Approximate calculation of the binding energy between 17 β -estradiol and human estrogen receptor alpha
AApproximate calculation of the binding energy between 17 β -estradiol andhuman estrogen receptor alpha Ricardo Ugarte a) Instituto de Ciencias Quimicas, Facultad de Ciencias, Universidad Austral de Chile. Independencia 641, Valdivia,Chile.
Estrogen receptors (ERs) are a group of proteins activated by 17 β -estradiol. The endocrine-disrupting chemi-cals (EDCs) mimic estrogen action by bind directly to the ligand binding domain of ER. From this perspective,ER represent a good model for identifying and assessing the health risk of potential EDCs. This ability isbest reflected by the ligand-ER binding energy. Multilayer fragment molecular orbital (MFMO) calculationswere performed which allowed us to obtain the binding energy using a calculation scheme that considers themolecular interactions that occur on the following model systems: the bound and free receptor, 17 β -estradioland a water cluster. The bound and free receptor and 17 β -estradiol were surrounded by a water shell contain-ing the same number of molecules as the water cluster. The structures required for MFMO calculations wereobtained from molecular dynamics simulations and cluster analysis. Attractive dispersion interactions wereobserved between 17 β -estradiol and the binding site hydrophobic residues. In addition, strong electrostaticinteractions were found between 17 β -estradiol and the following charged/polarized residues: Glu 353, His 524and Arg 394. The FMO2-RHF/STO-3G:MP2/6-31G(d) weighted binding energy was of -67.2 kcal/mol. Wehope that the model developed in this study can be useful for identifying and assessing the health risk ofpotential EDCs. I. INTRODUCTION
The chemical industry is introducing around 700 syn-thetic compounds on the market every year . Thesechemicals come on top of the 85000 substances listed inthe EPA’s chemical inventory. These compounds have avery wide range of applications and humans will come incontact to most of them through various routes. Theymay take a long time to degrade into harmless products.Some may not break down and persist in the environ-ment. A large number of synthetic chemicals have beenshown to damage wildlife populations, and pose large-scale hazards to human health . Despite their negativeeffects, humanity is increasingly dependent on syntheticchemicals. According to the UN, output will grow seventimes faster than the global population between 1990 and2030 . This chemical explosion is perhaps one of the mostformidable challenges confronting mankind today .Nuclear receptors (NRs) are evolutionary conservedintracellular proteins responsible for transmitting exter-nal signals to the cell nucleus. Most of these proteinsact as ligand-inducible transcription factors and respondto endogenous (endobiotics) and exogenous (xenobiotics)chemicals in order to regulate gene expression. NRs af-fect a variety of biological functions, such as reproductivedevelopment or detoxification of foreign substances andfatty acid metabolism. NRs mediate chemical communi-cation between different organs via the endocrine system,but also the interaction between organisms and their en-vironment. They act as xenosensors and endocrine regu-lators, which connect and integrate endogenous hormone-regulated functions with external dietary and/or environ-mental stimuli . a) Electronic mail: [email protected]
Figure 1. Chemical structure of 17 β -estradiol ( C H O ) The endocrine system is sensitive to stimulationsby low concentrations of hormones. Chemicals act-ing as endocrine-disrupting chemicals (EDCs) , eithernatural or synthetic, alters the hormonal and homeo-static systems that enable the organism to communi-cate with and respond to its environment. EDCs af-fect the endocrine system by mimicking natural hor-mones, antagonizing their action or modifying theirsynthesis, metabolism and transport. A large num-ber of industrial chemicals have polycyclic aromaticstructures which confer them the ability to bindNRs involved in steroid hormone metabolism. TheseEDCs include synthetic chemicals used as industrialsolvents/lubricants and their byproducts (polychlori-nated biphenyls, polybrominated biphenyls, dioxins),plastics (bisphenol A), plasticizers (phthalates), pes-ticides (methoxychlor, dichlorodiphenyltrichloroethaneor DDT), fungicides (vinclozolin), and pharmaceuticalagents (diethylstilbestrol). Natural chemicals found inhuman and animal food chains (e.g., phytoestrogens, in-cluding genistein and coumestrol) can