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Article

Inductive QSAR Descriptors. Distinguishing Compounds with Antibacterial Activity by Artificial Neural Networks

Division of Infectious Diseases, Faculty of Medicine, University of British Columbia, 2733, Heather street, Vancouver, British Columbia, V5Z 3J5, Canada
Int. J. Mol. Sci. 2005, 6(1), 63-86; https://doi.org/10.3390/i6010063
Submission received: 20 September 2004 / Revised: 14 January 2005 / Accepted: 15 January 2005 / Published: 31 January 2005

Abstract

:
On the basis of the previous models of inductive and steric effects, ‘inductive’ electronegativity and molecular capacitance, a range of new ‘inductive’ QSAR descriptors has been derived. These molecular parameters are easily accessible from electronegativities and covalent radii of the constituent atoms and interatomic distances and can reflect a variety of aspects of intra- and intermolecular interactions. Using 34 ‘inductive’ QSAR descriptors alone we have been able to achieve 93% correct separation of compounds with- and without antibacterial activity (in the set of 657). The elaborated QSAR model based on the Artificial Neural Networks approach has been extensively validated and has confidently assigned antibacterial character to a number of trial antibiotics from the literature.

Introduction.

Nowadays, rational drug design efforts widely rely on building extensive QSAR models which currently represent a substantial part of modern ‘in silico’ research. Due to inability of the fundamental laws of chemistry and physics to directly quantify biological activities of compounds, computational chemists are led to research for simplified but efficient ways of dealing with the phenomenon, such as by the means of molecular descriptors [1]. The QSAR descriptors came to particular demand during last decades when the amounts of chemical information started to grow explosively. Nowadays, scientists routinely work with collections of hundreds of thousands of molecular structures which cannot be efficiently processed without use of diverse sets of QSAR parameters. Modern QSAR science uses a broad range of atomic and molecular properties varying from merely empirical to quantum-chemical. The most commonly used QSAR arsenals can include up to hundreds and even thousands of descriptors readily computable for extensive molecular datasets. Such varieties of available descriptors in combination with numerous powerful statistical and machine learning techniques allow creating effective and sophisticated structure-bioactivity relationships [1,2,3]. Nevertheless, although even the most advanced QSAR models can be great predictive instruments, often they remain purely formal and do not allow interpretation of individual factors influencing activity of drugs [3]. Many molecular descriptors (in particular derived from molecular topology alone) lack defined physical justification. The creation of efficient QSAR descriptors also possessing much defined physical meaning still remains one of the most important tasks for the QSAR research.
In a series of previous works we introduced a number of reactivity indices derived from the Linearity of Free Energy Relationships (LFER) principle [4]. All of these atomic and group parameters could be easily calculated from the fundamental properties of bound atoms and possess much defined physical meaning [5,6,7,8]. It should be noted that, historically, the entire field of the QSAR has been originated by such LFER descriptors as inductive, resonance and steric substituent constants [4]. As the area progressed further, the substituent parameters remained recognized and popular quantitative descriptors making lots of intuitive chemical sense, but their applicability was limited for actual QSAR studies [9]. To overcome this obstacle, we have utilized the extensive experimental sets of inductive and steric substituent constants to build predictive models for inductive and steric effects [5]. The developed mathematical apparatus not only allowed quantification of inductive and steric interactions between any substituent and reaction centre, but also led to a number of important equations such as those for partial atomic charges [8], analogues of chemical hardness-softness [7] and electronegativity [6].
Notably, all of these parameters (also known as ‘inductive’ reactivity indices) have been expressed through the very basic and readily accessible parameters of bound atoms: their electronegativities (χ), covalent radii (R) and intramolecular distances (r). Thus, steric Rs and inductive σ* influence of n - atomic group G on a single atom j can be calculated as:
R s G j = α i G , i j n R i 2 r i j 2
σ G j * = β i G , i j n ( χ i 0 χ j 0 ) R i 2 r i j 2
In those cases when the inductive and steric interactions occur between a given atom j and the rest of N-atomic molecule (as sub-substituent) the summation in (1) and (2) should be taken over N-1 terms. Thus, the group electronegativity of (N-1)-atomic substituent around atom j has been expressed as the following:
χ N 1 j 0 = i j N 1 χ i 0 ( R i 2 + R j 2 ) r i j 2 i j N 1 R i 2 + R j 2 r i j 2
Similarly we have defined steric and inductive effects of a singe atom onto a group of atoms (the rest of the molecule):
R s j N 1 = α i j N 1 R j 2 r j i 2 = α R j 2 i j N 1 1 r j i 2
σ j N 1 * = β i j N 1 ( χ j 0 χ i 0 ) R j 2 r j i 2 = β R j 2 i j N 1 ( χ j 0 χ i 0 ) r j i 2
In the works [7,8] an iterative procedure for calculating a partial charge on j-th atom in a molecule has been developed:
Δ N j = Q j + γ i j N 1 ( χ j χ i ) ( R j 2 + R i 2 ) r j i 2
(where Qj reflects the formal charge of atom j).
Initially, the parameter χ in (6) corresponds to χ0 - an absolute, unchanged electronegativity of an atom; as the iterative calculation progresses the equalized electronegativity χ’ gets updated according to (7):
χ χ 0 + η 0 Δ N
where the local chemical hardness η0 reflects the “resistance” of electronegativity to a change of the atomic charge. The parameters of ‘inductive’ hardness ηi and softness si of a bound atom i have been elaborated as the following:
η i = 1 2 j i N 1 R j 2 + R i 2 r j i 2
s i = 2 j i N 1 R j 2 + R i 2 r j i 2
The corresponding group parameters have been expressed as
η M O L = 1 s M O L = 1 2 j i N 1 R j 2 + R i 2 r j i 2
s M O L = j i N j i N R j 2 + R i 2 r j i 2 = j i N 2 R j 2 + R i 2 r j i 2 = i N s i
The interpretation of the physical meaning of ‘inductive’ indices has been developed by considering a neutral molecule as an electrical capacitor formed by charged atomic spheres [8]. This approximation related inductive chemical softness and hardness of bound atom(s) with the total area of the facings of electrical capacitor formed by the atom(s) and the rest of the molecule.
We have also conducted very extensive validation of ‘inductive’ indices on experimental data. Thus, it has been established that RS steric parameters calculated for common organic substituents form a high quality correlation with Taft’s empirical ES -steric constants (r2=0.985) [10]. The theoretical inductive σ* constants calculated for 427 substituents correlated with the corresponding experimental numbers with coefficient r = 0.990 [5]. The group inductive parameters χ computed by the method (3) have agreed with a number of known electronegativity scales [6]. The inductive charges produced by the iterative procedure (6) have been verified by experimental C-1s Electron Core Binding Energies [8] and dipole moments [6]. A variety of other reactivity and physical-chemical properties of organic, organometallic and free radical substances has been quantified within equations (1)-(11) [11,12,13,14,15,16]. It should be noted, however, that in our previous studies we have always considered different classes of ‘inductive’ indices (substituent constants, charges or electronegativity) in separate contexts and tended to use the canonical LFER methodology of correlation analysis in dealing with the experimental data. At the same time, a rather broad range of methods of computing ‘inductive’ indices has already been developed to the date and it is feasible to use these approaches to derive a new class of QSAR descriptors. In the present work we introduce 50 such QSAR descriptors (we called ‘inductive’) and will test their applicability for building QSAR model of “antibiotic-likeness”.

