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Seizure 1998; 7: 347-354

A computational quantitative structure-activity relationship study of carbamate anticonvulsants using quantum pharmacological methods

JENNIFER L. KNIGHT* & DONALD F. WEAVER-f

Department of Chemistry*, Department of Medicine? (Neurology), Queen’s University, Kingston, Ontario, Canada, K7L 3N6

Correspondence to: Donald F. Weaver, Department of Medicine (Neurology), Queen’s University, Kingston, Ontario, Canada, K7L 3N6.

A pattern recognition quantitative structure-activity relationship (QSAR) study has been performed to determine the molecular features of carbamate anticonvulsants which influence biological activity. Although carbamates, such as felbamate, have been used to treat epilepsy, their mechanisms of efficacy and toxicity are not completely understood. Quantum and classical mechanics calculations have been exploited to describe 46 carbamate drugs. Employing a principal component analysis and multiple linear regression calculations, five crucial structural descriptors were identified which directly relate to the bioactivity of the carbamate family. With the resulting mathematical model, the biological activity of carbamate analogues can be predicted with 85-90% accuracy.

Key words: felbamate, anticonvulsant, structure-activity.

INTRODUCTION carbamate fragment capable of producing desired anticonvulsant biological effects. The pattern recognition approach to QSAR The underlying mechanisms of action for the attempts to determine reasons for biological agents used to treat epilepsy are incompletely activity in some compounds and inactivity in understood. For example, felbamate (2-phenyl- others within the same drug class. This approach 1,3-propanediol dicarbamate), a newly-developed assumes the following: (1) a wide variety of a potential anticonvulsant, has an unknown mecha- drug’s physical and chemical properties can be nism of actionim5; moreover, a number of patients reduced to numerical quantities, termed who received this medication died from either descriptors’, (2) the descriptors which influence hepatoxicity or aplastic anemia6. Thus, just as its activity can be determined and calculated’ and (3) mechanism of efficacy is unknown, felbamate’s a mathematical relationship between the descrip- mechanism of toxicity has likewise not been tors and the compound’s biological activity can be elucidated’-‘. A thorough molecular-level study described”,’ ‘. This knowledge assists in the early of felbamate and other carbamates may shed stages of research as the therapeutic potential of a light on these mechanisms. Quantitative given class of compounds is investigated. The structure-activity relationship (QSAR) studies simplicity of some of the descriptors and the are a technique which aid in identifying the availability of high-powered computers for calcu- structural features which are responsible for lating the large number of equations facilitate biological activity. This process, in turn, has the this in-depth structural analysis. In a competitive potential to uncover possible mechanisms of market, sensitive, yet economical devices are of action for efficacy and toxicity’. Therefore, the great importance. In this study, a set of focused goal of this study is to perform a pattern carbamates is thoroughly described and a recognition QSAR on carbamate anticonvulsants mathematical model is developed which predicts to identify the bioactive pharmacophore, i.e. the the activity or inactivity of individual analogues three-dimensional arrangement of atoms within a against an animal model of epilepsy.

1059-131 l/98/050347 + 08 $12.00/O 0 1998 British Epilepsy Association 348 J. L. Knight & D. F. Weaver

