Quantum theory of QSAR

Es discuteix aquí la forma de desenvolupar un formalisme on les mesures de semblança quàntiques (QSM) es transformen en un producte natural, que sorgeix d'un marc de treball específic relacionat amb la teoria quàntica. Aquesta fita s'empra per establir una connexió fonamental entre la teoria quàntica i les QSAR, que s'estudien més endavant des del punt de vista de la química quàntica discreta. A fi d'assolir aquest objectiu es revisen en un primer pas diverses eines teòriques. D'aquesta manera la primera secció s'associa a la construcció del concepte de conjunt etiquetat. Més tard, la definició d'objecte quàntic (QO) s'aclareix emprant tant el rerefons de la teoria quàntica com els conceptes previs, que formen part del formalisme de conjunt etiquetat. Per definir un QO, es demostra que les funcions de densitat (DF) tenen un paper principal i es presenta una possible forma matemàtica simplificada amb propòsits computacionals. En el camí de preparar les eines per dilucidar el problema, els conjunts convexos resulten ser prominents, mentre que la noció de semiespai vectorial, apareix com a conseqüència. Les regles de transformació, un aparell dissenyat per connectar les funcions d'ona amb les DF, es defineixen en un proper pas. També es descriuen diversos aspectes d'aquest tipus de discussió preliminar, entre altres el concepte de distribucions d'energia cinètica, que apareixen dins la definició dels espais de Hilbert generals i els espais de Sobolev. Les QSM, com una font de la representació discreta de les estructures moleculars, es fan evidents dins d'aquest concepte. Un desenvolupament posterior de la teoria intenta estudiar els processos de discretització; això és: la transformació dels espais funcionals d'infinites dimensions en espais n-dimensionals. Aquest resultat afegeix noves perspectives a la representació discreta de QO, ja que: a) esdevé una font de nous descriptors, b) descriu el fonament de les QSAR, cosa que permet la construcció de models adequats comWays of developing the formalism where Quantum Similarity Measures (QSM) become a natural product issuing from a specific mathematical framework related to quantum theory are discussed. This fact is used to establish a fundamental connection between Quantum Theory and QSAR, which is analysed in turn within the realm of discrete quantum chemistry. In order to achieve such an objective several theoretical tools are revised in a previous step. The first section is devoted to constructing the concept of the Tagged Set. Next, the definition of Quantum Object (QO) is clarified by means of Quantum Theory background ideas and the previous Tagged Set formalism. In the definition of QO, Density Functions (DF) are shown to play a fundamental role and a possible simplified mathematical picture is presented for possible computational purposes. In the process of preparing the problem-solving tools, convex sets become prominent, and the notion of Vector Semispace appears as a consequence. The Transformation Rule, a device to connect Wavefunctions with DF, is defined in a new step. Various products of this preliminary discussion are described, among them the concept of Kinetic Energy distributions, issuing from the background concept of extended Hilbert and Sobolev spaces. QSM as a source of discrete representation of molecular structures is made evident in this context. Further theoretical development undertakes precise study of discretization, that is, the transformation of infinite-dimensional functional spaces into n-dimensional ones. This result adds new perspectives to the discrete representation of QO, because a) It provides a source of new QO descriptors, b) It describes the QSAR theoretical background enabling the construction of adequate models like tuned-QSAR, and c) It allows the construction of sound and general alternatives of Hammet?s ó or log P parameters. In this context, QSM appear to produce QSAR models constructed with unbiased descriptors, deducible from quant

Molecular fragment and substituent effect studies of styrene derivatives by electron density shape analysis