Results

QSAR models for drug-likeness in general and for antibiotic-likeness in particular are the emerging topics of the ‘in silico’ chemical research. These binary classifiers serve as invaluable tools for automated pre-virtual screening, combinatorial library design and data mining. A variety of QSAR descriptors and techniques has been applied to drug/non-drug classification problem. The latest series of QSAR works report effective separation of bioactive substances from the non-active chemicals by applying the methods of Support Vector Machines (SVM) [17,18], probability-based classification [19], the Artificial Neural Networks (ANN) [20,21,22] and the Bayesian Neural Networks (BNN) [23,24] among others. Several groups used datasets of antibacterial compounds to build the binary classifiers of general antibacterial activity (antibiotic-likeness models) utilizing the ANN algorithm [25,26,27], linear discriminant analysis (LDA) [28,29], binary logistic regression [29] or k-means cluster method [30]. Thus, in the study [31] the LDA has been used to relate anti-malarial activity of a series of chemical compounds to molecular connectivity QSAR indices. The results clearly demonstrate that creation of QSAR approaches for classification of molecules active against broad range of infective agents represents an important and valuable tack for the modern QSAR research.

Dataset

To investigate the possibility of using the inductive QSAR descriptors for creation an effective model of antibiotic-likeness, we have considered a dataset of Vert and co-authors [27] containing the total of 657 structurally heterogeneous compounds including 249 antibiotics and 408 general drugs. This dataset has been used in the previous studies [27,29] and therefore could allow us to comparatively evaluate the performance of QSAR model built upon the inductive descriptors.

