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Usual quantitative structure-activity relationship (QSAR) models are computed from unstructured input data, by using a vector of molecular descriptors for each chemical in the dataset. Another alternative is to consider the structural relationships between the chemical structures, such as molecular similarity, presence of certain substructures, or chemical transformations between compounds. We defined a class of network-QSAR models based on molecular networks induced by a sequence of substitution reactions on a chemical structure that generates a partially ordered set (or poset) oriented graph that may be used to predict various molecular properties with quantitative superstructure-activity relationships (QSSAR). The network-QSAR interpolation models defined on poset graphs, namely average poset, cluster expansion, and spline poset, were tested with success for the prediction of several physicochemical properties for diverse chemicals. We introduce the flow network QSAR, a new poset regression model in which the dataset of chemicals, represented as a reaction poset, is transformed into an oriented network of electrical resistances in which the current flow results in a potential at each node. The molecular property considered in the QSSAR model is represented as the electrical potential, and the value of this potential at a particular node is determined by the electrical resistances assigned to each edge and by a system of batteries. Each node with a known value for the molecular property is attached to a battery that sets the potential on that node to the value of the respective molecular property, and no external battery is attached to nodes from the prediction set, representing chemicals for which the values of the molecular property are not known or are intended to be predicted. The flow network QSAR algorithm determines the values of the molecular property for the prediction set of molecules by applying Ohm’s law and Kirchhoff's current law to the poset network of electrical resistances. Several applications of the flow network QSAR are demonstrated.

Chemical and molecular graphs have fundamental applications in chemoinformatics, quantitative structureproperty relationships (QSPR), quantitative structure-activity relationships (QSAR), virtual screening of chemical libraries, and computational drug design. Chemoinformatics applications of graphs include chemical structure representation and coding, database search and retrieval, and physicochemical property prediction. QSPR, QSAR and virtual screening are based on the structure-property principle, which states that the physicochemical and biological properties of chemical compounds can be predicted from their chemical structure. Such structure-property correlations are usually developed from topological indices and fingerprints computed from the molecular graph and from molecular descriptors computed from the three-dimensional chemical structure. We present here a selection of the most important graph descriptors and topological indices, including molecular matrices, graph spectra, spectral moments, graph polynomials, and vertex topological indices. These graph descriptors are used to define several topological indices based on molecular connectivity, graph distance, reciprocal distance, distance-degree, distance-valency, spectra, polynomials, and information theory concepts. The molecular descriptors and topological indices can be developed with a more general approach, based on molecular graph operators, which define a family of graph indices related by a common formula. Graph descriptors and topological indices for molecules containing heteroatoms and multiple bonds are computed with weighting schemes based on atomic properties, such as the atomic number, covalent radius, or electronegativity. The correlation in QSPR and QSAR models can be improved by optimizing some parameters in the formula of topological indices, as demonstrated for structural descriptors based on atomic connectivity and graph distance.

Allergenic proteins must cross-link specific IgE molecules, bound to the surface of mast cells and basophils, to stimulate an immune response. A structural understanding of the allergen-IgE interface is needed to predict cross-reactivities between allergens and to design hypoallergenic proteins. However, there are less than 90 experimentally determined structures available for the approximately 1500 sequences of allergens and isoallergens catalogued in the Structural Database of Allergenic Proteins (SDAP). To provide reliable structural data for the remaining proteins, we previously produced over 500 3D-models using an automated procedure, with strict controls at template choice and model quality evaluation. Here we assessed how well the fold and residue surface exposure of 10 of these models correlated with recently published experimental 3D structures determined by X-ray crystallography or NMR. We also discuss the impact of intrinsically disordered regions on the structural comparison and epitope prediction. Overall, for seven allergens with sequence identities to the original templates higher than 27%, the backbone root-mean square deviations were less than 2A between the models and the subsequently determined experimental structures for ordered regions. Further, the surface exposure of known IgE epitopes on the models of three major allergens, from peanut (Ara h 1), latex (Hev b 2) and soy (Gly m 4) was very similar to the experimentally determined structures. For three remaining allergens with lower sequence identities to the modeling templates, the 3D folds were correctly identified. However the accuracy of those models is not sufficient for a reliable epitope mapping.

