Orientador: João Ruggiero Neto / Banca: Sergio Paulo Campana Filho / Banca: Márcio José Tiera / Resumo: No presente trabalho, foram avaliados modelos teóricos para a descrição da autodissociação de poliácido fraco, e para a formação de complexos entre polieletrólitos de cargas opostas. Os modelos descritos utilizam simetria cilíndrica e o modelo celular para representar a solução polieletrolítica. A equação de Poisson-Boltzmann, com condições de contorno que levam em conta a regulação carga-potencial, é utilizada nos modelos teóricos para descrever as interações eletrostáticas. Para auto-dissociação de poliácidos fracos, foram obtidos valores teóricos de pH, calculados em função da concentração de polímeros e de sal, os quais estão em boa concordância com resultados experimentais da diluição do ácido poligalacturônico e alginato. Na formação de complexos, a energia livre eletrostática e energia livre de mistura de Flory-Huggins foram combinadas para obter diagramas de estabilidade teóricos, em diferentes condições, para analisar alguns parâmetros críticos. Estes diagramas apresentam boa concordância quando comparados com resultados experimentais da complexação entre: goma arábica e gelatina, alginato e quitosana, DNA e quitosana, poli-L-lisina e sulfato de condroitina. / Abstract: In the present work, theoretical models for the weak polyacid self-dissociation and polyelectrolyte complexation were evaluated. The models described use cylindrical symmetry and the polyelectrolyte solution is represented by the cell model. The Poisson-Boltzmann equation with boundary conditions which take into account the charge-potential regulation were used to describe the electrostatic interactions. For weak polyacid self-dissociation, theoretical values of pH, calculated as a function of polymer and salt concentrations, were obtained, and are in good agreement with experimental data of dilution of polygalacturonic acid and alginate. In the complex formation the electrostatic and the Flory- Huggins mixture free energies were combined to obtain stability diagrams in different conditions in order to analyze some critical parameters. The theoretical diagrams have shown good agreement when compared with experimental data for the complexation of: arabic gum/gelatin, alginate/chitosan, DNA/chitosan, poly-L-lysine/chondroitin sulfate. / Mestre

Cette thèse est consacrée à étudier et à améliorer les modèles mathématiques et les méthodes utilisées pour les modèles de solvatation implicite en chimie quantique. Ce manuscrit est composée de deux parties. Dans la première partie où nous analysons l'interface soluté-solvant, nous donnons, pour la première fois, une caractérisation complète de la surface moléculaire lisse, c'est-à-dire la surface exclue du solvant (SES). À partie de cette caractérisation, nous développons un algorithme de maillage par morceaux pour les surfaces moléculaires différentes, en particulier pour la SES, en utilisant la triangulation à front avançant. De plus, la cavité de la SES (la région entourée par la SES) est une description plus précise de la cavité de soluté. Dans la deuxième partie, nous construisons donc un modèle de continuum polarisable basé (PCM) sur la SES, dans lequel le paramètre de permittivité diélectrique est continu. Le problème électrostatique de ce modèle consiste à résoudre une équation de Poisson définie sur R3. Nous développons ensuite une méthode de Schwarz particulière, où seules les équations locales restreintes à des boules doivent être résolues. Enfin, nous étudions le modèle de solvatation de Poisson-Boltzmann, un autre modèle de solvatation implicite, qui tient compte à la fois de la permittivité diélectrique et de la force ionique du solvant. Une méthode de Schwarz similaire est proposée pour résoudre l'équation de Poisson-Boltzmann associée en résolvant des équations locales restreintes aux boules comme pour le PCM basé sur la SES. / This thesis is devoted to study and improve the mathematical models and methods used in implicit solvation models in quantum chemistry. The manuscript is composed of two parts. In the first part where we analyze the solute-solvent interface, we give, for the first time, a complete characterization of the so-called “smooth” molecular surface, i.e., the solvent excluded surface (SES). Based on this characterization, we develop a piecewise meshing algorithm for different molecular surfaces, especially the SES, using the advancing-front triangulation. Further, it has been pointed out in the literature that the SES-cavity (the region enclosed by the SES) is a more accurate description of the solute cavity. In the second part, we therefore construct an SES-based polarizable continuum model (PCM), in which the dielectric permittivity parameter is continuous. The electrostatic problem of this model involves solving a Poisson equation defined in R3. We then develop a particular Schwarz domain decomposition method where only local equations restricted to balls need to be solved. Finally, the Poisson-Boltzmann solvation model, another implicit solvation model, is also investigated, which takes into account both the dielectric permittivity and the ionic strength of the solvent. A similar Schwarz domain decomposition method is proposed to solve the associated Poisson-Boltzmann equation by solving local equations restricted to balls as it is for the SES-based PCM.