Descriptors

50 inductive QSAR descriptors introduced on the basis of formulas (1)-(11) have been described in the greater details in Table 1. Those include various local parameters calculated for certain kinds of bound atoms (for instance for most positively/negatively charges, etc), groups of atoms (say, for substituent with the largest/smallest inductive or steric effect within a molecule, etc) or computed for the entire molecule. One common feature for all of the introduced inductive descriptors is that they all produce a single value per compound. Another similarity between them is in their relation to atomic electronegativity, covalent radii and interatomic distances. It should also be noted, that all descriptors (except the total formal charge) depend on the actual spatial structure of molecules. The choice of particular inductive descriptors in Table 1 was driven by our expectation to have a limited set of QSAR parameters reflecting the greatest variety of different aspects of intra- and intermolecular interactions a molecule can be engaged into. It should be mentioned, however, that some inductive descriptors may reflect related or similar molecular/atomic properties and therefore can be correlated in certain cases (even though the analytical representation of those descriptors does not directly imply their co-linearity). Thus, a special precaution should be taken when using such parameters for QSAR modeling. The procedure of selection of appropriate inductive descriptors has been outlined in the following section.
Table 1. Inductive QSAR descriptors introduced on the basis of equations (1)-(11).
Table 1. Inductive QSAR descriptors introduced on the basis of equations (1)-(11).
DescriptorCharacterizationParental formula(s)
χ (electronegativity) – based
EO_EqualizedaIteratively equalized electronegativity of a moleculeCalculated iteratively by (7) where charges get updated according to (6); an atomic hardness in (7) is expressed through (8)
Average_EO_PosaArithmetic mean of electronegativities of atoms with positive partial charge i n + χ i 0 n + where n + is the number of atoms i in a molecule with positive partial charge
Average_EO_NegaArithmetic mean of electronegativities of atoms with negative partial charge i n χ i 0 n where n is the number of atoms i in a molecule with negative partial charge
η (hardness) – based
Global_HardnessaMolecular hardness - reversed softness of a molecule(10)
Sum_HardnessaSum of hardnesses of atoms of a moleculeCalculated as a sum of inversed atomic softnesses in turn computed within (9)
Sum_Pos_HardnessaSum of hardnesses of atoms with positive partial chargeObtained by summing up the contributions from atoms with positive charge computed by (8)
Sum_Neg_HardnessaSum of hardnesses of atoms with negative partial chargeObtained by summing up the contributions from atoms with negative charge computed by (8)
Average_HardnessaArithmetic mean of hardnesses of all atoms of a moleculeEstimated by dividing quantity (10) by the number of atoms in a molecule
Average_Pos_HardnessArithmetic mean of hardnesses of atoms with positive partial charge i n + η i n + where n + is the number of atoms i with positive partial charge.
Average_Neg_HardnessaArithmetic mean of hardnesses of atoms with negative partial charge i n η i n where n is the number of atoms i with negative partial charge.
Smallest_Pos_HardnessaSmallest atomic hardness among values for positively charged atoms(8)
Smallest_Neg_HardnessaSmallest atomic hardness among values for negatively charged atoms.(8)
Largest_Pos_HardnessLargest atomic hardness among values for positively charged atoms(8)
Largest_Neg_HardnessLargest atomic hardness among values for negatively charged atoms(8)
Hardness_of_Most_PosAtomic hardness of an atom with the most positive charge(8)
Hardness_of_Most_NegaAtomic hardness of an atom with the most negative charge(8)
s (softness) - based
Global_SoftnessMolecular softness – sum of constituent atomic softnesses(11)
Total_Pos_SoftnessaSum of softnesses of atoms with positive partial chargeObtained by summing up the contributions from atoms with positive charge computed by (9)
Total_Neg_SoftnessaSum of softnesses of atoms with negative partial chargeObtained by summing up the contributions from atoms with negative charge computed by (9)
Average_SoftnessArithmetic mean of softnesses of all atoms of a molecule(11) divided by the number of atoms in molecule
Average_Pos_SoftnessArithmetic mean of softnesses of atoms with positive partial charge i n + s i n + where n + is the number of atoms i with positive partial charge.
Average_Neg_SoftnessArithmetic mean of softnesses of atoms with negative partial charge i n s i n where n is the number of atoms i with negative partial charge.
Smallest_Pos_SoftnessaSmallest atomic softness among values for positively charged atoms(9)
Smallest_Neg_SoftnessaSmallest atomic softness among values for negatively charged atoms(9)
Largest_Pos_SoftnessLargest atomic softness among values for positively charged atoms(9)
Largest_Neg_SoftnessLargest atomic softness among values for positively charged atoms(9)
Softness_of_Most_PosaAtomic softness of an atom with the most positive charge(9)
Softness_of_Most_NegaAtomic softness of an atom with the most negative charge(9)
q (charge)- based
Total_ChargeSum of absolute values of partial charges on all atoms of a molecule i N | Δ N i | where all the contributions Δ N i derived within (6)
Total_Charge_FormalaSum of charges on all atoms of a molecule (formal charge of a molecule)Sum of all contributions (6)
Average_Pos_ChargeaArithmetic mean of positive partial charges on atoms of a molecule i n + Δ N i n + where n + is the number of atoms i with positive partial charge
Average_Neg_ChargeaArithmetic mean of negative partial charges on atoms of a molecule i n Δ N i n where n is the number of atoms i with negative partial charge
Most_Pos_ChargeaLargest partial charge among values for positively charged atoms(6)
Most_Neg_ChargeLargest partial charge among values for negatively charged atoms(6)
σ* (inductive parameter) – based
Total_Sigma_mol_iaSum of inductive parameters σ*(molecule→atom) for all atoms within a molecule i N σ G i * where contributions σ G i * are computed by equation (2) with n=N-1 – i.e. each atom j is considered against the rest of the molecule G
Total_Abs_Sigma_mol_iSum of absolute values of group inductive parameters σ*(molecule→atom) for all atoms within a molecule i N | σ G i * |
Most_Pos_Sigma_mol_iaLargest positive group inductive parameter σ*(molecule→atom) for atoms in a molecule(2)
Most_Neg_Sigma_mol_iaLargest (by absolute value) negative group inductive parameter σ*(molecule→atom) for atoms in a molecule(2)
Most_Pos_Sigma_i_molaLargest positive atomic inductive parameter σ*(atom→molecule) for atoms in a molecule(5)
Most_Neg_Sigma_i_molaLargest negative atomic inductive parameter σ*(atom→molecule) for atoms in a molecule(5)
Sum_Pos_Sigma_mol_iSum of all positive group inductive parameters σ*( molecule →atom) within a molecule i n + | σ G i * | where σ G i * >0 and n + is the number of N-1 atomic substituents in a molecule with positive inductive effect (electron acceptors)
Sum_Neg_Sigma_mol_iaSum of all negative group inductive parameters σ*( molecule →atom) within a molecule i n | σ G i * | where σ G i * <0 and n is the number of N-1 atomic substituents in a molecule with negative inductive effect (electron donors)
Rs (steric parameter) – based
Largest_Rs_mol_iaLargest value of steric influence Rs(molecule→atom) in a molecule(1) where n=N-1 - each atom j is considered against the rest of the molecule G
Smallest_Rs_mol_iaSmallest value of group steric influence Rs(molecule→atom) in a molecule(1) where n=N-1 - each atom j is considered against the rest of the molecule G
Largest_Rs_i_molLargest value of atomic steric influence Rs(atom→molecule) in a molecule(4)
Smallest_Rs_i_molaSmallest value of atomic steric influence Rs(atom→molecule) in a molecule(4)
Most_Pos_Rs_mol_iaSteric influence Rs(molecule→atom) ON the most positively charged atom in a molecule(1)
Most_Neg_Rs_mol_iaSteric influence Rs(molecule→atom) ON the most negatively charged atom in a molecule(1)
Most_Pos_Rs_i_molSteric influence Rs(atom→molecule) OF the most positively charged atom to the rest of a molecule(4)
Most_Neg_Rs_i_molaSteric influence Rs(atom→molecule) OF the most negatively charged atom to the rest of a molecule(4)
a – descriptors selected for building the antibiotic-likeness QSAR model.

