General Theory for Multiple Input-Output ...

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General Theory for Multiple Input-Output Perturbations in Complex Molecular Systems. 1. Linear QSPR Electronegativity Models in Physical, Organic, and Medicinal Chemistry Humberto González-Díaz1,2,*, Sonia Arrasate1, Asier Gómez-SanJuan1, Nuria Sotomayor1, Esther Lete1, Lina Besada-Porto3 and Juan M. Ruso3 1

Department of Organic Chemistry II, University of the Basque Country UPV/EHU, 48940, Bilbao, Spain; IKERBASQUE, Basque Foundation for Science, 48011, Bilbao, Spain; 3Department of Applied Physics, University of Santiago de Compostela (USC), 15782, Santiago de Compostela, Spain

2

Abstract. In general perturbation methods starts with a known exact solution of a problem and add "small" variation terms in order to approach to a solution for a related problem without known exact solution. Perturbation theory has been widely used in almost all areas of science. Bhor’s quantum model, Heisenberg's matrix mechanincs, Feyman diagrams, and Poincaré’s chaos model or "butterfly effect” in complex systems are examples of perturbation theories. On the other hand, the study of Quantitative Structure-Property Relationships (QSPR) in molecular complex systems is an ideal area for the application of perturbation theory. There are several problems with exact experimental solutions (new chemical reactions, physicochemical properties, drug activity and distribution, metabolic networks, etc.) in public databases like CHEMBL. However, in all these cases, we have an even larger list of related problems without known solutions. We need to know the change in all these properties after a perturbation of initial boundary conditions. It means, when we test large sets of similar, but different, compounds and/or chemical reactions under the slightly different conditions (temperature, time, solvents, enzymes, assays, protein targets, tissues, partition systems, organisms, etc.). However, to the best of our knowledge, there is no QSPR general-purpose perturbation theory to solve this problem. In this work, firstly we review general aspects and applications of both perturbation theory and QSPR models. Secondly, we formulate a general-purpose perturbation theory for multiple-boundary QSPR problems. Last, we develop three new QSPR-Perturbation theory models. The first model classify correctly >100,000 pairs of intra-molecular carbolithiations with 75-95% of Accuracy (Ac), Sensitivity (Sn), and Specificity (Sp). The model predicts probabilities of variations in the yield and enantiomeric excess of reactions due to at least one perturbation in boundary conditions (solvent, temperature, temperature of addition, or time of reaction). The model also account for changes in chemical structure (connectivity structure and/or chirality paterns in substrate, product, electrophile agent, organolithium, and ligand of the asymmetric catalyst). The second model classifies more than 150,000 cases with 85-100% of Ac, Sn, and Sp. The data contains experimental shifts in up to 18 different pharmacological parameters determined in >3000 assays of ADMET (Absorption, Distribution, Metabolism, Elimination, and Toxicity) properties and/or interactions between 31723 drugs and 100 targets (metabolizing enzymes, drug transporters, or organisms). The third model classifies more than 260,000 cases of perturbations in the self-aggregation of drugs and surfactants to form micelles with Ac, Sn, and Sp of 94-95%. The model predicts changes in 8 physicochemical and/or thermodynamics output parameters (critic micelle concentration, aggregation number, degree of ionization, surface area, enthalpy, free energy, entropy, heat capacity) of self-aggregation due to perturbations. The perturbations refers to changes in initial temperature, solvent, salt, salt concentration, solvent, and/or structure of the anion or cation of more than 150 different drugs and surfactants. QSPR-Perturbation Theory models may be useful for multi-objective optimization of organic synthesis, physicochemical properties, biological activity, metabolism, and distribution profiles towards the design of new drugs, surfactants, asymmetric ligands for catalysts, and other materials.

Keywords: Perturbation theory, QSPR/QSAR models, ADMET process, Organometalic addition, Carbolithiation reactions, Asymmetric synthesis, Self-aggregation, Markov Chains, Complex networks. INTRODUCTION In the wider sense perturbation methods starts with a known exact solution of a problem and continue adding "small" terms to the mathematical description in order to approach a solution to a related problem without known *Address correspondence to this author at the Department of Organic Chemistry II, University of the Basque Country UPV/EHU, 48940, Bilbao, Spain; Email: [email protected] 1/13 $58.00+.00

exact solution. The use of small corrections to predict planets orbits in epicycles theory on early celestial mechanics is perhaps the first recorded use of a perturbational theory. It led in turn to the Copernican revolution in the 16th century [1]. Any case, epicycles stuf are not only about history. Bouzarth et al. [2], observed micron-sized particles which exhibit epicyclic orbits with coherent fluctuations distinguishable from comparable amplitude thermal noise. In the 19th century, Charles-Eugène Delaunay studied perturbations in the ex© 2013 Bentham Science Publishers

1714 Current Topics in Medicinal Chemistry, 2013, Vol. 13, No. 14

pansion for the Earth-Moon-Sun system and appeared the perturbation theory for differential equations. This in turn led Henri Poincaré to deduce the existence of chaos or "butterfly effect": small perturbations that can produce large non-linear effects on a complex system [3]. With the advent of Quantum Mechanics (QM) the application of perturbation methods in molecular sciences has exploded. Some examples of early applications of perturbation theory in quantum mechanics are the semi-classical Bohr’s theory of the atoms, Heisenberg's matrix mechanics, Stark’s effect (energy levels shift upon external electric field), and Zeeman’s effect, as well as first models of the structure of hydrogen and helium atoms. Even when Stark’s effect in physical and chemistry context are not exactly the same both and other related phenomena called Vibrational Stark’s Effect (VSE) are an important field for the application of perturbation methods. Laberge [4] reviewed the applications of Strak’s spectroscopy in proteins. In 1992, Fernandez and Morales [5], reported an interesting Perturbation theory for the Zeeman’s effect in hydrogen without wave functions. This year, Marshall and Chapman [6] developed a comprehensive approach to model associating fluids with small bond angles using Wertheim's perturbation theory. On the other hand, the study of Quantitative StructureProperty Relationships (QSPR) problems is of the major importance in almost all areas of modern science with special emphasis in bio-molecular sciences. Different QSPRlike methods have been used to study the chemical reactivity of compounds in the organic synthesis of drugs, the biological activity of drugs, as well as the ADMET (Absorption, Distribution, Metabolism, Elimination, and Toxicity) process of drugs, xenobiotic chemicals, or natural metabolites. In almost all cases, these techniques involve one out of two general stages: stage (1) numerical codification of molecular structure, and stage (2) search of a quantitative connection between the structure and biological process. QM and/or Graph theory are computational techniques typical of stage (1); while Statistical and/or Machine Learning (ML) techniques are commonly used in stage (2) [7-11]. All these techniques have been implemented in different user-friendly software. For instance, DRAGON [12-14], TOPS-MODE [15-18], TOMOCOMD [19, 20], CODESSA [21, 22], and MOE [23] are some of the more used software to solve stage (1) problems. STATISCA [24] and WEKA [25] are software that implement Linear Discriminant Analysis (LDA) and many other ML methods useful in stage (2). The same problem but a higher structural level appears in the study of structure-function or activity relationships for proteins, RNA, drug-protein complexes, or protein-protein complexes related to drug ADMET or biological activity profiles [2635]. A more elaborated formulation of this idea is the development of QSPR-like methodology to seek Quantitative Proteome-Disease Relationship (QPDR) or Quantitative Proteome-Toxicity Relationship (QPTR) connecting the information contained on full tissue proteomes to disease or drug toxicity detection in a sort of QSPR-like biomarkers discovery [36-40]. In this context, different researchers/journals have edited important monographic issues in order to discuss different computational methods. Current Topics in Medicinal Chem-

González-Díaz et al.

istry have published some of the more recent. For instance, Bisson has edited one special issue about computational chemogenomics in drug design and discovery [41]. SpeckPlanche and Cordeiro guest-edited a special issue about computer-aided techniques for the design of anti-hepatitis C agents [42]. Prado-Prado and García-Mera has also guestedited one special issue about computer-aided drug design and molecular docking for disorders of the central nervous system and other diseases [43]. Gonzalez-Diaz has guestedited two special issues about multi-target QSAR (mtQSAR) and Complex Networks applied to medicinal chemistry [44, 45]. In all these issues, and others of the same journal, have been published several review and research papers in this area [23, 46-80]. In any case, the development of perturbation theory for QSPR-like problems should falls by its own weight. In QSPR, we have several complex problems of multivariate nature and without exact solution. Two general situations of this type appear in the construction of new drugs by organic synthesis and in the subsequent characterization of the pharmacological activity and ADMET process of these drugs. For instance, we often know the yield (exact solution) of large collections of organic reactions given the initial conditions of temperature, time, solvents, reactants, etc. We also know the biological activity or ADMET properties (known solution) of large sets of compounds assayed at multiplexing boundary conditions (organisms, assays, parameters, targets). For instance, we often would like to know the yield (unknown solution) of new organic reactions given some “small” changes or perturbations of the initial conditions of temperature, time, solvents, or structural changes in the reactants. We would like to know also the biological activity or ADMET properties (unknown solution) of new organic compounds and/or the same compounds if we change the structure and/or the assay conditions (organisms, assays, parameters, targets). In organic synthesis the problem gains in relevance if we consider large libraries or databases of compounds against several molecular or cellular targets. In all cases discussed above (organic synthesis, ADMET process, and self-aggregation), we have large databases of examples of problems with known solution but a notably larger list of related problems without known solutions. However, despite of the high potential of a perturbation theory for QSPR there is not a general perturbation theory for these problems until the best of our knowledge. In this work, firstly we review different applications of perturbation theory in biomolecular sciences with emphasis in quantum chemistry, spectroscopy, drug-target interactions, chemical reactivity, drug discovery, metabolomics, and ADEM process. We also review general aspects of QSPR models applied to chemical reactivity and ADMET properties. Secondly, we develop a general-purpose perturbation theory for QSPR-like problems. Last, we give three examples of concept-of-proof experiments with the application of the new theory to predict drugs synthetic reactomes, distribution fluxomics in biphasic systems, and drug-target interactions of interest in Metabolomics. In this regard, the index of the issues reviewed/discussed here is:

General Theory for Multiple Input-Output Perturbations

Current Topics in Medicinal Chemistry, 2013, Vol. 13, No. 14

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BIO-MOLECULAR APPLICATIONS OF PERTURBATION THEORY

Møller–Plesset Perturbation Theory for Reactivity, Organo-Metallic Catalysis, and Drug Discovery

Applications of Perturbation Theory in Bio-Molecular Spectroscopy

The Møller and Plesset (MP) perturbation theory is a special application of RS perturbation theory [87]. Indeed they introduced a perturbation theory for treating a system of n electrons in which the Hartree-Fock solution appears as the zero-order approximation. Head-Gordon, Pople, and Frisch Second, third, and fourth order MP methods (MP2, MP3, and MP4) calculations for calculation of small molecules have been implemented in many computational chemistry software but higher order MPn calculations like MP5 are less common and costly in computational resources. Kristensen and Jørgensen [88]; developed a molecular gradient for MP2 perturbation theory using the divide-expand-consolidate (DEC) scheme. This year, Bozkaya and Sherrill [89] reported the analytic energy gradients for the orbital-optimized second-order MP perturbation theory (OMP2). OMP2 calculations outperfom the results obtained by MP2 perturbation method in the description of some difficult chemical systems. Hollman, Wilke, and Schaefer [90]; presented working equations MP2 perturbation theory with explicitly correlated atomic orbital basis. Also Kobayashi and Nakai [91], reported an effective energy gradient expression for divideand-conquer MP2 perturbation theory.