also act as en-docrine disruptors .A large range of xenobiotics have been found to bindand activate estrogen receptors (ERs), a group of pro- a r X i v : . [ q - b i o . B M ] J u l teins activated by the sex steroid hormone 17 β -estradiol(E2) (Figure 1). Two subtypes of ER exist: ER α andER β , which are members of the nuclear receptors su-perfamily. Both ER subtypes possess a modular organi-zation that is characteristic of the NRs; five functionaldomains from the N- to C-termini, designated A/B, C(DNA-binding domain, DBD), D, E (ligand-binding do-main, LBD), and F . Numerous crystal structureshave been determined for the LBDs of both subtypes,and these have given a detailed insight into the structureand alterations during the ligand binding. The structureof ER LBD reveals a conserved core of twelve α -helicesand a short two-stranded antiparallel β -sheet arrangedinto a three-layered sandwich fold; this arrangement gen-erates a mostly hydrophobic cavity in the lower part ofthe domain which can accommodate the ligand (Figure2). Since different classes of compounds might bind toER LBD and elicit hormone-like effects in humans, ERrepresent a good model system for identifying and as-sessing the health risk of potential EDCs. This ability isbest reflected by the ligand-ER binding energy. A num-ber of experimental and theoretical studies have beenperformed to investigate the ligand-ER interaction − ,and since 1997 about 100 crystal structures of ER LBDwith several ligands have been solved and deposited inthe Research Collaboratory for Structural Bioinformatics(RCSB) Protein Data Bank (PDB). On the basis of theabove information, the mode of binding between ERs andtheir ligands has been determined. The specific recogni-tion between ER and its ligand mainly depends on hy-drogen bonds and hydrophobic contacts .Most of the theoretical studies which use the structuresdeposited in RCSB PDB are carried out using molecu-lar dynamics (MD) simulations. These simulations arebased on empirical force fields that may not be accurateenough to predict ligand-ER binding energies. Accuracyrequirements could be provided by ab initio quantummechanical calculations, but these can be very compu-tationally expensive and time consuming. The hybridQM/MM (quantum mechanics/molecular mechanics) isa method that combines the precision of quantum me-chanics and the speed of empirical force fields. In thisapproach, part of the system that includes the chemicallyrelevant region is treated quantum mechanically (QM)while the remainder, often referred to as the environ-ment, is treated at the classical level using empirical ormolecular mechanics (MM) force fields. This multiscaleapproach reduces the computational cost significantly ascompared to a QM treatment of the entire system andmakes simulations possible . An efficient alternativeto either the full ab initio QM, MM or QM/MM, lies inthe fragment-based methods, which form an actively de-veloped field of research . Fragment Molecular Orbital(FMO) method is one such method that has beenused for efficient and accurate QM calculations in verylarge molecular systems . FMO involve fragmenta-tion of the chemical system, and from ab initio or den-sity functional quantum-mechanical calculations of each Figure 2. Model of ER α LBD (ribbon) complexed with EST(ball and stick) . The model based on the RSCB PDB crystalstructure (PDB code 1A52) includes 258 amino acid residues. fragments (monomers) and their dimers (and trimers ifgreater accuracy is required) one can construct the totalproperties. The distinctive feature of FMO is the inclu-sion of the electrostatic field from the whole system ineach individual fragment calculation, and in using thesystematic many-body expansion. The FMO method issuited to various analyses, as it provides information onfragments and their interactions that are naturally builtinto the method.In the present article, we report a study on an ap-proximate calculation of the binding energy between 17 β -estradiol and LBD of human estrogen receptor alpha inaqueous medium. Briefly, the main steps of the calcula-tion are as follows: 1) Search for representative structuresof the conformational space around the crystallographicstate of E2-ER α LBD by means of MD simulations andcluster analysis; 2) Geometry optimization of the repre-sentative structures using QM/MM approach; 3) Singlepoint FMO calculation on the optimized structures inorder to obtain the inter-fragment interaction energies.In general, the same steps were applied to other relatedmodel systems (vide infra).