Selection of variables

To build a binary QSAR model enabling effective separation of antibacterials we have initially calculated all 50 individual inductive descriptors for each molecule from the Vert’s dataset. We have used the hydrogen suppressed representation of the molecular structures – i.e. only the heavy atoms have been taken into account. The inductive QSAR descriptors have been calculated within the MOE package [32] from values of atomic electronegativities and radii taken from our previous publications [5]. To avoid the mentioned cross-correlation among the independent variables we have computed pair wise regressions between all 50 sets of the QSAR parameters and removed those inductive descriptors which formed any linear dependence with R≥0.9. As the result of this procedure, only 34 inductive QSAR descriptors have been selected for the further processing (see the legend to Table 1). The average values of these 34 parameters independently calculated for antibacterial and non- antibacterial compounds have been plotted onto Figure 1. As it can be seen, the corresponding curves for two classes of compounds are clearly separated on the graph and, hence, the selected 34 inductive descriptors should allow building an effective QSAR model of “antibiotic likeness”.
Figure 1. Averaged values of 34 selected inductive QSAR descriptors calculated independently within studied sets of antibiotics (dashed line) and non-antibiotics (solid line).
Figure 1. Averaged values of 34 selected inductive QSAR descriptors calculated independently within studied sets of antibiotics (dashed line) and non-antibiotics (solid line).
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QSAR model

In order to relate the inductive descriptors to antibiotic activity of the studied molecules we have employed the Artificial Neural Networks (ANN) method – one of the most effective pattern recognition techniques. During the last decades the machine-learning approaches have became an essential part of the QSAR research; the detailed description of the ANN’s fundamentals can be found in numerous sources [33 for example].
In our study we have used the standard back-propagation ANN configuration consisting of 34 input and 1 output nodes. The number of nodes in the hidden layer was varied from 2 to 14 in order to find the optimal network that allows most accurate separation of antibacterials from other compounds in the training sets. For effective training of the ANN (to avoid its over fitting) we have used the training sets of 592 compounds (including 197 antibiotics) randomly derived as 90 percent of the total of 657 molecules. In each training run the remaining 10 percents of the compounds were used as the testing set to assess the predictive ability of the model. It should be noted, that we the condition of non-correlation amongst the descriptors has been monitored within the training and the testing sets of compounds as well.
During the learning phase, a value of 1 has been assigned to the training set’s molecules possessing antibacterial activity and value 0 to the others. For each configuration of the ANN (with 2, 3, 4, 6, 8, 10, 12, and 14 hidden nodes respectively) we have conducted 20 independent training runs to evaluate the average predictive power of the network. Table 2 contains the resulting values of specificity, sensitivity and accuracy of separation of antibacterial and non-antibacterial compounds in the testing sets. The corresponding counts of the false/true positive- and negative predictions have been estimated using 0.4 and 0.6 cut-off values for non-antibacterials and antibacterials respectively. Thus, an antibiotic compound from the testing set, has been considered correctly classified by the ANN only when its output value ranged from 0.6 to 1.0. For each non-antibiotic entry of the testing set the correct classification has been assumed if the corresponding ANN output lay between 0 and 0.4. Thus, all network output values ranging from 0.4 to 0.6 have been ultimately considered as incorrect predictions (rather than undetermined or non-defined).
Table 2. Parameters of specificity, sensitivity, accuracy and positive predictive values for prediction of antibiotic and non-antibiotic compounds by the artificial neural networks with the varying number of hidden nodes. The cut-off values 0.4 and 0.6 have been used for negative and positive predictions respectively.
Table 2. Parameters of specificity, sensitivity, accuracy and positive predictive values for prediction of antibiotic and non-antibiotic compounds by the artificial neural networks with the varying number of hidden nodes. The cut-off values 0.4 and 0.6 have been used for negative and positive predictions respectively.
Hidden nodesSpecificitySensitivityAccuracyPPV
20.80.920.8460.751
30.9260.9280.9230.884
40.9250.920.9230.884
60.910.9380.862
80.90.920.9070.851
100.90.920.9070.851
120.90.920.9070.851
140.81510.9230.833
Considering that one of the most important implications for the “antibiotic-likeness” model is its potential use for identification of novel antibiotic candidates from electronic databases, we have calculated the parameters of the Positive Predictive Values (PPV) for the networks while varying the number of hidden nodes. Taking into account the PPV values for the networks with the varying number of the hidden nodes along with the corresponding values of sensitivity, specificity and general accuracy we have selected neural network with three hidden nodes as the most efficient among the studied. The ANN with 34 input-, 3 hidden- and 1 output nodes has allowed the recognition of 93% of antibiotic and 93% of non-antibiotic compounds, on average. The output from this 34-3-1 network has also demonstrated very good separation on positive (antibiotics) and negative (non-antibiotics) predictions. Figure 2 features frequencies of the output values for the training and testing sets consisting of ⅓ of antibiotic and ⅔ of non-antibiotics compounds. As it can readily be seen from the graph, the vast majority of the predictions has been contained within [0.0°0.4] and [0.6°1.0] ranges what also illustrates that 0.4 and 0.6 cut-offs values provide very adequate separation of two bioactivity classes (Table 3 and Table 4 feature the outputs values from the 34-3-1 ANN for the training and testing sets respectively).
Figure 2. Distribution of the output values from the ANN with three nodes in the hidden layer and trained on the set containing 90% of the studied compounds
Figure 2. Distribution of the output values from the ANN with three nodes in the hidden layer and trained on the set containing 90% of the studied compounds
Ijms 06 00063 g002
It should be mentioned, that the estimated 93% accuracy of the prediction by the 34-3-1 ANN is similar or superior to the results by several similar ‘antibiotic-likeness’ studies where the overall cross—validated accuracy can range from 78 [20] to 98% [26] depending of the QSAR methodology, size of antibiotics/non-antibiotics dataset, cross-correlation technique and statistics utilized.
We have also applied the developed techniques on the non-hydrogen suppressed molecular structures. The estimated accuracy of antibiotic/non-antibiotic classification was very close to the results for the hydrogen suppressed molecules. In contrast, the time for the calculation of the inductive QSAR descriptors in the former case is much shorter as the total number of all atoms nearly doubles.

