Geometry optimization of steroid sulfatase inhibitors - the influence on the free binding energy with STS
In the paper we review the application of two techniques (molecular mechanics and quantum mechanics) to study the influence of geometry optimization of the steroid sulfatase inhibitors on the values of descriptors coded their chemical structure and their free binding energy with the STS protein. We selected 22 STS-inhibitors and compared their structures optimized with MM+, PM7 and DFT B3LYP/6–31++G* approaches considering separately the bond lengths, angles, dihedral angles and total energies. We proved that different minimum energy conformers could be generated depending on the choice of the optimization method. However, the results indicated that selection of the geometry optimization method did not affect the optimal STS inhibitor coordinates, and hence the values of molecular descriptors which describe the 3D structure of the molecule. To study the interaction pattern of the STS inhibitors (optimized using different methods) with the target receptor we applied two strategies: AutoDock and PathDock. The docking studies point out that selection of software to docking simulation is one of the crucial factors determining the binding mode of STS inhibitors with their molecular target. Other factor is related to the ligand orientation in the binding pocket. Finally, obtained results indicate that MM+ and PM7 methods (faster and less expensive) could be successfully employed to geometry optimization of the STS inhibitors before their docking procedure as well as for molecular descriptors calculations.
KeywordsSteroid sulfatase inhibitors Geometry optimization Molecular docking Molecular mechanics Quantum mechanics
Over the past decades, numerous reports have suggested that the biologically active hormone precursors may affect on cellular proliferation in various cancers . These compounds (including androgens and estrogens) play an important role in the development of many diseases, such as hormone-dependent breast cancer (HDBC) . One approach for treatment of the HDBC involves inhibitors of enzymes responsible for the biosynthesis of estrogens in peripheral tissues, e.g., steroid sulfatase (STS) . The STS catalyses the hydrolysis reaction of steroid sulphates to their active forms and therefore plays a crucial role in the formation of biologically active hormones. The STS hydrolyses, among other, estrone sulfate (E1S) and dehydroepiandrosteronesulfate (DHEAS) into estrone (E1) and dehydroepiandrosterone (DHEA), respectively. The detailed studies have shown that E1 and DHEA can act as precursors for the formation of the estrogenic steroids estradiol (E2) and androstenediol (Adiol) . Furthermore, the wide distribution of the STS in various tissues indicates that the STS enzyme is involved in numerous physiological and pathological conditions .
The described above process of development of new steroid sulfatase inhibitors is expensive, time consuming, and requires collaboration of experts from different disciplines, such as: biology, chemistry, biochemistry, pharmacology, etc. However, according to recently recommended ideas in designing new drugs , this challenging process could be supported by a computational chemistry [12, 13]. The computer-aided drug design (CADD) is a valuable and promising tool , especially in the contexts of the rational drug discovery. Recently, the world’s major pharmaceutical and biotechnology companies more frequently follow the effectiveness strategies that allow reducing the costly failure of pharmaceutical candidates in clinical trials by applying different types of the computational techniques .
The computational methods employed in drug discovery can be classified into two main approaches: ligand-based drug design (LBDD) and structure-based drug design (SBDD) [15, 16, 17]. The first approach is applicable in the absence of information regarding the 3D structure of target molecules . In this case, the quantitative-structure activity relationships (QSAR)  and pharmacophore modelling  could be applied. The presence of experimentally determined structure of target molecule would allow following the second type of methodology. This includes the molecular docking (MD) , QM-Polarized Ligand Dicking (QPLD)  or/and the three-dimensional quantitative-structure activity relationships (3D QSAR) [22, 23].
In the presented work, the application of the SBDD approach for the rational designing of new steroid sulfatase inhibitors is verifying. Due to the fact that the initial step both in molecular docking and 3D QSAR modelling involves the geometry optimization of the STS inhibitors, the main goal of our study (the first step according to application of SBDD) is to: (i) compare the geometries of the STS inhibitor structures after the optimization with methods differ in theory level; (ii) evaluate the impact of the geometry optimization on the values of descriptors coded chemical structure of STS inhibitors, and then, (iii) verify if the method applied to optimize the structures influence their free binding energy with the STS protein.
