Computational Biology and Chemistry 49 (2014) 36–44

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Research Article

Affinity of HIV-1 antibody 2G12 with monosaccharides: A theoretical study based on explicit and implicit water models Yuka Koyama a , Kaori Ueno-Noto b , Keiko Takano a,∗ a Department of Chemistry and Biochemistry, Graduate School of Humanities and Sciences, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610, Japan b Center for Natural Sciences, College of Liberal Arts and Sciences, Kitasato University, 1-15-1 Kitasato, Minami-ku, Sagamihara, Kanagawa 252-0373, Japan

a r t i c l e

i n f o

Article history: Received 29 September 2013 Received in revised form 14 January 2014 Accepted 14 January 2014 Available online 4 February 2014 Keywords: HIV-1 antibody 2G12 d-Mannose and d-fructose FMO-PCM In silico ligand structure Solvation effect Binding free energy

a b s t r a c t In order to develop potential ligands to HIV-1 antibody 2G12 toward HIV-1 vaccine, binding mechanisms of the antibody 2G12 with the glycan ligand of d-mannose and d-fructose were theoretically examined. d-Fructose, whose molecular structure is slightly different from d-mannose, has experimentally shown to have stronger binding affinity to the antibody than that of d-mannose. To clarify the nature of dfructose’s higher binding affinity over d-mannose, we studied interaction between the monosaccharides and the antibody using ab initio fragment molecular orbital (FMO) method considering solvation effect as implicit model (FMO-PCM) as well as explicit water model. The calculated binding free energies of the glycans were qualitatively well consistent with the experimentally reported order of their affinities with the antibody 2G12. In addition, the FMO-PCM calculation elucidated the advantages of d-fructose over d-mannose in the solvation energy as well as the entropic contribution term obtained by MD simulations. The effects of explicit water molecules observed in the X-ray crystal structure were also scrutinized by means of FMO methods. Significant pair interaction energies among d-fructose, amino acids, and water molecules were uncovered, which indicated contributions from the water molecules to the strong binding ability of d-fructose to the antibody 2G12. These FMO calculation results of explicit water model as well as implicit water model indicated that the strong binding of d-fructose over d-mannose was due to the solvation effects on the d-fructose interaction energy. © 2014 Elsevier Ltd. All rights reserved.

1. Introduction In physiological systems, a large variety of biological functions are regulated by various interactions between biomolecules. Aiming for the understanding of the functions as well as drug developments, it is necessary to investigate biochemical mechanisms of the interactions that trigger a disease. It is known that the interaction between saccharides and their receptors is involved in many biological systems especially in viral infection (Smith and Helenius, 2004), e.g., influenza virus hemagglutinin–saccharides interaction (Gamblin et al., 2004; Skehel and Wiley, 2000; Zhang et al., 2010). The quantitative analysis of the interaction between saccharides and their receptor by theoretical calculations is challenging because of saccharides’ weaker, but sensitive affinities compared with other biomolecules such as proteins or DNAs. In the present study, we employ the fragment molecular orbital (FMO) method proposed by Kitaura et al. (Kitaura et al., 1999; Fedorov and Kitaura, 2007a). FMO method enables us to evaluate

∗ Corresponding author. Tel.: +81 359785353; fax: +81 59785335. E-mail address: [email protected] (K. Takano). 1476-9271/$ – see front matter © 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compbiolchem.2014.01.013

the physical properties of fragments as well as the interaction between them (Fedorov and Kitaura, 2007a). It is also possible to examine the binding affinity between a ligand and its receptor based on chemical fragments. These days, various investigations of ligands’ interaction with proteins in large biochemical systems have been reported using FMO method (Fukuzawa et al., 2006; Ito et al., 2008; Yamagishi et al., 2010; Ozawa et al., 2011; Nomura et al., 2012), which are summarized in reviews (Fedorov and Kitaura, 2007a; Gordon et al., 2012). With regard to saccharides–protein interaction, FMO calculations on charged saccharides with influenza hemagglutinin (Iwata et al., 2008; Sawada et al., 2007, 2008; Takematsu et al., 2009) and a neutral highmannose ligand complex with griffithsin (Nagata et al., 2012) were recently reported. For the application of calculations to biochemical target, it is important to properly consider solvent effects. Among various continuum solvation models, the polarizable continuum model (PCM) (Tomasi et al., 2005) is one of the most widely used ones. The FMObased PCM was introduced for the energy by Fedorov et al. (2006) and various enhancements of the FMO-PCM method, such as gradient (Li et al., 2010) and pair interaction energy decomposition analysis (PIEDA) (Fedorov and Kitaura, 2012), have been developed.

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Fig. 1. Antibody 2G12–glycan complex and ligand structures (PDB ID: 1OP3). (A) Fab 2G12–mannose complex; (B) d-mannose bound to Fab 2G12.

