Laddningsbeteendet hos amingruppen vid ytgränsskiktet mellan vatten och luft har studerats under ändring av vattenfasens pH och NaCl-koncentration via den ickelinjära laserspektroskopiska tekniken, vibrationssumfrekvensspektroskopi (VSFS). Modellen som användes för ytan bestod av ett Langmuirmonolager av 1-docosanamin, en icke-löslig fettkedjeamin med NH2-gruppen riktad mot vattenfasen. En av de huvudsakliga syftena med projektet var att bestämma det skenbara samt yt-pKa:t för amingruppen, såväl som att testa gränserna för de klassiska Poisson-Boltzmann-formuleringarna av teorin för det elektriska dubbellagret. Molekylär information av laddningsbeteendet hos aminen erhölls från VSFS-spektra genom att följa NH-, OH- och CH-sträckningsvibrationsmoderna. Specifikt så identifierades de spektrala dragen från den neutrala formen (R-NH2) och den laddade formen (R-NH3+) av aminen, vilka direkt korrelerades med monolagrets ytladdning. Intensiteten hos OH-banden från vattenmolekylerna i det diffusa dubbellagret kunde länkas till ytpotentialen och CH-vibrationerna från alkylkedjan av amino-tensiden kopplades slutligen till packningstätheten hos monolagret. Ytterligare experiment utfördes med en deutererad vattenfas (D2O) för att bekräfta sträckningsvibrationsmoderna hos NH3+, vilka aldrig tidigare har rapporterats. Resultaten visar på att fettkedjeaminen får ett avsevärt lägre yt- och skenbart pKa jämfört med bulken (∼ 4 jämfört med 10,5). Detta är i enlighet med vad Gouy-Chapmann-modellen av det elektriska dubbellagret förutser. Dessutom så indikerar datat att det inneboende pKa:t hos aminen också blir lägre vid ytan än för bulken (9,7±0,7 jämfört med 10,5), vilket kan beskrivas som en effekt av begränsningen i frihetsgrader hos den ytbundna aminen. Dock, så hindrades en mer utförlig kvantitativ jämförelse mot teorin av ett sämre val av det experimentella referensvärdet som användes för att jämföra data mellan olika dagar. Dessutom så var anpassningsrutinen för datat begränsad på grund av spektrala vibrationsöverlapp mellan de relativt svaga aminbanden och de mycket starkare vatten- och alkylsträckningssignalerna. Intressant nog, för högre pH-värden, då aminen är helt oladdad, bevisade sumfrekvensspektra att hydroxidjonen föredrar att adsorbera till ytan genom att monolagret fick en negativ nettoladdning. Överlag så förbättrar studierna som presenteras i denna master-projektuppsats vår molekylära förståelse kring hur den biofysiskt betydande amingruppen beter sig vid ytgränsskikt. / The charging behaviour of the amine moiety at the water-air interface upon changes in the aqueous subphase pH and NaCl concentration has been studied using  the non-linear laser spectroscopy technique, Vibrational Sum Frequency Spectroscopy (VSFS).  The model surface consisted of a Langmuir monolayer of 1-docosaneamine, an insoluble fatty amine that exposes its NH2  group to solution. One of the main purposes of the project is to determine the surface, and the apparent pKa of the amine moiety, as well as testing the limits of validity of classical formulations of the electrical double layer theory within the Poisson-Boltzmann formalism. Molecular information of the charging behaviour was obtained from the VSFS spectra by targeting the NH, OH and CH stretching modes. Specifically, spectral features from the neutral amine (i.e. R-NH2) and charged (R-NH3+) groups could be identified and directly correlated to the surface charge of the monolayer. The intensity of the  OH bands from water molecules in the diffuse double layer, were linked to the surface potential, and finally, the CH modes from the surfactant alkyl chain gave information of the packing density in the monolayer. Additional experiments were also carried out in D2O to help confirm the assignment of the NH3+ stretching modes that had not been previously reported. The results show that as predicted from the Gouy-Chapman electric double layer model, the apparent pKa of the fatty amine monolayer is significantly lower than in the bulk  (∼ 4 compared with 10.5) . However, the data show indication that the intrinsic pKa at the surface is also lower than in the bulk (9.7+/- 0.7, compared to 10.5), an effect that is ascribed to the 2D molecular confinement in the monolayer. A more quantitative comparison with the theoretical predictions was nonetheless hampered by a poor selection of the experimental reference for comparing data collected in different days, and the limitations in the fitting routines due spectral overlap of the relatively weak amine bands with the OH and CH stretching modes. Interestingly, at high pH when the fatty amine is fully uncharged, the sum frequency spectra show evidence that OH- ion preferentially adsorbed to the surface, making it effectively net negatively charged. Overall, the studies presented in this master thesis, improve our molecular understanding of the behaviour of the biophysically relevant amine-functionality at interfaces.