There are interesting applications of perturbation theory to biomolecular spectroscopy. In fact, Strak’s spectroscopy and VSE spectroscopy are modern methods useful in the characterization of chemical structures. The review paper entitled: Stark spectroscopy: applications in chemistry, biology, and materials science, after Bublitz and Boxer [81], discuss the topic. For an immobilized, isotropic molecule, the Stark spectrum can be described as the sum of derivatives of the absorption spectrum [81]: B C d A( )

d 2 A( ) 2 A = (Fext f ) A A( )+ + 2 2 d 30h c d 2 15hc

(1)

The equation is a clear example of the definition given in the first sentence of this work. It takes exact values of functions of molecular properties of the system (A() and coefficients A, B, and C) and continue adding deviation terms (derivatives d(A())/d) to approach to a final solution. Park et al. [82], reported the first measurement of the VSE in a protein. They used this equation to described vibrational shifts observed when protein undergoes a structural change associated with electric field perturbation. Rayleigh–Schrödinger Perturbation Theory Rayleigh–Schrödinger (RS) perturbation theory adds a small perturbation V pre-multiplied by the real parameter to one unperturbed Hamiltonian operator H0 to define the new operator obtained after the perturbation of the system. The perturbation is the correlation potential and the perturbed wave function and perturbed energy E are expressed as a power series in . We can obtain kth-order perturbation equations in k for different values of k = 0, 1, 2, ..., n. We can substitute these series into the timeindependent Schrödinger equation to obtain the following expression: n n n H = (H 0 + V ) k (k ) = k E (k ) k (k )

i =0 i =0 i =0

(2)

There have been different theoretical studies and modifications of RS perturbation theory formulation. For instance, Baik et al. [83], inverted RS perturbation series to study atomic stabilization by intense light. Znojil [84] also reported a modified RS perturbation theory approach. Patnaik [85] developed the RS perturbation theory for the anharmonic oscillator. Bloino and Barone developed in 2012 [86] a general formulation to compute anharmonic vibrational averages and transition properties at the second-order of RS perturbation theory. This modern RS approach is intended to be applicable to any property expanded as a Taylor series up to the third order. The equations are straightforward to implement and can be easily adapted to various properties, as illustrated for the case of electric and magnetic dipole moments an consequently infrared and vibrational circular dichroism spectra.

Aside from previous theoretical developments for MP perturbation theory, important applications have been reported. Some recent examples, to cite a few, are: Elm and Jørgensen et al. [92], used MP2 and other QM methods to study gas phase hydrogen abstraction reaction kinetics of short chained oxygenated hydrocarbons. These are compounds of atmospheric relevance. They predicted the rate constants for the reaction of the OH radical with CH3OH, CH3CH2OH, H2CO, CH3 CHO, CH3COCH3, CH3OCH3, HCOOH, CH3COOH, and HCOOCH3. A total of 18 individual hydrogen abstraction reactions were calculated and compared to experimental data. Jaufeerally et al. [93], studied isomerization and decomposition reaction pathways for telluro-ketones using MP2. Takagi and Sakaki [94]; carried out one MP2 study of the reactivity of Ge(II)-hydride compared with Rh(I)-hydride and prediction the full catalytic cycle by Ge(II)-hydride. Watanabe et al. [95]; developed an interfragment interaction energy (IFIE) analysis with fragment molecular orbital methods (FMO) to evaluate the interactions of functional groups in drug design. They performed FMO4 calculations with MP2 perturbation theory for an estrogen receptor and the 17-estradiol complex assessing the interaction for each ligands-binding site by the FMO4-IFIE analysis. Free Energy Perturbation (FEP) for Chemical Reactivity and Ligand-Protein Interactions Zwanzig [96], developed a free energy perturbation (FEP) theory that infers the thermodynamic properties of one system from those of a slightly different system and difference in the intermolecular potentials of the two systems. In FEP the free energy difference G0i for going from the intial state state to ith state is calculated with the Zwanzig equation:

1 (E Ei )

G0i = Gi G0 = k B T ln exp 0 n i k B T

(3)


Where, T is the temperature, kB is Boltzmann's constant, and the argument of the exponential function is an average over a simulation run for state initial state. Actually, each time a new configuration and energy is is also computed and accepted after the initial state E0 and for the perturbed state Ei. Once again, FEP resembles the idea of the first sentence, the addition of small perturbations of an initial state to approach a solution for a similar but unknown system. FEP use series of smaller “windows” computed independently to ensure convergence; which is possible only for small perturbations of free energy. Then FEP can be trivially parallelized (is embarrassingly parallel) by running each window in a different CPU. FEP calculations have been used for studying host-guest binding energetics, pKa predictions, solvent effects on reactions, and enzymatic reactions. The hybrid FEP-QM/MM method use both QM and MM calculations for the study of reactions. For instance, Zhan et al. [97]; investigated how the K24N mutation affects the affinity, structure, and dynamics of p53TAD binding to MDM2 using FEP and MD. Raman et al. [98], developed a computational algorithm that performs single step free energy perturbation (SSFEP) calculations for SILCS benzene derivatives. Computational Site Identification by Ligand Competitive Saturation (SILCS) is a method used to predict drug or ligands binding sites on protein surface. SSFEP reproduce the experimental trends for experimental relative binding free energies of congeneric series of ligands of the proteins -thrombin and P38 MAP kinase. Rathore et al. [99], reviewed the use of a QM/MM-FEP method to predict binding affinities. It applies QM to ligands/inhibitors and MM for the target protein. QM/MMFEP has been applied to predict fructose 1,6-bisphosphatase inhibitors and anomalous hydration behavior of amines and amides. Jiang and Roux developed a FEP method with Replica Exchange Molecular Dynamics (FEP/REMD) allowing random moves within an extended replica ensemble of thermodynamic coupling parameters "lambda" which in turn improve calculations of absolute binding free energy of ligands to proteins [100, 101]. In addition, Jiang and Roux [100], extended and combined FEP/REMD with an accelerated MD simulations method based on Hamiltonian replicaexchange MD (H-REMD). The method use new extensions to the REPDSTR module of the biomolecular simulation program CHARMM. They studied the absolute binding free energy of p-xylene to the nonpolar cavity of the L99A mutant of T4 lysozyme to illustrate the use of the method. This group also developed a user-friendly Web interface, CHARMM-GUI Ligand Binder (http://www.charmmgui.org/input/gbinding), for FEP/MD simulations [102-104]. Inhomogeneous Fluid Solvation and Perturbed-Chain Statistical Associating Fluid Theory Inhomogeneous fluid solvation theory (IFST) and Perturbed-Chain Statistical Associating Fluid Theory (PCSAFT); are two important theories that use perturbation theory ideas. IFST [105] is a statistical mechanical method for calculating solvation free energies by quantifying the effect of a solute acting as a perturbation to bulk water. Huggins and Payne [106], used two perturbation theories calculating the hydration free energies of simple solutes using IFST and comparing the results with FEP. Huggins [107], used simula-


tions of TIP4P-2005 and TIP5P-Ewald water molecules around a model beta sheet to investigate the orientational correlations and predicted thermodynamic properties of water molecules at a protein surface. Huggins et al. [108] also analysed the interaction of Polo-Like Kinase 1 (PLK1) with CDC25c one of its natural substrates. PLK1 is a central regulator of mitosis involved in a wide range of human tumours. Li and Lazaridis [109]; developed a computational package Solvation Thermodynamics of Ordered Water (STOW). Li and Lazaridis [110] studied also the complex formed by cyclophilin A and cyclosporin A. On the other hand, Yelash et al. [111]; carried out a global investigation of phase equilibrium using the PC-SAFT approach. The same authors studied PC-SAFT for a wide range of temperature, T, pressure, p, and (effective) chain length, m, to establish the generic phase diagram of polymers according to this theory [112]. Karakatsani and Economou [113]; extended PC-SAFT to polar molecular fluids, namely dipolar and quadrupolar fluids. Nhu, Singh, and Leonhard [114]; carried out a Quantitative Structure-Property Relationships (QSRR) analysis of (PCPSAFT) and equation of state (EOS) parameters with molecular descriptors for sizes, shapes, charge distributions, and dispersion interactions for 67 compounds using QM ab initio and Density Functional Theory (DFT) methods. BIO-MOLECULAR APPLICATIONS OF QSPR MODELS Quantitative Structure-Reactivity Relationships (QSRR) Computational methods for the prediction of reactivity based on QM and/or Quantitative Structure-Reactivity Relationships (QSRR) studies with molecular descriptors of chemical structure may become useful tools for the study of synthetic or biochemical reactions. The development of new models to predict the behaviour of large sets of interrelated synthetic or biochemical reactions (reactomes) is a goal of the major importance. SOPHIA (System for Organic Reaction Prediction by Heuristic Approach) is a reaction generator software developed by Satoh and Funatsu [115]. SOPHIA recognizes suitable Atoms and/or Atomic Groups given reaction condition in a reaction database (called reactome, in the present work a). In addition, Patel and coworkers have described a new approach, Iterated Reaction Graphs (IRG) that simulates complex chemical reaction systems [116]. For example, Ignatz-Hoover et al. describes QSRR for kinetic chain-transfer constants for 90 agents on styrene polymerization at 60 oC in which three- and five-parameter correlations were obtained with R2 of 0.725 and 0.818, respectively [117]. Satoh et al. [118]; studied changes of electronic features in synthetic reactome of 131 reactions using Principal Component Analysis (PCA) and Self-Organizing Neural Networks. Long and Niu [119]; found a QSPR model for rate constants (k) for the reaction of some radicals with alkylnaphthalenes. Mu et al. [120]; studied oxidoreductasecatalyzed reactions with atomic properties of metabolites. QSAR/QSPR Models of ADMET Process The study of ADMET process of drugs and xenobiotic chemicals using computational techniques is a promising goal. Specifically, Quantitative Structure-Activity/Property Relationships (QSPR/QSAR) models are among the more


used in this sense [71, 121-126]. The problem is in narrow relationship with toxicity, tissue distribution, membrane permeability, and partition to biphasic systems [127]. In 2010 Gonzalez-Diaz guest-edited one thematic issue focused in these techniques; this issue was published in the journal Current Drug Metabolism [128]. In one of the papers, Khan reviewed the prediction of the ADMET properties of candidate drug molecules utilizing different QSAR/QSPR modeling approaches [129]. In another paper, Mrabet & Semmar reviewed the mathematical methods to analysis of topology, functional variability and evolution of metabolic systems based on different decomposition concepts [130]. In the paper after Martinez-Romero et al., the authors discussed the use of artificial intelligence, ontology, and complex network techniques to study colorectal cancer drug metabolism [131]. The paper after Fouchecourt and Beliveau, et al. [132] presented the current methods in Quantitative StructurePharmacokinetic Relationship (QSPkR) modelling along with examples using chemicals of toxicological significance. The common method involves: (i) collecting pharmacokinetic data or determining pharmacokinetic parameters (e.g. elimination half-life, volume of distribution) by fitting to experimental data; and (ii) associating them with the structural features of chemicals using a Free-Wilson model. Such QSPkRs have been developed for a few series of chemicals but their usefulness is limited to the exposure scenario and conditions under which the experimental data were originally collected. The alternative approach involves the development of QSPR models for parameters blood:air partition coefficient, tissue: blood partition coefficient, maximal velocity for metabolism and Michaelis affinity constant, of physiologically-based pharmacokinetic (PBPK) models which are useful for conducting species, route, dose and scenario extrapolations of the tissue dose of chemicals. Integrated QSPR-PBPK modelling should facilitate the identification of chemicals of a family that possess desired properties of bioaccumulation and blood concentration profile in both test animals and humans. Beliveau and Krishnan [133] developed a spreadsheet program to simulate the ADMET of inhaled volatile organic chemicals (VOCs) in humans based on information from molecular structure. The approach involved the construction of a PBPK model, and the estimation of its parameters based on QSPRs in an Excel spreadsheet. Many authors [132-187] are trying to extend QSPR models to the study of as diverse as posible partition systems of biological relevance. Sedykh et al. [188], used DRAGON and MOE to develop a QSAR model of membrane transporters. These proteins are very important in drug ADMET process and drug resistance. The dataset studied contains more than 5,000 interaction for >3,700 molecules with transport and/or inhibition of several drug transporters such as MDR1, BCRP, MRP1-4, PEPT1, ASBT, OATP2B1, OCT1, and MCT1. TOMO-COMD Models of Drug Absorption


