Molecular electrostatic potential as a graph.

We present several procedures to represent molecular electrostatic potential as a graph, based on the pattern of critical points and their neighborhood relations. This representation is used for the molecular electrostatic comparison, which is reduced to a comparison of tree-type graphs. Several methods to compare trees are also presented. The applications of this algorithm to compare and classify molecules through their electrostatic potential are illustrated.

Funciones de cottorno para árboles como medida e similitud entre campos escalaares moleculares. un estudo de similitud molecular / Contour tree fucctions over molcular scalar fields representations. a moleculaar similarity study / Funções de conorrno de árvore em representaçõe de campos escalares molecularees. um estudo de similaridade molecular

En este trabajo se implementó una función de contorno de un árbol para establecer medidas de similitud molecular. El estudio se realizó con 73 moléculas orgánicas divididas en 8 grupos funcionales optimizadas con un nivel de teoría DFT//B3LYP/6-31G(d,p) a las cuales se les calculó el Potencial Electrostático Molecular y el Laplaciano de la Densidad Electrónica en una rejilla tridimensional. A partir de los valores de estas propiedades, caracterizando y codificando según su topología, se generaron grafos (árboles) que se compararon a través de la función propuesta. La caracterización y clasificación de las moléculas orgánicas con el Potencial Electrostático Molecular muestra una separación correspondiente a moléculas que en su estructura poseen heteroátomos con funciones químicas por lo menos estructuralmente similares, y con el Laplaciano de la Densidad Electrónica se obtuvo como resultado una clasificación acorde con el número de pares de electrones libres asociados a los heteroátomos en las moléculas y a la naturaleza de los átomos que los aportan. Lo anterior evidencia que las funciones de contorno de árbol propuestas en el estudio son una alternativa rápida para clasificar a grosso modo moléculas orgánicas.

In this job, Contour Tree Functions were implemented to establish molecular similarity measures. The study was carried by using 73 organic molecules, divided in 8 functional groups and optimized at theory level DFT//B3LYP/6-31G(d,p). The molecular electrostatic potential and the Laplacian of the electron density in a 3D grid for each one were calculated. From the values of these properties, characterizing and encoding the topology, we generated graphs (trees) that are compared with the proposed function. The characterization and classification of the organic molecules with the molecular electrostatic potential show a separation corresponding to molecules that have heteroatoms in their structure with at least similar chemical functions; with the Laplacian of the electron density we achieved a classification according to the number of free pairs of electrons associated to the heteroatoms in the molecules and to the nature provided by the heteroatoms. This is evidence that Contour Tree Functions proposed in this study are a quick alternative to broadly classify organic molecules.

Neste trabalho, funções de contorno de árvore foram implementadas para estabelecer medidas de similaridade molecular. O estudo foi conduzido com 73 moléculas orgânicas, divididas em 8 grupos funcionais, otimizadas com nível de teoria DFT//B3LYP/6-31G (d,p) para que eles calculassem o potencial eletrostático molecular e o Laplaciano da densidade de elétrons em uma grade tridimensional. A partir dos valores dessas propriedades, caracterização e codificação da topologia, geramos gráficos (árvores) que são comparados com a função proposta. A caracterização e classificação de moléculas orgânicas com potencial eletrostático molecular mostra uma separação correspondente ás moléculas que possuem heteroátomos em sua estrutura com funções químicas, pelo menos, estruturalmente semelhantes. Com o Laplaciano da densidade de elétrons foi obtido como resultado consistente com a classificação do número de pares de elétrons livres associados com heteroátomos nas moléculas e a natureza dos átomos que contribuem. Essa é uma evidência de que as funções de contorno de árvore proposto no estudo são uma alternativa rápida para classificar, grosso modo, moléculas orgânicas.

Variations in the electrostatic landscape of class II human leukocyte antigen molecule induced by modifications in the myelin basic protein peptide: a theoretical approach.

The receptor-ligand interactions involved in the formation of the complex between Class II Major Histocompatibility Complex molecules and antigenic peptides, which are essential for establishing an adaptive immunological response, were analyzed in the Class II Human Leukocyte Antigen (HLA)--Myelin Basic Protein (MBP) peptide complex (HLA-DRbeta1*1501-MBP) using a multipolar molecular electrostatic potential approach. The Human Leukocyte Antigen--peptide complex system was divided into four pockets together with their respective peptide fragment and the corresponding occupying amino acid was replaced by each of the remaining 19 amino acids. Partial atomic charges were calculated by a quantum chemistry approach at the Hatree Fock/3-21*G level, to study the behavior of monopole, dipole and quadrupole electrostatic multipolar moments. Two types of electrostatic behavior were distinguished in the pockets' amino acids: "anchoring" located in Pocket 1 and 4, and "recognition" located in Pocket 4 and 7. According to variations in the electrostatic landscape, pockets were ordered as: Pocket 1>Pocket 9>>Pocket 4 approximately Pocket 7 which is in agreement with the binding ability reported for Class II Major Histocompatibility Complex pockets. In the same way, amino acids occupying the polymorphic positions beta13R, beta26F, beta28D, beta9W, beta74A, beta47F and beta57D were shown to be key for this Receptor-Ligand interaction. The results show that the multipolar molecular electrostatic potential approach is appropriate for characterizing receptor-ligand interactions in the MHC-antigenic peptide complex, which could have potential implications for synthetic vaccine design.