Discussion

The accuracy of discrimination of antibiotic compounds by the artificial neural networks built upon the ‘inductive’ descriptors clearly demonstrates an adequacy and good predictive power of the developed QSAR model. There is strong evidence, that the introduced inductive descriptors do adequately reflect the structural properties of chemicals, which are relevant for their antibacterial activity. This observation is not surprising considering that the inductive QSAR descriptors calculated within (1)–(11) should cover a very broad range of proprieties of bound atoms and molecules related to their size, polarizability, electronegativity, compactness, mutual inductive and steric influence and distribution of electronic density, etc. The results of the study demonstrate that not extensive sets of inductive QSAR descriptors having much defined physical meaning can be sufficient for creating useful models of “antibiotic-likeness”. The accuracy of the developed QSAR model is superior or similar compared to other binary classifiers on the same set of molecules but using much more extensive collections of QSAR descriptors [27,29].
Presumably, accuracy of the approach operating by the inductive descriptors can be improved even further by expanding the QSAR descriptors or by applying more powerful classification techniques such as Support Vector Machines or Bayesian Neural Networks. Use of merely statistical techniques in conjunction with the inductive QSAR descriptors would also be beneficial, as they will allow interpreting individual descriptor contributions into molecular “antibiotic-likeness”. The selection of drugs used for the simulation can also be extended and/or refined. For instance, it has been experimentally confirmed that several non-antibacterial compounds from Vert’s dataset can, in fact, possess definite antibacterial activity. Thus, anti-inflammatory drugs diclofenac [34,35], piroxicam, mefenamic acid and naproxen [35], antihistamines – bromodiphenhydramine [36] diphenhydramine [36] and triprolidine [37], anti-psychotics – chlorpromazine [38,39] and fluphenazine [40,41], the tranquilizer promazine [42] and anti-hypertensive methyldopa [43] all exhibit moderate to powerful potential against microbes. It is obvious, that having all these compounds as the negative control can interfere with the training of efficient antibiotic-likeness model. We, however, did not remove these substances from the e training and testing sets for the sake of comparison of our results with the previous data. Nonetheless, despite the certain drawbacks, it is obvious that the developed ANN-based QSAR model operating by the inductive descriptors has demonstrated very high accuracy and can be used for mining electronic collections of chemical structures for novel antibiotic candidates.