to obtain the QSPR model able to discriminate higher absorption compounds from those with moderate-poorer absorption. The best LDA model has an accuracy of 90.58% and 84.21% for training and test set. The percentage of good correlation, in the virtual screening of 241 drugs with the reported values of the percentage of human intestinal absorption (HIA), was greater than 81%. In addition, Multiple Linear Regression (MLR) models were developed to predict Caco-2 permeability with determination coefficients of 0.71 and 0.72. These results suggest that the proposed method is a good tool for studying the oral absorption of drug candidates [189]. In a previous work, the Permeability Coefficients in Caco-2 cells (P) for 33 structurally diverse drugs were well described using quadratic indices calculated with TOMOCOND. A quantitative model that discriminates the highabsorption compounds from those with moderate-poor absorption was obtained for the training data set, showing a global classification of 87.87%. In addition, two QSPR models, through a multiple linear regression, were obtained to predict the P [apical to basolateral (AP-->BL) and basolateral to apical (BL-->AP)]. These results suggest that the proposed method is able to predict the P values and it proved to be a good tool for studying the oral absorption of drug candidates during the drug development process [190]. MARCH-INSIDE Mean Descriptors We have introduced, validated, applied, and reviewed the method MARCH-INSIDE; including applications in medicinal chemistry [77], and prediction of drugs ADMET process [191]. The MARCH-INSIDE approach use a Markov Chain method to calculate the kth mean values of different physicochemical molecular properties kt(mfi) of type (t) for molecules ith molecules (m) with different input roles or functions (f). These kt(mfi) values are calculated as an average of atomic properties (j) for all atoms in the molecule and its neighbors placed at a topological distance d k. The parameter k is called the parameter of the Markov Chain, the natural power of the Markov matrix. For instance, it is possible to derive average estimations of molecular refractivities k MR(mfi), partition coefficients kP(mfi), and hardness k(mfi ) for atoms placed at different topological distances d < k [192]. In this work, we use values of k = 5 only and omit the symbol k in for the sake of simplicity. It means molecules that play different roles in a transformation process (tp). For instance, in the first experiment of this work we are going to calculate the kt(mfi) for the molecules involved in a chemical reaction (cr) can be calculated for the ith substrates kt(si), organolithium reagents kt(oi), chiral ligands of catalysts k t(li), products t(pi). In the second experiment we are going to calculate kt(mfi) values only for drugs t(di). Last, in the third experiment we are going to calculate kt(mfi) values for the ations t(mi+) and anions t(mi-) ions of surfactants, respectively. In this first work we are going to calculate only one type of t(mqi) values, the mean electronegativities (mqi): k

The software TOMO-COND is a promising tool used in the stage (1) to calculate indices of drug structure in QSPR studies of drug ADMET process. Castillo-Garit et al., reported a QSPR study of the largest data set of measured P(Caco-2), consisting of 157 structurally diverse compounds. LDA, implemented in STATISTICA, was used in stage (2)

1717

t (mqi )= pk ( j ) j

( 4)

j

It is possible to consider isolated atoms (k = 0) in the estimation of the molecular properties 0, 0, 0 MR, 0, 0P. In this case the probabilities 0p(j) are determined without considering the formation of chemical bonds (simple additive



scheme). However, it is possible to consider the gradual effects of the neighboring atoms at different distances in the molecular backbone. In order to reach this goal the method uses a MM, which determines the absolute probabilities k p(j) with which the atoms placed at different distances k affect the contribution of the atom j to the molecular property in question. 1 p1, 2 1 p2,1 k t (mqi )= 0 p (1 )0 p (2 )…0 p (n ) . . 1 pn ,1

[

]

1

p1, 2

1

p1,3

.

1

p2, 2 .

1

p2,3 .

. .

.

.

.

.

.

.

k

p1,n 1 p 2 ,n 2 n . . = k p ( j ) j j =1 . . 1 pn , n n 1

1

(5)

Where, from left to right, the first term is k, which is the average molecular property considering the effects of all the atoms placed at distance k over every atomic property j. The vector on the left-hand side of the equation contains the probabilities 0p(j) for every atom in the molecule, without considering chemical bonds. The matrix in the centre of the equation is the so-called stochastic matrix. The values of this matrix (1pij) are the probabilities with which every atom affects the parameters of the atom bonded to it. Both kinds of probabilities 0p(j) and 1pij are easily calculated from atomic parameters (j) and the chemical bonding information: 0

p ij =

j

(6)

n

k =1

k

1

p ij =

ij j n

ik

k

(7 )

k =1

The only difference is that in the probabilities 0p(j) we consider isolated atoms by carrying out the sum in the denominator over all n atoms in the molecule. On the other hand, for 1pij chemical bonding is taken into consideration by means of the factor ij. This factor has the value 1 if atoms i and j are chemically bonded and it is 0 otherwise. All calculations were performed using the program MARCH-INSIDE version 3.0 [193]; which can be obtained for free academic use, upon request, from the corresponding author of the present work. MARCH-INSIDE Perturbation Models for Drug-Tissue Distribution Profiles One can consider a hypothetical situation in which a molecule is, as a whole, at one side or phase (s1) of the biphasic system (s1/s2) at an arbitrary initial time (t0). It is interesting to model the gradual passage of all the interconnected atoms in the molecule from s1 to s2. For the sake of simplicity, all the partition coefficients P(s1/s2) were written in such a way that partition undergoes from the less organized system (s1) to the more organized (s2), i.e. from water to vegetable oil, or from plasma to tissue. Based on this picture one can characterize distribution of one specific chemical in one specific system with the spectral moments k(s2/s1), entropies k(s2/s1), or changes in free-energy Gk(s2/s1). We can calculate these parameters for environment-dependent molecular Markov matrices using the software MARCH-INSIDE [193-196]. In a previous work [194], we calculated total and local k(s2/s1) values for a large data series of 413 chemicals and >10 different partition systems, to seek this model: 5.79 + 2.49 PS s2 = 0.84 0 s2 1 s2 5 s2 7.21 s1 s1 Cunst s1 H Het s1 Csat

(8)

Where, PS(s1/s2) is a real-value output variable called the partition score (PS) used to predict the propensity of the drug to undergo partition in the system under study. The subindices Cunst, H-Het and Csat express that we calculate local spectral moments summing up only unsaturated carbon atoms, labile hydrogen or saturated carbon atoms rather than all of the atoms present. The present LDA model showed a p-level < 0.01, which means that accepting the model as valid presupposes an error level of less than 1% in the separation of L and U-type of compounds with respect to different release systems. Bellow the model appear the number of Total, L, and U-type compounds (N(T), N(L), N(U)) as well as the ratios of classification in training and cross-validation. The values of accuracy in all these experiments are enough high to be accepted as correct according to previous uses of LDA in literature [197-200]. In this recent work, we constructed a multi-species complex network based on the mtQSPR model developed. This drug-drug network has 2060 pairs. The construction of drug-target networks is of the highest importance for the discovery of drugs with direct effect and/or long-range network effect over different targets, like allo-network drugs [201-204]. In a another work [195], we propose by the first time a MARCH-INSIDE model for thermodynamic parameters of the drug-biphasic system partition process. The model includes variables like time, the chemical structure of 423 drugs, and 14 different partition systems; including distribution to biological tissues of different biological species (fluxomics): (8) PS s2 = 3.03 0 s2 + 87.49 2 s2 220.41 3 s2 + 133.87 5 s2 s1 s1 Tot s1 Het s1 Het s1 Het s s s s 2 2 2 2 + 5.81 7.98 + 3.85G0 3.55G1 0 1 1.32 s1 H Het s1 H Het s1 H Het s1 H Het

The model present an overall Ac of 92.1 % (293 / 318 cases) in training series the model have shown 90% (36 out of 40 cases) in predicting ones, which are excellent values. In the third work of the same series [196], we redefined the free energy based descriptor (Gk). Based on Gk, we developed a model to predict the partition behavior of 1300 drugs and other chemicals for 38 different partition systems of biological and environmental significance with Ac of 91.7988.92 %. We check out inversion of the partition direction for each one of the 38 partition systems evidencing that our models correctly classified 89.08% of compounds with an uncertainty of only ± 0.17% independently of the direction of the partition process used to seek the model. This model do not incorporated entropy terms as in the work of AgüeroChapin, et al.: PS s 2 = 0.36 + 3.1!G5 s 2 1.01!G5 s 2 s1 s1 Tot s1 H Het s s + 1.54!G0 2 0.89!G1 2 s1 Tot s1 Csat

(9 )

A close inspection to the three models reveals that the terms used, more clearly in the case of (Gk), resemble a perturbation function useful for a QSPR-Perturbation model. They depend and can model changes on the structure of the drug and the partition system. However, we cannot predict directly with the model perturbations (changes) in both the structure and one of the phases of the partition system with respect to other known partition process.



Previous QSRR-Perturbation Models of 1,2-Additions of Organometallic Reagents to Imines In a previous work, we used a QSRR model to investigate which variables more strongly influence the change on enantioselectivity in a set of reactions that were previously reported in the literature [205-217]. The asymmetric reactions studied are 1,2-additions of organometallic reagents to imines is a powerful tool to form carboncarbon bonds [218227]. This allows preparing enantiomerically enriched amines with a stereogenic centre at the -position, important as chiral auxiliary ligands, resolving agents, and building blocks for the synthesis of natural and unnatural compounds, and their pharmacological properties [228-232]. Using the QSPR-perturbation theory the best model found for this synthetic reactome was: ee(R )nr = ee(R )rr # 6.60 + 5.80 ! Pp # 4.63 ! H l # 23.08 ! Ds + 44.18 ! t r # 1.23 ! Tr

(37 )

# 0.18! Ta + 0.24! A e + 1.90 ! S o # 8.22 ! P o # 0.24 ! M i n = 17404

R 2 = 0.803 R 2 adjusted = 0.803 F = 7120.7 p < 0.00001

Previous QSPR Model of Drugs and Surfactants Micelle Self-Aggregation In a recent work [236], we developed a linear mt-QSPR model able to predict the probability which with the compound (i-th) presents an experimental value of the property (j-th) higher than the average value of this property for this data set. The best model found using LDA was the following:

( ) ( )

( ) ( )

+ 0,244894 mi 0,047320 mi 5

5

+ 1,919078 mi

avg

5

n = 1085 2 = 221,24m29

(42)

+

+ 3,4360775 mi

addition, n is the number of cases used to train the model and 2 is Chi-square statistics with a given p-level = p(2). In this previous work [236], we also developed some MIANN models that improve the results obtained by LDA. For instance, the MIANN model MLP1 with profile MLP 6:6-8-1:1 improves LDA in terms of Sensitivity in both train and external validation series. Sensitivity of LDA was 72% whereas this MIANN model presented a sensitivity > 84% in both series. It means that MIANN is able to improve LDA in 10 percent points. However, this at cost of complicating the linear model transforming it into a non-linear ANN with H1 = 8 (hidden neurons). Notably both the MLP1 and MLP2 have an AUROC = 0.89. However, is well known that MLP2 needs a second hidden layer of neurons, 10 more neurons in the present case (profile MLP 6:6-10-1:1), which complicates the model to gain nothing in terms of Sensitivity and Specificity with respects to MLP1. NEW QSPR-PERTURBATION THEORY

Where, n is the number of cases (reaction pairs) used to train the model, R2 and R2adjusted are the train and adjusted square regression coefficients, F is Fisher ratio, and p the level of error. This model, with ten variables, predicts correctly 80.3% of variance of the data set with a standard error of 29.35%. These results indicate that we developed an accurate model according to previous reports of QSRR models [233-235]. It is straightforward to realize that the previous model used different structural descriptors (mqi) for each type molecule and ideally forms of both the variation state V(qi) and the *(qi) functions to construct the perturbation terms V(qi). The perturbation terms used are the differences in: the partition coefficient of products (Pp), hardness of chiral ligands (Hl), dipolar moment of solvents (Ds), reaction times (tr), reaction temperatures (Tr), addition temperatures (Ta), average enantiomeric excess for reactions using same procedure (Ae), substrate molar refractivity (Mi), steric constant (So) and hardness (Po) of organolithium compounds, respectively.

