- Research article
- Open Access

# High-quality and universal empirical atomic charges for chemoinformatics applications

- Stanislav Geidl†
^{1}, - Tomáš Bouchal†
^{1}, - Tomáš Raček†
^{1, 2}, - Radka Svobodová Vařeková
^{1}Email author, - Václav Hejret
^{1}, - Aleš Křenek
^{3}, - Ruben Abagyan
^{4}and - Jaroslav Koča
^{1}Email author

**Received:**7 July 2015**Accepted:**16 November 2015**Published:**2 December 2015

## Abstract

### Background

Partial atomic charges describe the distribution of electron density in a molecule and therefore provide clues to the chemical behaviour of molecules. Recently, these charges have become popular in chemoinformatics, as they are informative descriptors that can be utilised in pharmacophore design, virtual screening, similarity searches etc. Especially conformationally-dependent charges perform very successfully. In particular, their fast and accurate calculation via the Electronegativity Equalization Method (EEM) seems very promising for chemoinformatics applications. Unfortunately, published EEM parameter sets include only parameters for basic atom types and they often miss parameters for halogens, phosphorus, sulphur, triple bonded carbon etc. Therefore their applicability for drug-like molecules is limited.

### Results

We have prepared six EEM parameter sets which enable the user to calculate EEM charges in a quality comparable to quantum mechanics (QM) charges based on the most common charge calculation schemes (i.e., MPA, NPA and AIM) and a robust QM approach (HF/6-311G, B3LYP/6-311G). The calculated EEM parameters exhibited very good quality on a training set (\(R^2 > 0.9\)) and also on a test set (\(R^2 > 0.93\)). They are applicable for at least 95 % of molecules in key drug databases (DrugBank, ChEMBL, Pubchem and ZINC) compared to less than 60 % of the molecules from these databases for which currently used EEM parameters are applicable.

### Conclusions

We developed EEM parameters enabling the fast calculation of high-quality partial atomic charges for almost all drug-like molecules. In parallel, we provide a software solution for their easy computation (http://ncbr.muni.cz/eem_parameters). It enables the direct application of EEM in chemoinformatics.

## Keywords

- Partial atomic charges
- Electronegativity Equalization Method
- EEM
- Quantum mechanics
- QM
- Drug-like molecules

## Background

Partial atomic charges are real numbers describing the distribution of electron density in a molecule, thus providing clues as to the chemical behaviour of molecules. The concept of charges began to be used in physical chemistry and organic chemistry. Afterwards, partial atomic charges were adopted by computational chemistry and molecular modelling, where they serve for calculating electrostatic interactions, describe the reactivity of the molecule etc. Specifically, they are applied in molecular dynamics, docking, conformational searches, binding site predictions etc. Recently, partial atomic charges also became popular in chemoinformatics, as they proved to be informative descriptors for QSAR and QSPR modelling [1–9] and for other applications [10–12]; they can be utilised in pharmacophore design [13–15], virtual screening [16–18], similarity searches [19–21], molecular structure comparison [22–24] etc.

The partial atomic charges cannot be determined experimentally or derived straightforwardly from the results of quantum mechanics (QM), and many different methods have been developed for their calculation. The most common method for charge calculation is an application of the QM approach and afterwards the utilisation of a charge calculation scheme. Charge calculation schemes can be based on orbital-based population analysis, on wave-function-dependent physical observables or on reproducing charge-dependent observables. Examples of orbital-based population analyses are Mulliken population analysis (MPA) [25, 26], Löwdin population analysis [27] and Natural population analysis (NPA) [28, 29]. Wave-function-dependent physical observables are used in the atoms-in-molecules (AIM) approach [30, 31], Hirshfeld population analysis [32–34], CHELPG [35] and Merz-Singh-Kollman (MK) [36, 37] method. The reproduction of charge-dependent observables is applied in the CM1, CM2, CM3, CM4, and CM5 approaches [38, 39].