II. METHODSA. Model Building
Crystal structure of the ER α LBD in complex withE2 (PDB code 1A52) were downloaded from the RSCBPDB . The model was constructed from chain A of thehomodimer. Atomic coordinates for missing amino acidresidues (297-305, 545-554), missing heavy atoms and hy-drogen atoms, were reconstructed with the LEaP mod-ule of AmberTools 15 package . AMBER FF14SB forcefield was selected for the proteins and general AMBERforce field (GAFF) parameters were employed for E2.In order to parameterize E2, electrostatic potential wascalculated by Gaussian 09 program at the HF/6-31G(d)level of theory . Partial charges were fitted by RESPmethod of the Antechamber module of AmberTools 15 .Arg, Lys, Asp, Glu residues were modeled as chargedspecies, all tyrosines as neutral, and histidine residueswere modeled according to information obtained fromanother source . Three of the 13 residues of histidine,were protonated in order to preserve the electroneutral-ity of the system. The N- and C-terminus residues wereprotonated and deprotonated, respectively. The modelwas solvated with TIP3P water in a pre-equilibrated boxmeasuring 111 x 100 x 62 ˚A . The E2-ER-W system con-tains 258 amino acid residues (4190 atoms), E2 and 19979water molecules (W). The total number of atoms in thesystem is 64171. E2-ER-W was subjected to three suc-cessive steps of minimization using the SANDER moduleof the AmberTools 15. First, 1000 steps of steepest de-scent followed of 1500 steps of conjugate gradient, allow-ing only H atoms and water to move while holding therest of the system fixed. Next, the same minimizationalgorithm is used as the previous one, but allowing onlyE2-ER-W to move. Finally, the whole system was min-imized without any restraints for 2000 steps of steepestdescent followed by 1000 steps of conjugate gradient. B. Molecular Dynamics Simulations
All simulations were carried out with the SANDERmodule of the AmberTools 15 with periodic boundaryconditions, using Particle Mesh Ewald method to treatlong-range electrostatics interactions with a non-bondedcutoff of 12 ˚A. All bonds involving hydrogen atoms wererestrained using the SHAKE algorithm. Temperatureregulation was done using a Langevin thermostat withcollision frequency of 1 ps − . The Berendsen barostatwas used for constant pressure simulation at 1 atm, witha relaxation time of 1 ps. The time step was 1 or 2fs. The final energy-minimized system (E2-ER-W) wasthen submitted to the following protocol:Scheme 1: [0 →
310 K: 100 ps 1 fs NVT] −→ [310 K:500 ps 2 fs NPT] −→ [310 → . By combining the sampling ability ofthe multiple trajectories, we expect to sample more conformational space than single trajectory of the samelength. The aforementioned restart file was used as seedfor 30 short-time simulations that obey the protocolestablished in Scheme 2:Scheme 2: [5 →
150 K: 30 ps 1 fs NVT] −→ [150 →
310 K:70 ps 1 fs NPT] −→ [310 K: 500 ps 1 fs NVE]The initial velocities (Scheme 2) were assigned ran-domly from a Maxwell-Boltzmann distribution at 5 K.The trajectories start with the same structure and differonly in the initial velocity assignment. At the end of theequilibration, from ∼
40 ps NPT ensemble, the averagetemperature of the final 30 ps was 310 K, and the averagedensity was 1.0 g/ml. All production runs of 0.5 ns wereperformed in an NVE ensemble at 310 K.