Many concerns have been raised about the potential allergenicity of novel, recombinant proteins into food crops. Guidelines, proposed by WHO/FAO and EFSA, include the use of bioinformatics screening to assess the risk of potential allergenicity or cross-reactivities of all proteins introduced, for example, to improve nutritional value or promote crop resistance. However, there are no universally accepted standards that can be used to encode data on the biology of allergens to facilitate using data from multiple databases in this screening. Therefore, we developed AllerML a markup language for allergens to assist in the automated exchange of information between databases and in the integration of the bioinformatics tools that are used to investigate allergenicity and cross-reactivity. As proof of concept, AllerML was implemented using the Structural Database of Allergenic Proteins (SDAP; http://fermi.utmb.edu/SDAP/) database. General implementation of AllerML will promote automatic flow of validated data that will aid in allergy research and regulatory analysis.

In many countries regulatory agencies have adopted safety guidelines, based on bioinformatics rules from the WHO/FAO and EFSA recommendations, to prevent potentially allergenic novel foods or agricultural products from reaching consumers. We created the Structural Database of Allergenic Proteins (SDAP, http://fermi.utmb.edu/SDAP/) to combine data that had previously been available only as flat files on Web pages or in the literature. SDAP was designed to be user friendly, to be of maximum use to regulatory agencies, clinicians, as well as to scientists interested in assessing the potential allergenic risk of a protein. We developed methods, unique to SDAP, to compare the physicochemical properties of discrete areas of allergenic proteins to known IgE epitopes. We developed a new similarity measure, the property distance (PD) value that can be used to detect related segments in allergens with clinical observed cross-reactivity. We have now expanded this work to obtain experimental validation of the PD index as a quantitative predictor of IgE cross-reactivity, by designing peptide variants with predetermined PD scores relative to known IgE epitopes. In complementary work we show how sequence motifs characteristic of allergenic proteins in protein families can be used as fingerprints for allergenicity.

Reaction networks are viewed as derived from ordinary molecular structures related in reactant-product pairs so as to manifest a chemical super-structure. Such super-structures then are candidates for applications in a general combinatoric chemistry. Notable additional characterization of a reaction super-structure occurs when such reaction graphs are directed, as for example when there is progressive substitution (or addition) on a fixed molecular skeleton. Such a set of partially ordered entities is in mathematics termed a poset, which further manifests a number of special properties, as then might be utilized in different applications. Focus on the overall “super-structural” poset goes beyond ordinary molecular structure in attending to how a structure fits into a (reaction) network, and thereby brings an extra “dimension” to conventional stereochemical theory. The possibility that different molecular properties vary smoothly along chains of interconnections in such a super-structure is a natural assumption for a novel approach to molecular property and bioactivity correlations. Different manners to interpolate/ extrapolate on a poset network yield quantitative super-structure/activity relationships (QSSARs), with some numerical fits, e.g., for properties of polychlorinated biphenyls (PCBs) seemingly being quite reasonable. There seems to be promise for combinatoric posetic ideas.

Major histocompatibility complex (MHC) molecules bind short peptides resulting from intracellular processing of foreign and self proteins, and present them on the cell surface for recognition by T-cell receptors. We propose a new robust approach to quantitatively model the binding affinities of MHC molecules by quantitative structure-activity relationships (QSAR) that use the physical-chemical amino acid descriptors E1–E5. These QSAR models are robust, sequence-based, and can be used as a fast and reliable filter to predict the MHC binding affinity for large protein databases.

