Lowell H. Hall

An electrotopological-state index for atoms in molecules

A new method for molecular structure description is presented in which both electronic and topological characteristics are combined. The method makes use of the hydrogen-suppressed graph to represent the structure. The focus of the method is on the individual atoms and hydride groups of the molecular skeleton. An intrinsic atom value is assigned to each atom as I = (δV + l)/δ, in which δV and δ are the counts of valence and sigma electrons of atoms associated with the molecular skeleton. The electrotopological-state value, Si, for skeletal atom i is defined as Si, = Ii, + ΔIi, for second row atoms, where the influence of atom j on atom i, ΔIi, is given as Σ(Ii −Ij)/rij2; rij is the graph separation between atom i and atom j, counted as the number of atoms. The characteristics of the electrotopological state values are indicated by examples of various types of organic structures, including chain lengthening, branching, heteroatoms, and unsaturation. The relation of the E-state value to NMR chemical shift is investigated for a series of alkyl ethers. The E-state oxygen value gives an excellent correlation with the 17O NMR: r = 0.993 for 10 ethers. A biological application of the E-state values in QSAR analysis is given for the binding of barbiturates to beta-cyclodextrin.

The electrotopological state: structure information at the atomic level of molecular

The electrotopological state, a novel representation of atoms in molecules, is developed from chemical graph theory as an index of the graph vertex (or skeletal group). This new index combines both the electronic character and the topological environment of each skeletal atom in a molecule. The electrotopological state (E-state) of a skeletal atom is formulated as an intrinsic value I i plus a perturbation term, ΔI i , arising from the electronic interaction and modified by the molecular topological environment of each atom in the molecule

Modeling Blood-Brain Barrier Partitioning Using the Electrotopological State

The challenging problem of modeling blood-brain barrier partitioning is approached through topological representation of molecular structure. A QSAR model is developed for in vivo blood-brain partitioning data treated as the logarithm of the blood-brain concentration ratio. The model consists of three structure descriptors: the hydrogen E-State index for hydrogen bond donors, HS(T)(HBd); the hydrogen E-State index for aromatic CHs, HS(T)(arom); and the second order difference valence molecular connectivity index, d(2)chi(v) (q(2) = 0.62.) The model for the set of 106 compounds is validated through use of an external validation test set (20 compounds of the 106, MAE = 0.33, rms = 0.38), 5-fold cross-validation (MAE = 0.38, rms = 0.47), prediction of +/- values for an external test set (27/28 correct), and estimation of logBB values for a large data set of 20 039 drugs and drug-like compounds. Because no 3D structure information is used, computation of logBB by the model is very fast. The quality of the validation statistics supports the claim that the model may be used for estimation of logBB values for drug and drug-like molecules. Detailed structure interpretation is given for the structure indices in the model. The model indicates that molecules that penetrate the blood-brain barrier have large HS(T)(arom) values (presence of aromatic groups) but small values of HS(T)(HBd) (fewer or weaker H-Bond donors) and smaller d(2)chi(v) values (less branched molecules with fewer electronegative atoms). These three structure descriptors encode influence of molecular context of groups as well as counts of those groups.

An index of electrotopological state for atoms in molecules

A new method for molecular structure quantitation is described, in which both electronic and topological attributes are united. The method uses the hydrogen-suppressed skeleton to represent the structure and leads to a graph invariant index for the individual atoms and hydride groups of the molecular skeleton. An intrinsic atom value is calculated for each atom asI = (δν + 1)/δ, in whichδν andδ are the counts of valence and sigma electrons of atoms in the molecular skeleton, that is, exclusive of bonds to hydrogen atoms. The electrotopological state valueSi for an atomi is defined asSi =Ii + ΔIi, where the influence of atom j on atom i, ΔIi, is given as Σ(Ii-jj)/r2;r is the graph separation between atoms i and j, counted as number of atoms, includingi andj. The information in the electrotopological state values is revealed by examples of various types of organic structures, including chain branching and heteroatom variation. The relation of the E-state value to NMR chemical shift is demonstrated for a series of carbonyl compounds.