In 2010, Sawada et al. performed the FMO-PCM calculations at the MP2/6-31G* level to disaccharides complexes with influenza virus hemagglutinin resulted in good agreement with the experimental binding energies (Sawada et al., 2010a, 2010b; Sawada, 2012). HIV infection is a target system of our research, where an interaction of saccharides–protein plays a key role in the infection. In order to elucidate the nature of glycan–protein binding at the molecular level toward the contribution to the medications, we studied monosaccharides bound with the antibody involved in HIV1 infection system by FMO calculations. HIV-1 infection is the etiologic cause of Acquired Immune Deficiency Syndrome (AIDS) and has been investigated since the virus was recognized 30 years ago. At the end of 2010, UNAIDS (Joint United Nations Programme on HIV and AIDS) reported that an estimated 34 million people were living with HIV worldwide and the number of people dying of AIDS-related causes was 1.8 million (AIDS Epidemic Update, 2012). An effective vaccine is, therefore, paramount to combat the epidemic. A remarkable feature of HIV is the dense glycan array that surrounds the exposed envelope antigens. The envelope protein gp120 of HIV-1 is one of the most heavily glycosylated proteins in nature, with many of high-mannose type glycan (Morelli et al., 2011). The glycan epitope of gp120 has been considered as potential antigenic targets for the development of an antibody-based HIV-1 vaccine. The human monoclonal antibody 2G12 is capable of recognizing sugars on the high-mannose carbohydrate of gp120 with high affinity (Calarese et al., 2003). In 2003, Calarese et al. solved X-ray crystal structures of Fab region of 2G12 and its complexes with the disaccharide Man␣1-2Man (Fig. 1) and the high-mannose oligosaccharide Man9 GlcNAc2 (Calarese et al., 2003). Their study indicated the importance of the oligomannose D1 arm in the interaction between gp120 high-mannose and 2G12 (Calarese et al., 2003, 2005). Antigens that resemble these natural high-mannose epitopes of 2G12 would be highly desirable components for an HIV-1 vaccine. In 2010, Davis and his co-workers reported X-ray crystal structures of Fab 2G12 with d-fructose (Doores et al., 2010). They also found that d-fructose had higher affinity with 2G12 than self glycan d-mannose (Doores et al., 2010). From a structural point of view, they investigated the effects of C-5 hydroxyl group of d-fructose on the ligand binding as well as water molecules in the vicinity of the binding site found in the X-ray structure. This non-self glycan could be an important component of a carbohydrate anti-HIV-1 vaccine. Therefore, the understanding of the glycans’ binding mechanisms of the antibody 2G12 is critical in developing HIV-1 vaccines. Details of the antibody–neutral carbohydrate ligand interaction are still unclear. To investigate the glycan ligand binding mechanisms of 2G12, we have shown the physicochemical

picture of the interaction between 2G12 and its high-mannose Man9 GlcNAc2 ligand (Koyama et al., 2013). We herein report the binding free energies of neutral monosaccharides, d-mannose and d-fructose, with HIV-1 antibody 2G12 using FMO-PCM calculations at the MP2/6-31G* level. This is the first application of the FMO-PCM calculations to the HIV-1 system where human HIV-1 antibody 2G12 binds to its ligand saccharides. From an aspect of the saccharide–protein interaction, the higher-level calculation considering solvation effects would be necessary for the appropriate evaluation of this neutral monosaccharids’ moderate interaction. For this objective, explicit water molecules detected in the X-ray structure were also examined extensively by means of pair interaction energy analysis. 2. Computational details 2.1. FMO calculation in the gas phase To elucidate the nature of a higher binding affinity of d-fructose over d-mannose, we carried out FMO calculation utilizing X-ray crystal structures of the Fab 2G12–d-fructose/d-mannose complexes as calculation models. At first we cut out the ligand-binding site from the original X-ray crystal structure in order to reproduce systems with minimum computational loads. The model used in the present study consists of peptides of a binding region of the antibody 2G12 (L-chain Val2-Val110, H-chain Glu1-Lys117) with one monosaccharide ligand. Hydrogen atoms were subsequently added to the model by means of MOE Protonate 3D program under the experimental condition; pH 7.0 and T = 300 K (MOE (The Molecular Operating Environment) Version 2009.10). All the protonated states of histidines of d-mannose–antibody complex (PDB ID: 1OP3) and of d-fructose–antibody complex (PDB ID: 3OAY) were same except H32; positively charged H32 (with hydrogen atoms on the ␦ and ␧ nitrogens, with d-mannose) and neutral H32 (with a hydrogen atom on the ␦ nitrogen, with d-fructose). This difference mainly aroused from the position as well as the direction of the hydroxyl group of the mannose (Figs. 3 and 4). Regarding the glycan ligand, the crystal structure of Fab ˚ was 2G12 with d-fructose (PDB ID: 3OAY, Resolution 1.95 A) utilized for the d-fructose–antibody complex model. The model for d-mannose–antibody complex was prepared using mannose disaccharide–Fab 2G12 complex crystal structure (PDB ID: 1OP3, ˚ The ligand mannose disaccharide was cut into Resolution 1.75 A). monosaccharide d-mannose and protonated without any other refinement for X-ray structure. Using the software Facio (Suenaga, 2008), the peptides of Fab 2G12 proteins were fragmented into mono amino acid residue-fragments, except Cys-S-S-Cys