Unfortunately, QM charge calculation approaches are very time-consuming. A markedly faster alternative is to employ empirical charge calculation approaches, which can also provide high-quality charges. These approaches can be divided into conformationally-independent, which are based on 2D structure (e.g., Gasteiger’s and Marsili’s PEOE [40, 41], GDAC [42], KCM [43], DENR [44]) and conformationally-dependent, calculated from 3D structure (e.g., EEM [45], QEq [46] or SQE [47, 48]). We would like to highlight that conformationally-dependent charges are considered to be more suitable for chemoinformatics applications [1–3, 7, 12, 20]. The reason is that these charges contain extensive information not only about chemical surrounding of atoms, i.e., its topology (2D structure based charges) but also geometry and “chemical quality” of the surrounding. Such information is missing, for example, in force field charges which use averaged atomic charges from large sets of structures. Therefore we only focus on conformationally-dependent atomic charges.

*i*; \(R_{i,j}\) is the distance between atoms

*i*and

*j*;

*Q*is the total charge of the molecule;

*N*is the number of atoms in the molecule; \(\kappa\) is the molecular electronegativity, and \(A_i\), \(B_i\) and \(\kappa\) are empirical parameters. The parameters \(A_i\) and \(B_i\) vary for individual atom types, where atom type is a combination of element type and maximal bond order of the atom

*i*. For example, atom type C2 means that the atom is carbon and it creates at least one double bond with its neighbors. An atom X in the aromatic ring is therefore also included into X2 atom type. The parameters \(A_i\), \(B_i\) and \(\kappa\) are molecule independent and they are calculated from QM atomic charges by a process of EEM parameterization [49]. EEM is not only a fast charge calculation approach, but it can also provide highly accurate charges, i.e., they can mimic the QM charges for which EEM has been parameterized. On the other hand, EEM charges can be outperformed in certain situations. Specifically, QEq showed better agreement with experimental dipole moments [46] and SQE is presented as an extension of the EEM to obtain the correct size-dependence of the molecular polarizability [47]. But this drawback is compensated by a fact that the quality of EEM charges was documented by many successful applications [2, 3, 50–55] and they are clearly the most cited empirical conformationally-dependent charges.

Summary information about published EEM parameters evaluated in this study

QM theory Level + basis set | Charge calc. scheme | EEM parameter set name | Published by | Elements and bond orders included\(^\dag\) |
---|---|---|---|---|

HF/STO-3G | MPA | Baek1991 | Baekelandt et al. [56] | C, O, N, H, P, Al, Si |

Svob2007_cbeg2 | Svobodova et al. [49] | C1, C2, O, N1, N2, H, S1 | ||

Svob2007_cmet2 | Svobodova et al. [49] | C1, C2, O, N1, N2, H, S1, Fe, Zn | ||

Svob2007_chal2 | Svobodova et al. [49] | C1, C2, O, N1, N2, H, S1, Br, Cl, F, I | ||

Svob2007_hm2 | Svobodova et al. [49] | C1, C2, O, N1, N2, H, S1, F, Cl, Br, I, Fe, Zn | ||

HF/6-31G* | MK | Jir2008_hf | Jirouskova et al. [57] | C1, C2, O, N1, N2, H, S1, F, Cl, Br, Zn |

B3LYP/6-31G* | MPA | Bult2002_mpa | Bultinck et al. [58] | C, O, N, H, F |

NPA | Bult2002_npa | Bultinck et al. [58] | C, O, N, H, F | |

Ouy2009\(^\ddag\) | Ouyang et al. [59] | C, O, N, H | ||

Ouy2009_elem | Ouyang et al. [59] | C, O, N, H | ||

Hir. | Bult2002_hir | Bultinck et al. [58] | C, O, N, H, F | |

MK | Bult2002_mk | Bultinck et al. [58] | C, O, N, H, F | |

Jir2008_mk | Jirouskova et al. [57] | C1, C2, O, N1, N2, H, S1, F, Cl, Br, Zn | ||