MATERIALS AND METHODS molecular fragment (i.e. ‘the bioactive fragment’) which constituted the region of structural com- monality among active anticonvulsants. Background to methods The selection of descriptors capable of com- pletely encoding the significant and structural aspects of carbamate molecular structure was The correlation of biological activity with mole- crucial. The carbamate numbering scheme is cular structure is central to modem neurophar- shown in Fig. 1. The descriptors are listed in macology and enables an enhanced mechanistic Table 1, and are catagorized into four classes: understanding of drug action at the molecular geometric, electronic, topological and physio- level of reality. Accordingly, contemporary chemical (42 descriptors were employed in this approaches to the study and design of bioactive study). Geometric descriptors represent three- molecules are based on the notion that bioactivity dimensional properties and reflect aspects of may be related quantitatively to molecular molecular shape and size. The geometric descrip- structure through the application of QSAR tors employed in this study were derived from techniques’2-‘4. The establishment of QSAR theoretical quantum mechanics and molecular relationships for anticonvulsants has been hin- mechanics calculations. The carbamate analogues dered by the chemical diversity of the moelcules under study were conformationally and geomet- and by the complexity of the physiological and rically optimized using the AM1 Hamiltonian biochemical processes that initiate and propagate after a preliminary scanning of their conforma- seizure activity. tional space using multiple molecular mechanics A vareity of QSAR techniques are available, force field optimizations. Electronic descriptors including free energy models (Hansch such as charge densities, bond moments, orbital equation15”6), mathematical models (Free- energies and frontier electron densities, reflect Wilson equation”), statistical models” (dis- molecular properties arising from variable el- criminant analysis, cluster analysis), quantum ectron distribution through a compound’s str- mechanics and molecular mechanics methods”, uctural framework. The electronic descriptors topological methods2’ and pattern recognition used in this study were obtained from the methods2’-24. In recent years, the pattern recog- Mulliken population analyses of theoretical AM1 nition technique described by Stuper and Jurr?‘, semi-empirical quantum mechanics calculations. Kirschner and Kolalski26 and Wold et al”*24 has Topological descriptors encode aspects of mole- emerged as one of the most all-encompassing cular composition and connectivity, and describe and versatile techniques. patterns of interatomic interconnections that The initial objective of this theoretical pattern determine ultimate molecular architecture. The recognition study was to identify a theoretical topological descriptors used in this study were ‘classification rule’ capable of correctly categoriz- derived from graph theory calculations2635. In ing carbamate compounds into pharmacologically graph theory calculations, a graph G is a active and inactive classes based solely upon an examination of their structural properties. This problem was approached in two stages. First, a set (a) 04 (b) of carbamates of known biological activity was 0 selected and designated as the ‘training set’. A group of theoretical ‘descriptors’ was then gener- ated to describe each compound in this training set. Statistical techniques (regression analyses) were then employed to identify the minimal number of descriptors (i.e. the ‘essential descrip- (c) tor set’) capable of distinguishing active from inactive carbamates. This essential descriptor set -1 AN/H constitutes a classification algorithm or rule. This CH-CH.--0 classification rule was next applied to a second set Cb’ of carbamates, termed the ‘test set’, to evaluate the validity and predictability of the rule. As a Fig. 1: Carbtimate numbering scheme. Representations of corollary to developing a classification rule which the carbamates evaluated in the study. The generalized designated activity from inactivity, it was possible form is represented by A while f3 and C represent specific through complementarity arguments, to identify a analogues Cl and C2, respectively. A structure-activity relationship study of carbamate anticonvulsants 349

Table 1: List of descriptors the Schrodinger partial differential equation: Geometric descriptors (from AM1 semi-empirical W = W, where H is the Hamiltonian calculations) differential operator and Ic, is the wave function. 1-3 Bond lengths Molecular quantum mechanics calculations may NI-C2,C2-03,C2-04. be ab initio or semi-empirical. Semi-empirical 4-6 interatomic distances Nl -R, Nl - Rl, Nl - R2. calculations use a simpler Hamiltonian than the 7-9 Bond angles correct molecular Hamiltonian and incorporate Nl-C2-03,Nl-C2-04,03-C2-04. additional parameters designed to fit experimen- 10 Torsional angle tal data. In contrast, ab initio calculations use the Nl -C2-03-04. full correct Hamiltonian and attempt a solution Electronic descriptors (from AMI semi-empirical calculations) through a rigorous first principles treatment. 1 I-14 Atomic charge densities Classical mechanics force field calculation is Nl, C2, 03. 04. conceptually quite different: it is an empirical 15-16 Molecular dipole moments technique which employs multiple classical equa- 17 Heath of formation tions of motion to provide a priori geometries for 18 E HOMO-LUMO Topological descriptors (from graph theory calculations) varying conformations of large molecules. The 19-20 Zagreb topological indices sum of the individual classical equations constit- M,. M2 utes a multi-dimensional potential energy func- 21 Piatt topological index tion (termed the ‘force field’), which expresses 22-29 Randic topological indices the restoration forces acting on a molecule when ‘x, 2x, ‘x, Jx txv, *xv, TX‘., “xv the minimum potential energy conformation is 30-32 Volume of the substituents perturbed. By minimizing the force field equa- Voi R, Vol R, + R,, Vol R + R, + R,. tion, it is possible to determine the lowest energy 33 Number of carbon atoms in molecule native conformation of a large biomolecule. 34 Number of oxygen atoms in molecule 35 Number of haiide atoms in molecule 36 Number of rings in molecule Application of methods to carbamate QSAR 37 Number of atoms in molecule 38 Number of hydrogen atoms in molecule The biological activity data for the carbamate 39 Number of double bonds in molecule fa’mily were obtained from published literature 40 Number of triple bonds in molecule source?‘. The compounds were subdivided into 41 Molecule weight of molecule Physicochemical descriptor groups designated ‘active’ (bioactivity = 1) or 42 Lipophilicity of molecule ‘inactive’ (bioactivity = 0) as determined using a loe. P maximal electroshock assay. Seventy-five per cent of the compounds were randomly selected for inclusion in the training set and the remainder of mathematical structure consisting of vertices the molecules became the test set (which was then (atoms) connected by edges (bonds). The reserved for the validation of discovered predic- mathematical structure that maps a certain tive models”). Table 2 contains the training and molecule (molecular graph G) is the adjacency test set assignments. All molecules were then matrix A[G]. For an N-atom molecule, A[G] is an structurally optimized. N X N matrix with entries aij having values of All optimizations were perfromed on an IBM either 1 or 0, since any two atoms in a given RS/6000 RISC 355 processor using Spartan molecule are in binary relation being either modelling software3’ operating under the AIX connected or not connected. Physiochemical Windows operating system. The compounds were descriptors, such as the partition coefficient first optimized using molecular mechanics (MM) (1% I-7 describe molecular lipophilicity, calculations, with Sybyl force fields, and were representing the ability of a drug to traverse further optimized using AMl, a semi-empirical biological membrane barriers. quantum mechanical method, to obtain the Calculations were done using both classical and geometric and electronic descriptors. The topolo- quantum mechanical methods. New conceptual/ gical descriptors were calculated using a PC- computational methodologies are permitting based program38 while log P values were deter- pharmacologically useful studies to be achieved mined by ClogP3’. The substituent volumes were using quantum mechanics and classical mechan- calculated utilizing fragment values from Motoc ics. Quantum mechanics is a non-empirical and Marshal14’. A PCA computer program4’ method in which the properties of a stationary operating on the IBM RS/6000 RISC 355 state of a molecule are obtained by solution of processor was employed in the data reduction 350 J. L. Knight & D. F. Weaver