No description available.

Neste trabalho efetuamos uma análise quantitativa das forças que atuam entre partículas coloidais. Para isto integramos a Equação de Poisson-Boltzmann não linearizada levando em consideração o tamanho finito dos íons. Os resultados são aplicados a sistemas formados por esferas de poliestireno em dispersão aquosa. Concluímos que as forças repulsivas são dominantes nestes sistemas permitindo-nos negligenciar as forças atrativas. Também efetuamos algumas comparações dos mesmos resultados com dados experimentais / We present a quantitative analisis of the forces acting in colloidal particles. For this purpose we integrated the non linerized Poisson- Boltzmann Equation by a numerical method. We took in accont the finite size of the ions and applied the results to systems formed by polystirene spheres in aqueous dispersion. We were able to conclude that the attractive forces can be neglicted in front of the repulsive forces. We also were able to perform same comparasion com experimental data

Nous nous intéressons aux effets électrostatiques induits dans un système amphiphile neutre (constitué de triton X-100 et d'octanol en solution dans l'eau) faiblement dopé par un tensioactif ionique, le chlorure de cétylpyridinium. La principale méthode expérimentale utilisée est la diffusion des neutrons aux petits angles, complétée par des mesures en diffusion de lumière et en conductimétrie. Lorsqu'on dope le système avec de faibles quantités de tensioactif ionique, on observe de nouvelles morphologies: i) de très petites vésicules unilamellaires à grande dilution et ii) de grandes vésicules multilamellaires à concentration modérée. Nous avons mesuré l'évolution du rayon des vésicules unilamellaires en fonction des paramètres expérimentaux en modélisant quantitativement les spectres de diffusion des neutrons. D'autre part nous avons caractérisé l'ensemble des agrégats autres que vésicules.<br /><br />Nous proposons un modèle thermodynamique quantitatif permettant de décrire la phase de vésicules. Il repose sur une résolution numérique de l'équation de Poisson-Boltzmann dans une cellule de Wigner-Seitz. Les prédictions sont en très bon accord avec les résultats expérimentaux.

Neste trabalho efetuamos uma análise quantitativa das forças que atuam entre partículas coloidais. Para isto integramos a Equação de Poisson-Boltzmann não linearizada levando em consideração o tamanho finito dos íons. Os resultados são aplicados a sistemas formados por esferas de poliestireno em dispersão aquosa. Concluímos que as forças repulsivas são dominantes nestes sistemas permitindo-nos negligenciar as forças atrativas. Também efetuamos algumas comparações dos mesmos resultados com dados experimentais / We present a quantitative analisis of the forces acting in colloidal particles. For this purpose we integrated the non linerized Poisson- Boltzmann Equation by a numerical method. We took in accont the finite size of the ions and applied the results to systems formed by polystirene spheres in aqueous dispersion. We were able to conclude that the attractive forces can be neglicted in front of the repulsive forces. We also were able to perform same comparasion com experimental data

No description available.