C. Cluster Analysis
Cluster analysis methods have been developed for an-alyzing simulation trajectories of biomacromolecules andused for the analysis of their conformational behaviorin solution . These methods group together similarconformers from molecular simulations. A clustering ap-proach based on the C α -RMSD (root mean square devia-tion) was applied to the snapshots of the MD simulations.We selected the alpha carbon atoms because they de-scribe the backbone conformations. The C α -RMSD wascalculated after rigid body alignment of C α atoms of eachframe of the trajectory with respect to C α atoms of theaverage structure of the protein. Prior to clustering, theindividual E2-ER-W trajectories from the 30 short-timesimulations were combined into a single file and the wa-ter molecules removed. In our analysis, 15000 snapshotswere grouped into five clusters. Each cluster is describedby a centroid structure, which in itself is not physicallysignificant as it is effectively a mathematical constructbased on the members of a cluster. However, the ac-tual structure closest to the centroid (rmsd) is significantand representative of each cluster. Therefore, each ofthese structures corresponds to snapshots of the MD tra-jectory. Thus, five representative structures (E2-ER) ofeach cluster, and therefore of the conformers population,were obtained . Finally, from E2-ER we return to thecorresponding E2-ER-W representative structures. D. QM/MM Optimization
All E2-ER-W systems representative of the populationwere subjected to geometry optimization using Gaus-sian 09 at the MM/Amber level of theory. Then, to fa-cilitate the QM/MM calculations, the water moleculesbeyond 10 ˚A of the protein surface were deleted us-ing VMD program . As a consequence, new modelsystems (E2-ER-w) with a water layer of 10 ˚A aroundof receptor surface were generated. ONIOM, a hy- Figure 3. FMO2 calculation model: ∆ E Binding = (cid:104) ∆ E E − ER − wInteraction + ∆ E wInteraction (cid:105) − (cid:104) ∆ E ER − wInteraction + ∆ E E − wInteraction (cid:105) brid QM/MM method implemented in Gaussian 09, withelectronic embedding was used for the geometry opti-mization of E2-ER-w model systems. Electronic embed-ding procedure best describes the electrostatic interac-tion between the QM (E2) and MM (ER-w) regions,because it includes the partial charges of the MM re-gion into the quantum mechanical Hamiltonian. In thisway, the wave function of the QM region can be polar-ized. In the present study we used a two-layer ONIOM(B3LYP/6-31+G(d):AMBER) scheme: E2 (B3LYP/6-31+G(d)); ER-w(AMBER). E. Related Model Systems
In order to calculate the binding energy we also re-quire ER-w, E2-w and water (w) model systems (Figure3). ER-w and E2-w are derived, respectively, of MD sim-ulations of ER-W and E2-W systems. Practically thesame protocol described in the methods section was re-quired to obtain five representative ER-w structures andtwo representative E2-w structures. In addition, by re-moving 17 β -estradiol from E2-ER-w and E2-w followedby optimizing the geometries of the resulting systems atthe appropriate level of theory, five new ER-w and twow model systems were obtained. F. FMO Calculations
Fragment-based approaches allude to the chemical ideaof parts of the system retaining their identity to a largeextent (e.g., functional groups and residues). FMOmethod not only reduces the computational cost, butit also provides a wealth of information on the proper-ties of fragments and their interactions. In this study,the calculation of the binding energy is based on ob-taining the following interaction energies between pairof fragments: E2-amino acid residue (est-aa), E2-water(est-wat), amino acid residue-amino acid residue (aa-aa),amino acid residue-water (aa-wat) and water-water (wat- wat). These pair interaction energies (PIEs) will be com-puted in the following model systems: ER-w, E2-w, E2-ER-w and w (Figure 3).The energy expression in the two-body FMO expansion(FMO2) is : E = N (cid:88) I E I + N (cid:88) I>J ( E IJ − E I − E J ) (1)The total energy E of the system is written as the sumof the monomer energies E I , and the pair interaction en-ergies ( E IJ − E I − E J = ∆ E IJ ), where E IJ is the energyof the dimer made of two fragments I and J . The orderof the fragments in the FMO input file is very important:water → ER amino acid residues → β -estradiol. LetA = number of water fragments, B = number of water+ amino acid residue fragments and C = total numberof fragments (water + amino acid residue + E2). Ac-cording to the above schema and the FMO2 calculationmodel (Figure 3):∆ E Binding = [ E E − ER − w + E w ] − [ E ER − w + E E − w ] (2) E E − ER − w = N = C (cid:88) I =1 E I + N = C (cid:88) J =1 I>J ∆ E IJ (3) E w = N = A (cid:88) I =1 E I + N = A (cid:88) J =1 I>J ∆ E IJ (4) E ER − w = N = B (cid:88) I =1 E I + N = B (cid:88) J =1 I>J ∆ E IJ (5) Table I. Number of fragments in the model systemsFragments ER-w E2-w E2-ER-w w17 β -estradiol 1 1Amino acid residue 257 257Water 5153 5153 5153 5153Total 5410 5154 5411 5153 E E − w = N = A (cid:88) I =1 E I + E A +1 + N = A (cid:88) J =1 I>J ∆ E IJ + N = A (cid:88) J =1 ∆ E ( A +1) J (6)We assume that the monomer energies are practicallyindependent of the model systems and since these termsare subtracted from each other, then:∆ E Binding = N = C (cid:88) J =1 I>J ∆ E IJ + N = A (cid:88) J =1 I>J ∆ E IJ − N = B (cid:88) J =1 I>J ∆ E IJ − N = A (cid:88) J =1 I>J ∆ E IJ − N = A (cid:88) J =1 ∆ E ( A +1) J (7)The right-side terms of equation (7) represent sumsof pair interaction energies (PIEs). For the purpose ofsimplifying notation:∆ E Binding = (cid:104) ∆ E E − ER − wInteraction + ∆ E wInteraction (cid:105) − (cid:104) ∆ E ER − wInteraction + ∆ E E − wInteraction (cid:105) (8)From the FMO output file we obtain the values of theterms on the right-side of the previous equation. TheAFO (adaptive frozen orbitals) scheme was used through-out for fragmentation across peptide bonds, with the de-fault settings for bond definitions. The fragmentation ofthe model system was as follows: The first two aminoacid residues and each remaining amino acid residue ofER, 17 β -estradiol molecule, and the water molecule weretreated as a single fragment. Table I shows the numberof fragments in the different model systems.For the binding energy (∆ E Binding ) calculation thepart of the system that is of particular interest corre-sponds to the ligand and the binding site. In FMO,one can address this by using multilayer FMO (MFMO),when several fragments are assigned to a higher layer.Wavefunctions and basis sets can be defined separatelyfor each layer. In this work we used the two-layer two-body FMO method: FMO2-RHF/STO-3G:MP2/3-21Gand FMO2-RHF/STO-3G:MP2/6-31G(d) level of theory. For example, the latter means the two-layer two-bodyFMO method with layer 1 (environment) described byRHF and the STO-3G basis set, and layer 2 (E2 andbinding site) described by MP2 and the 6-31G(d) basisset .The binding site consists of all residues that have atleast one atom within 3.5 ˚A from any 17 β -estradiol atomin E2-ER-w. This generally gives a good representationof the important residues in the binding pocket of a pro-tein. The amino acids residues that form the binding siteof E2-ER-w and ER-w are: Leu 346, Leu 349, Ala 350,Glu 353, Leu 384, Leu 387, Met 388, Leu 391, Arg 394,Phe 404, Met 421, Ile 424, Leu 428, Gly 521, His 524,Leu 525, Met 528. The binding site was constructed byusing the ArgusLab software . III. RESULTS AND DISCUSSION
In cluster analysis, 15000 snapshots from MD simu-lations were processed and grouped into five (E2-ER-w,ER-w) and two (E2-w) clusters. Thus, representativestructures (RS) of each cluster, and therefore of the con-formers population, were obtained (Table II). The popu-lation of each cluster is important for the calculation ofa weighted binding energy.
A. Binding energy using ER-w structures from MDsimulations of ER-W system
Table II shows the cluster population of each systemand the symbol assigned to their representative struc-tures. Because E2 is a relatively rigid molecule, its pop-ulation of conformers could be described by only two RS(X, Y). In order to calculate the binding energy, all pos-sible combinations between RS were made. For exam-ple, Aω X X symbolizes the following calculation scheme(Figure 3): 1 + X → A + ω X . In this notation ω X is thewater representative structure obtained from X.Table III shows the binding energies calculated at theFMO2-RHF/STO-3G:MP2/3-21G level of theory. As wecan see there is a large dispersion in the binding energyobtained with the proposed calculation scheme; the ex-treme values are the result of the remarkable differenceof the interaction energies, ∆ E E − ER − wInteraction − ∆ E ER − wInteraction ,between some of the RS (data not shown). The basisof this dispersion is structural and is corroborated bythe protein backbone RMSD between pairs of superim-posed representative structures: E2-ER-w//ER-w. TheRMSD across all 258 pairs of amino acids on the twentyfive combinations (A//1, A//2... E//5) of the RS wasmeasured. By averaging all these measurements, the cal-culated RMSD mean value is 5.0 ± . This flexibility of the ter-minal ends has a strong impact on the aa-aa, aa-wat andwat-wat interactions. Table II. Cluster Analysis of MD trajectories in the different model systems(MS). E2-ER-w ER-w E2-wCP ( a ) ( b ) A B C D E 1 2 3 4 5 X Y ( a ) Cluster population. ( b ) Representative structure of the respective clus-ter.
