New Fragmentation of Fragment Molecular Orbital Method
Applicable to Fragment Based Drug Design
Chiduru Watanabe 1, Kaori Fukuzawa 1, 2, Yoshio Okiyama 1, Takayuki Tsukamoto 1, 2, Akifumi Kato 2,Shigenori Tanaka 3, Tatsuya Nakano 1, 4, and Yuji Mochizuki 1, 5
1Institute of Industrial Science, The University of Tokyo, Japan
2
Mizuho Information & Research Institute Inc., Japan
3
Graduate School of System Informatics, Department of Computational Science, Kobe University, Japan
4
Division of Medicinal Safety Science, National Institute of Health Sciences, Japan
5
Department of Chemistry & Research Center for Smart Molecules, Faculty of Science, Rikkyo University, Japan1

Introduction

Estrogen receptor (ER), which is a ligand-dependenttranscription factor, is an important drug target of breast cancer.
Inter-fragment interaction energy (IFIE) analysis based on theab initio fragment molecular orbital (FMO) method has revealed
ligand binding mechanism of the ER [1, 2]. The IFIE is one of
the advantages of FMO method and can represent detailed
interactions at the amino acid residue and the ligand levels. On
the other hand, the IFIE analysis for each ligand binding site at
the functional unit (e.g., by fragmentation of ligand) will bevaluable to Fragment Based Drug Design (FBDD). However, aligand fragmentation in the two-body FMO (FMO2) method has
not kept appropriate accuracy to discuss chemical reactions.
Recently, the four-body corrected fragment molecular orbital(FMO4) method [3, 4] was developed and applied with highaccuracy to the subdivision into main and side chain fragments,
which are smaller than conventional main chain fragment.
Following this, we attempt to perform the FMO4 calculation byusing the fragmentation of ligand distinguishing each functionalgroup along with the fragmentation of protein divided into mainand side chains. In this study, the IFIE of complex between ERand 17-estradiol (EST) was analysed at the FMO4-MP2/6-31G
level with new fragmentation in FBDD context.
2
2.1

and 50 residues of ER around EST, at the FMO4-MP2/6-31G
level with the ABINIT-MP program [4].
2.2

New Fragmentation applicable to FBDD

Fig. 1 shows fragmentation of protein: (a) Main and (b)Main/Side chains. Each amino acid residue of ER was divided
into main and side chain fragments in order to discriminate theircontributions. In Fig. 2, the ligand was split into two fragments,EST(1) and EST(2) including “A ring” and “D ring” of steroidal
EST, respectively, along with two ligand binding sites of EST,
as shown in green and orange areas.

MethodFMO4 method

A brief description of the ab initio FMO4 method [3] is given
here. In the FMO4 method, a molecule or a molecular cluster isdivided into small fragments, and the MO calculations on eachfragment monomer, dimer, trimer, and tetramer are performed toobtain the properties of the whole system. The many-bodyeffects are considered through the environmental electrostatic
potentials. The total energy of FMO4 calculation was given by~~E FMO4   EI   EIJ   EIJK II JI J KFig. 1. Fragmentation of protein (a) Main chain and (b)Main/Side chain~ EI J K L

IJKL

where E I is monomer energy without the environmental~~~

electrostatic potential, E IJ , E IJK and E IJKL are two-body,there-body and four-body inter-fragment interaction energies
and I, J, K, and L are fragment indices. Intermolecularinteraction between ER and EST was calculated by apharmacophore model, which consists of EST, a water molecule,Fig. 2. (a) Ligand binding network of ER-EST complexand (b) Fragmentation of ligand

3Results

43.1

Accuracy of total energy of FMO2, FMO3, andFMO4 calculations with new fragmentation
Table 1 lists the total energy errors of FMO2, FMO3, andFMO4 calculations with the fragmentations of Main andMain/Side chains for protein and that of Model1 and 2 forligand, where the reference energies (in units of hartree) by theFMO calculations with the conventional Main chain
fragmentation are included. It is clear that the accuracies ofFMO2 calculations are not chemically sufficient at all levels.
The accuracy of FMO4-HF/STO3-G calculations with theMain/Side chain fragmentations is equivalent to that of FMO3
calculation with the conventional Main chain fragmentation.
These tendencies of energy errors more significantly appear at
HF and MP2 levels with 6-31G basis. Here, the total energies ofModel1 and Model2 are not very different. Thus, it is reasonable
to employ FMO4 calculation instead of FMO2/3 calculation inorder to perform the Main/Side chain and the ligand
fragmentations. Next, we show intermolecular interactions
between ER and each functional group of EST by using theFMO4-IFIE analysis with the Main/Side chain and the ligand(Model1) fragmentations.