Comparison of the STS-inhibitors’ geometries obtained at different theory level
After geometry optimization we performed a Wilcoxon’s tests for examining if the selected optimization methods influence the average bond lengths of the studied STS inhibitors. Subsequently, in order to obtain a deeper insight into the geometry optimization of selected compounds we compared individually their bond lengths, angles and dihedral angles at used data obtained in all calculations’ levels (MM+, PM7, DFT B3LYP/6–31++G*).
The influence of the geometry optimization on the values of descriptors coded the chemical structure of the STS inhibitors
For compounds optimized at different theory level we calculated the 3D so-called molecular descriptors (840 descriptors), which describe the three dimensional structure of a particular compound. The descriptors were calculated with Dragon (version 6.0) software . Then, we performed a series of statistical calculation (Wilcoxon’s tests) for examining if the selected optimization methods influence on the descriptors’ values. In this way, we were able to establish if the differences between value descriptors were significant.
The influence of the geometry optimization on the free binding energy of steroid sulfatase inhibitors with STS – molecular docking
The X-ray structure of the human steroid sulfatase (STS) was taken from the Protein Databank (PDB ID: 1P49) and prepared for docking using the following procedure: (i) the catalytic amino acid FGly75 (formylglycine) was converted to the gem-diol form using the Discovery Studio visualizer (http://accelrys.com/products/collaborative-science/biovia-discovery-studio/visualization.html), (ii) the waters of crystallization were removed from the structure, (iii) polar hydrogen atoms were added to the protein, and (iv) gasteiger charges were added to each atom and the non-polar hydrogen atoms were merged to the protein structure employing Autodock Tools 1.5.6. .
The distance between donor and acceptor atoms that form a hydrogen bond was defined as 1.9 Å with a tolerance of 0.5 Å, and the acceptor–hydrogen–donor angle was not less than 120°. The structure was then saved in PDB file format for PatchDock docking and in PDBQT file format for docking studies in Autodock Vina 1.1.2 software , (http://autodock.scripps.edu/resources/references).
The STS inhibitors presented in Table 1 (optimized at above describe three levels of theory: (i) MM+, (ii) PM7 and (iii) DFT B3LYP 6–31++G*) were analysed in order to select compounds structurally similar to 667-COUMATE that was thoroughly studied according to mode of inhibitor binding to STS . Hierarchical cluster analysis (HCA) with Euclidian distances and Ward’s method of linkage  was applied. Selected inhibitors were saved as PDB file format for input to PatchDock software . To carry out docking study in AutodockVina 1.1.2 software, all the ligand structures were saved also in PDBQT file format in Autodock Tools 1.5.6. .
The docking of the optimized inhibitors into the prepared rigid structure of the human steroid sulfatase protein was performed using the Autodock Vina 1.1.2 software . For all the docking studies, a grid box size of 30 Å × 30 Å × 30 Å centred on the Cβ atom of the amino acid FGly75 was used. The centre of the box was set at ligand centre and grid energy calculations were carried out. For the AutoDock docking calculation, default parameters were used and the 20 docked conformations were generated for each compound. The energy calculations were performed employing the genetic algorithms (GAs). All dockings were taken into 2.5 million energy evaluations for each of the test molecules. In order to verify the reproducibility and validation of the docking calculations, 667-COUMATE was submitted as reference molecule for one-ligand run calculation. The active pocket consisted of identical amino acid residues for 667-COUMATE from literature  suggesting that this method is valid enough to be used for docking studies of other test ligands. Docking of all ligands to protein was performed using AutoDock following the same protocol used for reference compound. Docked ligand conformations were analysed in terms of energy, hydrogen bonding, and hydrophobic interaction between ligand and receptor protein human STS.
The PatchDock  is geometry-based molecular docking open source web software designed to find docking transformations facilitating excellent molecular shape complementarity. Such transformations, when applied, induce both wide interface areas and small amounts of steric clashes which ensured to include numerous matched local features of the docked molecules that have complementary characteristics. Therefore, we decided to use PatchDock docking to compare the results of AutoDock and make the study using the approach proved to be more accurate one.
As it is a web-based software, both the prepared rigid protein and ligands saved in the PDB format were uploaded. Followed by root mean square deviation (RMSD) value set to 1.5 clustering is applied to the candidate solutions to discard redundant solutions. Each candidate transformation is further evaluated by a scoring function that considers both geometric fit and atomic desolvation energy . The geometric score, the desolvation energy, the interface area size and the actual rigid transformation of the solution were provided in the output file to judge the best possible docked conformations. The main reason behind PatchDock’s high efficiency is its fast transformational search, which is driven by local feature matching rather than brute force searching of the six-dimensional transformation space.