CARACTERIZACIÓN DEL TALLO ACEPTOR DEL tARN MEDIANTE DESCRIPTORES LOCALES BASADOS EN CARGAS PARCIALES / tRNA ACCEPTOR STEM CHARACTERIZATION BY MEANS OF LOCAL DESCRIPTORS BASED ON PARTIAL CHARGES / CARACTERIZAÇÃO DO TALO ACEITADOR DO tRNA MEDIANTE DESCRITORES LOCAIS BASEADOS EM CARGAS PARCIAIS

En este trabajo se caracteriza la distribución de carga del tallo aceptor del tARN, considerando todas las posibles combinaciones de pares Watson-Crick. El estudio se realizó con 256 fragmentos moleculares de 10 nucleótidos que modelan los tres primeros pares del tallo aceptor, la base diferenciadora y el extremo CCA. Para caracterizar los nucleótidos se proponen dos descriptores locales basados en la distribución de carga de la base nitrogenada de cada nucleótido, los cuales se calculan a partir de las cargas parciales de Mulliken obtenidas de cálculos HF/6-31G. La caracterización y clasificación de los tallos según estos descriptores mostró cómo la base diferenciadora tiene un comportamiento particular respecto a los demás nucleótidos del tallo y una fuerte influencia sobre el extremo CCA. La clasificación de nueve variaciones del tallo aceptor del tARNAla mostró una buena relación estructura-actividad que pone en evidencia la bondad de los descriptores propuestos para caracterizar de manera local la distribución de carga de estas biomoléculas.

In this work the charge distribution of the tRNA acceptor stem is characterized, considering all the possible Watson- Crick base pair combinations. 256 RNA fragments modeled by 10 nucleotides were used in order to model the first three pairs of the acceptor stem, the discriminator base and the CCA end. We propose two local charge descriptors based on the charge distribution of the nitrogenated base to characterize each nucleotide. These descriptors were computed from atomic partial charges derived from HF/6-31G calculations. From the characterization and classification of the stems according to the proposed descriptors, we found a special behavior for the discriminator base (in contrast to the other positions) and a strong effect of this position on the CCA end. The classification of nine variations of the tRNAAla acceptor stem showed a good structure-activity relationship that makes evident the usefulness of the proposed descriptors to characterize the local charge distributions of these biomolecules.

Nesse estudo é caracterizada a distribuição da carga do talo aceitador considerando- se todas as combinações possíveis dos pares Watson-Crick. O estudo realizouse com 256 fragmentos moleculares dos 10 nucleotídeos que modelam os três primeiros pares do talo aceitador, a base diferenciadora e o extremo CCA. Com o intuito de caracterizar cada nucleotídeo, foram propostos dois descritores locais baseados na distribuição de carga da base nitrogenada de cada nucleotídeo, os quais se calculam a partir das cargas parciais de Mulliken obtidas de cálculos HF/6-31G. A caracterização e classificação dos talos segundo esses descritores demonstrou um particular comportamento da base diferenciadora em relação aos demais nucleotídeos do talo e uma forte influência sobre o extremo CCA. A classificação de nove variações do talo aceitador do tRNA mostrou uma boa relação estrutura-atividade que colocam em evidência a utilidade dos descritores propostos para caracterizar de maneira local a distribuição de carga dessas bio-moléculas.

Graph theoretical similarity approach to compare molecular electrostatic potentials.

In this work we introduce a graph theoretical method to compare MEPs, which is independent of molecular alignment. It is based on the edit distance of weighted rooted trees, which encode the geometrical and topological information of Negative Molecular Isopotential Surfaces. A meaningful chemical classification of a set of 46 molecules with different functional groups was achieved. Structure--activity relationships for the corticosteroid binding affinity (CBG) of 31 steroids by means of hierarchical clustering resulted in a clear partitioning in high, intermediate, and low activity groups, whereas the results from quantitative structure--activity relationships, obtained from a partial least-squares analysis, showed comparable or better cross-validated correlation coefficients than the ones reported for previous methods based solely in the MEP.

tRNA structure from a graph and quantum theoretical perspective.

One of the objectives of theoretical biochemistry is to find a suitable representation of molecules allowing us to encode what we know about their structures, interactions and reactivity. Particularly, tRNA structure is involved in some processes like aminoacylation and genetic code translation, and for this reason these molecules represent a biochemical object of the utmost importance requiring characterization. We propose here two fundamental aspects for characterizing and modeling them. The first takes into consideration the connectivity patterns, i.e. the set of linkages between atoms or molecular fragments (a key tool for this purpose is the use of graph theory), and the second one requires the knowledge of some properties related to the interactions taking place within the molecule, at least in an approximate way, and perhaps of its reactivity in certain means. We used quantum mechanics to achieve this goal; specifically, we have used partial charges as a manifestation of the reply to structural changes. These charges were appropriately modified to be used as weighted factors for elements constituting the molecular graph. This new graph-tRNA context allow us to detect some structure-function relationships.