En sjukdom kan många gånger härledas till en kaskadereaktion mellan proteiner, co-faktorer och substrat. Denna kaskadreaktion blir många gånger målet för att behandla sjukdomen med läkemedel. För att designa nya läkemedelsmoleyler används vanligen datorbaserade verktyg. Denna design av läkemedelsmolekyler drar stor nytta av att målproteinet är känt och då framförallt dess tredimensionella (3D) struktur. Är 3D-strukturen känd kan man utföra så kallad struktur- och datorbaserad molekyldesign, 3D-geometrin (f.f.a. för inbindningsplatsen) blir en vägledning för designen av en ny molekyl. Många faktorer avgör interaktionen mellan en molekyl och bindningsplatsen, till exempel fysikalisk-kemiska egenskaper hos molekylen och bindningsplatsen, flexibiliteten i molekylen och målproteinet, och det omgivande lösningsmedlet. För att strukturbaserad molekyldesign ska fungera väl måste två viktiga steg utföras: i) 3D anpassning av molekyler till bindningsplatsen i ett målprotein (s.k. dockning) och ii) prediktion av molekylers affinitet för bindningsplatsen. Huvudsyftena med arbetet i denna avhandling var som följer: i) skapa modeler för att prediktera affiniteten mellan en molekyl och bindningsplatsen i ett målprotein; ii) förfina molekyl-protein-geometrin som skapas vid 3D-anpassning mellan en molekyl och bindningsplatsen i ett målprotein (s.k. dockning); iii) karaktärisera proteiner och framför allt deras sekundärstruktur; iv) bedöma effekten av olika matematiska beskrivningar av lösningsmedlet för förfining av 3D molekyl-protein-geometrin skapad vid dockning och prediktion av molekylers affinitet för proteiners bindningsfickor. Ett övergripande syfte var att använda kemometriska metoder för modellering och dataanalys på de ovan nämnda punkterna. För att sammanfatta så presenterar denna avhandling metoder och resultat som är användbara för strukturbaserad molekyldesign. De rapporterade resultaten visar att det är möjligt att skapa kemometriska modeler för prediktion av molekylers affinitet för bindningsplatsen i ett protein och att dessa presterade lika bra som andra vanliga metoder. Dessutom kunde kemometriska modeller skapas för att beskriva effekten av hur inställningarna för olika parametrar i dockningsprogram påverkade den 3D molekyl-protein-geometrin som dockingsprogram skapade. Vidare kunde kemometriska modeller andvändas för att öka förståelsen för deskriptorer som beskrev sekundärstrukturen i proteiner. Förfining av molekyl-protein-geometrin skapad genom dockning gav liknande och ickesignifikanta resultat oberoende av vilken matematisk modell för lösningsmedlet som användes, förutom för ett fåtal (sex av 30) fall. Däremot visade det sig att användandet av en förfinad geometri var värdefullt för prediktion av molekylers affinitet för bindningsplatsen i ett protein. Förbättringen av prediktion av affintitet var markant då en Poisson-Boltzmann beskrivning av lösningsmedlet användes; jämfört med prediktionerna gjorda med ett dockningsprogram förbättrades korrelationen mellan beräknad affintiet och uppmätt affinitet med 0,7 (R2). / A disease is often associated with a cascade reaction pathway involving proteins, co-factors and substrates. Hence to treat the disease, elements of this pathway are often targeted using a therapeutic agent, a drug. Designing new drug molecules for use as therapeutic agents involves the application of methods collectively known as computer-aided molecular design, CAMD. When the three dimensional (3D) geometry of a macromolecular target (usually a protein) is known, structure-based CAMD is undertaken and structural information of the target guides the design of new molecules and their interactions with the binding sites in targeted proteins. Many factors influence the interactions between the designed molecules and the binding sites of the target proteins, such as the physico-chemical properties of the molecule and the binding site, the flexibility of the protein and the ligand, and the surrounding solvent. In order for structure-based CAMD to be successful, two important aspects must be considered that take the abovementioned factors into account. These are; i) 3D fitting of molecules to the binding site of the target protein (like fitting pieces of a jigsaw puzzle), and ii) predicting the affinity of molecules to the protein binding site. The main objectives of the work underlying this thesis were: to create models for predicting the affinity between a molecule and a protein binding site; to refine the geometry of the molecule-protein complex derived by or in 3D fitting (also known as docking); to characterize the proteins and their secondary structure; and to evaluate the effects of different generalized-Born (GB) and Poisson-Boltzmann (PB) implicit solvent models on the refinement of the molecule-protein complex geometry created in the docking and the prediction of the molecule-to-protein binding site affinity. A further objective was to apply chemometric methodologies for modeling and data analysis to all of the above. To summarize, this thesis presents methodologies and results applicable to structure-based CAMD. Results show that predictive chemometric models for molecule-to-protein binding site affinity could be created that yield comparable results to similar, commonly used methods. In addition, chemometric models could be created to model the effects of software settings on the molecule-protein complex geometry using software for molecule-to-binding site docking. Furthermore, the use of chemometric models provided a more profound understanding of protein secondary structure descriptors. Refining the geometry of molecule-protein complexes created through molecule-to-binding site docking gave similar results for all investigated implicit solvent models, but the geometry was significantly improved in only a few examined cases (six of 30). However, using the geometry-refined molecule-protein complexes was highly valuable for the prediction of molecule-to-binding site affinity. Indeed, using the PB solvent model it yielded improvements of 0.7 in correlation coefficients (R2) for binding affinity parameters of a set of Factor Xa protein drug molecules, relative to those obtained using the fitting software.