Table 2: Carbamate analogues ID# R Rl R2 Activity

Training set Cl i-C3H7- 1 c2 i-C4H9- 1 c3 set-C4H9- 1 c4 n-C5Hl l- 0 C5 n-C3H7CH(CH3)- 1 C6 tert-C5Hl l- 1 Cl Cl+CC(CH=CH2)(CH3)- 1 C8 n-C4H9CH(CH3)- 1 c9 Cl+CC(CH=CH2)(CH=CHZ)- 1 1 Cl0

H H 1

Cl1 H H 1

Cl2 C6HSCH2- H H 1 Cl3 C6H5CH2CH2- H H 1 Cl4 C2H5- C6H5- H 1 Cl5 C6H5CH(C2H5)- H H 1 Cl6 C2H5 C6HSCHZCH(CH H 0 Cl7 n-C6H13- C6H5CH2- H 0 Cl8 C2H5- C6H5- C6H5- 0 Cl9 C2H5- Cl3CCH(OH)- H 1 c20 (CH3)2C(CH20H)CH2- H H 0 c21 (C2H5)2C(CH20H)CHZ- H H 1 C22 n-C3H7C(CH3)(CH20H)CH2- H H 1 C23 (C2H5)2C(CH20H)CH2- CH3- CH3- 1 C24 n-C4H9C(CZH5)(CH20H)CH2- H H 1 c25 o-CH3C6H5OCH2CH(OH)CH2- H H 1 C26 CSHSC(C2HS)(CH2OH)CH2- H H 1 C27 I I

p- H H 1

I I C28 o-CH3C6H4OCH2CH(OH)CH2- C6H5- H 0 C29 o-CH30C6H40CHZCH(OH)CH2- C6H5- H 0 c30 CkCC(CH3)(CH=CHCI)- H H 1 Test set Tl C2H5 H H 1 T2 tert-C4H9 H H 1 T3 (C?.H5)2CH- H H 1 T4 CMC(CH=CH2)(i-C2H7)- H H 1 T5 C6H5CH(CH3)- H H 1 T6 (C6H5)2CH- H H 0 T-7 C6H5CH2- C6H5- H 0 T8 (C2H5)2C(CH20H)CH2- CH3- H 1 T9 o-CH~OC~H~OCH~CH(OH)CH~- H H ,l TlO (C6H5)2C(CH20H)CH2- H H 1 Tll