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pairs (disulfide bonds). In the FMO fragmentation scheme, each carbonyl group of the peptide bond was allocated to the next residue fragment (Yoshioka et al., 2011). Each ligand monosaccharide was treated as one fragment. These fragmentation techniques were applied to all FMO calculations in the present work. All FMO calculations were performed at the MP2/6-31G* level (Hehre et al., 1972) using the GAMESS program package (Schmidt et al., 1993; Fedorov and Kitaura, 2004). Pair interaction energy decomposition analysis (PIEDA) (Fedorov and Kitaura, 2007b) was applied to clarify the characteristics of the interaction between the antibody and the ligand. The pair interaction energy is divided into the electrostatic (ES), exchange-repulsion (EX), charge-transfer plus higher order mixed terms (CT + mix), and dispersion (DI) contributions. There is no entropic contribution in PIEDA scheme. EIJint = EIJES + EIJEX + EIJCT+mix + EIJDI Although Fedorov and Kitaura recently expanded the PIEDA analysis into problems in solution by combining the fragment molecular orbital (FMO) method with the polarizable continuum model (PCM) (Fedorov and Kitaura, 2012), we did not utilize the method because it has not been implemented in the GAMESS program package at this time. It would be considered for further study. 2.2. FMO-PCM calculation To include solvation effects in calculation models, there are two main computational methods, explicit and implicit models. While considering solvents as explicit molecules is the most ideal calculation model, it requires large computational loads. On the other hand, polarizable continuum model (PCM) (Tomasi et al., 2005) implicitly considers the liquid solvation state as a parameter and requires less computational cost. It has been extensively used to introduce solvent effects to the calculation model as mentioned above. Thus, we carried out FMO combined with PCM (FMO-PCM) calculation to examine the binding free energy of d-fructose–2G12 and d-mannose–2G12 complexes in the physiological condition. The antibody 2G12 complexes with d-mannose/d-fructose, free ligands, and the antibody 2G12 were prepared using their X-ray crystal structures (PDB ID: 3OAY, 1OP3) as noted above. In FMOPCM calculations, conductor-like PCM (Cammi and Tomasi, 1995) under water solvent (ε = 78.39) at 298 K was employed. Although biological reactions occur in vivo at around 310 K, the calculation at 298 K was selected for the comparison with the affinity investigation in vitro (Doores et al., 2010). A cavity in the solvent was constructed surrounding the solute with the simplified united ˚ C: 1.77 A, ˚ N: 1.68 A, ˚ O: 1.59 A, ˚ and S: 2.10 A˚ atomic radii H: 0.01 A, (Barone et al., 1997). All FMO-PCM calculations were performed at the MP2/6-31G* level. To consider the interaction as the binding free energy Gbind , we estimated the solute entropic contributions using normal-mode analysis implemented in sander and nmode programs in AMBER10 package (Case et al., 2008). Ten snap-shot structures were extracted every 100 ps from 2 to 3 ns trajectories of the MD simulations of the complex, unbound 2G12 as well as unbound ligand. The binding free energy Gbind was evaluated by following expressions. Gbind = GPCM − TS GPCM = GPCM,complex − GPCM,2G12 − GPCM,ligand S = Ssolute,complex − Ssolute,2G12 − Ssolute,ligand The binding free energy Gbind corresponds to the sum of the binding energy in PCM-FMO scheme GPCM and the entropic

Table 1 Studied ligands and substituents. PDB ID

Original ligand

Ligand compared

Examined ligand substituent

1OP3 3OAY

d-Mannose d-Fructose

Model-ligand Model-ligand

C-1 hydroxyl C-5 hydroxyl

contribution estimated by normal-mode analysis −TS. Each energy component was computed as the difference between the complex and its free systems. The binding free energy in PCM-FMO scheme GPCM is the sum of two energy terms of the binding energy in the gas phase Egas and the solvation energy Gsolvation . GPCM = Egas + Gsolvation Gsolvation shows the change in the solvation free energy during the complex formation, when some surface of the interacting systems is desolvated. The solvation free energy Gsolvation is further divided into five energy components by following equation. Gsolvation = Gpold + Ges + Gcav + Gdisp + Grep Gpold is the destabilization component of the solvent-induced polarization of the solute, Ges is the solute–solvent electrostatic interaction energy, Gcav is the cavitation energy (describing the loss of the solvent free energy necessary to create a cavity for the solute), Gdisp is the solute–solvent dispersion interaction energy, and Grep is the solute–solvent exchange-repulsion interaction energy (i.e., the nonelectrostatic part of the interaction excluding the dispersion). 2.3. Ligand structure investigation To clarify the effect of the difference in the ligand structures between d-mannose and d-fructose on the binding energy Egas , we prepared calculation model complexes with Model-ligand (see Scheme 1). Scheme 1 graphically shows the differences among substituents of monosaccharides investigated in the present study. The difference between d-mannose and d-fructose was the position of one hydroxyl group, at C-1 and C-5, respectively. To analyze the effects of the substituent on the interaction energy in each crystal structure, we prepared a complex with a model-ligand, which was simply modified at the position investigated. The Model-ligand had the structure without hydroxyl group on C-1 nor C-5 position. C-1 hydroxyl substituent effect on the interaction was investigated using the complexes with d-mannose (PDB ID: 1OP3) and those with Model-ligand, which were prepared by substituting C-1 hydroxyl in d-mannose with hydrogen atom. C-5 hydroxyl substituent effect was investigated by calculating the complexes with d-fructose (PDB ID: 3OAY) and those with the Model-ligand. Ligands and substituents examined in the present study are summarized in Table 1. 2.4. Explicit water investigation For further investigation of the solvation energy contribution in the ligand binding mechanism, crystal waters of the Fab 2G12–dfructose complex were considered explicitly. In the X-ray crystal structure of the Fab 2G12–d-fructose complex, there were six water molecules around 5 A˚ from the ligand. We prepared the complex model including those water molecules to examine how they were involved in the ligand–2G12 interaction. For comparison, the Model-ligand–antibody complex with waters’ model was also prepared by modifying the model of d-fructose–antibody complex with six waters by in silico modification module implemented in the MOE program package. Using the module, C-5 hydroxyl group