The Structural Database of Allergenic Proteins (SDAP) brings together data from diverse sources on over 800 allergen sequences and their epitopes in a cross-referenced format. Special methods developed for SDAP, such as the property distance (PD) scale, automatically detect peptides in the ensemble of allergen sequences that have physicochemical properties similar to known immunoglobulin E (IgE) epitopes. Comparing the structure of food allergens with allergenic proteins from exposure to pollens, insect dust, or other aeroallergens can give valuable information about the sensitization process. Any novel protein introduced into a food crop should have a low potential to be an allergen. This chapter deals with database approaches to determine the allergenic potential of a test protein, based on similarity to known allergens. It outlines basic methodology to identify cross-reacting proteins in food sources and predict the potential allergenicity of novel proteins. The chapter concentrates on the SDAP, which has been specifically designed to allow combined analysis of the sequence, structure, and epitopes of allergens. It also shows how SDAP and the methods for sequence and peptide comparison incorporated therein can be used to predict cross-reactive allergens in foods and determine common properties of their IgE epitopes. The second half of the chapter demonstrates how SDAP has allowed one to rapidly collect data pertinent to very basic questions about allergens, such as whether enzymatic activity is related to allergenicity. The chapter provides an overview of the information and methods incorporated into the cross-referenced (MySQL-Linux) lists of data.

Due to their widespread use in bactericides, insecticides, herbicides, andfungicides, chlorophenols represent an important source of soil contaminants. Theenvironmental fate of these chemicals depends on their physico-chemical properties. In theabsence of experimental values for these physico-chemical properties, one can use predictedvalues computed with quantitative structure-property relationships (QSPR). As analternative to correlations to molecular structure we have studied the super-structure of areaction network, thereby developing three new QSSPR models (poset-average, cluster-expansion, and splinoid poset) that can be applied to chemical compounds which can behierarchically ordered into a reaction network. In the present work we illustrate these posetQSSPR models for the correlation of the octanol/water partition coefficient (log Kow) and thesoil sorption coefficient (log KOC) of chlorophenols. Excellent results are obtained for allQSSPR poset models to yield: log Kow, r = 0.991, s = 0.107, with the cluster-expansionQSSPR; and log KOC, r = 0.938, s = 0.259, with the spline QSSPR. Thus, the poset QSSPRmodels predict environmentally important properties of chlorophenols.

During bioconcentration, chemical pollutants from water are absorbed by aquatic animals via the skin or a respiratory surface, while the entry routes of chemicals during bioaccumulation are both directly from the environment (skin or a respiratory surface) and indirectly from food. The bioconcentration factor (BCF) and the bioaccumulation factor (BAF) for a particular chemical compound are defined as the ratio of the concentration of a chemical inside an organism to the concentration in the surrounding environment. Because the experimental determination of BAF and BCF is time-consuming and expensive, it is efficacious to develop models to provide reliable activity predictions for a large number of chemical compounds. Polychlorinated biphenyls (PCBs) released from industrial activities are persistent pollutants of the environment that produce widespread contamination of water and soil. PCBs can bioaccumulate in the food chain, constituting a potential source of exposure for the general population. To predict the bioconcentration and bioaccumulation factors for PCBs we make use of the biphenyl substitution-reaction network for the sequential substitution of H-atoms by Cl-atoms. Each PCB structure then occurs as a node of this reaction network, which is some sort of super-structure, turning out mathematically to be a partially ordered set (poset). Rather than dealing with the molecular structure via ordinary QSAR we use only this poset, making different quantitative super-structure/activity relationships (QSSAR). Thence we developed cluster expansion and splinoid QSSARs for PCB bioconcentration and bioaccumulation factors. The predictive ability of the BAF and BCF models generated for 20 data sets (representing different conditions and fish species) was evaluated with the leave-one-out cross-validation, which shows that the splinoid QSSAR (r between 0.903 and 0.935) are better than models computed with the cluster expansion (r between 0.745 and 0.887). The splinoid QSSAR models for BAF and BCF yield predictions for the missing PCBs in the investigated data sets.

