types and spatial constraints. In order to evaluate the surface geometric properties of these bonds, we compute the alpha shapes of the protein and the ligand in each complex separately. After that, we search for the atoms of the hydrogen bonds in the alpha shape model to obtain the solid angles corresponding to the surface curvature of the atoms. In order to ensure the atoms on the surface of the alpha shape are solvent accessible, we set the alpha value to 0 and use a probe radius of 1.4 Å.
Figure 1. The alpha shape (A) and solvent accessible surface (B) of protein ‘1a07’ from the PDB.
W. Zhou et al. / Chemical Physics Letters 545 (2012) 125–131
Figure 2. Illustration for the calculation of the solid angle for point O in tetrahedron OABC.
There are 1072 hydrogen bonds extracted from the experimental data. We first classify the hydrogen bonds into two groups according to the hydrogen bond donor: Group I for (protein donor) – (hydrogen atom) – (ligand acceptor) and Group II for (ligand donor) – (hydrogen atom) – (protein acceptor). Group I and Group II contain 631 and 441 hydrogen bonds, respectively. The data selection process ensures that both H and A are on the surface of the
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alpha shape. Therefore, there should be two situations: (a) H is on the surface of the alpha shape but D is not; (b) both D and H are on the surface of the alpha shape. Finally, we can classify the hydrogen bonds into four types (Figure 3) for further analysis: DPHSALS DPSHSALS, DLHSAPS, and DLSHSAPS, where D, H and A stand for donor, hydrogen and acceptor atoms respectively, subscripts P and L represent protein and ligand respectively, and subscript S indicates that the atom is on the surface of the alpha shape. According to the definition, solid angle values ranging from 1 to 0 represent a convex shape on the surface while values ranging from 0 to 1 represent a concave shape. The distributions of the solid angle values for the four types of hydrogen bonds are shown in Figure 4. Geometrically, the two atoms match well in the interface if they have opposite solid angle values. Figure 4A and C show that there are spatial matches between hydrogen atoms and acceptor atoms in DPHSALS and DLHSAPS hydrogen bonds. Similarly, Figure 4B and D indicate spatial matches between donor atoms and acceptor atoms in DPSHSALS and DLSHSAPS hydrogen bonds. However, we notice that each ligand is a small molecule and its atoms that are in contact with a protein surface usually have small solid angles, which result in high positive solid angle values. In the present study, we use the following basic condition to check for a potential spatial match: the solid angles of the two atoms involved in the matching should have opposite signs. We have examined two patterns: H-A matching pair and D-A matching pair. In the following discussions, if the solid angles of the two atoms (H–A or D–A) have opposite signs, we call the hydrogen bond a spatially matched one. Otherwise, we call it a spatially unmatched one.
Figure 3. Different types of hydrogen bonds. Donor, hydrogen and acceptor atoms are shown in blue, white and red respectively. (A) DPHSALS hydrogen bond. (B) DPSHSALS hydrogen bond. (C) DLHSAPS hydrogen bond. (D) DLSHSAPS hydrogen bond. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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W. Zhou et al. / Chemical Physics Letters 545 (2012) 125–131 D H A
D
P S LS
B
1
1
0.8
0.6
0.6
0.4
0.4
0.2 0 −0.2
0.2 0 −0.2
−0.4
−0.4
−0.6
−0.6 −0.8
−0.8
−1
−1 Hydrogen
Donor
Acceptor
D H A
L S PS
1
D1
0.8
0.8
0.6
0.6
0.4
0.4 Solid angle
Solid angle
C
H A
PS S LS
0.8
Solid angle
Solid angle
A
0.2 0
Hydrogen
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DLSHSAPS
0.2 0 −0.2
−0.2
−0.4
−0.4
−0.6 −0.8
−0.6
−1 Hydrogen
Acceptor
Donor
Hydrogen
Acceptor
Figure 4. Distribution of solid angles of different types of hydrogen bonds: (A) DPHSALS, (B) DLHSAPS, (C) DPSHSALS and (D) DLSHSAPS.