CHELPG | Bult2002_che | Bultinck et al. [58] | C, O, N, H, F | |

AIM | Bult2004_aim | Bultinck et al. [60] | C, O, N, H, F |

Information about freely available software tools enabling EEM charge calculation

Software | EEM parameters used by a software |
---|---|

OpenBabel [61] | It contains the embedded EEM parameter set Bult2002_mpa, which was parameterized for B3LYP/6-31G*/MPA charges. It does not allow any other EEM parameter set to be used |

Balloon [23] | It contains an embedded EEM parameter set published by Puranen et al. [62], which was calculated by fitting to the MEP field. Balloon’s developers claim that the EEM charges calculated via Balloon should be comparable to B3LYP/cc-pVTZ/MPA. It does not allow any other EEM parameter set to be used |

EEM SOLVER [63] | It allows the use of any input EEM parameter sets provided by the user. It does not contain any embedded EEM parameter sets |

## Methods

### EEM parameterization (step 1)

All the steps performed during our work are depicted in Fig. 1a. The most challenging part of our work was the EEM parameterization. This step required several tasks (see Fig. 1b) and the quality of the calculated EEM parameters sets depends on the proper accomplishment of all these tasks.

#### EEM parameterization: selection of atom types to be parameterized

Occurrence of atom types in the training set

Denotation of atom type | Element symbol | Maximal bond order | Number of atoms with this atom type in the training set | Number of molecules containing this atom type in the training set |
---|---|---|---|---|

H1 | H | 1 | 57,119 | 4442 |

C1 | C | 1 | 15,220 | 3447 |

C2 | 2 | 38,097 | 4149 | |

C3 | 3 | 345 | 266 | |

N1 | N | 1 | 4151 | 2483 |

N2 | 2 | 3383 | 1879 | |

N3 | 3 | 345 | 266 | |

O1 | O | 1 | 5016 | 2525 |

O2 | 2 | 5793 | 3069 | |

F1 | F | 1 | 938 | 395 |

P1 | P | 1 | 153 | 143 |

P2 | 2 | 251 | 213 | |

S1 | S | 1 | 1034 | 770 |

S2 | 2 | 1391 | 1211 | |

Cl1 | Cl | 1 | 1084 | 676 |

Br1 | Br | 1 | 336 | 261 |

I1 | I | 1 | 1734 | 1365 |

Total | – | – | 136,390 | 4475 |

#### EEM parameterization: preparation of the training set

Our training set contains the 3D structures of 4475 distinct small organic molecules. The molecules were obtained from the DTP NCI database [66] and their 3D structures were generated with CORINA 3.60 [67], without any further geometry optimization. The DTP NCI database collects compounds tested as anticancer drugs (with positive or negative results), therefore it is a database of common drug-like molecules. The training set was created in such a way that each selected atom type is contained in at least 100 molecules. The occurrences of individual atom types in the training set are summarized in Table 3. The list of training set molecules, including their NSC numbers and summary formulas, can be found in (Additional file 1: Table S1).

#### EEM parameterization: selection of QM charge calculation approach

Quality criteria of our EEM parameter sets

EEM parameter set name | Relevant QM charges | R | RMSD | \({{\bar{\Delta }}}\) |
---|---|---|---|---|

Cheminf_b3lyp_mpa | B3LYP/6-311G/MPA | 0.9007 | 0.1038 | 0.0727 |

Cheminf_b3lyp_npa | B3LYP/6-311G/NPA | 0.9651 | 0.0746 | 0.0540 |

Cheminf_b3lyp_aim | B3LYP/6-311G/AIM | 0.9499 | 0.0785 | 0.0558 |

Cheminf_hf_mpa | HF/6-311G/MPA | 0.9178 | 0.1125 | 0.0776 |

Cheminf_hf_npa | HF/6-311G/NPA | 0.9633 | 0.0805 | 0.0574 |

Cheminf_hf_aim | HF/6-311G/AIM | 0.9441 | 0.0919 | 0.0651 |

#### EEM parameterization: calculation of QM charges

For each molecule from the training set, six sets of QM charges were calculated via the above-mentioned six QM charge calculation approaches. The calculations of QM charges were carried out using Gaussian09 [68]. With the AIM population analysis, the output from Gaussian03 was further processed with the software package AIMAll [69].