Boiling Point and Critical Temperature of a Heterogeneous Data Set: QSAR with Atom Type Electrotopological State Indices Using Artificial Neural Networks†

Two sets of heterogeneous organic compounds were analyzed with artificial neural networks using atom type electrotopological state indices. The first set contains the boiling point for 298 compounds; 30 were placed in a testing set. The neural network model used atom type E-state indices for the 19 atom types present in the data set; the actual network used for prediction had a 19:5:1 architecture. This model produced a mean absolute error (MAE) of 3.93 K for the overall set, 3.86 for the training set, and 4.57 for the test set. The average relative percent error for 10 runs is 0.94% for the whole data set and 1.12% for the test set. The second set contains critical temperatures for 165 compounds; 18 were placed in the testing set. The neural network possessed a 19:4:1 architecture and produced an MAE of 4.52 K for the whole set, 4.39 K for the training set, and 5.59 K for the test set. The average relative percent error for 5 runs is 0.77% for the whole data set and 0.95% for the test set.

E-STATE FIELDS : APPLICATIONS TO 3D QSAR

SummaryThe derivation of a new 3D QSAR field based on the electrotopological state (E-state) formalism is described. A complementary index and its associated field, the HE-state, describing the polarity of hydrogens is also defined. These new fields are constructed from a nonempirical index that incorporates electronegativity, the inductive influence of neighboring atoms, and the topological state into a single atomistic descriptor. The classic CoMFA steroid test data set was examined with models incorporating the E-state and HE-state fields alone and in combination with steric, electrostatic and hydropathic fields. The single best model was the E-state/HE-state combination with q2=0.803 (three components) and r2=0.979. Using the E-state and/or HE-state fields with other fields consistently produced models with improved statistics, where the E-state fields provided a significant, if not dominant, contribution.

Intermolecular accessibility: the meaning of molecular connectivity

The molecular connectivity indices are shown to be the numerical possibilities of a molecule encountering another identical molecule, derived from the bond accessibilites of each. The meaning of the delta values and the significance of all suppressed X-H bonds is described. A new concept of the meaning of molecular connectivity, built around bimolecular encounter accessibility, is presented.

Issues in representation of molecular structure: The development of molecular connectivity

Significant issues in the representation of molecular structure and the development of the molecular connectivity paradigm are presented. In the molecular connectivity paradigm, molecular structure is represented directly. Kier and Hall developed the method by creating ways to encode electronic information based on the paradigm developed from the Randić branching index. The simple and valence delta values were created to encode atomic and valence-state electronic information through counts of sigma, pi, and lone pair electrons. A family of indices was created to provide a wide range of structure information. The key aspects of the development are presented and discussed in such a way as to reveal, at least in part, the imaginative thinking involved in the process. Possible future roles for molecular connectivity chi indices are discussed.

The E-State as the Basis for Molecular Structure Space Definition and Structure Similarity

The electrotopological state (E-state) is presented as a representation of molecular structure useful for definition of a space for chemical structures. This E-state representation provides the basis for chemical database management. The E-state formalism is presented along with its extension to the atom-type E-state. An approach to database organization, using polychlorobiphenyls (PCBs) as examples, reveals the descriptive power of the E-state paradigm. A well-organized chemical database, as described here, may be searched to find structures similar to a target structure with the expectation that such structures may exhibit properties similar to the target. Searches using the atom-type E-state indices are demonstrated with two example drug molecules.

QSAR MODELING WITH THE ELECTROTOPOLOGICAL STATE INDICES : CORTICOSTEROIDS

A structure-activity analysis of a series of steroids binding to corticosteroid-binding globulin was made using the electrotopological state index for each atom in the molecule. Two indices were found to correlate well with the binding affinity. The indices encode structural characteristics in the A and the D rings of the steroids in the study. One of the indices was formulated as the difference between two indices in the A ring. The two were not intercorrelated, suggesting that the composite index signals the influence of structure changes in or near the A ring that can be monitored by the composite index. This is a new observation using this structure-activity method. It is suggested that this model makes some contributions towards detection of the pharmacophore.