Vibrational sum frequency spectroscopy har använts för att studera interaktionerna mellan monovalenta joner och laddade fettsyramonolager. Subfasen bestod av utvalda alkalihydroxidsaltlösningar med pH12, med huvudfokus på cesiumjonen. Molekylär information erhölls genom att rikta in sig på vibrationerna hos karboxylsyragruppen, alkylkedjor, och vattenmolekyler i kontakt med monolagret, samt i det diffusa dubbellagret. Ytans laddning uppskattades genom att observera sträckningsvibrationerna hos hydratiserade karboxylat och protonerade karboxylsyror. Ytans potential beräknades utifrån signalresponsen hos vattenmolekylerna i det diffusa dubbellagret. Beteendet hos ytans laddning och potential överensstämmer väl med Gouy-Chapman-teorin för stora områden per molekyl, men avviker avsevärt vid kompression av monolagret. Vid små områden per molekyl, eller hög laddningsdensitet, stämmer resultaten bättre överens med en storleksmodifierad version av Poisson-Boltzmann-teorin. Resultaten från experiment med en cesiumhydroxidsubfas jämfördes med motsvarande experiment med natrium och litium, vilket beskriver cesiumjonen i relation till de andra alkalijonerna vad gäller jonspecifika effekter. Resultaten som har samlats in här ger insikt i hur effektiv jonstorlek kan användas för att modellera och förutsäga jonspecifika effekter med karboxylsyragruppen i ett Langmuir-monolager. / Vibrational sum frequency spectroscopy has been used to study the interactions of monovalent ions with highly charged fatty acid monolayers. The subphase consisted of selected alkali hydroxide salt solutions of pH 12, primarily focusing on the cesium ion. Molecular information was obtained by targeting the vibrational modes of the carboxylic acid headgroups, alkyl chains, and water molecules in the immediate surface and diffuse double layers. The surface charge was estimated by monitoring the stretching modes of the hydrated carboxylate and protonated carboxylic acid. The surface potential was estimated from the signal response of the water molecules in the diffuse double layer. The behaviour of the surface charge and surface potential agrees well with Gouy-Chapman theory for large areas per molecule, but deviates significantly upon monolayer compression. At small areas per molecule or high surface charge density, the results better align with a size-modified version of the Poisson-Boltzmann theory. The results obtained with a cesium hydroxide subphase were compared to equivalent experiments with sodium and lithium, which puts the cesium ion into context with the other alkali ions in terms ion specific effects. The results collected here provide insight into how effective ion size can be used in modelling and predicting ion specific effects with the carboxylic acid moiety in a Langmuir monolayer.

In this study, we consider electrostatics contributed from the molecules in the ionic solution. It plays a significant role in determining the binding affinity of molecules and drugs. We develop the overall framework of computing electrostatic properties for three-dimensional molecular structures, including potential, energy, and forces. These properties are derived from Poisson-Boltzmann equation, a partial differential equation that describes the electrostatic behavior of molecules in ionic solutions. In order to compute these properties, we derived new boundary integral equations and designed a boundary element algorithm based on the linear time fast multipole method for solving the linearized Poisson-Boltzmann equation. Meanwhile, a higher-order parametric formulation called algebraic spline model is used for accurate approximation of the unknown solution of the linearized Poisson-Boltzmann equation. Based on algebraic spline model, we represent the normal derivative of electrostatic potential by surrounding electrostatic potential. This representation guarantees the consistent relation between electrostatic potential and its normal derivative. In addition, accurate numerical solution and fast computation for electrostatic energy and forces are also discussed. In addition, we described our hierarchical modeling and parameter optimization of molecular structures. Based on this technique, we can control the scalability of molecular models for electrostatic computation. The numerical test and experimental results show that the proposed techniques offer an efficient and accurate solution for solving the electrostatic problem of molecules. / text