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Scheme 1.

in d-fructose was changed to hydrogen atom and relaxation for hydrogen atoms of the Model-ligand was performed without any other refinement for heavy atoms in X-ray structure. Crystal water molecules were assigned a number from 1 to 6 (residue names in PDB 3OAY are WAT H242, H252, H259, H275, H451, and H457) (Fig. 2).

3. Results and discussion 3.1. FMO-PCM binding free energy Table 2 lists calculated FMO-PCM binding free energies and those energy components of the glycan–Fab 2G12 complexes.

Fig. 2. Calculation model of d-fructose–Fab 2G12 complex with crystal water molecules at the binding site. d-Fructose and water molecules considered in the calculation are only shown for simplicity.

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Table 2 Glycan–antibody binding free energy and its components (kcal/mol) (MP2-PCM/6-31G*) (−TS was calculated by normal-mode analysis in Amber10 at 300 K using 10 snap shots every 100 ps from 2 to 3 ns trajectories. STE values are shown in the parentheses.). FMO-PCM energy components

d-Mannose d-Fructose (frc-man)

Total FMO-PCM Egas + Gsolv

Entropic term

Total GPCM − TS

Gas phase

Solvation energy components

Egas

Gpold

Ges

Gcav

Gdisp

Grep

Total solvation energy Gsolv

GPCM

−TS

Gbind

−100.3 −88.1 12.1

−9.9 −7.5 2.4

64.5 57.4 −7.0

−12.7 −12.9 −0.2

30.5 29.2 −1.3

−9.0 −8.1 0.9

63.4 58.2 −5.3

−36.8 −30.0 6.8

28.8 (2.2) 17.2 (2.8) −11.5 (3.5)

−8.0 (2.2) −12.8 (2.8) −4.8 (3.5)

Gsolv = Gpold + Ges + Gcav + Gdisp + Grep . GPCM = Egas + Gsolv = Egas + (Gpold + Ges + Gcav + Gdisp + Grep ). Gbind = GPCM − TS.

By comparing the binding free energy Gbind of d-fructose (−12.8 kcal/mol) and d-mannose (−8.0 kcal/mol), d-fructose was theoretically shown to have greater affinity than d-mannose. It was qualitatively consistent with the experimental results that d-fructose bound the antibody 2G12 stronger than the original ligand d-mannose (Doores et al., 2010). This order was attained after considering the solvation energy and entropic contribution. The difference between d-fructose and d-mannose in the binding energy in PCM-FMO scheme (GPCM ) was 6.8 kcal/mol, which was smaller than the difference in the binding energy in the gas phase (Egas , 12.1 kcal/mol). After considering the contribution of entropic term −TS, the absolute value of Gbind of d-fructose (−12.8 kcal/mol) was larger than that of d-mannose (−8.0 kcal/mol), which was consistent with the experimentally observed order. Regarding the solvation free energy components, there were both exothermic and endothermic energy contributions to the ligands’ bindings (Table 2). In solvation energies of the both d-mannose and d-fructose, electrostatic solute–solvent interaction Ges and solute–solvent dispersion energy Gdisp were endothermic energy contributions. These destabilization solvation energies of d-fructose were smaller than that of d-mannose, which were advantageous for d-fructose’s binding over d-mannose. Especially, the electrostatic component Ges was the dominant energy contribution causing the largest difference in the solvation energy components between d-fructose and d-mannose (Ges = −7.0 kcal/mol). On the other hand, solvent-induced polarization of the solute Gpold , cavitation energy Gcav and solute–solvent exchange-repulsion interaction energy Grep were exothermic energies in both ligands’ bindings. These stabilizing solvation energies were more advantageous for d-mannose than d-fructose, however, the contribution to the total solvation energy was smaller than the endothermic penalty of d-fructose’s binding. Namely, the difference in the exothermic energy contribution between d-mannose and d-fructose (Gpold = 2.4 kcal/mol and Grep = 0.9 kcal/mol) was smaller than that in the endothermic contribution (Ges = −7.0 kcal/mol, Gcav = −0.2 kcal/mol, and Gdis = −1.3 kcal/mol). As a whole, the total solvation

free energy was more favorable for d-fructose’s binding (Gsolv = 58.2 kcal/mol) than d-mannose (Gsolv = 63.4 kcal/mol). Although calculations of −TS were carried out using MD simulation and there were standard error (STE) values comparable to the differences of the binding free energy between d-fructose and d-mannose (4.8 kcal/mol), entropic contribution to the binding free energy was also a significant factor to reproduce the experimental results. It should be noted that STE value of the binding free energy differences (3.5 kcal/mol) due to the entropy largely affected the final result (−4.8 kcal/mol). For more accurate evaluation of the binding free energy, STE improvement in the entropy calculated by MD simulation would be necessary. From FMO-PCM binding free energy calculations, we found that the solvation energy and moderate penalty of entropic term were the advantage for d-fructose’s binding to the Fab 2G12.