Si (z ( s (mi )) > 0) = 3,91375 +0,011557!e c (si ) 0,012303 T (K )j

1719

+

avg

p ( 2 )< 0.01

It means, surfactants with a higher or lower-than-theaverage value of the observed property j-th. The independent terms of the equation are the following. The first c(si) is the concentration of the salt in the solution used. The two next (mi-) and (mi+) are the mean electronegativities of the anion or cation. The two last (mi-)savg and (mi+)savg are average value of (mi-) and (mi+) for those ions of surfactants with z(s) > 0 for a given property of type s. These terms were calculated using the software MARCH-INSIDE. In

Introduction to New QSPR-Perturbation Theory Let be a set of molecules mqi that undergoes a transformation process tp. The tp involve at least chemical reaction (cr) and/or one physicochemical process (pp) like organic synthesis reactions, biochemical reactions, or drug metabolism and/or physicochemical processes like drug-target interaction, self-aggregation in complex systems, or absorption, distribution, and excretion in a living organism. It means that the tp involve at least one cr that change the structure and/or at least one pp that shift the state of this set of ith molecules (mqi). We also have to consider that a tp may involve more than one input/output molecules; which play different distinguishable roles or functions fth in the crth reaction or ppth process. Another important fact is the existence of multiple classes sth of output efficiency parameters s(mqi) to quantify the efficiency with which the molecules are transformed by the crth reaction or ppth process involved in the transformation process tpth . In this work, we propose a general chemo-informatics theory for complex molecular systems that incorporates ideas taken from QSRR models and perturbation theories in order to account for all the aspects mentioned in the previous paragraph. As a result, we should state that the model presented is neither a classic QSPR nor a quantum perturbation theory commonly used in physics. We shall focus mainly in the prediction of multiple classes of output efficiency parameters s(pi)ntp with which a new transformation process (ntp) transforms the chemical structure and/or the physicochemical state of the molecules with respect to the values of multiple efficiency parameters s(pi)itp of one initial, known, or reference transformation process of (itp). We put special emphasis in the fact that this ntp is essentially a perturbation, shift, or change in output efficiency s(mpi) that takes place after a change, variation, or perturbation (V) in the initial or input structure and/or physicochemical boundary conditions of the itp. Both the ntp and the itp may involve at least one cr and/or pp. It means that ntp = new chemical reaction (ncr) + new physicochemical process (npp) and itp = reference or initial physicochemical process (ipp) and/or chemical reaction (icr). Shortly, we can annotate this as follow ntp = npp + ncr 0) is a real-valued score (output of the linear model) that can be used to discriminate between surfactants with high probability p(zij > 0) of showing a high zij > 0 and others with high probability p(zij 0) of presenting a zij 0. Considering that zij is an standardization coefficient used to scale the values of the different properties to a single adimensional scale. We calculated this parameter as follow: zij = (yij - j)/SDj. Where, yij is the value of the jth property of the ith molecule; j is the average value of his property in the data set and SDj the standard deviation. These parameters allowed us to classify the surfactants as “active” => C = 1 => zij > 0 => yij > j or “non-active” => C = -1 => zij 0 => yij j. (z ij > 0)n = a r (d i )r + bqi V (qi )ad + cqi V (qi )dm + d qi V (qi )md + e0

(35)

(z ij > 0)n = ad z (d i )itp + at z (ti )ntp + ad z (Ti )ntp + z (ci )ntp + (qi )ntp + exp(p (ev ))

(36)

t

t

t

mi

mi

mi

t

+ cqi [z (ti )n z (Ti )n z (ci )n (qi )n exp(p (ev )) z (ti )r z (Ti )r z (ci )r (qi ) exp(p (ev ))] mi

+ d qi z (ti )n z (Ti )n z (ci )n (qi )n exp(p (ev ))+ e0

NEW QSPR-PERTURBATION MODELS New QSRR-Perturbation Model for Intra-Molecular Carbolithiations A particular class of reaction of high interest in organic synthesis is the so-called carbolithiation. The carbolithiation reaction offers an attractive pathway for the efficient construction of new carbon-carbon bonds by addition of an organo-lithium reagent to non-activated alkenes or alkynes, with the possibility of introducing further functionalization on the molecule by trapping the reactive organolithium intermediates with electrophiles. The intramolecular variant of this reaction has been applied mainly with alkyl- and alkenyllithiums, though there are also some examples of cycloisomerization of alkenyl substituted aryllithiums, generated by metal-halogen exchange. In particular, this type of intramolecular carbolithiation reaction has found application in the synthesis of both carbocycles and heterocycles, with a high degree of regio- and stereoselectivity in the formation of five-membered rings, although its application to larger rings is still not general [237-246]. When alkenes are used, up to two contiguous stereogenic centers may be generated, which may be controlled by using chiral ligands for lithium, and so opening new opportunities for application of this



methodology to asymmetric synthesis. The naturally occurring alkaloid (–)-sparteine is the most widely used chiral ligand in enantioselective carbolithiation reaction [247]. The procedure has been successfully applied for the formation of five membered rings with high levels of stereocontrol. Thus, Bailey and Groth reported independently the intramolecular carbolithiation of N-allyl substituted o-haloanilines in the enantioselective synthesis of indolines ee [248-251], while Barluenga described the preparation of dihydrobenzofurans in high ee, starting from allyl o-haloaryl ethers [252]. However, few examples of enantioselective intramolecular 6-exo carbolithiation reactions have been described. In this context, Lete et. al. previously reported the preparation of 4substituted 2-phenyltetrahydroquinolines from Nalkenylsubstituted 2-iodoanilines via intramolecular carbolithiation reactions. The stereochemical outcome of the carbolithiation reactions depends on the nature of organolithium employed to perform the lithium-halogen exchange, the solvent, or the use of additives, for example, TMEDA or chiral bidentated ligands such as ()-sparteine [253]. Thus, the 2,4disubstituted tetrahydroquinolines are obtained with moderate diastereoselectivities (up to 77:23) and with ee up to 94% when Weinreb amide derivatives are used. On the other hand, we have shown that although the intramolecular carbolithiation reactions of 2-alkenyl substituted N-benzylpyrroles constitutes an efficient route to pyrrolo[1,2-b]isoquinolines, the use of (–)-sparteine as a chiral ligand led to low levels of enantioselection [254]. In the first example studied in this paper, we are going to develop a QSPR model for a very large set of input-output perturbations in the enantioselective intramolecular carbolithiation reactions via aryllithiums generated by halogen-lithium exchange, developed by us and others (see Fig. 1). We consider the following six roles or types of molecules substrates (q = s), solvents (q = v), ligands of chiral catalysts (q = l), organolithium reactants (q = o), electrophiles (q = e), and products (q = p). Consequently, we can at least calculate six molecular descriptors of the same type; one per each one of the ith molecules that play the different roles in the reactome. We refer to, molecular descriptors of substrates (mqi), solvents (mvi), electrophiles (mei), ligands (mli), organolithium reactants (moi), and products (mpi). As a results, we can calculate six values of *(mqi) and five perturbations V(mqi) for a given set of initial and final conditions. The general equation of this model is the following: ( s (pi ))nr = e ppi ( s (pi ))rr + bpipi * (pi )nr e pipi * (pi )nr + esis V (si )+ evivi V (vi ) nr + eeiei V (ei )+ ellii V (li )+ eooi V (oi )+ e0

(38)

We propose herein, for the first time, a QSRR model able to predict both the change in yield and enantiomeric excess for two pair of reactions after at least one change in chemical structure and/or perturbation of reaction variables of at least one of the molecules involved. After optimization of coefficients the best model found with LDA was: ( s (pi ))ncr = -0.00105976 V (pi )icr + 0.13496123 V (si )+ -0.00000065 V (vi )

+ 0.08477068 V (ei )- 0.00029331 V (li )- 0.00029331 V (oi )+ 0.01087415

(39)

In this model, we used an identity functions for conditions of both the new (ncr) and the initial chemical reaction (icr): (T(qi)) = T(qi), (t(qi)) = t(qi), and (c(qi)) = c(qi). The definition of the different perturbation terms is as follow. The perturbation term for the product pi is V(pi) =

s(pi)icr·[(pi)·exp(p(R/pi)] = s(pi)icr·[(pi)·exp(p(R/pi)ncr (pi)·exp(p(R/pi)icr]. The perturbation term for the substrate si is V(si) = ((si)·exp(p(R/si)) = [(si)·exp(p(R/si)ncr (si)·exp(p(R/si)icr]. The perturbation term for the solvent vi is V(vi) = (vi). The perturbation term for the electrophile ei is V(ei) = (ei). The perturbation term for the ligand li is V(li) = (c(li)·(Lig)·exp(p(R/li)). The perturbation term for the organolithium reagent oi is V(oi) = (c(oi)·T(oi)add·(oi)·exp(p(add)). We used here only one type of molecular descriptor for all molecules (qi). The parameter (qi) is the average value of electronegativity for each atom and all its closer neigbour atoms placed at topological distance d 5. This parameter approximates the distribution of electrons in the molecule that can be calculated very fast for large libraries of compounds using the software MARCH-INSIDE. This model uses an additive approach to calculate the perturbation functions V(qi) but combines additive and multiplicative *(qi) functions. In Table 1 we give the classification results for this model. Notably, we found another QSPR-Perturbation model exactly with the same variables but applicable only to predict ee(pi) and not yld(pi). This model can be used in the case we are interested on improving the ee and less interested on the yield. The coefficients of this second model, written in the same order than in equation (39) are the following: 0.02658387, 0.16603794, -0.00000756, 0.11320999, 0.00060486, 0.00037813, -0.00151956. This is a more specific model useful to predict only ee(pi) and not for yield but has notably higher values of Ac, Sp, and Sn >95% in training and validation, see Table 1. A very notable feature is related to the perturbation term for the product V(pi) = s(pi)rr·((pi)·exp(p(R/pi)). Here, s(pi)rr is called efficiency of reference and may be either the yield of this reaction s(pi)rr = yld(pi)rr or the enantiomeric excess of the same reaction 0(pi)rr = ee(pi)rr. If we make the substitution 1(pi)rr = yld(pi)rr in the model we can predict the probability with which the new reaction has a yield yld(pi)nr >95%. On the other hand, if we substitute 0(pi)rr = ee(pi)rr in the model we can predict the probability with which the new reaction produce an enantiomeric excess ee(pi)nr >95%. This is a very strong result because it determines that this is probably the first multi-objective optimization (MOOP) model for the effect of structural or condition perturbations in reactions. In particular, a MOOP model that predict both changes in reaction yield and enantiomeric excess with a single equation. Nicolau et al. [255], discussed the importance of MOOP methods for molecular optimization. In addition, Cruz-Monteagudo et al. [250-254], published a series of seminar works about MOOP methods combined with the analysis of desirability to optimize various aspects of the same compound. In fact, this QSRR-Perturbation model may predict the formation of different chirality patterns in the product of the new reaction. The parameter p(R/pi)nr describe the different chirality patterns in the product. This prediction depends on the chirality patterns of the ligand p(R/si)nr of this reaction. The prediction depends also on the chirality patterns of both ligand p(R/li)rr and products p(R/pi)rr of the reaction of reference. In Table 2, we give the values of p(R/qi) for different chirality patterns and explain the calculation of these input probabilities.