An application of the model

We have decided to test the developed model of “antibiotic-likeness” on the series of early-stage antibiotic compounds featured in the free issue of the Drug Data Report – a journal presenting preliminary drug research results appearing for the first time in patent literature [44]. The “experimental” antibiotic compounds cited by the issue included one penicillin- and two cephalosporin- derivatives as well as a number of high molecular weight chemicals with complex spatial structures such as five C11-carbamate azalides and four eremomycin carboxamides (the corresponding structural formulas are presented on Figure 3).
Figure 3. Chemical structures of twelve early stage antibiotics from the Drug Data Report used for validation for the developed ANN – based QSAR model.
Figure 3. Chemical structures of twelve early stage antibiotics from the Drug Data Report used for validation for the developed ANN – based QSAR model.
Ijms 06 00063 g003aIjms 06 00063 g003b
For each of 12 compounds from the validation set we have calculated 34 inductive descriptors used earlier. The normalized patterns of the independent variables have then been passed through 34-3-1 network with its node–associated weights pre-assigned during the training. The ANN has produced the output parameters presented in Table 5. As it can be seen from the data, all of the estimated output values score well above 0.60 threshold what confidently assigns all of the trial molecules to the class of antibiotics.
Table 3. Compounds of the training set and output values from the trained neural network with three hidden nodes.
Table 3. Compounds of the training set and output values from the trained neural network with three hidden nodes.
NameOutputNameOutput
antibiotics apicycline0.975
4'-(methylsulfamoyl)sulfanilanilide0.973 apramycin0.980
4'-formylsuccinanilic acid thiosemicarbazone azidocillin0.979
0.259 arbekacin0.980
4-sulfanilamidosalicylic acid0.938 aspoxicillin0.975
acediasulfone0.828 azidamfenicol0.966
acetyl sulfamethoxypyrazine0.855 azlocillin0.850
acetyl sulfisoxazole0.964 aztreonam0.981
amidinocillin0.702 bacampicillin0.982
amidinocillin pivoxil0.938 benzylpenicillinic acid0.924
amifloxacin0.881 benzylsulfamide0.733
amikacin0.984 biapenem0.830
apalcillin0.981 brodimoprim0.585
butirosin0.984 cephalothin0.977
carbenicillin0.974 cephapirin sodium0.984
carfecillin sodium0.970 cephradine0.897
carindacillin(a,e,f,i)0.938 chloramphenicol0.606
carumonam0.985 chloramphenicol palmitate0.604
cefaclor0.860 chloramphenicol pantothenate0.983
cefadroxil0.915 chlortetracycline0.984
cefamandole0.964 cinoxacin0.770
cefatrizine0.973 clinafloxacin0.920
cefazedone0.984 clindamycin0.926
cefazolin0.979 clometocillin0.953
cefbuperazone0.984 clomocycline0.982
cefcapene pivoxil0.983 cloxacillin0.935
cefclidin(a,i,j)0.985 cyclacillin0.960
cefdinir(e,i)0.984 dibekacin0.952
cefditoren0.984 dichloramine0.253
cefepime0.982 dicloxacillin0.983
cefetamet0.983 difloxacin0.835
cefixime0.984 diphenicillin sodium0.767
cefmenoxime0.984 doxycycline0.981
cefmetazole0.984 enoxacin0.915
cefminox0.985 enrofloxacin0.630
cefodizime0.985 epicillin0.963
cefonicid0.984 fenbenicillin0.967
ceforanide0.974 fleroxacin0.980
cefotiam0.985 flomoxef0.985
cefoxitin0.984 florfenicol0.955
cefozopran0.982 floxacillin0.983
cefpimizole0.985 fortimicin a0.978
cefpiramide0.985 fortimicin b0.700
cefpirome0.984 furaltadone0.901
cefpodoxime proxetil0.985 gentamicin c10.850
cefprozil0.902 gentamicin c20.940
cefroxadine0.970 gentamicin c30.956
cefsulodin0.982 grepafloxacin0.862
ceftazidime0.984 guamecycline0.977
cefteram0.979 imipenem0.577
ceftezole0.984 isepamicin0.985
ceftizoxime0.984 kanamycin a0.962
cefuroxime0.980 kanamycin b0.976
cefuzonam0.985 kanamycin c0.971
cephacetrile sodium0.982 lenampicillin0.985
cephalexin0.847 lincomycin0.907
cephaloglycin0.951 lomefloxacin0.946
cephaloridine0.960 loracarbef0.862
cephalosporin c0.976 lymecycline0.978
meclocycline0.984 propicillin0.814
meropenem0.977 quinacillin0.984
methacycline0.983 ribostamycin0.965
methicillin sodium0.951 rifamide0.979
mezlocillin0.976 rifamycin sv0.984
micronomicin0.966 rifaximin0.984
miloxacin0.786 ritipenem0.977
moxalactam0.984 rolitetracycline0.979
n2-formylsulfisomidine0.919 rosoxacin0.265
n4-sulfanilylsulfanilamide0.980 rufloxacin0.975
nadifloxacin0.658 salazosulfadimidine0.970
nafcillin sodium0.919 sancycline0.980
nalidixic acid0.268 sisomicin0.909
neomycin a(c,i,j)0.983 sparfloxacin0.975
neomycin b(a,d,h,i)0.981 spectinomycin0.628
netilmicin0.938 succinylsulfathiazole0.977
nifuradene0.600 sulbenicillin0.884
nifuratel0.980 sulfabenzamide0.895
nifurfoline0.963 sulfacetamide0.955
nifurprazine0.267 sulfachlorpyridazine0.915
nifurtoinol0.694 sulfachrysoidine0.975
nitrofurantoin0.291 sulfacytine0.971
norfloxacin0.523 sulfadiazine0.937
N-sulfanilyl-3,4-xylamide0.956 sulfadicramide0.933
ofloxacin0.972 sulfadimethoxine0.958
oxytetracycline0.984 sulfadoxine0.965
panipenem0.939 sulfaethidole0.918
paromomycin0.984 sulfaguanidine0.904
pasiniazide0.236 sulfaguanol0.943
pazufloxacin0.926 sulfalene0.938
pefloxacin0.563 sulfaloxic acid0.857
penamecillin0.636 sulfamethazine0.912
penethamate hydriodide0.704 sulfamethizole0.759
penicillin G potassium0.848 sulfamethomidine0.940
penicillin N0.901 sulfamethoxazole0.908
penicillin O0.978 sulfamethoxypyridazine0.912
penicillin V0.912 sulfamidochrysoidine0.952
phenethicillin potassium0.822 sulfamoxole0.954
phthalylsulfathiazole0.976 sulfanilamide0.653
pipacycline0.921 sulfanilic acid0.841
pipemidic acid0.882 sulfanilylurea0.938
piperacillin0.982 sulfaphenazole0.929
piromidic acid0.696 sulfaproxyline0.957
pivampicillin0.916 sulfapyrazine0.934
pivcefalexin0.946 sulfathiazole0.873
p-nitrosulfathiazole0.893 sulfathiourea0.849
sulfisomidine0.909 bamipine0.036
sulfisoxazole0.963 biclofibrate0.247
sultamicillin0.983 befunolol0.252
talampicillin0.911 benfluorex0.258
temocillin0.985 benorylate0.259
tetracycline0.983 benserazide0.259
tetroxoprim0.837 benzitramide0.259
thiamphenicol0.942 benzotropine mesylate0.000
ticarcillin0.983 benzpiperylon0.000
tigemonam0.985 benzydamine0.000
trimethoprim0.739 bermoprofen0.257
trospectomycin0.850 betaxolol0.174
trovafloxacin(b)0.960 bevantolol0.154
non-antibiotics bevonium methyl sulfate0.032
2-amino-4-picoline0.258 bezafibrate0.256
5-bromosalicylic acid acetate0.258 binifibrate0.319
5-nitro-2propoxyacetanilide0.280 bisoprolol0.184
acecarbromal0.259 bitolterol0.004
aceclofenac0.431 bucloxic acid0.258
acefylline(c,d,e,g)0.841 bopindolol0.001
acetaminophen(b,i)0.258 bromfenac0.258
acetanilide0.258 bromisovalum0.258
acetazolamide0.023 bromodiphenhydramine0.057
acetophenazine0.265 brompheniramine0.006
acetylsalicylic acid0.258 bucetin0.247
acrivastine0.260 bucolome0.253
ahistan0.000 bucumolol0.256
albuterol0.258 bufetolol0.157
alclofenac0.258 bufexamac0.258
alminoprofen0.256 bufuralol0.008
alphaprodine0.106 bumadizon0.205
alprenolol0.239 bunitrolol0.258
aminochlorthenoxazin0.257 butabarbital0.258
aminopyrine0.000 butaclamol0.123
amosulalol0.078 butallylonal0.262
amtolmetin guacil0.001 butanilicaine0.206
anileridine0.262 butibufen0.255
antipyrine0.017 butidrine hydrochloride0.183
antrafenine0.283 butoctamide0.252
apazone0.001 butofilolol0.256
apronalide0.258 caffeine0.159
arotinolol0.293 capuride0.257
atenolol0.258 carazolol0.027