The implicit-solvent model uses continuum electrostatic theory to represent the salt solution around dissolved biomolecules, leading to a coupled system of the Poisson-Boltzmann and Poisson equations. This thesis uses the implicit-solvent model to study solvation, binding and adsorption of proteins. We developed an implicit-solvent model solver that uses the boundary element method (BEM), called PyGBe. BEM numerically solves integral equations along the biomolecule-solvent interface only, therefore, it does not need to discretize the entire domain. PyGBe accelerates the BEM with a treecode algorithm and runs on graphic processing units. We performed extensive verification and validation of the code, comparing it with experimental observations, analytical solutions, and other numerical tools. Our results suggest that a BEM approach is more appropriate than volumetric based methods, like finite-difference or finite-element, for high accuracy calculations. We also discussed the effect of features like solvent-filled cavities and Stern layers in the implicit-solvent model, and realized that they become relevant in binding energy calculations. The application that drove this work was nano-scale biosensors-- devices designed to detect biomolecules. Biosensors are built with a functionalized layer of ligand molecules, to which the target molecule binds when it is detected. With our code, we performed a study of the orientation of proteins near charged surfaces, and investigated the ideal conditions for ligand molecule adsorption. Using immunoglobulin G as a test case, we found out that low salt concentration in the solvent and high positive surface charge density leads to favorable orientations of the ligand molecule for biosensing applications. We also studied the plasmonic response of localized surface plasmon resonance (LSPR) biosensors. LSPR biosensors monitor the plasmon resonance frequency of metallic nanoparticles, which shifts when a target molecule binds to a ligand molecule. Electrostatics is a valid approximation to the LSPR biosensor optical phenomenon in the long-wavelength limit, and BEM was able to reproduce the shift in the plasmon resonance frequency as proteins approach the nanoparticle.

Neste trabalho abordam-se alguns aspectos numéricos relacionados ao movimento de uma partícula carregada em um fluido ionizado, constituindo assim o fenômeno de eletroforese. A equação de Navier-Stokes governa a hidrodinâmica do sistema, sendo atribuída a esta um termo forçante relacionado a equação de Poisson-Boltzmann que descreve a interação com o campo elétrico. A simulação foi realizada utilizando a linguagem Fortran 90 e as discretizações foram feitas pelo método de diferenças finitas junto as equações governantes. Para descrever a posição da partícula foi usada a técnica de fronteira virtual, onde são criados pontos lagrangeanos sobre,o contorno da partícula formando uma espécie de segunda malha. Foram feitos testes com objetivo de validar as equações governantes e identificar a influencia das condições de contorno direção da partícula. / In this work we study some of the numerical aspects related to the motion of a charged particle in an ionized fluid, known as the phenomenon of electrophoresis. The Navier-Stokes equations models the ,hydrodynamics of the system, with the addition of a forcing term, related to the Poisson-Boltzmann equation, which describes the interaction of the electric field. The simulation was performed using Fortran 90 and discretizations were made by the method of finite differences applied to the governing equations. To describe the position of the particle the technique of virtual boundary is used, where Lagrangean points are created around the circumference of the particle forming a sort of second mesh. Tests were made with the objective of validating the governing equations and to identify the influence of boundary conditions in the direction of the particle.