The research work leading to the content of this thesis and to the related publications represents a novel way to analyze and characterize some aspects of the most fundamental interactions within molecules, namely through-space and through-bond interactions, which are also relevant to substituent effects. The approach and the results give quantum chemical justification for some components of the associated fundamental phenomena which are often difficult or even impossible to examine separately by experimental means. The results are obtained using well-established, thoroughly tested and verified methods of electron density shape analysis approaches, based on input electron densities obtained by various established quantum chemistry computational methods, such as Hartree-Fock, Density Functional, and Møller-Plesset methodologies. The shape analysis methods, applicable to both complete molecules and locally to molecular fragments such as functional groups, are based on two fundamental theorems of quantum chemistry: the Hohenberg-Kohn theorem and the Holographic Electron Density theorem. The first of these theorems establishes that the molecular electron density must contain all molecular properties, whereas the second of these theorems gives justification that even small molecular fragments, such as a vinyl group in our studies, can be used as a “fingerprint”, fully representing all the unique intramolecular interactions within each molecule. As a consequence of these theorems, the electron density shape analysis methods, when applied to the complete electron density cloud of a target molecule, or locally to that of a molecular fragment, yield shape information which can, in principle, give highly detailed theoretical information about all molecular properties, hence, providing a suitable basis for establishing correlations with experimentally available data about various measured chemical properties. In earlier studies, such shape analysis approaches have been used in various applied fields of chemistry, such as pharmacology and toxicology. The present study describes the use of a series of small molecules, specifically, substituted styrenes for the analysis and shape correlations involving through-bond and through-space correlations. As a consequence of their specific structural features, the chosen molecules appear as ideal candidates to study both effects separately. In spite of their specificity, the results provide some general conclusions which are likely to contribute to a better understanding of far more complex phenomena, such as some of the components contributing to the complex folding pattern of globular proteins and more general interaction problems in the emerging field of molecular design. Even in these latter fields, these two types of interactions, through-space and through-bond, play significant roles as well. The presence of aromatic rings in these styrene derivatives is very useful as through-bond transmitting media whilst the distance between the studied molecular fragments obtained after removing the ring is also nearly optimal to be used in through-space interaction studies. The structural specificities of the model molecules have played an important role in all three publications constituting the main chapters of this thesis. Therefore, there is a strong emphasis on the effect transmitting capabilities of the aromatic ring in all 3 of these papers

Information-theoretic approaches to atoms-in-molecules : Hirshfeld family of partitioning schemes

Many population analysis methods are based on the precept that molecules should be built from fragments (typically atoms) that maximally resemble the isolated fragment. The resulting molecular building blocks are intuitive (because they maximally resemble well-understood systems) and transferable (because if two molecular fragments both resemble an isolated fragment, they necessarily resemble each other). Information theory is one way to measure the deviation between molecular fragments and their isolated counterparts, and it is a way that lends itself to interpretation. For example, one can analyze the relative importance of electron transfer and polarization of the fragments. We present key features, advantages, and disadvantages of the information-theoretic approach. We also codify existing information-theoretic partitioning methods in a way, that clarifies the enormous freedom one has within the information-theoretic ansatz

Defining binding efficiency and specificity of auxins for SCF(TIR1/AFB)-Aux/IAA co-receptor complex formation.

Structure-activity profiles for the phytohormone auxin have been collected for over 70 years, and a number of synthetic auxins are used in agriculture. Auxin classification schemes and binding models followed from understanding auxin structures. However, all of the data came from whole plant bioassays, meaning the output was the integral of many different processes. The discovery of Transport Inhibitor-Response 1 (TIR1) and the Auxin F-Box (AFB) proteins as sites of auxin perception and the role of auxin as molecular glue in the assembly of co-receptor complexes has allowed the development of a definitive quantitative structure-activity relationship for TIR1 and AFB5. Factorial analysis of binding activities offered two uncorrelated factors associated with binding efficiency and binding selectivity. The six maximum-likelihood estimators of Efficiency are changes in the overlap matrixes, inferring that Efficiency is related to the volume of the electronic system. Using the subset of compounds that bound strongly, chemometric analyses based on quantum chemical calculations and similarity and self-similarity indices yielded three classes of Specificity that relate to differential binding. Specificity may not be defined by any one specific atom or position and is influenced by coulomb matrixes, suggesting that it is driven by electrostatic forces. These analyses give the first receptor-specific classification of auxins and indicate that AFB5 is the preferred site for a number of auxinic herbicides by allowing interactions with analogues having van der Waals surfaces larger than that of indole-3-acetic acid. The quality factors are also examined in terms of long-standing models for the mechanism of auxin binding

Computational Approaches to Drug Profiling and Drug-Protein Interactions

Despite substantial increases in R&D spending within the pharmaceutical industry, denovo drug design has become a time-consuming endeavour. High attrition rates led to a long period of stagnation in drug approvals. Due to the extreme costs associated with introducing a drug to the market, locating and understanding the reasons for clinical failure is key to future productivity. As part of this PhD, three main contributions were made in this respect. First, the web platform, LigNFam enables users to interactively explore similarity relationships between ‘drug like’ molecules and the proteins they bind. Secondly, two deep-learning-based binding site comparison tools were developed, competing with the state-of-the-art over benchmark datasets. The models have the ability to predict offtarget interactions and potential candidates for target-based drug repurposing. Finally, the open-source ScaffoldGraph software was presented for the analysis of hierarchical scaffold relationships and has already been used in multiple projects, including integration into a virtual screening pipeline to increase the tractability of ultra-large screening experiments. Together, and with existing tools, the contributions made will aid in the understanding of drug-protein relationships, particularly in the fields of off-target prediction and drug repurposing, helping to design better drugs faster