Substitution-reaction networks frequently arise in chemistry and are naturally identifiable as “partially ordered sets” (or posets). The direction of the reaction identifies the partial ordering of the set of the member molecular species, for which various properties may be developed in light of the partial ordering. Here some general characteristics of such posets are noted, and a chemically appealing posetic cluster-expansion analysis of molecular properties is described and illustrated for methyl substitutions on cyclobutane. The results for computed energies and a few further selected properties are compared to alternative posetic approaches.

In a previous paper on large “pillow” fullerenes, various systems were described with 12 pentagons connecting 2 parallel hexagonal arrays of benzenoid rings (graphene fragments functioning as the faces of the “pillow”) on top of each other. Additional bonds between these identical arrays formed only from sp2‐hybridized carbon atoms gave rise to hexagons and 12 pentagons along the “seam” or “rim.” High steric strain was associated with curvature around the pentagons due to connections between the 2 pillow faces involving bonds between 2 sp2‐hybridized carbon atoms. The present paper examines similar “quasi‐graphitic” structures in which some carbon atoms of the rim between the two raphene faces have hydrogen atoms attached to them, i.e., have sp3‐hybridization, alleviating thereby some strain.

Homology modeling has become an essential tool for studying proteins that are targets for medical drug design. This paper describes the approach we developed that combines sequence decomposition techniques with distance geometry algorithms for homology modeling to determine functionally important regions of proteins. We show here the application of these techniques to targets of medical interest chosen from those included in the CASP5 (Critical Assessment of Techniques for Protein Structure Prediction) competition, including the dihydroneopterin aldolase from Mycobacterium tuberculosis, RNase III of Thermobacteria maritima, and the NO-transporter nitrophorin from saliva of the bedbug Cimex lectularius. Physical chemical property (PCP) motifs, identified in aligned sequences with our MASIA program, can be used to select among different alignments returned by fold recognition servers. They can also be used to suggest functions for hypothetical proteins, as we illustrate for target T188. Once a suitable alignment has been made with the template, our modeling suite MPACK generates a series of possible models. The models can then be selected according to their match in areas known to be conserved in protein families. Alignments based on motifs can improve the structural matching of residues in the active site. The quality of the local structure of our 3D models near active sites or epitopes makes them useful aids for drug and vaccine design. Further, the PCP motif approach, when combined with a structural filter, can be a potent way to detect areas involved in activity and to suggest function for novel genome sequences.

The high incidence of food allergies, including oral allergy syndrome, represent major considerations when introducing new crops and foods. A new structural database of allergenic proteins, SDAP-Food, http://fermi.utmb.edu/SDAP/, has been developed to aid in predicting the IgE-binding potential of novel food proteins and cross-reactivities among known allergens. The site is designed to facilitate the first steps of a decision tree approach to determine the allergenicity of a given protein, based on the sequence and structural similarity to known allergens and their IgE binding sites. Immunological tests can then be used to confirm the predictions. A hierarchical procedure for identifying potential allergens, using a physical property-based sequence similarity index, has been designed to identify regions that resemble known IgE binding sites. As an example, SDAP tools were used to find food allergen sequences similar to an IgE binding site of the Jun a 3 allergen from mountain cedar pollen. The SDAP sequence similarity search matched the Jun a 3 epitope to regions in several food allergens, including cherry (Pru av 2), apple (Mal d 2) and pepper (Cap a 1), which are, like Jun a 3, members of the plant pathogenesis-related (PR-5) protein family. Homology modeling, using our EXDIS/DIAMOD/FANTOM program suite, indicated a similar surface location and structure for the potential epitope region on all of these allergens. The quantitative approach presented here can be used as part of a screening process for potential allergenicity of recombinant food products.