C6H5- H 0

T12 H H 1 T13 C6H5CH2- H 0 T14 H H 1 T15 H H 1 T16 o-CH3C6H40CH2CH(CH20-i-C3H7)- H H 1 A structure-activity relationship study of carbamate anticonvulsants 351

stage. All other calculations were perfromed on further analysis”. Chemical rationalization was an IBM compatible PC using Quattro ProTMJ2. used to decide which descriptor should be eliminated. For example, the direct correlation RESULTS between the Vol R, + Rz and the N, - CZ bond length was not surprising since the larger the Data analysis volume of the substituent, the further away N, An initial multiple linear regression (MLR) could will pull from the rest of the molecule to alleviate only be perfromed on descriptors which were any steric hindrance. Accordingly, N, - C2 was completely uncorrelated, i.e. descriptors which dropped in favour of the volume parameter. If are ‘orthogonal’ to each other. To address this there was not an apparent chemical rationaliza- problem, a principal components analysis (PCA) tion, the degeneracy index was consulted. The was used to transform correlated descriptors into degeneracy index, D%, indicates the ability to a new, orthogonal descriptors which were linear given parameter to discriminate between combinations of the original descriptors4”A”. The different compounds3’; therefore, since the de- refurbished descriptors of the training set were scriptor with the better discernment has the lower employed to develop a predictive model by the the index value, the descriptor with the smaller ‘leave-one-out’ method, which also functions as a D% was retained. The number of descriptors was technique for cross-validation46.‘7. This method reduced- initially from forty-two to twenty-eight involves performing a MLR on all the compounds and then to thirteen and tinahy to ten by this except for one. A model was then developed and method. Based on additional information from implemented to predict the activity of the crystallographic studies4x.4” and from documented compound which was originally omitted46. This ab initio” experiments on carbamates, the num- process was repeated while each compound was ber of descriptors was successfully reduced to left out sequenitally and systematically. The five. Table 3 outlines which descriptors were PRESS (PRedicted Error Sum of Squares) retained at each stage. A separate PCA and series recorded the error between the true and pre- of leave-one-out trials, as well as an assessment of dicted activities of each trial. PRESS(i) = (at - the precision of the average model on the training a:)*, where ai is the true or measured activity and and test sets respectively were perfromed at each a; is the predicted activity of the ith compound. level to confirm the effectiveness of the elimina- The smaller the PRESS, the more precise the tion of the descriptors. prediction. The total PRESS indicated the error The trials with five transformed descriptors in ability of the models to predict the individual yielded the mathematical model with optimal members of the training set. When the values for predictive ability (see Table 3). Since the number a; were rounded off to 1 or 0 the PRESS equalled of descriptors had been reduced to five and there zero for a correctly predicted activity and the were thirty compounds in the training set, the PRESS equalled one for an incorrect prediction’. QSAR ‘rule of thumb’ is achieved whereby there A summary table was constructed to illustrate the should be at least four compounds for every results. Once it was confirmed that the individual independent variable for the ‘chance of correla- models were promising, an average model was tion risk to be acceptably 10~‘~‘. Thus a MLR derived and re-applied to the entire training set. perfromed on the raw data is justified; however, New PRESS values were recorded. If this model the raw data must first be ‘auto-scaled’, i.e. predicted well (i.e. had a low PRESS value), then re-scaled to the same (unit) variance giving each the model was applied to each of the compounds variable the same opportunity at the onset to belonging to the test set while the errors were influence the MLR result’***. The following monitored. equation was determined: When these steps were followed with forty-two descriptors, the predictive ability was significant. Activity = - 0.019 G-0, + 0.054 N, However, there was a need to reduce the number - 0.057 Dipole - 0.072 Vol R of descriptors to increase the chemical sig- nificance of the findings. - 0.285 vol RI + R2 + 0.781.

The average error of the prediction (i.e. Data reduction average PRESS) of bioactivity for the training The correlation matrix of the initial 42 descriptors and test sets were 0.100 and 0.126, respectively, or revealed a high degree of correlation between 10.0% and 12.6%. various descriptors. Only one descriptor from Since the coefficients of the MLR are derived each highly correlated pair was selected for from autoscaled data, ideal absolute values for 352 J. L. Knight & D. F. Weaver