atropine0.258 carbamazepine0.015
bambuterol0.032 carbidopa0.259
bamifylline0.290 carbinoxamine0.066
carbiphene0.258 diethylbromoacetamide0.257
carbocloral0.313 difenamizole0.006
carbromal0.257 difenpiramide0.009
carbuterol0.258 diflunisal0.258
carfimate0.258 dilevalol0.255
carphenazine0.263 dioxadrol0.000
carprofen0.258 dipyrocetyl0.315
carsalam0.258 dipyrone0.041
carteolol0.259 disulfiram0.001
carvedilol0.000 doxefazepam0.270
celiprolol0.211 doxofylline0.629
cetamolol0.245 doxylamine(b,f,g,i)0.000
cetirizine0.261 droperidol0.259
chlorhexadol0.288 droxicam0.022
chlorobutanol0.258 dyphylline0.410
chloropyramine0.050 ectylurea0.244
chlorothen0.070 embramine0.122
chlorpheniramine0.095 emorfazone0.010
chlorprothixene0.017 enfenamic acid0.256
chlorthenoxacin enprofylline0.246
(chlorthenoxazine)0.258 epanolol0.258
chlorcyclizine0.078 ephedrine0.229
cinchophen0.251 epirizole0.002
cinmetacin0.248 eprozinol0.237
cinnarizine0.388 estazolam0.000
cinromida0.197 etafedrine0.179
ciprofibrate0.251 etamiphyllin0.118
clemastine0.039 etaqualone0.000
clenbuterol0.234 eterobarb0.001
clidanac0.258 etersalate0.260
clinofibrate0.282 ethenzamide0.243
clofibric acid0.256 ethinamate0.258
clometacin0.292 ethoheptazine0.000
clometiazol0.255 ethoxazene0.248
clonixin0.254 etodolac0.259
clopirac0.257 etofibrate0.260
cloranolol0.247 etofylline0.266
clordesmetildiazepam0.257 etomidate0.000
clorprenaline0.249 etymemazine0.002
clothiapine0.003 felbinac0.258
clozapine0.051 fenadiazole0.230
codeine0.062 fenbufen0.258
cropropamide0.002 fenclofenac0.259
crotethamide0.035 fenethazine0.000
deserpidine0.005 fenofibrate0.254
diclofenac0.262 fenoprofen0.258
fenoterol0.258 lornoxicam0.031
fentanyl0.066 loxapina0.004
fentiazac0.259 loxoprofen0.258
floctafenine0.266 mazindol(i)0.162
flufenamic acid0.259 meclofenamic acid(f)0.276
fluoresone0.459 mecloqualone0.000
fluphenazine0.260 medibazine0.004
flupirtine0.260 medrylamine0.001
fluproquazone0.258 meparfynol0.258
flurazepam0.010 mepindolol0.211
flurbiprofen0.258 meprobamate0.259
fluspirilene0.259 mequitazine0.001
flutropium bromide0.259 methafurylene0.000
formoterol0.259 methaphenilene0.000
fosazepam0.258 methotrimeprazine0.002
fusaric acid0.258 methoxyphenamine0.000
gemfibrozil0.248 methyldopa0.258
gentisic acid0.258 methyltyrosine0.256
glafenine0.259 methyprylon0.232
glucametacin0.335 metiapine0.002
glutethimide0.258 metipranolol0.258
haloperidide0.259 metofoline0.094
haloperidol0.258 metoprolol0.179
hexapropymate0.258 metron0.275
hexobarbital0.274 mexiletine0.251
hexoprenaline0.258 mofezolac0.340
histapyrrodine0.004 molindone0.000
hydroxyethylpromethazine moperone0.259
(N-Hydroxyethylpromethazine)0.261 moprolol0.213
hydroxyzine0.261 morazone0.000
ibufenac0.258 morphine0.289
ibuprofen0.258 moxastine0.000
ibuproxam0.258 nadoxolol0.258
indenolol0.179 naproxen0.256
indomethacin0.323 narcobarbital0.265
ipratropium bromide0.259 nefopam0.000
isoetharine0.258 niceritrol0.981
isofezolac0.183 nicoclonate0.095
isonixin0.125 nicofibrate0.214
isopromethazine0.000 nifenalol0.256
isoxicam0.003 nifenazone0.000
ketoprofen0.250 niflumic acid0.260
ketorolac0.259 nimetazepam0.512
labetalol0.252 nipradilol0.611
lefetamine0.068 nitrazepam0.337
lorazepam0.268 nordiazepam0.254
novonal0.255 propyphenazone0.000
octopamine0.258 protokylol0.260
orphenadrine0.000 proxibarbital0.262
oxaceprol0.259 proxyphylline0.210
oxametacine0.284 pyrilamine0.000
oxanamide0.254 pyrrobutamine0.000
oxaprozin0.259 quazepam0.331
oxitropium bromide0.265 ramifenazone0.000
oxprenolol0.221 reproterol0.296
oxypertine0.000 rimiterol0.258
paramethadione0.258 ronifibrate0.259
parsalmide0.259 salacetamide0.258
p-bromoacetanilide0.258 salicylamide0.257
pemoline0.258 salicylamide O-acetic acid0.258
penbutolol0.099 salsalate0.258
penfluridol0.259 salverine0.000
perisoxal0.034 scopolamine0.278
perphenazine0.284 secobarbital0.257
phenacemide0.258 setastine0.035
phenacetin0.247 simetride0.028
phenoperidine0.191 simfibrate0.259
phenopyrazone0.243 simvastatin0.355
phenylbutazone0.000 sotalol0.013
phenyltoloxamine(a,c,g)0.000 soterenol0.099
pindolol0.055 sulfinalol0.062
pipebuzone0.001 sulpiride0.017
piperacetazine0.261 suprofen0.258
piperidione0.253 talastine0.000
piperylone0.000 talinolol0.245
pirbuterol0.259 talniflumate0.399
pirifibrate(g,h)0.258 temazepam0.207
piroxicam0.013 tenoxicam0.008
pirprofen0.258 terbutaline0.258
p-lactophenetide0.257 tertatolol0.129
p-methyldiphenhydramine0.000 tetrabarbital0.257
pravastatin0.438 thenaldine0.000
prazepam0.008 thenyldiamine0.000
primidone0.133 theobromine0.251
probucol0.000 theofibrate(b,f,i)0.435
procaterol0.260 theophylline(f,h,i,j)0.224
proglumetacin0.292 thioridazine0.003
prolintane0.024 thiothixene0.003
promazine0.000 thonzylamine0.001
pronethalol0.237 tiaprofenic acid0.258
propanolol0.067 timolol0.030
toliprolol0.127 tripelennamine0.000
tolmetin0.254 triprolidine0.000
tolpropamine0.001 tulobuterol0.169
tretoquinol0.418 viminol0.028
triazolam0.003 vinylbital0.258
triclofos0.276 xenbucin0.256
trifluoperazine0.298 xibenolol0.148
trifluperidol0.259 zolamine0.035
trimethadione0.258 zomepirac0.263
triparanol0.248
Table 4. Compounds of the testing set and the corresponding output values from the trained neural network with three hidden nodes.
Table 4. Compounds of the testing set and the corresponding output values from the trained neural network with three hidden nodes.
NameOutputNameOutput
antibiotics butacetin0.147
amoxicillin0.152 chlorpromazine0.169
ampicillin0.728 ciramadol0.150
cefoperazone0.997 clocinizine0.125
cefotaxime0.999 clofibrate0.142
cefotetan0.568 diazepam0.997
cefteram0.999 diphenhydramine0.125
ceftriaxone0.999 diphenylpyraline0.101
ciprofloxacin0.999 esmolol0.151
demeclocycline0.999 ethclorvinol0.047
flumequine0.998 feprazone0.118
hetacillin0.992 flunitrazepam0.069
mafenide0.999 fosfosal0.134
metampicillin0.978 indoprofen0.287
minocycline0.984 isoproterenol0.151
nifurpirinol0.998 levobunolol0.150
noprylsulfamide0.998 lovastatin0.151
oxacillin0.999 mabuterol0.149
oxolinic acid0.991 mefenamic acid0.097
sulfamerazine0.999 mefexamide0.000
sulfametrole0.999 meperidine0.146
sulfanitran0.998 mephobarbital0.160
sulfaperine0.997 methapyrilene0.000
temafloxacin0.987 nadolol0.151
thiazolsulfone0.994 pheniramine0.134
tobramycin0.994 phenocoll0.000
tosufloxacin0.995 phenyramidol0.000
non-antibiotics pimozide0.029
acetaminosalol0.110 practolol0.152
acetobutolol0.150 proheptazine0.149
aminopropylon0.000 propacetamol0.166
benoxaprofen0.150 sulindac0.975
brotizolam0.004 talbutal0.063
bupranolol0.144
Table 5. Output values from the neural network for the validation set’s antibiotics.
Table 5. Output values from the neural network for the validation set’s antibiotics.
CompoundStructural formulaPrediction
2865473a0.984
2867243c0.985
2867253c0.985
2867263c0.985
2867273c0.985
2867283c0.985
2868473b0.915
2868483b0.914
2871323d0.985
2871333d0.985
2871353d0.985
2871363d0.985
These results demonstrate that the developed ANN-based binary classifier of antibacterial activity is adequate and can be considered an effective tool for ‘in silico’ antibiotics discovery. The results also demonstrate that the inductive parameters readily accessible by formulas (1)-(11) from atomic electronegativities, covalent radii and interatomic distances can produce a variety of useful QSAR descriptors to be used ‘in silico’ chemical research.