#### EEM parameterization: calculation of EEM parameter sets

*i*; \(q^{QM}_i\) is the QM charge of an atom

*i*; \(\overline{q}^{EEM}\) is an average of all EEM charges; \(\overline{q}^{QM}\) is an average of all QM charges,

*N*is the number of atoms in the molecule.

### Coverage comparison (step 2)

Size of database, used for comparison of EEM parameter set coverages

Database | Number of compounds |
---|---|

DrugBank | 6874 |

ChEMBL | 1,456,020 |

PubChem | 63,676,639 |

ZINC | 21,957,378 |

### Quality comparison (step 3)

This evaluation was done for the 21 above-mentioned tested EEM parameter sets and was performed on two data sets—a test set (657 molecules) and an extended test set (1226 molecules). The extended test set contained all approved drugs (i.e., drugs which have received approval in at least one country) from the DrugBank database (downloaded 10th February 2015), for which it was possible to calculate all QM charges necessary for testing. The test set was a subset of the extended test set, which contained only molecules covered by all the tested EEM parameter sets. The 2D structures of all molecules were obtained from DrugBank. The lists of molecules from the test set and the extended test set, including their DrugBank IDs and summary formulas, can be found in (Additional file 3: Table S2a; Additional file 4: Table S2b, respectively). The 3D structures of all the molecules were generated with CORINA 2.6 [67], without any further geometry optimization. For all the molecules, we calculated all the types of QM charges which corresponded to the tested EEM parameters. This means we used the 8 QM charge calculation approaches mentioned in Table 1 and the six QM charge calculation approaches employed for calculating our EEM parameter sets. The calculations of QM charges were done with Gaussian09 and the AIMAll software package was used for AIM charges. We compared the quality of the tested EEM parameter set on both the test set and the extended test set. The comparison was done using NEEMP, which provided quality criteria for all the tested EEM parameter sets. In the extended test set, some molecules were not covered by certain EEM parameter set(s). Therefore, we calculated quality criteria based purely on the covered molecules and in parallel, we also computed the coverage.

#### Quality comparison: EEM parameter sets embedded in software tools

The calculation of EEM charges can be done with a few software tools, e.g., EEM SOLVER, OpenBabel or Balloon. The software tools OpenBabel and Balloon contain embedded EEM parameter sets (see Table 2). Therefore, we also evaluated the quality of these embedded EEM parameter sets. This evaluation was done for the same data sets and via the same procedure as with the tested EEM parameter sets. The only difference was that the EEM charges were not calculated with NEEMP, but with OpenBabel and Balloon. Afterwards, these EEM charges were compared with the relevant QM charges using R statistical software [76], which provided their quality criteria.

### Software solution (step 4)

We provide the user two such solutions, the first based on EEM SOLVER and the second on OpenBabel.

## Results and discussion

### EEM parameterization (step 1)

EEM parameterization was performed for six QM charge calculation approaches, and a training set containing 4475 drug-like molecules was used. Squared Pearson correlation coefficient (\(R^2\)), root mean square deviation (RMSD) and average absolute error (\({\overline{\Delta }}\)) of the obtained EEM parameter sets, calculated for the training set, are summarized in Table 4. These quality criteria describe the correlation between QM charges and the corresponding EEM charges and they were calculated using NEEMP software.

These results show that the quality of our EEM parameter sets is very high, i.e., all the \(R^2\) values are higher or equal to 0.9. Table 4 also illustrates that QM theory levels B3LYP and HF are both applicable for EEM parameterization, and EEM charges based on them have similar accuracy. From this table, we can also see that the quality of EEM parameters based on NPA and AIM population analysis is slightly better than for MPA.