Conclusion

The FMO4 calculation with the new fragmentations ofprotein and ligand was performed for ER-EST complex in orderto quantitatively reveal the key substructures of amino acidresidue (main and side chains) and functional groups of ligand(EST(1) and EST(2)) with important roles for the ligand binding
mechanism. In order to subdivide fragments into smaller ones,
we confirmed that the total energy of FMO4 calculation is more
appropriate than that of FMO2/3 calculation. The FMO4-IFIEs
between ER and EST revealed that the functional group
including “A ring” of EST (EST(1)) interacts with the main
chain of Thr347 and the side chains of Glu353, Arg349, andPhe404; EST(2) including “D ring” of EST interacts mainlywith the side chain of His524. Thus, the FMO4 calculation isavailable for analysis of intermolecular interaction for eachligand binding site at the functional unit. In addition, the FMO4IFIE analysis with the new fragmentation and CHPI analysis [5]will be useful to specify a weak interaction such as CH/interaction. Altogether, the FMO4-IFIE analysis by using thefragmentation of ligand may be helpful in drug discovery forFBDD.

Table 1. Total energy of FMO2, FMO3 and FMO4 calculations
c-e

Fragmentation
ProteinDifference of total energy (hartree)

Ligand

FMO2

FMO3

FMO4cHF/STO-3G ( Rerefence of total energy: -22578.9424 hartree)
ac0.0167-0.0010Main chain
Nob

Main/Side chain-cNo

10.1236-0.0068

0.0024cModel1

10.1247-0.0066

0.0027cModel2

10.1256-0.0065

0.0028

Acknowledgementsd

HF/6-31G ( Rerefence of total energy: -22855.8634 hartree)
ad-0.0227
0.0032Main chain
Nob

Main/Side chainba

Main/Side chain-dNo

10.0978-0.0423-0.0028dModel110.0988-0.0421-0.0027dModel210.1007-0.0420-0.0028

MP2/6-31G (eRerefence of total energy: -22898.2895 hartree)
ae-0.0026-0.0001
Main chain
Noe

Noe
Model1eModel210.3742
10.3776
10.3797-0.0479-0.0461-0.0462-0.00150.0002-0.0001b

Divided at C atoms. Divided at C and C atoms.
Compared with the FMO4 calculation at each level with theconventional Main chain fragmentation.
c-e

3.2

Fig. 3. FMO4-IFIEs at MP2/6-31G level of EST(1) and EST(2)Inter fragment Interaction between ER and EST

Fig. 3 shows the FMO4-IFIEs of EST(1) and EST(2) withsurrounding residues. Subscripts of residue name, “M” and “S”,are show the Main and Side chain fragments, respectively (e.g.
Thr347M and Glu353S). Either EST(1) or EST(2) are coloured
yellow, and the attractive and the repulsive interactions arecoloured red and blue, respectively. The ligand binding
mechanism of ER was elucidated in detail by analyzing theinteractions between each functional group of EST and either
main or side chain of each amino acid residue. EST(1) interacts
with the main chain of Thr347, the side chains of Glu353,
Arg394, and Phe404. In contrast, EST(2) interacts mainly withthe side chain of His524. Thus, the intermolecular interactions
between ER and EST at each ligand binding site are specified by
the FMO4-IFIE analysis with the new fragmentation.

The authors would thank Mr. Katsumi Yamashita for technicalsupport. This research was done in “Research and Developmentof Innovative Simulation Software” project supported by
Research and Development for Next-generation Information
Technology of Ministry of Education, Culture, Sports, Scienceand Technology (MEXT).
References[1] K. Kitaura, E. Ikeo, T. Asada, T. Nakano, M. Uebayasi,Fragment molecular orbital method: an approximate
computational method for large molecules, Chem. Phys.
Lett., 313, 701-706 (1999).
[2] K. Fukuzawa, Y. Mochizuki, S. Tanaka, K. Kitaura, and T.
Nakano, Molecular Interactions between Estrogen Receptor
and Its Ligand Studied by the ab Initio Fragment MolecularOrbital Method, J. Phys. Chem. B, 110, 16102-16110(2006).
[3] T. Nakano, Y. Mochizuki, K. Yamashita, C. Watanabe, K.
Fukuzawa, K. Segawa, Y. Okiyama, T. Tsukamoto, S.
Tanaka, Development of the four-body corrected fragment
molecular orbital (FMO4) method, Chem. Phys. Lett., 523,128–133 (2012).
[4] BioStation 6.0: ABINIT-MP and BioStation Viewer. The
program package is due to be released.
[5] Y. Umezawa, S. Tsuboyama, K. Honda, J. Uzawa, M.
Nishio, CH/ interaction in the conformation of organic
compounds. A database study, Tetrahedron, 55, 1004710056 (1999).