R2

Y

RLi, L*

R3 n

R1

1723

R4

R3

X R1


n R2

Y

R4

X = Br, I; Y = NMe, NBn, N-allyl, O; n = 0,1 R1 = H, Me, F, OBn, OMe, t Bu, TMS R2 = H, Ph R3 = H, i Pr, Ph, CH2OH, CH2OMe, CH2OTIPS, CH2SPh, CH2NMe2 R4 = H, CONEt2, CONMe(OMe)

R2

R2

I R1

RLi, L*

R1

N

N

R1 = H, OMe R2 = H, CONEt2, CONMe(OMe)

L*:

H N

N H

(–)-sparteine

N

H

N

H

N

H (+)-sparteine surrogate

R1 N

R3

Ph R2

R1 = OMe, OEt R2 =OMe, NMe2, NMeEt, NMei Pr R3 = Me, Ph

Fig. (1). General scheme for intramolecular carbolithiations studied here.

QSPR-Perturbation Hunt of Sparteine Surrogates as Chiral Ligand for Asymmetric Synthesis ()-Sparteine, a naturally occurring lupin alkaloid, is widely used as a chiral ligand for asymmetric synthesis. To address the limitation that sparteine is only available in significant quantities as its ()-antipode, O'Brien’s group has introduced a family of (+)-sparteine surrogates that are structurally similar to (+)-sparteine but lack the D-ring. In 2003, O’Brien et al. [261] synthesized and evaluated three chiral diamines towards the design of new sparteine surrogates in the lithiation-substitution of N-(tert-butoxycarbonyl)pyrrolidine. These authors concluded that, for the asymmetric lithiation substitution of N-Boc pyrrolidine, a rigid bispidine framework and only three of the four rings of ()-sparteine are needed for high enantioselectivity. They also shown that diamine (1R,2S,9S)-11-methyl-7,11diazatricyclo[7.3.1.0(2,7)]tridecane is the first successful (+)-sparteine surrogate. In 2004, O’Brien [262] prepared three new (+)-sparteine-like diamines from ()-cytisine and evaluated them as sparteine surrogates in the alpha-lithiation rearrangement of cyclooctene oxide and the palladium(II)/diamine catalyzed oxidative kinetic resolution of 1indanol. The new diamines exhibited opposite enantioselectivity to that observed with ()-sparteine. The optimal N-Me diamine was evaluated with much success in five other ()sparteine-mediated processes involving different metals

(lithium, magnesium, and copper) and different types of reaction mechanisms. In 2008, O'Brien [263] published the paper entitled “Basic instinct: design, synthesis and evaluation of (+)-sparteine surrogates for asymmetric synthesis”. In this feature article the authors gave a detailed comparison of (+)-sparteine derivatives with ()-sparteine in a range of asymmetric reactions. The main O'Brien’s conclusions are: (i) the (+)-sparteine surrogates are most easily prepared starting from ()-cytisine extracted from Laburnum anagyroides seeds; (ii) in nearly all examples, use of the (+)-sparteine surrogates produced essentially equal but opposite enantioselectivity compared to ()-sparteine and (iii) the N-Mesubstituted (+)-sparteine surrogate is the most useful and versatile of those investigated till now. Previously, O'Brien et al. [264] studied enantioselective lithiation of N-Bocpyrrolidine using sec-butyllithium and isopropyllithium in the presence of sparteine-like diamines using different computationally levels through to B3P86/6-31G*. From these works, we can conclude that we can introduce structural changes (perturbations) in the structure of sparteine to design new chiral ligands for asymmetric synthesis. Another interesting conclusion is that computational technique may help us to rationalize somehow this process. In any case, we cannot guarantee that the new chiral ligand obtained after perturbation of sparteine structure shall work optimally in the same conditions (t, T, Tadd, Solvent, etc.)


Table 1.


Results of QSPR-Perturbation Models.

Perturbation

*(qi)

Stat.

Data

Pred.

Synthetic Reactions (ee and yld)

type

type

Param.

sub-set

%

s(pi)nr 95%

s(pi)nr > 95%

Additive

Additive

Sp

s(pi)nr 95%

98.7

81794

1040

+

Sn

s(pi)nr > 95%

73.1

382

1040

Multiplicative

Ac

Total train

98.3

Sp

s(pi)nr 95%

98.7

27264

346

Sn

s(pi)nr > 95%

73.0

128

346

Ac

Total cv

98.3

Perturbation

*(qi)

Stat.

Data

Pred.

Synthetic Reactions (ee only)

type

type

Param.

sub-set

%

ee(pi)nr 95%

ee(pi)nr > 95%

Additive

Additive

Sp

ee(pi)nr 95%

100.0

41062

0

+

Sn

ee(pi)nr > 95%

97.6

26

1040

Multiplicative

Ac

Total train

99.9

Sp

ee(pi)nr 95%

100.0

13686

0

Sn

ee(pi)nr > 95%

97.2

10

346

Ac

Total cv

99.9

Perturbation

*(qi)

Stat.

Data

Pred.

ADMET process

type

type

Param.

sub-set

%

zi(mj)n 1

zi(mj)n > 1

Additive

Additive

Sp

zi(mj)n 1

100.0

110901

5

+

Sn

zi(mj)n > 1

85.6

341

2028

Multiplicative

Ac

Total train

99.7

Sp

eff(pi)nr 95%

100.0

36989

2

Sn

eff(pi)nr > 95%

85.9

113

686

Ac

Total cv

99.7

Perturbation

*(qi)

Stat.

Data

Pred.

type

type

Param.

sub-set

%

zi(mj)n 0

zi(mj)n > 0

Additive

Additive

Sp

zi(mj)n 0

95.0

97205

5082

+

Sn

zi(mj)n > 0

94.4

5478

93181

Multiplicative

Ac

Total train

94.7

Sp

zi(mj)n 0

94.9

32326

1748

Sn

zi(mj)n > 0

94.7

1726

31135

Ac

Total cv

94.8

than sparteine does. Consequently, we have good reasons to open a computer-aided “hunting season” for sparteine-like derivatives for asymmetric catalysis. We need to predict not only the efficiency of transformation 0(li) = yld(%) and 0(li ) = ee(%) for the new ligand (li) in the optimal conditions for reactions with sparteine. We have to predict also the optimal conditions (perturbations in t, T, Solvent, etc.) for the new ligands with respect to sparteine. In this sense, our new

Self-Aggregation

QSRR-Perturbation model may become a useful tool to shed some light about the potential of new sparteine surrogates. In Fig. 1 (bottom), we show the structure of O’Brien’s (+)sparteine surrogate. One of these compounds called our attention specially. We refer to the ligand O’Brien (+)sparteine surrogate 1 (in this work ligand L36). As a sort of example, we have predicted the values of (ee > 95%) as well as probability scores p for > 9000 perturbations of


Table 2.


1725

Probability of Chirality Patterns.

Chirality

p(R/qi)

Center order and p(R)center values for different centers

patterns

valuesa

Products chirality

p(R/pi)

2R4R

0.60

1

1

0.5

R

0.53

1

0.5

R or S

0.50

0.5

2S4R

0.55

10R10aS

1st

2nd

3rd

4th

Chiral 5th

centers

0.5

0.5

2

0.5

0.5

0.5

1

0.5

0.5

0.5

0.5

1

0.25

1

0.5

0.5

0.5

2

0.50

1

0.25

0.5

0.5

0.5

2

2SR4RS

0.50

0.5

0.5

0.5

0.5

0.5

2

2RS4RS

0.50

0.5

0.5

0.5

0.5

0.5

2

S

0.48

0.25

0.5

0.5

0.5

0.5

1

Non-chiral product

0.50

0.5

0.5

0.5

0.5

0.5

0

Ligand chirality

p(R/li)

7S7aR14S14aS

0.43

0.25

1

0.25

0.25

0.5

4

2S

0.48

0.25

0.5

0.5

0.5

0.5

1

S

0.48

0.25

0.5

0.5

0.5

0.5

1

4S4'S

0.50

1

0.25

0.5

0.5

0.5

2

1R2R

0.60

1

1

0.5

0.5

0.5

2

1S2S

0.45

0.25

0.25

0.5

0.5

0.5

2

1S4S

0.45

0.25

0.25

0.5

0.5

0.5

2

4aR8aR

0.60

1

1

0.5

0.5

0.5

2

1R2S

0.50

1

0.25

0.5

0.5

0.5

2

1S2R

0.45

0.25

0.25

0.5

0.5

0.5

2

R

0.53

1

0.5

0.5

0.5

0.5

1

3R3aR6S6aR

0.68

1

1

0.25

1

0.5

4

3R3aR6R6aR

0.83

1

1

1

1

0.5

4

3aR5R6S6aR1S

0.75

1

1

1

1

0.25

4

3aR5R5aS8aS8bR

0.65

1

1

0.25

0.25

1

5

1R5S11aS

0.45

1

0.25

0.25

0.5

0.5

3

Non-chiral ligand

0.50

0.5

0.5

0.5

0.5

0.5

0

No ligand

0.00

0

0

0

0

0

0

R or S chiral substrate

0.53

1

0.5

0.5

0.5

0.5

1

Stereogenic products atom centers

Stereogenic products atom centers

a

p(R/qi) = SUM(order·p(R)center)/SUM(orders) is the probability of finding a center with chirality R if we inspect the atoms in a predetermined order according to IUPAC nomenclature numbering, for instance: p(R/qi) for 3R3aR6S6aR is p(R/qi) = 0.68 = (1·p(R) + 2·p(R) + 3·p(S) +4·p(R) + 5·p(NC))/15 = (1·1 + 2·1 + 3·0.25 +4·1 + 5·0.5)/15, the elemental event probabilities are p(R) = 1 > p(NC) = 0.5 > p(S) = 0.25 > p(NL) = 0.

theoretic intramolecular carbolithiations using L36 as the chiral ligand. We do not used the general model useful for 0(li) = yld(%) and 0(li) = ee(%) but the second more specific model useful only for 0(li) = ee(%) but very much accurate. The other conditions (t, T, solvent, organolithium,

electrophiles, etc.) were taken from known reactions of the literature. In this context, the values of p = p(ee > 95%) help to select the top-ranked reactions. In a sub-set of predictions, we used exactly the same conditions of reactions of reference (rr) reported for already-known reactions based on ()-


sparteine. Theoretically, the value of ee of these reactions should be higher than 95%. It should be also in many cases higher than the ee for the reactions of reference if we use L36 instead of () sparteine. The model also predicts an inversion of configuration in the product. This coincides with the expected results due to an inversion of configuration in the chiral ligand with the substitution of ()-sparteine by L36 a (+)-sparteine surrogate. We present these reactions in Table 3. The structures of all compounds involved in these reactions have been stored in the form of SMILE codes in a supplementary material file (SM1.pdf), available upon request to corresponding author. New QSRR-Perturbation Model for Drug ADMET Process CHEMBL is one of the largest databases containing biological activity information for a large number of compounds. Currently, the database contains 5.4 million bioactivity measurements for more than 1 million compounds and 5200 protein targets. Access is available through a webbased interface, data downloads and web services at: https://www.ebi.ac.uk/chembldb [265]. In addition, despite of the large number of assays described many drugs have been assayed only for some selected tests. Consequently, predictive models may become also an important tool to carry out an “in silico” mining of CHEMBL predicting new results for drugs already released. The mining of CHEMBL using different computational tools have been recognized by Mok et al. as a very interesting source of new knowledge [266]. In special, Quantitative Structure-Toxicity Relationships (QSTR), or the same QSAR in toxicology, have been widely used to predict toxicity from chemical structure and corresponding physicochemical properties [267]. Unfortunately, almost current QSAR/QSTR models are able to predict new outcomes only for one specific assay of pharmacological activity or ADMET process. We can evade this drawback of classic QSAR/QSPR models using multi-target QSAR/QSPR approaches (mt-QSAR/QSPR) to predict complex datasets determined in multiplexing assay conditions (mj) as is the case of CHEMBL [68, 268]. In this second example, studied in this paper, we develop a QSPR-Perturbation model for metabolomic-fluxomic data useful in drug discovery. The model classify with Ac, Sn, and Sp of 85-100% more than 150,000 cases. The data contains experimental shifts in upto 18 different pharmacological parameters determine >3000 assays used to quantify the ADMET properties and/or interactions between 31723 drugs and 100 targets (metabolizing enzymes, drug transporters, or organisms). We need molecular descriptors for only two molecules, new drug (n) used in the new assay and reference drug (rd) used in the assay of reference; which are of the same class of molecular entity (drugs). Consequently, we can at least calculate two molecular (di)n and (di)r descriptors of the same type; one per each one of drugs. We propose herein, for the first time, a QSRR-Perturbation model able to predict shifts in a high number of output experimental measures of efficiency for drug ADMET process due to initial perturbations in chemical structure and/or assay variables. The best QSPR-Perturbation model found here with LDA was:

González-Díaz et al. (z s (d i ))ntp = 0.357310 z s (d i )itp - 0.255938 (d i )Cins + 0.000026 V (d i )Tot

+ 0.00025 V (d i )Hal - 0.000264 V (d i )Het + 0.00025 V (d i )H Het + 0.357310

(41)

The first input term is the value zs(di)itp of z-score for the efficiency of the initial process (s(di) standardized). The other are V(di)g = [z(mej)·z(aj)·z(tj)·z(atj)·(di)g·exp(p(cj))]ntp - [z(mej)·z(aj)·z(tj)·z(atj)·(di)g·exp(p(cj))]itp. These are perturbation terms of the type additive-multiplicative. It means that we calculate a difference (additive perturbation function) between two state functions V(di)g formed by products of variables. The variables multiplied are the z-scores used to define all the conditions of assay and a molecular descriptor used to codify structural information. The z-scores have been = s(di) – calculated as follow zs(s(di)) (AVG(s(di))/SD(s(di)). The values s(di) and SD(s(di) are the values of average and standard deviation of zs(s(di)) for all molecules in the same set s. The sets here are s1 = experimental parameter measured (me), s2 = biological assay (a), s3 = molecular or cellular target, s4 = assay type. The corresponding z-scores for these sets are z(mej), z(aj), z(tj), z(atj). It means, that if we change the values of these scores we simulate perturbations in assay conditions including the experimental parameter measured, biological assay), molecular or cellular target, and assay type. In Table 4, we give the values of these z-scores for 98 different molecular and cellular targets. The assay types are Binding (B), Functional (F), and ADMET (A). Here we used only one type of molecular descriptor for all molecules (di)g. The parameter (qi)g is the average value of electronegativity for each atoms in the group of atoms (g) and all its closer neighbor atoms placed at topological distance d 5, explained in the previous section. We also included one event represented by the probability p(cj). The values of this probability are p(cj) = 1, 0.75, and 0.5 when the data is reported as curated three different levels of accuracy. Gozález-Díaz et al. [269-273] and SpeckPlanche et al. [274-283] introduced multi-target/multiplexing QSAR models that incorporate this type of information using the resent and other schemes. In any case, the present is probably the first QSPR-Perturbation model useful to predict multiple input-output perturbations in ADMET processes in Metabolomics and Fluxomics. New QSPR-Perturbation Model for Drugs and Surfactant Micelle Self-Aggregation Molecular self-assembly is the process through which single molecules arrange themselves spontaneously into different structures [284]. One of the most ubiquitous selfassembly processes in physical chemistry is the hierarchical organization of amphiphile molecules into a huge variety of patterns as micelles, rods or liposomes among others [285, 286]. Such property has recently been employed to design and fabricate for a wide range of biotechnological applications because of their relatively simple structures and easy scale up commercial productions [287]. Some drugs exhibit amphiphile behavior, they tend to self-assembly, usually in a small aggregation number, when dispersed in aqueous solution in a surfactant like manner [288]. Although drug micelles normally form at concentrations well above the concentration of the drug appearing in body systems, micelles may be present in the pharmaceutical formulation to


Table 3.


1727

L36 Reactions Ranked with the QSPR-Perturbation Model and their Reaction Conditions.

IDRa

pb

R068

d

Cn Cr

eerr

t

T

RLi

Tadd

Eq(RLi)

Eq(L)

Solvent

Electrophile

SMILE of Product

1.00

S

R

80

14

25

t-BuLi

-78

2.2

4.4

Toluene

CH3OH

C[C@]1(C(C)C)C2=CC=CC=C2N(CC3 =CC=CC=C3)C1

R069

0.95

S

R

0

10

25

t-BuLi

-78

2.2

4.4

Toluene

CH3OH

C[C@]1(C2=CC=CC=C2)C3=CC=CC= C3N(CC4=CC=CC=C4)C1

R015

0.95

S

R

87

18

-90

t-BuLi

-90

2.2

1.1

Toluene

CH3OH

C[C@@]1([H])CN(CC2=CC=CC=C2)C 3=CC=CC=C31

R016

0.95

S

R

75

18

-90

t-BuLi

-90

2.2

1.1

iPrPh

CH3OH


R017

0.94

S

R

85

18

-90

t-BuLi

-90

2.2

1.1

Toluene

Br(CH2) 2Br

[H][C@]1(CBr)CN(CC2=CC=CC=C2)C 3=CC=CC=C31

R024

0.94

S

R

90

18

-90

t-BuLi

-90

2.2

1.1

Toluene

CH3OH

C[C@@]1([H])CN(CC2=CC=CC=C2)C 3=CC=C(F)C=C31

R025

0.94

S

R

88

18

-90

t-BuLi

-90

2.2

1.1

Toluene

Br(CH2) 2Br

[H][C@]1(CBr)CN(CC2=CC=CC=C2)C 3=CC=C(F)C=C31

R022

0.94

S

R

89

18

-90

t-BuLi

-90

2.2

1.1

Toluene

CH3OH

C[C@@]1([H])CN(CC2=CC=CC=C2)C 3=CC=C(C)C=C31

R023

0.94

S

R

87

18

-90

t-BuLi

-90

2.2

1.1

Toluene

Br(CH2) 2Br

[H][C@]1(CBr)CN(CC2=CC=CC=C2)C 3=CC=C(C)C=C31

R070

0.94

S

R

30

20

-80

t-BuLi

-78

2.2

1.1

Toluene

CH3OH

C[C@]1(CO)C2=CC=CC=C2N(CC3=C C=CC=C3)C1

R012

0.93

S

R

65

18

-78

t-BuLi

-78

2.2

1.1

Et2O

CH3OH


R013

0.93

S

R

0

18

-78

t-BuLi

-78

2.2

1.1

THF

CH3OH


R014

0.93

S

R

80

18

-78

t-BuLi

-78

2.2

1.1

Toluene

CH3OH


R018

0.91

S

R

87

18

-78

t-BuLi

-78

2.2

1.1

Toluene

CH3OH

C[C@@H]1C2=CC(OCC3=CC=CC=C3 )=CC=C2N(CC4=CC=CC=C4)C1

R020

0.91

S

R

88

18

-78

t-BuLi

-78

2.2

1.1

Toluene

CH3OH

C[C@@H]1C2=CC=C(OCC3=CC=CC= C3)C=C2N(CC4=CC=CC=C4)C1

R021

0.91

S

R

82

18

-78

t-BuLi

-78

2.2

1.1

Toluene

Br(CH2) 2Br

BrC[C@@H]1C2=CC=C(OCC3=CC=C C=C3)C=C2N(CC4=CC=CC=C4)C1

R019

0.91

S

R

85

18

-78

t-BuLi

-78

2.2

1.1

Toluene

Br(CH2) 2Br

BrC[C@@H]1C2=CC(OCC3=CC=CC= C3)=CC=C2N(CC4=CC=CC=C4)C1

R071

0.90

S

R

88

14

-80

t-BuLi

-78

2.2

1.1

Toluene

CH3OH

C[C@]1(COC)C2=CC=CC=C2N(CC3= CC=CC=C3)C1

R077

0.89

S

R

85

14

-80

t-BuLi

-78

2.2

1.1

Toluene

CH3OH

C[C@]1(CN(C)C)C2=CC=CC=C2N(CC 3=CC=CC=C3)C1

R074

0.89

S

R

72

6

25

t-BuLi

-78

2.2

4.4

Toluene

CH3OH

C[C@]1(CCCOC)C2=CC=CC=C2N(CC 3=CC=CC=C3)C1

R078

0.89

S

S

22

7

22

t-BuLi

-78

2.5

4.4

C5H12 / Et2O 9:1

CH3OH

C=CCN1C2=CC=CC(C)=C2[C@]([H])( C)C1

R075

0.88

S

R

87

12

-80

t-BuLi

-78

2.2

1.1

Toluene

CH3OH

C[C@]1(CSC2=CC=CC=C2)C3=CC=C C=C3N(CC4=CC=CC=C4)C1



(Table 3) contd… IDRa

pb

R068

d

Cn Cr

eerr

t

T

RLi

Tadd

Eq(RLi)

Eq(L)

Solvent

Electrophile

SMILE of Product

0.88

S

R

80

14

25

t-BuLi

-78

2.2

2.5

Toluene

CH3OH


R076

0.87

S

R

91

10

-80

t-BuLi

-78

2.2

1.1

Toluene

CH3OH

C[C@]1(CSC)C2=CC=CC=C2N(CC3= CC=CC=C3)C1

R068

0.86

S

R

80

14

25

t-BuLi

-78

2.2

2.3

Toluene

CH3OH


R073

0.86

S

R

60

3.5

25

t-BuLi

-78

2.2

4.4

Toluene

CH3OH

C[C@]1(CO[Si](C(C)C)(C(C)C)C(C)C) C2=CC=CC=C2N(CC3=CC=CC=C3)C1

R069

0.86

S

R

0

10

25

t-BuLi

-78

2.2

2.5

Toluene

CH3OH

C[C@]1(C2=CC=CC=C2)C3=CC=CC= C3N(CC4=CC=CC=C4)C1

R068

0.86

S

R

80

14

25

t-BuLi

-78

2.2

2.2

Toluene

CH3OH


R072

0.86

S

R

93

8

-80

t-BuLi

-78

2.2

1.1

Toluene

CH3OH

C[C@]1(COC2OCCCC2)C3=CC=CC=C 3N(CC4=CC=CC=C4)C1

R080

0.85

S

R

84

5

20

t-BuLi

-78

2

4.4

iPr2O

Ph2CO

[H][C@]1(CC(C2=CC=CC=C2)(C3=CC =CC=C3)O)COC4=C(C(C)(C)C)C=C(C) C=C41

R088

0.85

S

R

87

5

20

t-BuLi

-78

2

4.4

iPr2O

Ph2CO

[H][C@]1(CC(C2=CC=CC=C2)(C3=CC =CC=C3)O)COC4=C(C(C)C)C=CC=C4 1

R082

0.85

S

R

77

5

20

t-BuLi

-78

2

4.4

iPr2O

Ph2CO

[H][C@]1(CC(C2=CC=CC=C2)(C3=CC =CC=C3)O)COC4=C(C)C=C(C)C=C41

R081

0.85

S

R

86

5

20

t-BuLi

-78

2

4.4

iPr2O

PhNCO

[H][C@]1(CC(NC2=CC=CC=C2)=O)C OC3=C(C(C)(C)C)C=C(C)C=C31

R085

0.85

S

R

80

5

20

t-BuLi

-78

2

4.4

iPr2O

PhNCO

[H][C@]1(CC(NC2=CC=CC=C2)=O)C OC3=C([Si](C)(C)C)C=C(C)C=C31

R005

0.85

RoS

R

84

1.5

-40

t-BuLi

-78

2.2

1.1

C5H12 / Et2O 9:1

CH3OH

C=CCN1C2=CC=CC=C2[C@](C)([H]) C1

R086

0.85

S

R

82

5

20

t-BuLi

-78

2

4.4

iPr2O

PhNCO

[H][C@]1(CC(NC2=CC=CC=C2)=O)C OC3=C([Si](C)(C)C)C=CC=C31

R084

0.85

S

R

80

5

20

t-BuLi

-78

2

4.4

iPr2O

Ph2S2

[H][C@]1(CSC2=CC=CC=C2)COC3=C (C)C=C(C)C=C31

R087

0.85

S

R

81

5

20

t-BuLi

-78

2

4.4

iPr2O

Me2SO 4

[H][C@]1(CC)COC2=C([Si](C)(C)C)C= CC=C21

R068

0.85

S

R

80

14

25

t-BuLi

-78

2.2

2.1

Toluene

CH3OH


R083

0.85

S

R

79

5

20

t-BuLi

-78

2

4.4

iPr2O

D 2O

[H][C@]1(C[2H])COC2=C(C)C=C(C)C =C21

R021

0.10

S

R

82

18

-78

t-BuLi

-78

2.2

4.4

Toluene

Br(CH2) 2Br

BrC[C@@H]1C2=CC=C(OCC3=CC=C C=C3)C=C2N(CC4=CC=CC=C4)C1

R019

0.10

S

R

85

18

-78

t-BuLi

-78

2.2

4.4

Toluene

Br(CH2) 2Br

BrC[C@@H]1C2=CC(OCC3=CC=CC= C3)=CC=C2N(CC4=CC=CC=C4)C1

R070

0.01

S

R

30

20

-80

t-BuLi

-78

2.2

4.4

Toluene

CH3OH

C[C@]1(CO)C2=CC=CC=C2N(CC3=C C=CC=C3)C1

R015

0.00

S

R

87

18

-90

t-BuLi

-90

2.2

4.4

Toluene

CH3OH




1729

(Table 3) contd…

a d

IDRa

pb

R016

d

Cn Cr

eerr

t

T

RLi

Tadd

Eq(RLi)