Table 1 Analysis of spatial properties of the hydrogen bonds. H–bond type
H–A matching pairs
D–A matching pairs
Total number of Hbonds
H–A distance (Å)
D–A distance (Å)
D–H– A angle (°)
DPHSALS DPSHSALS DLHSAPS DLSHSAPS
255 96 45 238
278 250
287 344 71 370
1.98 2.02 2.08 2.02
2.89 2.89 3.00 2.86
154.66 149.44 155.87 145.16
A statistical analysis is shown in Table 1. Out of a total of 287 DPHSALS H–A pairs, 255 H–A pairs meet the basic condition. This result indicates that 88.8% of the DPHSALS hydrogen bonds form potential matches between their hydrogen atoms and acceptor atoms. For DLHSAPS hydrogen bonds, 45 H–A pairs out of 71 H–A pairs are matched. Compared to the high percentage of spatial matches of H–A pairs in DPHSALS, the percentage of that in DLHSAPS is low. In order to find out why DLHSAPS hydrogen bonds show a low H–A spatial match, we calculate the average H–A distance and D–A distance for DPHSALS and DLHSAPS hydrogen bonds, respectively. As it is shown in Table 1, we can see that the average H–A distances for DPHSALS and DLHSAPS hydrogen bonds are 1.98 and 2.08 Å, respectively. The average D–A distances for the two types of bonds are 2.89 and 3.00 Å, respectively. The standard deviation for the H–A and D–A distances of both types of hydrogen bonds are 0.22 and 0.21 Å, respectively. This implies the variance of the distance values is very small. The differences between the average H–A distance and the average D–A distance for two types of bonds are 0.1 and 0.11 Å, which are 45% and 52% of the standard
deviation. From this comparison, we can see that DLHSAPS hydrogen bonds have larger H–A and D–A distances. This means that they are formed in places with larger distances between the protein and ligand molecules. On the contrary, DPHSALS hydrogen bonds are formed in places with small distances between two molecules. At the same time, smaller H–A and D–A distances correspond to stronger hydrogen bond strength. This shows why more spatially matched H–A pairs appear in DPHSALS hydrogen bonds. We have examined both H–A and D–A matching pairs in DPSHSALS and DLSHSAPS hydrogen bonds. The result shows that H– A matching pairs are only a minor part in DPSHSALS hydrogen bonds, while D–A matching pairs are a majority part. Comparing the average H–A distances, D–A distances and D–H–A angles of DPSHSALS and DPHSALS hydrogen bonds shown in Table 1, we can see that DPSHSALS hydrogen bonds show a larger H–A distance, a medium D–A distance and a smaller D–H–A angle. This result indicates that the acceptor atom is bending towards the donor atom side, which means a spatial match is required for the acceptor and donor atoms. The situation is different in DLSHSAPS hydrogen bonds, where there are both H–A and D–A matching pairs. The distribution of the solid angle values for DLSHSAPS hydrogen bonds show that both donor and hydrogen atoms have mainly positive values while acceptor atoms have negative values. This is the reason why there are spatial matches for both H–A and D–A pairs. An analysis is carried out to study the average D–H–A angles of the H– A and D–A matching pairs and spatially unmatched hydrogen bonds. The result shows that their values are 155.16°, 147.24° and 148.72°, respectively. We can see that H–A matched hydrogen bonds have a significantly larger average D–H–A angle than D–A matched ones and unmatched ones. The reason is that H-A matched hydrogen bonds come from DPHSALS and DLHSAPS types.
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W. Zhou et al. / Chemical Physics Letters 545 (2012) 125–131 Table 2 Association energy (kcal/mol) of different hydrogen bond types. Donor
O.3 N.3 N.am N.pl3
Acceptor O.2
O.3
O.co2
N.2
3.69 20.64 3.02 3.40
2.69 15.61 3.99 4.13
16.02 N/Aa 21.72 22.58
4.62 25.32 4.45 6.17
a Liu et al. [29] report that the energy does not reflect the formation of this type of hydrogen bonds.