Finally, we compared the free binding energy from the docking calculations with the experimental values. This was performed in order to investigate the influence of the geometry optimization method on the free binding energy of the ligand and the STS active site.
Results and discussion
Comparison of geometries of STS-inhibitors obtained at different theory level
The geometries of the 22 steroid sulfatase inhibitors (see Table 1) were optimized with application of two methods differing in theory level. We have applied: (i) the molecular mechanics using the MM+ force field and the Polak-Ribiere conjugate gradient algorithm terminating at the gradient of 0.05 kcal mol−1 Å−1; (ii) the quantum-mechanics using semi-empirical PM7 level; and DFT B3LYP with the 6–31++G* basis set. The application of DFT B3LYP 6–31++G* method for coumarin derivatives was previously verified [36, 37].
Results of Wilcoxon test for comparison of average bond lengths of each STS-inhibitor
MM+ vs. PM7
MM+ vs. DFT B3LYP 6-31++G*
PM7 vs. DFT B3LYP 6-31++G*
Due to the fact that there are differences in geometries suggesting that optimization method influences the type of conformer creation, we decided to evaluate the energies of structures obtained in each optimization. Therefore, we have calculated for each structure its total energy.
Comparison of total energy calculated with the DFT B3LYP 6–31++ G* method for geometries obtained at different theory levels
Method of geometry optimization
Total energy ×10−6 [kJ mol−1]
Moreover, we have compared also the geometry of compounds optimized with MM+/DFT B3LYP/6–31++G* approach with the previously applied ones. According to the obtained results, Figures S1-S3, one can notice that the choice of the applied method poses the highest impact on the dihedral angles between planes including the central atom that can be rotated (e.g. dihedral angle created by atoms of functional group of compound j). Taking into account that the total energies computed for STS-inhibitors are similar, as we have proven above, one can conclude that the method of optimization has impact on the type of molecular conformer creation [36, 42]. The application of the PM7 and the DTF B3LYP/6-31++G* approach allow obtaning the same conformer. Application of the method based on molecular mechanics forces the creation of another type of conformer.
The influence of the geometry optimization on the values of the descriptor coded chemical structure of the STS inhibitors
In order to obtain deeper insight into the geometry optimization results we have performed further analysis that tested the influence of the chosen optimization method (MM+, PM7, DFT B3LYP/6-31++G*) on the molecular descriptor values. In the comparison study we chose descriptors, which might be affected by the 3D structure of the molecule. We selected groups of 3D descriptors such as: Radial Density Function descriptors (RDF), 3D-MOlecule Representation of Structures based on Electron diffraction (3D-MoRSE), Weighted Holistic Invariant Molecular descriptors (WHIM), GEometry, Topology and Atom-Weight Assembly descriptors (GETAWAY), Molecular properties and Drug-like indices. Then, each group of selected descriptors was divided into smaller sub-groups connected to their weighting scheme (unweighted (u), weighted by mass (m), by van der Waals volume (v), by Sanderson electronegativity (e), by polarizability (p), by ionization potential (i), and by I-state (s). Afterwards, we have compared descriptor values for each STS inhibitor with its analogue from the sub-group optimized with different optimization methods. We have applied a series of statistical Wilcoxon’s tests (at 1% level of confidence). The number of performed test was equal to the number of the descriptor’s sub-group for each STS inhibitor.
Summarizing, we have proved that the selection of the geometry optimization method did not affect the optimal STS inhibitor coordinates, and hence the values of molecular descriptors which describe the 3D structure of the molecule. This trend was noticed in most classes of calculated 3D descriptors. In the next step, in order to verify, if the optimization methods influence the binding mode of the STS inhibitor to the active site we performed further analysis.
The influence of the geometry optimization on the free binding energy of the steroid sulfatase inhibitors with STS – molecular docking
To compare the influence of the inhibitors’ geometries on their free binding energy with the steroid sulfatase we have selected inhibitors structurally similar to 667-COUMATE that was proven to bind with the binding pocket of the protein . The selection was performed with the application of HCA with Euclidian distances and Ward’s method of linkage . The similarities were analysed in space of the topological descriptors.