Eq(L)

Solvent

Electrophile

SMILE of Product

0.00

S

R

75

18

-90

t-BuLi

-90

2.2

4.4

iPrPh

CH3OH


R017

0.00

S

R

85

18

-90

t-BuLi

-90

2.2

4.4

Toluene

Br(CH2) 2Br

[H][C@]1(CBr)CN(CC2=CC=CC=C2)C 3=CC=CC=C31

R024

0.00

S

R

90

18

-90

t-BuLi

-90

2.2

4.4

Toluene

CH3OH

C[C@@]1([H])CN(CC2=CC=CC=C2)C 3=CC=C(F)C=C31

R025

0.00

S

R

88

18

-90

t-BuLi

-90

2.2

4.4

Toluene

Br(CH2) 2Br

[H][C@]1(CBr)CN(CC2=CC=CC=C2)C 3=CC=C(F)C=C31

R022

0.00

S

R

89

18

-90

t-BuLi

-90

2.2

4.4

Toluene

CH3OH

C[C@@]1([H])CN(CC2=CC=CC=C2)C 3=CC=C(C)C=C31

R023

0.00

S

R

87

18

-90

t-BuLi

-90

2.2

4.4

Toluene

Br(CH2) 2Br

[H][C@]1(CBr)CN(CC2=CC=CC=C2)C 3=CC=C(C)C=C31

IDR = ID of Reaction, p(ee > 95%)min = 0 p(ee > 95%) = [(ee > 95%) - (ee > 95%)min]/[(ee > 95%) - (ee > 95%)min] p(ee > 95%)max = 1 Cn = Chirality of new product predicted, Cr = Chirality of product obtained with (-)-sparteine

overcome different challenges including poor bioavailability, stability, side effects, or plasma fluctuations of drugs. Previous studies have focused on the study of self-aggregation properties of drugs by means of a great variety of experimental techniques such as: electrical conductivity, light scattering, fluorescence spectroscopy, density and ultrasound velocities or NMR. On the other hand, recently QSPR techniques have emerged as a rational alternative in the search of novel drugs. It may become useful in order to reduce costs in terms of material resources and time in the exploration of large databases. This technique is not aimed to replace experimentation at all; we should understand these methods only as a guide to “seek the needle in the haystack”. The main section of the present work is precisely to evaluate the accuracy of complex network in characterizing the spontaneously formation of drug aggregates in the solution. In a recent work (see review section above), we developed a linear QSPR model able to predict the probability which with the compound (ith) presents an experimental value of the property (j-th) higher than the average value of this property for this data set. The model predicts Si(zij>0) values for a given drug or surfactant micelle but it is unable to predict directly the effect perturbation effect in the response due to perturbations in the input parameters. To solve this problem, we applied the new QSPR-Perturbation theory introduced here to this problem. The first QSPR-Perturbation model obtained in this work was the following: (zs (mi ) > 0)ntp = 0.05333 zs (mi )itp 5.66967 z ( s (mi ))avg 0.16655z (c(si ))+ 0.14605 z (T j )

( )

( ) +

( )

0.14789 mi 0.23664 mi 0.04258 V mi

n = 267881 2 = 163258.3 p ( 2 )< 0.01

dm

( )

+ 0.05632 V mi

(42)

+

dm

Where, n is the number of cases used to train the model and 2 is Chi-square statistics with a p-level = p(2). In Table 1, we show the classification results obtained for this model in training and validation series. The output of the model (z(mi)ntp >0) is a real-value function to score the propensity with which the new transformation process or ntp will present a z(mi)ntp > 0. The value zs(mi)ntp = [s(mi)ntp – AVG(s(mi)ntp)]/SD(s(mi)ntp). This is the z-scored or stan-

dardized of physicochemical and/or thermodynamic property s(mi) used to measure the efficiency of the ntp. The ntp is the process of transformation of the drug or industrial surfactant (mi) obtained after perturbation of the initial conditions of known or initial transformation process itp (see previous theory sections). In this study both the ntp and the itp are process of self-aggregation of the molecules of the drug or industrial surfactant (mi). On the other side, the input or independent terms of the equation are the following. The first term is zs(mi)itp = [s(mi)itp – AVG(s(mi)itp)]/SD(s(mi)itp). This is the z-scored or standardized value of the physicochemical and/or thermodynamic property s(mi)itp used to measure the efficiency of the itp. Then AVG(s(mi)itp and SD(s(mi)itp) are the average and the standard deviation for the s(mi)itp of type s of the itp, respectively. The meaning and detailed expressions for the other independent terms of the equation are the following. The second term is zs(s)avg = AVG(zs(s)itp) – AVG(zs(s)ntp). The parameters AVG(zs(s)itp) and AVG(zs(s)ntp are the average value of z(mi)ntp for a given property s(mi)ntp or s(mi)ntp, respectively. Consequently, AVG(zs(s)itp) and AVG(zs(s)ntp are constant parameters for a property. In consonance, zs(s)avg measures a perturbation in the type of experimental property we used to measure micelle self-aggregation. When zs(s)avg = 0, we are using the same physicochemical or thermodynamic parameters to characterize both the itp and the ntp. When we set zs(s)avg 0 we can predict for instance the level of a other aggregation parameter for the same molecule. In plain English, the values of zs(s)avg define which s(mi) we want to study. Similarly to previous examples, we used only two molecular descriptors of the same type (mi-) and (mi+); the mean electronegativities of the anion and cation. The expressions we have used are the following. The first is V(m-)dm = (z(c(si))·z(T)·(z(s(mi)) + 1)·(mi-)·exp(p1(mi-))·exp(p1(si))·exp(p1(vi))), for anions. The other is V(m+)dm = (z(c(si))·z(T)·(z(s(mi+)) + 1)·(mi+)·exp(p1(mi+))·exp(p1(si))3exp(p1(vi))), for cations. These two last terms are additive-multiplicative perturbations. A very notable fact is that this model is both a multiple-input and output equation. Then, it can predict seven


Table 4.


Values of z Score for Important Cellular and Molecular Targets of Drugs.

TARGET NAME (tj)

z

TARGET NAME (tj)

z

1-acylglycerol-3-PO4-acyltransferase

-0.029

Glycogendebranchingenzyme

-0.014

Acetyl-CoAacetyltransferase,mitochondrial

-0.027

H sapiens

0.003

AcylcoenzymeA:cholesterolacyltransferase1

-0.029

Histone-argininemethyltransferaseCARM1

-0.029

Adenosinekinase

-0.030

Histone-lysineN-methyltransferaseSETD7

0.023

AICARtransformylase

-0.015

Ilealbileacidtransporter

-0.031

Beta-1,4-galactosyltransferase1

-0.034

IndolethylamineN-methyltransferase

0.021

Bileacidtransporter

-0.019

Kynurenine-oxoglutaratetransaminaseI

0.059

Branched-chain-amino-acidtransferase

0.004

Multidrugresistance-associatedprotein1

-0.027

Caco-2

0.000

Musmusculus

-0.120

CatecholO-methyltransferase

2.234

Musmusculus(BALB/c)

-0.098

Ceramideglucosyltransferase

-0.030

Musmusculus(C57B16/J)

-0.101

CoagulationfactorXIII

-0.022

Musmusculus(C57BL/6)

-0.056

CytP45011B1

-0.030

Musmusculus(CD-1)

-0.044

CytP45011B2

-0.031

Musmusculus(DBA/1)

-0.271

CytP45017A1

-0.030

Musmusculus(SCID)

-0.101

CytP45019A1

-0.029

Norepinephrinetransporter

-0.032

CytP4501A1

-0.026

Oligopeptidetransportersmallintestineisoform

0.980

CytP4501A2

0.018

PeptideN-myristoyltransferase2

-0.021

CytP4501B1

-0.032

PeroxisomalcarnitineO-octanoyltransferase

0.972

CytP45024A1

-0.009

P-glycoprotein1

-0.019

CytP45026A1

-0.031

PhenylethanolamineN-methyltransferase

-0.031

CytP4502A6

0.120

Plasma

-0.006

CytP4502B6

-0.013

Plasma(Sprague-Dawley)

-0.211

CytP4502C18

-0.013

Plasma(Wistar)

-0.102

CytP4502C19

-0.013

Poly[ADP-ribose]polymerase2

-0.035

CytP4502C8

-0.017

Poly[ADP-ribose]polymerase3

-0.031

CytP4502C9

0.003

Protein-arginineN-methyltransferase1

0.125

CytP4502D6

0.030

ProteinarginineN-methyltransferase3

-0.027

CytP4502E1

-0.021

ProteinarginineN-methyltransferase6

-0.009

CytP4502J2

-0.028

Protein-beta-aspartatemethyltransferase

-0.007

CytP4503A4

-0.026

Protein-glutamine -glutamyltransferase K

-0.024

CytP4503A5

-0.014

Protein-tyrosinesulfotransferase2

0.061

CytP4504A11

-0.031

QueuinetRNA-ribosyltransferase

-0.036

CytP4504F2

-0.031

Rattusnorvegicus

0.004

CytP45051A1

-0.019

Rattusnorvegicus(Fischer344)

-0.098

CytP4508A1

0.064

Rattusnorvegicus(Lewis)

-0.104

Dihydroorotase

-0.036

Rattusnorvegicus(Sprague-Dawley)

-0.002



1731

(Table 4) contd… TARGET NAME (tj)

z

TARGET NAME (tj)

z

DipeptidylpeptidaseI

-0.026

Rattusnorvegicus(Wistar)

-0.013

DNA(cytosine-5)-methyltransferase3B

-0.011

Rattusnorvegicus(WistarHan)

-0.137

Equilibrativenucleosidetransporter1

0.014

Serinehydroxymethyltransferase,cytosolic

-0.035

Farnesyldiphosphatesynthase

-0.026

Serinepalmitoyltransferase1

-0.031

Fucosyltransferase10

22.326

Serotonintransporter

-0.032

Fucosyltransferase6

-0.033

Serum

-0.054

Gamma-amino-N-butyratetransaminase

0.126

Spermidine/spermineN(1)-acetyltransferase1

-0.006

Gamma-glutamyltranspeptidase1

-0.018

TARRNAbindingprotein1

-0.030

different output scores (zs(di) > 0) for 8 micelle properties. The output of the model and the respective variables are the following. Four are physicochemical properties. The value (zcmc(di) > 0) is the score of critical micelle concentration = cmc (in mol·kg-1); a(z1(di) > 0) for Sa = Surface area (nm2), (z1(di) > 0) for the degree of ionization , and (zN(di) > 0) for N = aggregation number. The other four are (zs(di) > 0) values are scores for classic thermodynamic properties. The two frist are (zcp(di) > 0) the score of heat capacity = CP,m0 (J·mol1·K1) and (zH(di) > 0) for enthalpy = HP,m0 (J·mol1). The two last are (zS(di) > 0) the score of entropy = SP,m0 (J mol1·K1) and (zG(di) > 0) is the score of Gibbs’ standard free energy = GP,m0 (J·mol1).

solvent exchange time of amphiphilic molecules and typical fusion time of the corresponding aggregates. Thus, the equilibrium is guaranteed a few seconds after dilution [293]. Dynamic light scattering measurements were made at 298.0 ± 0.1 K and at a scattering angle of 90º. Time correlation was analyzed by an ALV-5000 (ALV-GmbH) instrument with vertically polarized incident light of wavelength = 488 nm supplied by a CW diode-pumped Nd; YAG solid-state laser operated at 400 mW (Coherent. Inc.). Data were analyzed to determine diffusion coefficients using the software packages CONTIN. Hydrodynamic radii were calculated from measured diffusion coefficients by means of the Stokes- Einstein equation [294].