### Coverage comparison (step 2)

Information about the coverages of published EEM parameter sets and our EEM parameter sets are summarized in Table 6. The coverages were computed on four well-known databases of drug-like molecules—DrugBank, ChEMBL, PubChem and ZINC. Table 6 shows that the coverages of the published EEM parameter sets are low (\(<\)60 %). The only exception are the EEM parameter sets published by Svobodova et al. and Jirouskova et al., which have coverage between 70 and 80 %. In contrast, our EEM parameter sets have very high coverage—about 95 % or more for all the databases. The not covered molecules include atom types rare for drug-like molecules, e.g., metals or boron. An interesting fact is that the coverages are very similar for all four analyzed databases. Therefore, low EEM parameter set coverage is not merely an isolated issue related to one database, but a general problem.

### Quality comparison (step 3)

Table 6 summarizes the main quality criteria (i.e., \(R^2\) values) of all tested EEM parameter sets for the test set, which contained 657 approved drugs from DrugBank. Other quality criteria (RMSD and \({\overline{\Delta }}\)) can be found in (Additional file 5: Table S3) and all values of partial atomic charges (represented as tables and as graphs) are in (Additional file 6). The table shows that our EEM parameter sets are among the best performing EEM parameter sets to have been published so far. The table also illustrates that the quality of EEM parameters is strongly influenced by the selection of QM charge calculation scheme. Specifically, EEM parameters based on MPA, NPA and AIM charges are very high quality, and EEM parameters based on Hirshfeld charges are still acceptable. EEM parameters based on MK and CHELPG charges are very low quality, which is in agreement with published data [2, 58]. Both theory levels (HF and B3LYP) and all three basis sets used (STO-3G, 6-31G* and 6-311G) are applicable for EEM parameterization. These results also confirm that our selection of QM theory level, basis set and charge calculation schemes is appropriate.

For the extended test set, the quality criteria exhibit similar trends (see Additional file 7: Table S4). In parallel, the coverages for this data set are slightly higher than for the complete DrugBank database. An interesting fact is that even for such common compounds as approved drugs, the coverages of published EEM parameter sets are low. Specifically, most published EEM parameter sets have coverages between 55 and 65 %. Further remarkable fact is that quality criteria of our EEM parameters are better for the test set than for the training set. The reason is that the training set is much larger and heterogeneous than the test set.

#### Quality comparison: EEM parameter sets embedded in software tools

EEM charges produced with OpenBabel were compared with QM charges calculated with B3LYP/6-31G*/MPA. The quality criteria for the test set were the same as for the EEM parameters Bult2002_mpa (i.e., \(R^2\) about 0.97). This was expected, because OpenBabel uses Bult2002_mpa as its embedded EEM parameters. Very surprising was the behavior of OpenBabel on the extended set. The coverage was 100 %, but the quality criteria were markedly lower (e.g., \(R^2\) about 0.82). The reason for this is that OpenBabel replaces the EEM parameters for atom types which are not provided in Bult2002_mpa with the EEM parameters for some other atom types. Unfortunately, this approach is not very reliable, i.e., the quality criteria for molecules which are in the extended test set but are not in the test set are very low (\(R^2 = 0.66\)). Additionally, this approach is relatively tricky. The user does not know whether the correct or the estimated EEM parameters are used and, therefore, whether the resulting EEM charges will be of a good quality.

The EEM charges produced by Balloon were compared with the QM charges calculated by the B3LYP/cc-pVTZ/MPA approach. The coverage was close to 100 %, but the correlation was also low (\(R^2 < 0.8\)). On the other hand, the Balloon developers mentioned that the EEM charges provided by Balloon do not correspond directly to some particular QM charges, and they should only be close to B3LYP/cc-pVTZ/MPA charges.

All the quality criteria and coverages for EEM parameter sets embedded in OpenBabel and Balloon are summarized in (Additional file 8: Table S5).