3.2. Interaction energy and ligand structure investigation in the gas phase In order to analyze how the differences in the structures of dmannose and d-fructose affect their interaction energies with Fab 2G12, complex models with Model-ligand (Scheme 1) were prepared. Ligands and substituents examined here are summarized in Table 1. Since the purpose of the comparison of native ligand with Model-ligand was to assess the substituent effect in the native ligand, d-mannose and d-fructose, on the interaction, the Modelligand was prepared by simply modifying the substituents of the ligand without refinements of the Model-ligand complex. Their interaction energies between the ligand and Fab 2G12 calculated with FMO method were compared with the case of d-mannose/dfructose. It should be noted that the results of FMO calculations were based on FMO fragmentation scheme in which each carbonyl group was allocated to the next residue, so the residue names in Tables 4 and 5 as well as Figs. 2–5 indicate FMO fragments. The substituent effect of C-1 hydroxyl group in d-mannose on the pair interaction energy with Fab 2G12 was initially analyzed. d-mannose had stronger interaction with 2G12 than the

Table 3 Pair interaction energy and the number of hydrogen bonds between glycans and the antibody (kcal/mol) (MP2/6-31G*). Etot

Ees

Eex

Ect

Edi

d-Mannose (PDB ID: 1OP3) Model-ligand (PDB ID: 1OP3)  (d-mannose–Model-ligand)

−151.1 −148.0 −3.1

−150.1 −149.8 −0.4

92.2 91.9 0.3

−41.0 −39.6 −1.4

−52.1 −50.5 −1.6

11 10 1

d-Fructose (PDB ID: 3OAY) Model-ligand (PDB ID: 3OAY)  (d-fructose–Model-ligand)

−135.7 −142.0 6.3

−131.8 −139.4 7.6

83.9 83.8 0.1

−36.2 −35.8 −0.4

−51.5 −50.5 −1.0

11 11 0

15.4

18.3

−8.3

4.8

0.6

0

 (d-fructose–d-mannose)

# H bond

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Table 4 Pair interaction energy between amino acid and d-mannose (kcal/mol) and the number of hydrogen bonds between d-mannose and amino acid fragment in the gas phase. Nine amino acids that had hydrogen bonds with d-mannose and had large energy differences compared with Model-ligand are shown. The deviations from the corresponding values of Model-ligand are also listed in the parentheses. Fragment

Etot

(Etot )

Ees

(Ees )

Eex

(Eex )

Ect

(Ect )

Edi

(Edi )

His H32 Thr H33 Arg H71 Lys H95 Gly H96 Leu H100 Asp H100B Asp H100D Tyr L94

−17.3 −26.4 −4.0 −20.9 −5.9 −2.5 −27.0 −44.2 −10.7

(−5.1) (−0.8) (1.3) (−0.2) (−0.6) (−1.0) (3.1) (2.0) (−0.3)

−13.3 −31.9 −4.0 −15.1 −9.6 0.2 −27.3 −50.9 −10.9

(−4.2) (0.3) (1.3) (−0.2) (−0.5) (−0.3) (2.6) (1.8) (0.0)

4.8 22.8 0.0 5.2 13.8 1.7 8.9 25.4 6.5

(0.4) (0.1) (0.0) (0.0) (−0.1) (0.0) (−0.1) (0.0) (0.0)

−3.7 −8.2 0.0 −3.8 −5.2 −1.4 −4.3 −10.4 −3.1

(−0.7) (−0.8) (0.0) (−0.1) (0.0) (−0.3) (0.4) (0.1) (−0.2)

−5.1 −9.1 0.0 −7.2 −4.9 −3.0 −4.2 −8.3 −3.3

(−0.6) (−0.5) (0.0) (−0.1) (0.0) (−0.3) (0.1) (0.2) (−0.1)

Model-ligand by −3.1 kcal/mol in energy (Table 3). This stronger interaction indicated that C-1 hydroxyl of d-mannose had the stabilizing effect on the antibody binding. We further investigated the pair interaction energy between amino acids and d-mannose. As listed in Table 4 His H32 fragment had the largest contribution of −5.1 kcal/mol to the stabilization energy with C-1 hydroxyl of the ligand among the amino acids. Amino acids having hydrogen bonds with d-mannose are shown in Fig. 3a. The C-1 hydroxyl group points toward the oxygen atom in the carbonyl group of His H32 fragment (see Fig. 3b). This d-mannose interaction with His H32 corresponds to the difference with the Model-ligand in the number of hydrogen bonds as shown in Table 4. In contrast, Asp H100B, Asp H100D, and Arg H71 fragments give the positive Etot values and thus it means weaker interactions with d-mannose than those with the Model-ligand. These results indicated that C-1 hydroxyl group of d-mannose brought both advantage and disadvantage to the interaction with amino acids, and as a whole, played as a stabilization substituent in the ligand binding. We also compared the glycan–antibody pair interaction energies of d-fructose and of the Model-ligand (Table 3). It indicates that d-fructose had weaker interaction with 2G12 than the Modelligand (Etot = 6.3 kcal/mol). According to the PIEDA analysis, C-5 hydroxyl group of d-fructose contributed to the weaker interaction energy with 2G12 than that of Model-ligand, especially in the electrostatic energy (Ees = 7.6 kcal/mol). As stated in the structural investigation, C-5 hydroxyl group in d-fructose formed an additional direct hydrogen bond with the oxygen atom in the carbonyl