Although the calculation scheme combining the rep-resentative structures obtained through the MD simula-tions (except for ω X or ω Y which derives directly from Xor Y) seems reasonable and unbiased, it fails to calculatethe binding energy. B. Binding energies using ER-w structures from ofE2-ER-w model system
Table IV shows the binding energies calculatedat the FMO2-RHF/STO-3G:MP2/3-21G and FMO2-RHF/STO-3G:MP2/6-31G(d) level of theory. The bind-ing energy calculation schema is analogous to the above.For example, Aω X aX symbolizes the following calcula-tion scheme: a + X → A + ω X . Here, ”a” (without quotes)stands for the representative structure derived from A byprior elimination of 17 β -estradiol.All binding energy values are negative which, at leastat this level of calculation, would indicate a certain sta-bility of the system; furthermore, the dispersion in thevalues lie within a normal range. The RMSD mean valueobtained from the RMSD measurements on the five en-sembles (A//a... E//e) is 0.035 ± .In an FMO study of ER α LBD in complex with17 β -estradiol (PDB code 1ERE), the model system in-cluded 241 amino acid residues, one water moleculewhich directly mediates ER-E2 binding (where the hy-drogen bonded water molecule was included in the re-ceptor) and E2. The binding energy was estimated from:∆ E Binding = E E − ER − ( E ER + E E ). The total energies(E) were considered in the calculation and the geome-tries of ER and E2 were fixed in those found in E2-ERmodel system. The reported binding energy was -37.65kcal/mol at FMO2-RHF/STO-3G level of theory . Inanother FMO study with the same model system, FMO2interaction energy between E2 and ER was calculatedusing HF and MP2 methods with several basis sets .The calculated interaction energy was -40.26 kcal/mol atFMO2-RHF/6-31G(d) and -123.73 kcal/mol at FMO2- Figure 4. 17 β -estradiol in the binding site of ER with impor-tant amino acid residues. Four water molecules are present,and one of them (cylinder) links E2 and Leu 387. The fig-ure corresponds to the A representative structure and it wasmade with the ArgusLab software . MP2/6-31G(d) level of theory. The large interaction en-ergy difference between the RHF and the MP2 meth-ods is due to dispersion interaction, which can only bedescribed by electron correlation methods. In general,charged and polarized amino acid residues interact ei-ther strongly or weakly with the ligand, while hydropho-bic residues contribute to weak interactions. The sum ofthese weak dispersion interactions makes the differencebetween both methods.The interaction energies of E2 with each residuefragment of the ER binding site at the FMO2-RHF/STO-3G:MP2/3-21G and FMO2-RHF/STO-3G:MP2/6-31G(d) level of theory are shown in Figure 5.In all model systems, regardless of the calculation level,we observe that Glu 353 and His 524 are very stablestructures. These residues present a strong electrostaticinteraction with E2, and it is known that together withArg 394, they form a hydrogen bond network with E2.A water molecule is similarly responsible for yet anotherstabilizing hydrogen bond between E2 and the ER(Figure 4) . Therefore, the interactions between E2and these residues, together with the hydrogen bonds,play a key role in the E2-ER binding.Many binding site hydrophobic residues are stabilized(attractive interaction) through dispersion interactionswith E2. Therefore, the MP2 electron correlation is es-