The functional aspects of proteins are largely dictated by highly selective protein- protein and protein-ligand interactions, even in situations of high structural homology, where electrostatic factors are the major contributors to selectivity. The vibrational Stark effect (VSE) allows us to measure electrostatic fields in complex environments, such as proteins, by the introduction of a vibrational chromophore whose vibrational absorption energy is linearly sensitive to changes in the local electrostatic field. The works presented here seek to computationally quantify electrostatic fields measured via VSE, with the eventual goal of being able to quantitatively predict electrostatic fields, and therefore Stark shifts, for any given protein-interaction. This is done using extensive molecular dynamics in the Amber03 and AMOEBA force fields to generate large ensembles the GTPase Rap1a docked to RalGDS and [superscript p]²¹Ras docked to RalGDS. We discuss how side chain orientations contribute to the differential binding of different mutations of Rap1a binding to RalGDS, where it was found that a hydrogen-bonding pocket is disrupted by the mutation of position 31 from lysine to glutamic acid. We then show that multi-dimensional umbrella sampling of the probe orientations yields a wider range of accessible structures, increasing the quality of the ensembles generated. A large variety of methods for calculating electrostatic fields are presented, with Poisson- Boltzmann electrostatics yielding the most consistent, reliable results. Finally, we explore using AMOEBA for both ensemble-generation as well as the electrostatic description of atoms for field calculations, where early results suggest that the electrostatic field due to the induce dipole moment of the probe is responsible for predicting qualitatively correct Stark shifts.

Na presente Tese, vamos desenvolver teorias para eletrólitos próximos de interfaces e para suspensões coloidais carregadas. No caso de interfaces, a nova teoria permite-nos calcular quantitativamente tensões e potenciais superficiais, e perfis de densidade para ambas interfaces água-ar e água-óleo. Para suspensões coloidais hidrofóbicas, a teoria permite-nos calcular as concentrações críticas de coagulação (CCC) para várias soluções eletrolíticas. Os resultados teóricos estão em excelente acordo com dados experimentais. A interação iônica com interfaces é relacionada com a classificação dos íons em caotrópicos e cosmotrópicos. A teoria, portanto, traz novo enfoque a série de Hofmeister que governa a estabilidade de soluções proteicas. Em suspensões coloidais, estudamos também o papel das correlações eletrostáticas na distribuição de íons multivalentes próximos da superfície coloidal. Uma nova teoria é introduzida que nos permite incluir as correlações interiônicas como uma nova condição de contorno renormalizada para a equação de Poisson-Boltzmann. Os perfis de densidade calculados são comparados com simulações de Monte Carlo, demonstrando uma boa concordância. Finalmente, exploramos o papel da polarizabilidade coloidal na distribuição iônica. Encontramos que a polarizabilidade causa a repulsão superficial dos contraíons e pode afetar a mobilidade eletroforética de partículas coloidais. / In the present Thesis we will develop theories for electrolytes near interfaces and for charge stabilized colloidal suspensions. In the case of interfaces the new theory allows us to quantitatively calculate surface tensions, surface potentials, and the ionic density profiles both for the water-air and the water-oil interfaces. For the hydrophobic colloidal suspensions, the theory allows us to calculate the critical coagulation concentrations (CCC) for various electrolyte solutions. The theoretical results are found to be in excellent agreement with the experimental data. The ionic interaction with the interfaces is found to be related to the classification of ions into chatropes and kosmotropes. The theory, therefore, sheds new light on the Hofmeister series which governs the stability of protein solutions. For colloidal suspensions, we also study the role of electrostatic correlations on the distribution of multivalent ions near the colloidal surface. A new theory is introduced which allows us to include the interionic correlations as a renormalized boundary condition for the Poisson-Boltzmann equation. The calculated ionic density profiles are then compared with the Monte Carlo simulations, showing a good agreement. Finally, we explore the role of colloidal polarizability on the ionic distribution. We find that polarizability causes the counterion repulsion from the surface and can affect the electrophoretic mobility of colloidal particles.