# H bond 2(1) 2(0) 0(0) 1(0) 2(0) 0(0) 1(0) 2(0) 1(0)

group of Ser H100A, which caused the stabilization of the ligand (Doores et al., 2010). Pair interaction energy between d-fructose and Asp H100B fragment in which the carbonyl group of Ser H100A residue was allocated corresponded to that interaction (see Table 5 and Fig. 4). While Asp H100B fragment had significant interaction energy with d-fructose (−22.1 kcal/mol), it was weaker than that of the Model-ligand by 7.0 kcal/mol. In addition, there was no difference between d-fructose and the Model-ligand in the number of hydrogen bond with amino acids (Table 5). These results indicated that the strong interaction between d-fructose and 2G12 was not due to the C-5 hydroxyl group-amino acid interaction. It was different from the effect of C-1 hydroxyl group in d-mannose, which brought direct stabilization interactions to the binding. Next, the binding energy in the gas phase Egas , having the largest contribution in ligands’ binding free energies (Table 2), between d-fructose and d-mannose were compared. Pair interaction energies of Fab 2G12 with d-mannose/d-fructose are listed in Table 3. The total energy originated from three stabilization energies, electrostatic, charge transfer and dispersion energies, and one destabilization component of exchange repulsion. In every energy component, d-fructose had smaller interaction energies in absolute value than d-mannose. Electrostatic interaction energy was the dominant stabilization components causing the largest difference between d-mannose and d-fructose (Ees = 18.3 kcal/mol). Meanwhile, dispersion interaction energy of d-fructose, −51.5 kcal/mol, was comparable to d-mannose, −52.1 kcal/mol.

Fig. 3. d-Mannose and amino acids in the active site. Hydrogen bonds between d-mannose and amino acids are shown as dot lines. (a) Distances between His H32 fragment and C-1 hydroxyl group are shown (Å) (b).

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Table 5 Pair interaction energy between amino acid and d-fructose (kcal/mol) and the number of hydrogen bonds between d-fructose and amino acid fragment in the gas phase. Nine amino acids that had hydrogen bonds with d-mannose and had large energy differences compared with Model-ligand are shown. The deviations from the corresponding values of Model-ligand are also listed in the parentheses. The number of hydrogen bonds for Model−ligand was the same as that of d-fructose. Fragment

Etot

(Etot )

Ees

(Ees )

Eex

(Eex )

Ect

(Ect )

Edi

(Edi )

# H bond

His H32 Thr H33 Lys H95 Gly H96 Arg H99 Asp H100B Asn H100C Asp H100D Tyr L94

−10.4 −28.4 −20.3 −4.4 1.4 −22.1 −1.9 −35.8 −12.3

(0.2) (−0.5) (0.7) (0.0) (−0.7) (7.0) (−1.0) (2.4) (−2.1)

−6.2 −30.1 −14.9 −5.6 1.5 −19.7 1.2 −44.6 −16.5

(0.3) (0.3) (0.5) (−1.0) (−0.8) (6.8) (−0.8) (2.2) (−1.1)

2.9 18.4 4.2 9.3 0.0 6.0 2.6 23.3 14.0

(0.0) (0.1) (0.0) (0.1) (0.0) (0.4) (0.0) (−0.1) (−0.2)

−3.0 −7.4 −3.2 −3.7 0.0 −3.8 −2.2 −7.2 −5.2

(−0.1) (−0.6) (0.2) (0.0) (0.0) (0.2) (0.0) (0.2) (−0.5)

−4.1 −9.3 −6.4 −4.4 −0.1 −4.6 −3.5 −7.4 −4.7

(0.0) (−0.3) (0.1) (0.0) (0.1) (−0.4) (−0.3) (0.2) (−0.3)

1 2 1 2 0 2 0 2 1

3.3. Explicit water investigation Evaluations of solvation effects using PCM calculations showed that the solvation free energy was more advantageous for d-fructose’s binding to the antibody than d-mannose’s. PCM calculation is a useful way to introduce solvent effect implicitly. In some cases, however, it cannot evaluate where and how much explicit solvent molecules play significant roles in a system (Fedorov and Kitaura, 2007a). In the X-ray experimental study, several watermediated interactions between amino acids and d-fructose were observed (Doores et al., 2010). Doores et al. noted that solvent water molecules engaged in the d-fructose–2G12 complex (Doores et al., 2010). These results indicate that analyses of the solvents as explicit water molecules will provide a profound insight into the solvation effect on the d-fructose–2G12 binding. Thus, we evaluated how explicit water molecules contributed to the interaction between dfructose and the antibody 2G12 as well as the model-ligand and the antibody. Fig. 5 graphically shows the pair interaction energies among the ligand (d-fructose), waters, and amino acids at the binding site. It corresponds to the three-dimensional structure depicted in Fig. 2. The interaction energies of the Model-ligand are also shown in parentheses. Fig. 5 shows amino acids, which had pair interaction energy with d-fructose more than −5.0 kcal/mol (His H32, Thr