Meticulous analyses of the ligand-receptor interactions were carried out, and final coordinates of the ligand and receptor were saved. The Discovery Studio visualizer (http://accelrys.com/products/collaborative-science/biovia-discovery-studio/visualization.html) was employed for display of the receptor with the ligand-binding site. The docking of the inhibitors of the human STS with the receptor (1P49) exhibited well-established bonds with one or more amino acids in the receptor active pocket. The active pocket consisted of amino acid residues as Leu74, Arg98, Gly100, Val101, Leu167, His290, His346, Lys368, Asn447, Val 486 and Phe488.
Docking results for MM+ optimized geometries
Docking results for PM7 optimized geometries
Docking results for DFT B3LYP/6-31++G* optimized geometries
Docking results for MM+ optimized geometries
Docking results for PM7 optimized geometries
Docking results for DFT B3LYP/6-31++G* optimized geometries
Molecular docking results
ΔG (AuthoDock) (kcal mol−1)
ΔG (PathDock) (kcal mol−1)
ΔGa (kcal mol−1)
Analyses of Table 4 and Fig. 11 suggest that the PathDock approach is a more adequate method to study the free binding energy of STS-inhibitors with their molecular target. In the case of AutoDock the residuals between binding energies calculated by means of experimentally measuring the IC50 value and the ones computed in docking procedure are much more significant (e.g. residual for m compound optimized with MM+ method docked by means of AutoDock is equal to almost 10 kcal mol−1, while in the case of PathDock it is only 2,67 kcal*mol−1). Thus, based on our results the PathDock docking software is more recommended to study binding of STS-inhibitors with the STS protein.
According to the PathDock results, it was interesting to point out that the best agreement between the computed free binding energy and the experimentally measured ones (the lowest residuals observed in Fig. 11) is in the case of derivatives optimized with the MM+ method. However, differences in residuals obtained for compounds optimized with different approaches (MM+, PM7 and DFT B3LYP/6-31++G*) are, in the case of compounds j, k, and s, negligible, which indicate that the method of geometry optimization is not the crucial factor in free binding energy computation by means of docking procedure. This is reasonable taking into account that docking simulation includes exploration of the best conformation of the flexible ligand (the energetically most favourable) to increase the energy of the ligand-receptor interaction [33, 48]. Therefore, changes in ligand structure during docking simulation are possible.
The more important factor determining the free binding energy of STS-inhibitors with the STS protein is ligand orientation that influences their free binding energy. In almost all performed docking simulations, compounds l and m bind with the STS protein in different ways, having opposite orientation in comparison to other derivatives, regardless of the applied method of geometry optimization. Moreover, the residuals between the experimentally measured and the computed free for these two derivatives (l and m), regardless of the applied method of geometry optimization and docking procedure are the highest, which in fact confirms that the orientation opposite to the reference compounds is not adequate.
In the presented work, we have evaluated the influence of the method of geometry optimization on the geometry expression in bond lengths, angles and dihedral angles of steroid sulfatase inhibitors. We have employed two methods that differ in theory levels, such as: molecular mechanics (MM+) and quantum mechanics (DFT B3LYP/6-31++G* and PM7). The obtained results indicate that application of these techniques allows obtaining different conformers. Surprisingly, we have revealed that the selection of the geometry optimization method did not affect the optimal STS inhibitor coordinates, as well as the values of the molecular descriptors that describe the 3D structure of the obtained conformers.
Additionally, we have verified the impact of the geometry optimization method on the free binding energy of steroid sulfatase inhibitors with the STS protein. The results indicate that the geometry optimization did not influence significantly the binding of these compounds with their molecular target. More crucial factors include: (i) selection of the software to molecular docking; and (ii) proper orientation of ligand into its binding pocket.
Thus, taking into account that the time and computational cost required to perform calculation with MM+ or PM7 method are much less demanding than for the DFT one, these methods would be recommended to optimize geometries of STS inhibitors before their docking procedure, as well as for molecular descriptor calculations.
The authors (K. J., A. S. and T. P.) thank the Polish Ministry of Science and Higher Education (grant no. DS 530-8637-D510-15/16). We also would like to thank our colleague Maciej Barycki from University of Gdańsk for writing the Matlab code that allowed performing the Wilcoxon test for the large dataset. Calculations were carried out at the Academic Computer Center in Gdansk. S. K. and J. L. thank the National Science Foundation (NSF/CREST HRD-1547754, and EPSCoR (award no. 362492-190200-01/NSFEPS-090378) for the financial support.