Molecular graph descriptors are used, together with a large diversity of geometric, electrostatic, and quantum indices, to model physical, chemical, or biological properties with quantitative structure–property relationships and quantitative structure–activity relationships. The interest of developing new graph descriptors for organic compounds was stimulated in recent years by their use in virtual screening of combinatorial libraries, database mining, similarity and diversity assessment. Recently, we have extended topological indices by defining a series of molecular graph operators, providing an effective systematization and generalization of these structural descriptors. A graph operator uses a mathematical equation to compute a family of related molecular graph descriptors with different molecular matrices and various sets of parameters for atoms and bonds. In this paper we use structural descriptors computed with molecular graph operators to develop quantitative structure–activity relationships (QSAR) models for the dihydrofolate reductase inhibition with diaminopyrimidines. The molecular descriptors are derived from five molecular matrices, namely adjacency A , distance D , reciprocal distance RD , distance-path D p , and reciprocal distance-path RD p . The QSAR models are obtained by selecting descriptors with a genetic algorithm, and the best models are validated with the leave-one-out cross-validation method. The QSAR models with the highest prediction power are comparable with those obtained with substituent constants and neural networks, but they use a much lower number of parameters.

The expensive and time-consuming process of drug lead discovery is significantly accelerated by efficiently screening molecular libraries with a high structural diversity and selecting subsets of molecules according to their similarity toward specific collections of active compounds. To characterize the molecular similarity/diversity or to quantify the drug-like character of compounds the process of screening virtual and synthetic combinatorial libraries uses various classes of structural descriptors, such as structure keys, fingerprints, graph invariants, and various topological indices computed from atomic connectivities or graph distances. In this paper we present efficient algorithms for the computation of several distance-based topological indices of a molecular graph from the distance invariants of its subgraphs. The procedures utilize vertex- and edge-weighted molecular graphs representing organic compounds containing heteroatoms and multiple bonds. These equations offer an effective way to compute for weighted molecular graphs the Wiener index, even/odd Wiener index, and resistance-distance index. The proposed algorithms are especially efficient in computing distance-based structural descriptors in combinatorial libraries without actually generating the compounds, because only distance-based indices of the building blocks are needed to generate the topological indices of any compound assembled from the building blocks.

Three-dimensional quantitative structure-activity relationships (3D QSAR) are widely used for the prediction of in vitro or in vivo interactions between chemical compounds and their biological targets (transporters, receptors, ion channels, enzymes). Comparative receptor surface analysis (CoRSA) is a new 3D QSAR algorithm that can be applied to study ligand-receptor interactions whenever the structure of the biological target is not known. The steric and electrostatic features of the most active compounds from a QSAR set are used by CoRSA to generate a virtual receptor model, represented as points on a surface complementary to the van der Waals surface of the aligned compounds. The CoRSA structural descriptors, represented by the total interaction energies between each surface point of the virtual receptor and all atoms in a molecule, are used in a partial least squares data analysis to generate a structure-activity model. In this paper the calcium channel antagonist activity of 35 dihydropyridine derivatives is modeled with CoRSA, giving a 3D QSAR with r2 = 0.928 for calibration and r2cv = 0.921 for the leave-one-out cross-validation.

Chemical structures of organic compounds are characterized numerically by a variety of structural descriptors, one of the earliest and most widely used being the Wiener index W, derived from the interatomic distances in a molecular graph. Extensive use of distance-based structural descriptors or topological indices has been made in QSPR and QSAR models, drug design, toxicology, virtual screening of combinatorial libraries, similarity and diversity assessment. Novel topological indices are introduced representing a partitioning of the Wiener polynomial based on counts of even and odd molecular graph distances. During the QSAR/QSPR modeling process the variables of the even and odd power functions are optimized in order to offer an improved mapping of the investigated property. These novel topological indices are tested in QSPR models for the boiling temperature, molar heat capacity, standard Gibbs energy of formation, vaporization enthalpy, refractive index, and density of alkanes. In many cases, the even/odd Wiener polynomial indices proposed here give notably improved correlations or suggest simpler QSPR models.