Conclusions

The results of the present work demonstrate that a variety of atomic, substituent and molecular properties which can be computed within the framework of our previous models for inductive and steric effects, inductive electronegativity and molecular capacitance represent a powerful arsenal of 3D QSAR descriptors for modern ‘in silico’ drug research. Using only 34 inductive descriptors with no additional independent parameters we have achieved 93% correct classification of compounds with- and without antibacterial activity. The introduced inductive descriptors possess a number of important merits: they are 3D- and stereo- sensitive, can be easily computed from fundamental properties of bound atoms and molecules and possess much defined physical meaning. The developed ANN-based model for antibiotic-likeness prediction can be used as a powerful QSAR tool for filtering through the collections of chemical structures to discover novel antibiotic leads.

Methods

The names of the chemical compounds from the dataset from [27] have been translated into SMILES records and MOL files using the ChemIDPlus online service [45] and the MOE package [32]. 50 inductive descriptors have been calculated using by the SVL scripts – a specialized language of the MOE package. The interatomic distances have been calculated by the MOE from the molecular structures optimized with the MMFF94 force-field [46]. The atomic types have been assigned according to the name, valent state and a formal charge of atoms as it is defined within the MOE. The parameters of the corresponding atomic electronegativities and covalent radii have been taken from our works [5,8]. The inductive QSAR descriptors used in the study have been normalized into the range [0.0°1.0] and the non-overlapping training and testing sets have been randomly drawn by the customized Java scripts. The training and testing of the neural networks has been conducted using the Stuttgart Neural Network Simulator [47]. The training was performed through the feed-forward back-propagation algorithm with the weight decay and pattern shuffling. The values of initial rates were randomly assigned in a range [0.0°1.0], the learning rate has been set to 0.8 with the threshold 0.10.

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Cherkasov, A. Inductive QSAR Descriptors. Distinguishing Compounds with Antibacterial Activity by Artificial Neural Networks. Int. J. Mol. Sci. 2005, 6, 63-86. https://doi.org/10.3390/i6010063

AMA Style

Cherkasov A. Inductive QSAR Descriptors. Distinguishing Compounds with Antibacterial Activity by Artificial Neural Networks. International Journal of Molecular Sciences. 2005; 6(1):63-86. https://doi.org/10.3390/i6010063

Chicago/Turabian Style

Cherkasov, Artem. 2005. "Inductive QSAR Descriptors. Distinguishing Compounds with Antibacterial Activity by Artificial Neural Networks" International Journal of Molecular Sciences 6, no. 1: 63-86. https://doi.org/10.3390/i6010063

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