H33, Lys H95, Asp H100B, Asp H100D, and Tyr L94 fragments), and the values of “water-mediated” pair interaction energies among d-fructose, amino acids, and water molecules over −3.0 kcal/mol. The ligand structure is depicted as d-fructose in Fig. 5 though the calculations were performed on both d-fructose and Model-ligand complexes. Crystal water molecules 1–6 were also depicted (see Fig. 2). Asp H100B fragment had significant interaction energies with d-fructose (−20.6 kcal/mol), H2 O 3 (−12.0 kcal/mol) and H2 O 4 (−3.3 kcal/mol). In addition to those pair interaction energies, notable pair interaction energy between H2 O 3 and d-fructose (−4.7 kcal/mol) was observed, which could contribute to the stabilization of the ligand binding to Asp H100B in the active site. This interaction could be unique for the d-fructose–Fab 2G12 interaction, since H2 O 3 located in the vicinity of the C-5 hydroxyl group in d-fructose (C-5 hydroxyl group is absent in d-mannose) (see Scheme 1 and Fig. 2). Our results suggested that H2 O 3 also served as the stabilization factor of Asp H100D fragment–d-fructose interaction, which was not indicated by the experimental study though. Large interaction energies were observed between d-fructose and His H32 fragment (−10.5 kcal/mol) as well as between H2 O 2 and His H32 fragment (−7.9 kcal/mol). Nevertheless, there were no significant pair interaction energy between H2 O 2 and d-fructose

Fig. 4. d-Fructose and amino acids in the active site. Hydrogen bonds between d-fructose and amino acids are shown as dot lines. (a) Distances between Asp H100B fragment and the pyranose ring of d-fructose are shown (Å) (b).

Y. Koyama et al. / Computational Biology and Chemistry 49 (2014) 36–44

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Fig. 5. Pair interaction energies of d-fructose and Model-ligand (in the parentheses) with each amino acid fragment at the ligand binding site including water molecules (kcal/mol) (FMO-MP2/6-31G*). Amino acid fragments which had pair interaction energy with d-fructose more than −5.0 kcal/mol (His H32, Thr H33, Lys H95, Asp H100B, Asp H100D, and Tyr L94 fragments) and more than −3.0 kcal/mol pair interaction energies among amino acids, water molecules, and the ligand are shown.

(−0.1 kcal/mol, not shown in Fig. 5). It was reported that the C-5 hydroxyl in d-fructose formed water-mediated hydrogen bonds with the carbonyl groups in the peptide bond between His H32 and Ala H31, however, our result indicated that watermediated hydrogen bond between d-fructose and the carbonyl group did not directly contribute to the d-fructose’s binding to 2G12. Although the experimental study suggested the significant interaction between the hydroxyl group of Tyr L94 and H2 O 5, the pair interaction energy between Tyr L94 fragment and H2 O 5 was moderate (−1.9 kcal/mol, not shown in Fig. 5) compared to the other pair interaction energies shown in Fig. 5. H2 O 1 located near the oxygen atom of the d-fructopyranose ring had large pair interaction energies with d-fructose (−10.2 kcal/mol), Tyr L94 fragment (−3.6 kcal/mol), and Thr H33 fragment (−3.1 kcal/mol). This water molecule (H2 O 1) was found in the Fab 2G12 complex with d-mannose (PDB ID: 1OP3). The calculated interaction energy of d-mannose with the ligand (−10.7 kcal/mol, data not shown) was comparable to the one for d-fructose. Thus, this watermediated interaction did not relate directly to the higher affinity of d-fructose. Finally, in comparison with d-fructose, the pair interaction energies of the Model-ligand with the water molecules, H2 O 3 (+2.7 kcal/mol shown in the parentheses in Fig. 5) and H2 O 5 (−2.3 kcal/mol) which located in the vicinity of the C-5 hydroxyl group in d-fructose described above, were insignificant. This result indicated essential role of C-5 hydroxyl group of d-fructose in the water-mediated d-fructose–Fab 2G12 interactions.

4. Conclusions We calculated the binding free energy between the dmannose/d-fructose with the antibody 2G12 considering the solvation free energy as implicit model (FMO-PCM) at the MP2/631G* level. The stronger binding affinity of d-fructose over the original ligand of d-mannose was theoretically examined and natures of the ligand binding were clarified. The calculation results were well consistent with the experimentally observed order that d-fructose had higher binding affinities with Fab 2G12 than that of d-mannose. The FMO-PCM calculation along with MD simulations elucidated the advantage of d-fructose over d-mannose in the solvation energy as well as the entropic penalty terms. To clarify the nature of differences in the binding energy between d-fructose and d-mannose, the binding energy in the gas phase were further analyzed. We constructed Fab 2G12 complexes with the Model-ligand in which substituent C-1 hydroxyl of dmannose or C-5 hydroxyl of d-fructose were modified to hydrogen. It was found that C-1 hydroxyl group in d-mannose played as the stabilization substituent in the ligand binding where His H32 of the antibody mainly engaged in the stabilization. On the other hand, this was not the case with C-5 hydroxyl in d-fructose. By comparing the results obtained with d-fructose and the Model-ligand calculations, we found that C-5 hydroxyl group in d-fructose contributed as destabilization factor in the Fab 2G12 binding. Thus, the higher binding affinity of d-fructose does not arise from the direct interaction energy between the C-5 hydroxyl group in the ligand and Fab 2G12.