Table III. FMO2-RHF/STO-3G:MP2/3-21G binding energy ( a ) (BE) of the differentcombinations between the representative structures.Model BE Model BE Model BE Model BE Model BE Aω X X Bω X X Cω X X Dω X X Eω X X -46.1 Aω Y Y Bω Y Y Cω Y Y -16.1 Dω Y Y Eω Y Y -64.3 Aω X X Bω X X Cω X X -87.3 Dω X X Eω X X -135.5 Aω Y Y Bω Y Y Cω Y Y -105.5 Dω Y Y Eω Y Y -153.7 Aω X X -95.3 Bω X X -131.1 Cω X X -308.7 Dω X X Eω X X -356.9 Aω Y Y -113.5 Bω Y Y -149.3 Cω Y Y -326.9 Dω Y Y Eω Y Y -375.1 Aω X X Bω X X Cω X X -154.3 Dω X X Eω X X -202.5 Aω Y Y Bω Y Y Cω Y Y -172.5 Dω Y Y Eω Y Y -220.7 Aω X X -13.6 Bω X X -49.4 Cω X X -227.0 Dω X X Eω X X -275.2 Aω Y Y -31.8 Bω Y Y -67.6 Cω Y Y -245.2 Dω Y Y Eω Y Y -293.4 ( a ) All Energies in kcal/mol.Table IV. FMO2-RHF/STO-3G:MP2/3-21G & FMO2-RHF/STO-3G:MP2/6-31G(d) binding (BE)and interaction energy ( a ) (∆ E int ).FMO2-RHF/STO-3G:MP2/3-21GWeighted Binding Energy = -84.2Weighted ∆ E int = -92.3Model Aω X aX Aω Y aY Bω X bX Bω Y bY Cω X cX Cω Y cY Dω X dX Dω Y dY Eω X eX Eω Y eY BE -71.7 -89.9 -73.7 -91.9 -80.5 -98.7 -79.7 -97.9 -85.3 -103.5RS ( b ) A B C D E∆ E int -93.0 -88.6 -105.7 -91.3 -101.8FMO2-RHF/STO-3G:MP2/6-31G(d)Weighted Binding Energy = -67.2Weighted ∆ E int = -73.6Model Aω X aX Aω Y aY Bω X bX Bω Y bY Cω X cX Cω Y cY Dω X dX Dω Y dY Eω X eX Eω Y eY BE -54.6 -72.8 -57.4 -75.6 -66.9 -85.1 -62.1 -80.3 -64.0 -82.2RS A B C D E∆ E int -74.3 -69.6 -85.4 -74.0 -79.2 ( a ) Sum of all PIEs between 17 β -estradiol and each amino acid residue fragment in the ERbinding site. All Energies in kcal/mol. ( b ) Representative structure. sential to characterize these interactions, whose func-tion is possibly to accommodate the substrate at thehydrophobic binding pocket (Figure 4). Important hy-drophobic residues at the binding site are: Leu 346, Leu387, Leu 391, Phe 404 and Leu 525 . The behaviourof the Arg 394 PIE (Figures 5) with respect to the restof the amino acid residues is remarkable. In the latter,the behaviour is quite conservative; whereas in Arg 394it fluctuates from -12.4 to 5.0 kcal/mol and from -7.5 to4.6 kcal/mol, at FMO2-RHF/STO-3G:MP2/3-21G andFMO2-RHF/STO-3G:MP2/6-31G(d) level of theory, re-spectively. The above suggests that perhaps Arg 394could play a stabilizing-destabilizing role in the interac-tion between E2 and the ER binding site. According tothis hypothesis, conformational changes in the receptorcould influence the behavior of Arg 394, which would pos-sibly determine both the entry and exit of E2 from thebinding site.During the simulation a number of water moleculeswere trapped at the binding site. Table V shows the in-teraction energy calculated at the FMO2-RHF/STO-3Glevel of theory between E2 and each water fragment inthe ER binding site. The number of water molecules varies according to the representative structure and, atthis level of calculation, the interactions can be either at-tractive or repulsive. It was observed that only in the rep-resentative structure of the most populated cluster (A) awater molecule makes a bridge between E2 and Leu 387through the hydrogen bonds (∆ E int = -4.05 kcal/mol).The negative value in the interaction energy of the otherstructures (C, E) corresponds to an interaction by hydro-gen bond between the 17 β -OH group (D ring) of E2 anda water molecule.One shortcoming of this study is that we do not con-sider the binding site as a dynamic entity, subject tochange. These, are intrinsic to the dynamics of the sys-tem itself. The binding site is defined by the distancebetween E2 and the corresponding amino acid residue,and this distance is modified in the course of the sim-ulation. Therefore, some residues will cease to belongto the binding site, while others, which initially did notbelong, will become part of the binding site (Table VI).The above is also relevant for water molecules. We hopeto address this inconsistency in a future study.We have shown that if the structure representing thefree receptor (ER-w) differs significantly from that of the Figure 5. PIEs (kcal/mol) between 17 β -estradiol and each amino acid residue fragment of the ER binding site for each of therepresentative structures. Glu 353, Arg 394 and Hie 524 are charged/polar residues; the remaining residues are hydrophobic.Table V. FMO2-RHF/STO-3G interaction energy ( a ) (∆ E int ).RS ( b ) A B C D EWater fragment 4 1 3 2 3∆ E int -4.05 0.87 -4.01 1.38 -4.80 ( a ) Sum of all PIEs between E2 and each water frag-ment in the ER binding site. ( b ) Representativestructure. All Energies in kcal/mol. bound receptor (E2-ER-w), the binding energy calcula-tions are not reliable. However, if we obtain the freereceptor from