- 12.Hamzeh-Mivehroud M, Sokouti, B., Dastmalchi, S. (2015) An introduction to the basic concepts in QSAR - aided drug design. In: K. R (ed) Quantitative structure-activity relationships in drug design, predictive toxicology and risk assessment. IGI Global, Hershey PA, p 1–47Google Scholar
- 14.Kubinyi H, Bohm HJ (1997) Computer-aided drug design: current state and future perspectives. Abstr Pap Am Chem S 214:44-CINFGoogle Scholar
- 18.Roy K (2015) Quantitative structure-activity relationships in drug design, predictive toxicology and risk assessment. IGI Global, Hershey PAGoogle Scholar
- 21.Schrodinger Suite (2016) QM-Polarized Ligand Docking protocol, https://www.schrodinger.com/qmpolarized-ligand-docking
- 24.Dennington RKT, Millam J (2009) GaussView, 5th edn. Semichem Inc., Shawnee Mission, KansasGoogle Scholar
- 26.Stewart J (2012) MOPAC20012. Stewart Computational Chemistry, Colorado SpringsGoogle Scholar
- 31.Frisch MJT, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA Jr, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas Ö, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2009) Gaussian 09, revision A.02. Gaussian, Inc, Wallingford CTGoogle Scholar
- 32.Talete (2014) Dragon (software for molecular descriptor calculation http://www.talete.mi.it/
- 34.Woo LW, Fischer DS, Sharland CM, Trusselle M, Foster PA, Chander SK, Di Fiore A, Supuran CT, De Simone G, Purohit A, Reed MJ, Potter BV (2008) Anticancer steroid sulfatase inhibitors: synthesis of a potent fluorinated second-generation agent, in vitro and in vivo activities, molecular modeling, and protein crystallography. Mol Cancer Ther 7(8):2435–2444. doi:10.1158/1535-7163.MCT-08-0195 CrossRefGoogle Scholar
- 38.Momany FA, Willett JL (2000) Computational studies on carbohydrates: I. Density functional ab initio geometry optimization on maltose conformations. J Comput Chem 21(13):1204–1219. doi:10.1002/1096-987x(200010)21:13<1204::Aid-Jcc9>3.3.Co;2-6 CrossRefGoogle Scholar
- 40.Duan Y, Wu C, Chowdhury S, Lee MC, Xiong GM, Zhang W, Yang R, Cieplak P, Luo R, Lee T, Caldwell J, Wang JM, Kollman P (2003) A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations. J Comput Chem 24(16):1999–2012. doi:10.1002/jcc.10349 CrossRefGoogle Scholar
- 44.Durdagi S, Mavromoustakos T, Chronakis N, Papadopoulos MG (2008) Computational design of novel fullerene analogues as potential HIV-1 PR inhibitors: analysis of the binding interactions between fullerene inhibitors and HIV-1 PR residues using 3D QSAR, molecular docking and molecular dynamics simulations. Bioorgan Med Chem 16(23):9957–9974. doi:10.1016/j.bmc.2008.10.039 CrossRefGoogle Scholar
- 45.Tzoupis H, Leonis G, Durdagi S, Mouchlis V, Mavromoustakos T, Papadopoulos MG (2011) Binding of novel fullerene inhibitors to HIV-1 protease: insight through molecular dynamics and molecular mechanics Poisson-Boltzmann surface area calculations. J Comput Aided Mol Des 25(10):959–976. doi:10.1007/s10822-011-9475-4 CrossRefGoogle Scholar
- 46.Sengupta D, Verma D, Naik PK (2007) Docking mode of delvardine and its analogues into the p66 domain of HIV-1 reverse transcriptase: screening using molecular mechanics-generalized born/surface area an absorption, distribution, metabolism and excretion properties. J Biosci 32(7):1307–1316CrossRefGoogle Scholar
- 48.Morris GM, Huey R, Lindstrom W, Li CL, Zhao Y, Hart WE, Belew R, Sanner MF, Goodsell DS, Olson WJ (2004) Recent advances in autodock: search, representation and scoring. Abstr Pap Am Chem S 228:U508–U508Google Scholar
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.