Extracellular neuroelectronic interfacing has important applications in the fields of neural prosthetics, biological computation and whole-cell biosensing for drug screening and toxin detection. While the field of neuroelectronic interfacing holds great promise, the recording of high-fidelity signals from extracellular devices has long suffered from the problem of low signal-to-noise ratios and changes in signal shapes due to the presence of highly dispersive dielectric medium in the neuron-microelectrode cleft. This has made it difficult to correlate the extracellularly recorded signals with the intracellular signals recorded using conventional patch-clamp electrophysiology. For bringing about an improvement in the signalto-noise ratio of the signals recorded on the extracellular microelectrodes and to explore strategies for engineering the neuron-electrode interface there exists a need to model, simulate and characterize the cell-sensor interface to better understand the mechanism of signal transduction across the interface. Efforts to date for modeling the neuron-electrode interface have primarily focused on the use of point or area contact linear equivalent circuit models for a description of the interface with an assumption of passive linearity for the dynamics of the interfacial medium in the cell-electrode cleft. In this dissertation, results are presented from a nonlinear dynamic characterization of the neuroelectronic junction based on Volterra-Wiener modeling which showed that the process of signal transduction at the interface may have nonlinear contributions from the interfacial medium. An optimization based study of linear equivalent circuit models for representing signals recorded at the neuron-electrode interface subsequently iv proved conclusively that the process of signal transduction across the interface is indeed nonlinear. Following this a theoretical framework for the extraction of the complex nonlinear material parameters of the interfacial medium like the dielectric permittivity, conductivity and diffusivity tensors based on dynamic nonlinear Volterra-Wiener modeling was developed. Within this framework, the use of Gaussian bandlimited white noise for nonlinear impedance spectroscopy was shown to offer considerable advantages over the use of sinusoidal inputs for nonlinear harmonic analysis currently employed in impedance characterization of nonlinear electrochemical systems. Signal transduction at the neuron-microelectrode interface is mediated by the interfacial medium confined to a thin cleft with thickness on the scale of 20-110 nm giving rise to Knudsen numbers (ratio of mean free path to characteristic system length) in the range of 0.015 and 0.003 for ionic electrodiffusion. At these Knudsen numbers, the continuum assumptions made in the use of Poisson-Nernst-Planck system of equations for modeling ionic electrodiffusion are not valid. Therefore, a lattice Boltzmann method (LBM) based multiphysics solver suitable for modeling ionic electrodiffusion at the mesoscale neuron-microelectrode interface was developed. Additionally, a molecular speed dependent relaxation time was proposed for use in the lattice Boltzmann equation. Such a relaxation time holds promise for enhancing the numerical stability of lattice Boltzmann algorithms as it helped recover a physically correct description of microscopic phenomena related to particle collisions governed by their local density on the lattice. Next, using this multiphysics solver simulations were carried out for the charge relaxation dynamics of an electrolytic nanocapacitor with the intention of ultimately employing it for a simulation of the capacitive coupling between the neuron and the v planar microelectrode on a microelectrode array (MEA). Simulations of the charge relaxation dynamics for a step potential applied at t = 0 to the capacitor electrodes were carried out for varying conditions of electric double layer (EDL) overlap, solvent viscosity, electrode spacing and ratio of cation to anion diffusivity. For a large EDL overlap, an anomalous plasma-like collective behavior of oscillating ions at a frequency much lower than the plasma frequency of the electrolyte was observed and as such it appears to be purely an effect of nanoscale confinement. Results from these simulations are then discussed in the context of the dynamics of the interfacial medium in the neuron-microelectrode cleft. In conclusion, a synergistic approach to engineering the neuron-microelectrode interface is outlined through a use of the nonlinear dynamic modeling, simulation and characterization tools developed as part of this dissertation research.