In these two types of hydrogen bonds, the donor atoms are not on the surface of the molecule while the hydrogen atoms and acceptor atoms are spatially matched (Figure 3A and C). Under this configuration, the donor has more freedom to move to a position so that it can become collinear with the hydrogen and acceptor atom as much as possible. This results in a larger D–H–A angle. The D–A matched hydrogen bonds come from DPSHSALS and DLSHSAPS hydrogen bonds, in which both the donor atom and hydrogen atom are on the surface of the molecule (Figure 3B and D). Because the hydrogen bonds are formed in the interface between the protein and ligand molecules, the three atoms (D, H, A) are less likely to become collinear since all of them are on the molecular surface. From the analysis above, we can conclude that hydrogen bonds show two spatial patterns. The hydrogen and the acceptor atoms are spatially matched in DPHSALS and DLHSAPS hydrogen bonds with larger D–H–A angles. Donor and acceptor atoms are spatially matched in DPSHSALS and DLSHSAPS hydrogen bonds with smaller D–H–A angles. Various studies show that hydrogen bond strength can be estimated from the donor and acceptor atom types [27–29]. In this Letter, we assign the association energy to each hydrogen bond according to their donor and acceptor atom types. The association energy data in Table 2 are obtained from Liu et al. [29], which were calculated from the hydrogen bonds in the protein–ligand interface using quantum mechanics method. Here, we consider four types of donor atoms including O.3 (sp3 oxygen atom in a hydroxyl group), N.3 (sp3 nitrogen atom in an amine group), N.am (nitrogen atom in an amide group) and N.pl3 (sp3 or sp2 nitrogen atom with a
triangular geometry). For acceptor atoms, we consider O.2 (sp2 oxygen atom), O.3 (sp3 oxygen atom in a hydroxyl group), O.co2 (sp3 oxygen atom in a carboxylic group) and N.2 (sp2 nitrogen atom). The result shows that the spatially matched hydrogen bonds have average association energy of 10.65 kcal/mol while the unmatched ones 9.97 kcal/mol. We can see that the spatially matched hydrogen bonds require larger energy in the association process than the unmatched ones. In other words, the spatially matched hydrogen bonds have stronger bonding strength, which indicates they play a more important role than other hydrogen bonds in protein–ligand interactions. In order to reveal the importance of the hydrogen bonds with spatial match during protein–ligand interactions, we analyze the number of these hydrogen bonds in each structure. As discussed above, we define a hydrogen bond as a spatially matched one if the solid angle of the hydrogen atom or donor atom is of opposite sign with that of the acceptor atom. Figure 5 shows the total number of hydrogen bonds and the number of spatially matched ones in each protein–ligand complex. We can calculate from the diagram that 77.2% of the hydrogen bonds from all structures have either an H–A or a D-A matching pair. At least half of the hydrogen bonds show spatial match in 87.7% of the structures. Only 5% of the structures contain no spatially matched hydrogen bond. Out of all the hydrogen bonds in each structure, the average percentage of spatially matched ones is 77.5%. This analysis demonstrates that the spatially matched hydrogen bonds play a significant role in protein–ligand interactions. Comparing the four types of hydrogen bonds, we find that DPHSALS shows the largest percentage (88.8%) of H–A matching pairs and the smallest value of average H–A distance (1.98 Å). These properties imply that DPHSALS may show stronger bonding strength than the other three types of hydrogen bonds. This signifies its importance in protein–ligand interactions. In order to reveal the relation between these types of hydrogen bonds and their protein structure, we study the residue type of the donor atom. Here, we focus on the (protein donor) – (hydrogen atom) – (ligand acceptor) hydrogen bonds. The distribution of the residue type for DPHSALS and DPSHSALS donor atom is shown in Figure 6. We can see that the DPHSALS type of hydrogen bond appears with a high percentage in Phe, Glu, Cys, Met, Ala, Val, Leu and Asp residues.
Distribution of spatially matched hydrogen bonds in each protein−ligand structure 18 Number of spatially matched hydrogen bonds Total number of hydrogen bonds
16
Number of hydrogen bonds
14
12
10
8
6
4
2
0
0
50
100 150 Index of protein−ligand complex
200
Figure 5. Distribution of spatially matched hydrogen bonds in each protein–ligand structure.
250
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W. Zhou et al. / Chemical Physics Letters 545 (2012) 125–131 Distribution of residue type for donor atom 200 180
Number of DPHSALS hydrogen bonds Number of DPSHSALS hydrogen bonds
Number of hydrogen bonds
160 140 120 100 80 60 40 20 0
PHE GLU CYS MET ALA
ILE
TRP VAL HIS LEU GLN ASP THR LYS SER ASN TYR GLY ARG
Figure 6. Distribution of the residue type for DPHSALS and DPSHSALS donor atom.