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The solvation energy that provided the superior binding affinity with d-fructose was further investigated by considering solvation effect with the explicit water model. FMO calculations with crystal water molecules showed notable pair interaction energies among water molecules, amino acids, and d-fructose which contributed to the stabilization of the ligand binding to 2G12. These FMO calculation results of explicit water model as well as implicit water model indicated that the strong binding of d-fructose over d-mannose was due to the solvation effects on the d-fructose interaction energy. An essential first step and challenge toward a vaccine development by theoretical calculations is the reproduction of experimental results. Our calculation result that was qualitatively well consistent with experimental order only came after considering both the solvent effect in high-level FMO calculations and entropic contributions. This study provides the fundamental knowledge of the ligand–antibody interaction analysis by theoretical calculations toward a vaccine design. Acknowledgements A part of the calculations reported in the present study were performed using computing resources in the Research Center for Computational Science, Okazaki, Japan. This work was supported by JSPS KAKENHI Grant Number 24500363. References AIDS Epidemic Update, 2012. Joint United Nations Programme on HIV/AIDS. United Nations, Geneva. Barone, V., Cossi, M., Tomasi, J., 1997. A new definition of cavities for the computation of solvation free energies by the polarizable continuum model. J. Chem. Phys. 107, 3210–3221. Calarese, D.A., Lee, H.K., Huang, C.Y., Best, M.D., Astronomo, R.D., Stanfield, R.L., Katinger, H., Burton, D.R., Wong, C.H., Wilson, I.A., 2005. Dissection of the carbohydrate specificity of the broadly neutralizing anti-HIV-1 antibody 2G12. Proc. Natl. Acad. Sci. U. S. A. 102, 13372–13377. Calarese, D.A., Scanlan, C.N., Zwick, M.B., Deechongkit, S., Mimura, Y., Kunert, R., Zhu, P., Wormald, M.R., Stanfield, R.L., Roux, K.H., 2003. Antibody domain exchange is an immunological solution to carbohydrate cluster recognition. Science 300, 2065–2071. Cammi, R., Tomasi, J., 1995. Remarks on the use of the apparent surface charges (ASC) methods in solvation problems: Iterative versus matrix-inversion procedures and the renormalization of the apparent charges. J. Comput. Chem. 16, 1449–1458. Case, D., Darden, T., Cheatham Iii, T., Simmerling, C., Wang, J., Duke, R., Luo, R., Crowley, M., Walker, R.C., Zhang, W., 2008. AMBER 10. University of California, San Francisco, pp. 32. Doores, K.J., Fulton, Z., Hong, V., Patel, M.K., Scanlan, C.N., Wormald, M.R., Finn, M., Burton, D.R., Wilson, I.A., Davis, B.G., 2010. A nonself sugar mimic of the HIV glycan shield shows enhanced antigenicity. Proc. Natl. Acad. Sci. U. S. A. 107, 17107–17112. Fedorov, D.G., Kitaura, K., 2004. The importance of three-body terms in the fragment molecular orbital method. J. Chem. Phys. 120, 6832–6840. Fedorov, D.G., Kitaura, K., 2007a. Extending the power of quantum chemistry to large systems with the fragment molecular orbital method. J. Phys. Chem. A 111, 6904–6914. Fedorov, D.G., Kitaura, K., 2007b. Pair interaction energy decomposition analysis. J. Comput. Chem. 28, 222–237. Fedorov, D.G., Kitaura, K., 2012. Energy decomposition analysis in solution based on the fragment molecular orbital method. J. Phys. Chem. A 116, 704–719. Fedorov, D.G., Kitaura, K., Li, H., Jensen, J.H., Gordon, M.S., 2006. The polarizable continuum model (PCM) interfaced with the fragment molecular orbital method (FMO). J. Comput. Chem. 27, 976–985. Fukuzawa, K., Mochizuki, Y., Tanaka, S., Kitaura, K., Nakano, T., 2006. Molecular interactions between estrogen receptor and its ligand studied by the ab initio fragment molecular orbital method. J. Phys. Chem. B 110, 16102–16110. Gamblin, S.J., Haire, L.F., Russell, R.J., Stevens, D.J., Xiao, B., Ha, Y., Vasisht, N., Steinhauer, D.A., Daniels, R.S., Elliot, A., Wiley, D.C., Skehel, J.J., 2004. The structure and receptor binding properties of the 1918 influenza hemagglutinin. Science 303, 1838–1842. Gordon, M.S., Fedorov, D.G., Pruitt, S.R., Slipchenko, L.V., 2012. Fragmentation methods: a route to accurate calculations on large systems. Chem. Rev. 112, 632–672.

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