### Coverage comparison and quality comparison combined

### Software solution (step 4)

For the actual applicability of EEM in chemoinformatics, the user doesn’t just need EEM parameter sets that are high quality and cover almost all molecules. They also need a software package that embeds these EEM parameter sets and calculates EEM charges based on them. We provide the user with two such solutions. First, we provide our EEM parameter sets in a format that can be directly used in EEM SOLVER (Additional file 2: EEM parameter sets). Second, we provide an OpenBabel patch which allows our EEM parameter sets to be used directly in OpenBabel (Additional file 9: OpenBabel patch). All the information including documentation is also accessible on the web: http://ncbr.muni.cz/eem_parameters. The parameters are also accessible via ACC web application [77].

## Conclusion

We provide here six EEM parameter sets which enable the user to calculate EEM charges with quality comparable to frequently used QM charges computed by well-known charge calculation schemes (i.e., MPA, NPA and AIM) and based on a robust QM approach (HF/6-311G, B3LYP/6-311G). The training set for EEM parameterization contained more than 4000 molecules from the DTP NCI drug database, and all six calculated EEM parameter sets exhibited a very good quality on this training set (\(R^2 > 0.9\)).

The coverage of these computed EEM parameter sets was then compared with the coverages of 15 EEM parameter sets published in the past. This comparison was done on four key databases of drug-like molecules—DrugBank, ChEMBL, Pubchem and ZINC. The comparison showed that our EEM parameter sets enable us to calculate EEM charges for almost all molecules in these databases.

We then compared the quality of computed and published EEM parameter sets on two test data sets composed of approved drugs from DrugBank. This comparison also included EEM parameter sets embedded in the software tools OpenBabel and Balloon. The comparison showed that our EEM parameter sets are among the best performing EEM parameter sets published to date (\(R^2 > 0.93\)).

To summarize, charge calculation methodology suitable for chemoinformatics applications like virtual screening or QSAR should be fast, conformationally-dependent and accurate. EEM fulfils all these requirements. However, EEM parameter sets that would exhibit high coverage of drug-like molecule databases and provide high quality charges have not been available to date. The EEM parameters calculated in this paper solve this problem. They exhibit coverage close to 100 % and excellent quality criteria, therefore they are applicable in chemoinformatics.

Last but not least, we provide a software solution for the easy computing of EEM charges based on these EEM parameter sets—input files for EEM SOLVER and OpenBabel patch.

## Notes

## Declarations

### Authors' contributions

The concept of the study originated from JK and was reviewed and extended by RA, while the design was put together by RSV and SG and reviewed by JK and RA. TB and SG prepared the input data (molecules and published EEM parameters). TB, SG and VH performed QM charge calculation. TR updated and extended NEEMP software. TB and TR performed EEM parameterizations, EEM charges validation and calculation of statistical data. VH prepared an automatic workflow, which is able to reproduce all steps preformed in the article. AK reviewed, corrected and improved this workflow. TR wrote the OpenBabel patch. The data were analyzed and interpreted by RSV, SG and JK. The manuscript was written by RSV in cooperation with JK, and reviewed by all authors. All authors read and approved the final manuscript.

### Acknowledgements

This work was supported by the Grant Agency of the Czech Republic [13-25401S]; the European Community’s Seventh Framework Programme (CZ.1.05/1.1.00/02.0068) from the European Regional Development Fund; and by the European Social Fund and the state budget of the Czech Republic (CZ.1.07/2.3.00/20.0042, CZ.1.07/2.3.00/30.0009).

This work was also supported in part by NIH Grants R01 GM071872, U01 GM094612, and U54 GM094618 to R.A.. The access to MetaCentrum supercomputing facilities provided under research intent MSM6383917201 is greatly appreciated.

### Authors' information

Stanislav Geidl, Tomáš Bouchal and Tomáš Raček wish it to be known that, in their opinion, the first three authors should be regarded as joint First Authors. Radka Svobodová Vařeková and Jaroslav Koča wish it to be known that, in their opinion, they should be regarded as joint Corresponding Authors.

### Competing interests

The authors declare that they have no competing interests.

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## Authors’ Affiliations

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