Theoretic-Experimental Study of Perturbations Chlorpromazine Micelle Self-Aggregation

We obtained the isotherms of molality dependence of electrical conductivity for the compounds under study. For all temperatures, the concentration dependence of the electrical conductivity shows a monotonic increase with a gradual decrease in slope, this being an experimental confirmation of the self-assembly process. Then, the cmc values were calculated by fitting the experimental raw data of the isotherms to a simple nonlinear function obtained by direct integration of a Boltzmann type sigmoid function [295]. In Fig. 3, we show the curves of normalized cmc change with temperature for the present drug. Each plot appears to follow a U-shaped curved with a minimum at a certain temperature, Tmin. Zielinski [296] has postulated that the occurrence of a minimum on these plots suggests the existence of at least two factors affecting the cmc value in aqueous solution: hydrophilic hydration around the drug in the aggregate state and two types of hydration around drug molecules in the monomer state, hydrophobic around the aromatic rings and hydrophilic around the polar group.

in

In recent years, an interest in the properties of surfaceactive drugs has been greatly renewed, particularly for phenothiazine drugs [289, 290]. Chlorpromazine (2-chloro-10(3-(dimethylamino)propyl)-phenothiazine) is a phenothiazine drug with neuroleptic activity, has shown a large capacity to interact with biological membranes and sometimes used as a local anesthetic. It has an amino group and is essentially in charged form at physiological pH. Chlorpromazine is often regarded as model drug for the investigation of interactions between drug and biological or model membranes [291, 292]. At follows we give new results for the experimental characterization of the process of self-aggregation of Chlorpromazine in micelles. In order to carry out the experiments, Chlorpromazine (2-chloro-10-(3-(dimethylamino)propyl)-phenothiazine) was purchased from Sigma Chemical Co. and used without further purification. The drugs were used as received. All measurements were performed using distilled water with conductivity lower than 3 S·cm-1 at 298.15 K. Electrical conductivities were measured using a Kyoto Electronics conductometer model CM-117 with a K-121 cell type. The cell constant was determined using KCl solutions. All measurements were taken in a PolyScience Model PS9105 thermostatted waterbath, at a constant temperature within ± 0.05 K. The determination of the isotherms of conductivity was carried out by continuous dilution of a concentrated sample prepared by weight. The expected duration of the dynamics processes varies from 10-8 to 10-2 s, i.e., between typical aggregate-

Thus, the observed minimum reflects the effect of raising the temperature in a balance between a gradual dehydration of the hydration shell around the aromatic rings, promoting aggregate formation, and partial dehydration of the hydrophilic hydration, leading to an increase in repulsion between polar groups. Thermodynamic parameters corresponding to the aggregation process can be obtained by analyzing the cmc dependence on temperature by means of [297]:

1 T* 2

1 0 2 * * 2 0 * + ln xcmc = ln xcmc 1 + 1T 1 + + 2 T 1T 2 * 1T * CP0*,m

T *2 T 2 T* T

T

1 + ln * + + T * ln * T (2 ) R 2T T (2 ) R T

(43)



of aggregates. The correlation functions from dynamic light scattering were analyzed by the contin method. Polydispersity indices generated by this analytical method were less than 0.1, indicative of a reasonable degree of monodispersity of size. The Fig. 4 shows the size distributions obtained. We have obtained a single peak which corresponds to aggregates with a mean diameter of 2.91 for chlorpromazine. Aggregation number can be estimated from this value. Assuming that the aggregates have spherical shape, the aggregation numbers are obtained from the total surface area of the aggregates and the minimum area per molecule 1.32 nm2 for chlorpromazine (obtained from surface tension measurements). Thus, we obtain mean value of 20 molecules per aggregate of chlorpromazine.

Fig. (2). Plots of temperature dependence of the cmc of chlorpromazine; dash line fits experimental points (1).

Here, the degree of ionization depend on temperature, = 0 + 1T, and the standard change in isobaric molar heat capacity, C0P,m = C0*P,m + (T - T*), are explicitly considered. The values of ln(x cmc*) and T* correspond to the minimum. Results obtained from the fitting for chorpromazine were: 287.5 K, -7.91, -347.21 J mol-1 K-1 and 18.34; 292.8 K, -5.53, -306.27 J mol-1 K-1 for T*, ln(x cmc*), C0*P,m, and /R respectively. The standard changes in enthalpy and entropy due to aggregates formation at the minimum are given by: H 0m* = RT*21 ln x *CAC S m0* =

H T

0* m *

(44)

2 2 + 0 * 1T

Fig. (3). Diameter distributions of the aggregates of chlorpromazine in water at concentrations 2·cmc.

(45)

The dependence of the thermodynamic functions on temperature is obtained from the following expressions: H m0 = H m0* + CP0*, m (T T * )+ ( 2 )(T T * )

2

S = S + C 0 m

0* m

0* P ,m

(

) {

(46)

( )}

ln T T + T T T ln T T *

*

*

*

(47)

And the standard Gibbs energy of aggregates formation is given by: Gm0 = H m0 TS m0

(48)

Heat capacity, enthalpy, entropy, and standard free energy data corresponding to the aggregation process are listed in Table 5. Hm0 and Sm0 are quite sensitive to temperature. Hm0 values indicate that for both drugs the aggregation is increasingly more exothermic at higher temperatures. Negative Hm0 values suggest the importance of Londondispersion interactions as the major force for aggregation. However, Sm0 decreased with temperature and remained positive. This aggregation is entropic driven at low temperatures whereas enthalpic contributions become more important at high temperatures. The higher order of water molecules around hydrocarbon chains at lower temperatures could explain this. Continuing with the characterization of the systems, dynamic light-scattering measurements were performed to obtain a size distribution of the aggregates. The concentration chosen was twice the cmc, this way we ensured the presence

Last, we used the QSPR-Perturbation model to predict the effect of different perturbations in chlorpromazine micelle self-aggregation. In order to compare chlorpromazine with known cases with substitute in the model the values of for chlorpromazine self-aggregation in the ntp part of the model. We keep the original conditions for the itp part. In all cases the ipt was in a solution of salt NaBr in H2O at c(si) = 6.0 mol·Kg-1 at 298.15 but for different drugs and surfactants at different temperatures. In Table 6, we summarize some of the more interesting results. For instance, the model predict a higher score of aggregation number for chlorpromazine at 298.2 K without salt in solution with respect to other formulation based on NaBr in H2O at c(si) = 6.0 mol·Kg-1 at 298.15 K. The model also predict low score for cmc values for chlorpromazine in NaBr in H2O at c(si) = 3.0 mol·Kg-1at 298.2 K. In addition, interesting low cmc values are predicted in Glycine-NaOH. However, this results should be compared with other predictive methods before to corroborate them experimentally. CONCLUSION It is possible to develop general models to predict the results of multiple input-output perturbations using ideas of QSPR analysis and perturbation theory. The new QSPRPerturbation models may be used to study complex molecular systems. Some of the properties we can study are the yield and enantiomeric excess of reactions, the interaction of



Experimental Values Obtained for Chlorpromazine at Different Temperatures, T (K).

Table 5.

T (K)

cmc

, - , -0.

, - -0.

, - -0.

, - -0.

283.15

0.0209

-337.64

-13132

56.26

-29060

285.15

0.0205

-342.04

-13841

53.86

-29200

288.15

0.0204

-348.64

-14887

50.25

-29367

290.15

0.0206

-353.04

-15574

47.82

-29450

293.15

0.0212

-359.64

-16588

44.16

-29533

295.15

0.0214

-364.04

-17253

41.70

-29561

298.15

0.0228

-370.64

-18234

37.99

-29559

300.15

0.0238

-375.04

-18877

35.49

-29530

303.15

0.0254

-381.64

-19824

31.73

-29444

308.15

0.0282

-392.64

-21360

25.40

-29187

Table 6.

Prediction of Perturbations in Chlorpromazine Self-Aggregation with Respect to Other itps.

(zcmc(di) > 0)

Tntp

Saltntp

c(si)ntp

(zN(di) > 0)

Tntp

Saltntp

c(si)ntp

1.00

298.2

ns

0

0.39

298.2

NaBr

3

0.79

283.2

ns

0

0.52

298.2

NaBr

2

0.78

298.2

ns

0

0.64

313.2

Glycine-NaOH

1

0.78

298.2

NaBr

0

0.65

308.2

Glycine-NaOH

1

0.78

298.2

ns

0

0.65

303.2

Glycine-NaOH

1

0.78

298.2

NaCl

0

0.65

298.2

NaBr

1

0.77

298.2

NaCl

0.1

0.65

298.2

Glycine-NaOH

1

0.75

298.2

NaCl

0.2

0.65

293.2

Glycine-NaOH

1

0.75

298.2

NaBr

0.2

0.66

298.2

NaCl

0.9

0.74

298.2

NaCl

0.3

0.68

298.2

NaCl

0.8

0.74

298.2

NaBr

0.3

0.69

298.2

NaCl

0.7

0.73

298.2

NaBr

0.4

0.69

298.2

NaBr

0.7

0.73

298.2

NaCl

0.4

0.70

298.2

NaBr

0.6

0.72

298.2

NaCl

0.5

0.71

313.2

NaBr

0.5

0.72

298.2

NaBr

0.5

0.71

308.2

NaBr

0.5

0.69

298.2

NaBr

0.7

0.71

303.2

NaBr

0.5

0.69

298.2

NaCl

0.7

0.72

298.2

NaBr

0.5

0.68

298.2

NaCl

0.8

0.72

298.2

NaCl

0.5

0.66

298.2

NaCl

0.9

0.72

293.2

NaBr

0.5

0.65

298.2

NaCl

1

0.72

288.2

NaBr

0.5

0.39

298.2

NaBr

3

0.73

298.2

NaCl

0.4

0.27

298.2

NaBr

4

0.73

298.2

NaBr

0.4

1733


drugs with multiple targets, or the aggragation of drugs and industrial surfactants to form micelles. These models may include perturbations in a very high number of input-output variables like (time, temperature, solvent, catalyst, assay, pharmacological experimental measures, molecular and cellular targets, and many others). The electronegativity values calculated with MARCH-INSIDE seems to be good molecular descriptors for QSPR-Perturbation theory.

González-Díaz et al. [14]

[15] [16]

CONFLICT OF INTEREST The author(s) confirm that this article content has no conflicts of interest.

[17]

ACKNOWLEDGEMENTS

[18]

Financial support from Basque government by means of IKERBASQUE, Basque Foundation for Science and (GICIT623-13) are gratefully acknowledged. We also wish to thank the Ministry of Science and Innovation (Ministerio de Ciencia e Innovación -MICIN), (CTQ2009-07733), University of the Basque Country (UPV/EHU), (UFI11/22, and a postdoctoral grant to A.G), and Xunta de Galicia (10PXIB206258PR).

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Received: June 29, 2013

Revised: June 29, 2013

Accepted: June 30, 2013

Current Topics in Medicinal Chemistry, 2013, Vol. 13, No. 14 [295]

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