Table 3: Descriptors used for each model

28 Descriptors 13 Descriptors IO Descriptors 8 Descriptors 7 Descriptors 6 Descriptors 5 Descriptors

NI-C2, cz-03. CT?-04. C2-03, C2-04. CZ-03. (J-04. CZ-03. CZ-04. ““‘, C2-04. CZ-04. a-04. NI-R, NI-RI. Nl-R2. N I-R2. N I --Q-03, Nl-CZ-04, ,.I”, 03-C2-04. 03-C2-04. 03-C2-04. 03-CZ-04. 03-(x-04. (.lX.40, N 1-C2-03-04 N I -C-Z-03-04 N I -C2-03-04 NI. C2. 03. Nl. 04. Nl. 04. Nl. Iw1 NI. Nl. NI. 04. Dipole momenr. Dipole moment, Dipole moment, Dipole moment. Dipole moment. Dipole moment, Dipole moment. HP H,. H,. 6. HP H,. ~,MO.LL~MO~ ‘IX”‘. Vol R. Vol R, Vol R. Vol R. Vol R. Vol R. ‘X”. Vol R. Vol R, - R>. Vol RI-R,. Vol R,-R2. Vol R,-RI. Vol R,-RZ, Vol R,-R2. Vol R,-R,, Vol total. Number C. Number ol rings. number H. total atoms. MW double bonds, the physical descriptors cannot be readily semi-empirical protocol lack rigorous physical identified. A negative coefficient suggests that a meaning 52. However, the consideration of the measurement for a given descriptor which is small relative atomic charges between compounds may relative to the values of the compounds in the be valuable, and is particularly so, as the model training set will have a greater chance of being suggests, with respect to the N, charge. The biologically active than one with an extremely dipole moment of the molecule may also lead to large value. Conversely, a positive coefficient information about site specific receptor binding. indicates that values which are relatively large for Log P values are often identified as crucial the corresponding descriptor will be favoured. descriptors” because of their direct link to a compound’s capacity to cross the blood-brain barrier; the larger the log P value, the greater the DISCUSSION molecule’s ability to cross the membrane. How- Five descriptors are significant for predicting the ever, in this investigation, the combined volume anticonvulsant activity of carbamates: the Cz-0, of the N-substituents (R, and R,) was found to bond length, the electronic charge on the N, correlate directly with the log P values. There- atom, the dipole moment of the molecule and the fore, during the data reduction stage, the log P volumes of R (the ’ I)-substituent’) and R, + R2 value was eliminated as a descriptor because the (the ‘N-substituents’-refer to Fig. 1 for the R, and R2 volumes which were also highly carbamate numbering scheme). correlated with several other descriptors could The volume of the substituents (Vol R and account for the same information more succinctly Vol R, + R,) is a crucial factor in the activity or within a MLR analysis. inactivity of the compound, suggesting a space- Calculations such as those presented in this limiting feature for the biological mechanism. If a study may be of value in designing future substituent is too large the molecule will not carbamate analogues as improved anticonvul- interact effectively with the receptor site; if it is sants. For example, from the MLR equation, a too small the compound will not be in simul- carbamate analogue with optimally small Q- and taneous contact with all of the necessary regions N- substituents would have a greater degree of of the receptor to promote activity. The C,-0, biological activity than one with large sub- bond length may also affect how the molecule stituents. (However, if the substituent is too docks into a particular site. small, the drug will not be lipophilic enough to The electrostatic descriptors are similarly im- cross the BBB). A reduction of the dipole portant in ascertaining a compound’s ability to moment would also favour bioactivity; therefore, bind to a receptor. Because of the inherently the substituents ought to be able to ‘diffuse’ the subjective nature of charge partitioning methods, electron density of the -OC(=O)N- function- the absolute atomic charges calculated from a ality. To meet this need, a compact electron A structure-activity relationship study of carbamate anticonvulsants 353 withdrawing group could be included within the a positive biological effect. The positive results ester substituent (R substituent), such that the from this experiment suggests that further studies size requirements are not greatly compromised. should be perfromed to statistically confirm or The presence of a hydroxyl group, for instance, refine the predictive model. The structure of the while minimizing the over-all dipole moment, ideal, biologically active carbamate could be could also offer some potential hydrogen bonding improved, which might then lead to a better to a receptor site, although the model does not understanding about potential receptor sites. specifically recognize this mechanism. These calculations are also of value in provid- ing indirect insights concerning receptor struc- ACKNOWLEDGEMENTS ture. For example, this information suggests that the carbamate receptor site has volume limita- This work was supported in part by an operating tions, a situation which is generally favourable grant to DFW from the National Sciences and and which leads to more precise binding. (There Engineering Research Council of Canada. DFW would need to be several exposed functional also acknowledges an Ontario Ministry of Health groups which would serve as hydrogen bond Career Scientist Award. Useful conversations donors and acceptors.) 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