the respective bound receptor, the valuesof the binding energy are less dispersed and seeminglyreliable. In this particular case, the backbone RMSD isvery small between both representative structures; thatis, the conformations are very similar. The justificationfor the second calculation scheme is somewhat supportedby the conformational selection model, which postulatesthat the native state of a protein does not exist as a sin-gle, rigid conformation but rather as a ensemble of con-formers that coexist in equilibrium with different popu-lation distributions, and that the ligand can bind selec-tively to the most suitable conformer. In other words,the free protein can sample with a certain probabilitythe same conformation as that of the bound protein . Ifwe accept the above hypothesis, it is permissible to de-rive the free receptor from the bound receptor. Finally,we must mention that although it is true that the repre-sentative structures obtained from the independent MDsimulations of both systems differ significantly from eachother and, therefore, contradict one of the premises of theconformational selection, the reason for this possibly liesin the fact that the extension of the sampled space is in- sufficient for the free system. Increasing conformationalsampling of the free receptor will likely allow to obtainstructures more similar to those of the bound receptor. IV. CONCLUSIONS
The molecular interactions between 17 β -estradiol andER were calculated, and from these the binding energywas obtained. Two different schemes were used for thecalculation of the binding energy. In the first scheme, thefree receptor used in the calculations is obtained from MDsimulations, and the results are not reliable as the energyvalues are highly dispersed. This failure is a consequenceof the lack of structural similarity between the represen-tative structures of the free and the bound receptor. Thesecond scheme, which produces reliable results, uses thestructure of the free receptor obtained directly from thebound receptor by removal of E2. The above procedure isconsistent with the conformational selection model. Wethink that by increasing the conformational sampling ofthe free receptor it is possible to obtain structures similarto those of the bound receptor; indeed, if this were thecase, we could provide reasonable theoretical evidence infavor of the conformational hypothesis.In general, attractive dispersion interactions were ob-served between E2 and all surrounding hydrophobicresidues. These interactions play an important role instabilizing E2 at the binding site. Water molecules werefound at the binding site of all representative structures;in one of them (A), a water molecule makes a bridgebetween E2 and Leu 387 through the hydrogen bonds.Strong electrostatic interactions were observed betweenthe E2 and the following charged/polarized residues: Glu Table VI. Effect of the simulation on the amino acid residue ( a ) composition of theER binding site. The following original residues remained at the binding site: Leu346 → Leu 525. The binding site consists of all residues that have at least oneatom within 3.5 ˚A from any E2 atom in E2-ER-w model system. (∆ E int ).RS A B C D EMet 528 ( b ) Met 528 Met 528Met 343 Met 343 Met 343 Met 343Aa residue Leu 327Phe 425Thr 347 Thr 347Trp 383 ( a ) Charged/Polar residues are indicated by underlined characters. The remain-ing residues are hydrophobic. ( b ) Original amino acid residue. β -estradiol and ER LBD tend to forman enzyme-substrate complex and therefore validates ourcalculation model based on interactions. We hope thatthe model developed in this study can be useful for iden-tifying and assessing the health risk of potential EDCs. ACKNOWLEDGEMENTS
I wish to express my gratitude to each and every per-son who has contributed to the development and main-tenance of free and open source software. I thank Dr.Robin Mesnage for English assistance and constructivecomments on the manuscript.
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