According to the definition of the donor atom type, the donor atoms from these residues are all main chain nitrogen atoms. The donor atoms of the DPHSALS hydrogen bonds in these types of residues are not accessible by solvent. In these residues, the hydrogen atoms usually show a negative solid angle, which means they are concave spots on the protein surface. The acceptor atoms from the ligand are mostly on the convex spots on the ligand surface. Therefore, geometric complementarity is necessary for hydrogen bonding in these residues. In Figure 6, we can also see that a large number of donor atoms come from Arg. In the structure of arginine, besides the main chain nitrogen atom, there are three side-chain nitrogen atoms serving as donor atoms for hydrogen bonding. The three nitrogen atoms come from a guanidine in the side chain, which is a plane-like structure in the 3D space. Due to the planar structure, the nitrogen atoms from guanidine are likely to be on the surface of the protein structure. Therefore, arginine dominates the residue type in hydrogen bonding. Surface characteristics are important in molecular interactions, as demonstrated in our previous studies [10,18,30,31]. The result in this Letter indicates that geometric surface matching is a requirement in protein–ligand interactions. In these interactions, hydrogen bonds play the most significant role in the stability of the structure, and there is a higher probability for a hydrogen bond to be formed in places with a better geometric match. This property provides us with a deeper insight into the physical nature of hydrogen bonding. The findings in this Letter are useful for the study of protein–ligand interactions such as structure-based drug design. Two essential issues in structure-based drug design are docking and scoring. The aim of the docking process is to find the best binding site and the binding pose between a protein and a drug molecule. A number of docking methods have been proposed but most of them are computational expensive. Recently, researchers have applied hydrogen bonding to the docking process, which can reduce the computational complexity substantially [7,32]. According to the finding in this Letter, we can see that geometric complementary is an important element for the formation of hydrogen bonds in protein–ligand interactions. Therefore, we can apply this criterion in a docking method by considering spatially matched hydrogen bonds rather than all hydrogen bonds. This approach may further improve the accuracy and speed of the docking method. At the same time, hydrogen bonding is widely
used in the scoring process of structure-based drug design [33–36]. In this Letter, we have demonstrated that the spatially matched hydrogen bonds show stronger bonding strength than unmatched ones. This result can be applied to the scoring process by assigning the hydrogen bonds with different weights according to their spatially matching property, which increase the influence of the spatially matched hydrogen bonds in the scoring function. 4. Conclusions In this Letter, we apply 3D alpha shape modeling to the study of the surface geometric properties of hydrogen bonding in protein– ligand complexes. The hydrogen bonds are classified into four types according their surface geometric properties. We use solid angles to evaluate the spatial match within the H–A and D–A pairs. The result demonstrates that hydrogen bonds show spatially matching patterns protein–ligand complexes. Our study here indicates that surface match play an important role in hydrogen bond formation in protein–ligand interactions, which contributes to the stability of a protein–ligand structure. As the key element during protein–ligand interaction, hydrogen bonding requires not only charge complementarity but also geometric complementarity. Acknowledgement This work is supported by the Hong Kong Research Grant Council (Project CityU 123809). References [1] L.M. Amzel, Curr. Opin. Biotechnol. 9 (1998) 366. [2] C. DeWeese-Scott, J. Moult, Proteins 55 (2004) 942. [3] A.D. Buckingham, J.E. Del Bene, S.A.C. McDowell, Chem. Phys. Lett. 463 (2008) 1. [4] Y. Harano, R. Roth, Y. Sugita, M. Ikeguchi, M. Kinoshita, Chem. Phys. Lett. 437 (2007) 112. [5] R.E. Babine, S.L. Bender, Chem. Rev. 97 (1997) 1359. [6] H. Gohlke, M. Hendlich, G. Klebe, J. Mol. Biol. 295 (2000) 337. [7] W. Luo, J. Pei, Y. Zhu, J. Mol. Model. 16 (2010) 903. [8] R.L. Mancera, Chem. Phys. Lett. 399 (2004) 271. [9] A.T.R. Laurie, R.M. Jackson, Bioinformatics 21 (2005) 1908. [10] W. Zhou, H. Yan, Bioinformatics 26 (2010) 2541. [11] T.W. Siggers, A. Silkov, B. Honig, J. Mol. Biol. 345 (2005) 1027.
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