Neste trabalho abordam-se alguns aspectos numéricos relacionados ao movimento de uma partícula carregada em um fluido ionizado, constituindo assim o fenômeno de eletroforese. A equação de Navier-Stokes governa a hidrodinâmica do sistema, sendo atribuída a esta um termo forçante relacionado a equação de Poisson-Boltzmann que descreve a interação com o campo elétrico. A simulação foi realizada utilizando a linguagem Fortran 90 e as discretizações foram feitas pelo método de diferenças finitas junto as equações governantes. Para descrever a posição da partícula foi usada a técnica de fronteira virtual, onde são criados pontos lagrangeanos sobre,o contorno da partícula formando uma espécie de segunda malha. Foram feitos testes com objetivo de validar as equações governantes e identificar a influencia das condições de contorno direção da partícula. / In this work we study some of the numerical aspects related to the motion of a charged particle in an ionized fluid, known as the phenomenon of electrophoresis. The Navier-Stokes equations models the ,hydrodynamics of the system, with the addition of a forcing term, related to the Poisson-Boltzmann equation, which describes the interaction of the electric field. The simulation was performed using Fortran 90 and discretizations were made by the method of finite differences applied to the governing equations. To describe the position of the particle the technique of virtual boundary is used, where Lagrangean points are created around the circumference of the particle forming a sort of second mesh. Tests were made with the objective of validating the governing equations and to identify the influence of boundary conditions in the direction of the particle.

Neste trabalho abordam-se alguns aspectos numéricos relacionados ao movimento de uma partícula carregada em um fluido ionizado, constituindo assim o fenômeno de eletroforese. A equação de Navier-Stokes governa a hidrodinâmica do sistema, sendo atribuída a esta um termo forçante relacionado a equação de Poisson-Boltzmann que descreve a interação com o campo elétrico. A simulação foi realizada utilizando a linguagem Fortran 90 e as discretizações foram feitas pelo método de diferenças finitas junto as equações governantes. Para descrever a posição da partícula foi usada a técnica de fronteira virtual, onde são criados pontos lagrangeanos sobre,o contorno da partícula formando uma espécie de segunda malha. Foram feitos testes com objetivo de validar as equações governantes e identificar a influencia das condições de contorno direção da partícula. / In this work we study some of the numerical aspects related to the motion of a charged particle in an ionized fluid, known as the phenomenon of electrophoresis. The Navier-Stokes equations models the ,hydrodynamics of the system, with the addition of a forcing term, related to the Poisson-Boltzmann equation, which describes the interaction of the electric field. The simulation was performed using Fortran 90 and discretizations were made by the method of finite differences applied to the governing equations. To describe the position of the particle the technique of virtual boundary is used, where Lagrangean points are created around the circumference of the particle forming a sort of second mesh. Tests were made with the objective of validating the governing equations and to identify the influence of boundary conditions in the direction of the particle.

Na presente Tese, vamos desenvolver teorias para eletrólitos próximos de interfaces e para suspensões coloidais carregadas. No caso de interfaces, a nova teoria permite-nos calcular quantitativamente tensões e potenciais superficiais, e perfis de densidade para ambas interfaces água-ar e água-óleo. Para suspensões coloidais hidrofóbicas, a teoria permite-nos calcular as concentrações críticas de coagulação (CCC) para várias soluções eletrolíticas. Os resultados teóricos estão em excelente acordo com dados experimentais. A interação iônica com interfaces é relacionada com a classificação dos íons em caotrópicos e cosmotrópicos. A teoria, portanto, traz novo enfoque a série de Hofmeister que governa a estabilidade de soluções proteicas. Em suspensões coloidais, estudamos também o papel das correlações eletrostáticas na distribuição de íons multivalentes próximos da superfície coloidal. Uma nova teoria é introduzida que nos permite incluir as correlações interiônicas como uma nova condição de contorno renormalizada para a equação de Poisson-Boltzmann. Os perfis de densidade calculados são comparados com simulações de Monte Carlo, demonstrando uma boa concordância. Finalmente, exploramos o papel da polarizabilidade coloidal na distribuição iônica. Encontramos que a polarizabilidade causa a repulsão superficial dos contraíons e pode afetar a mobilidade eletroforética de partículas coloidais. / In the present Thesis we will develop theories for electrolytes near interfaces and for charge stabilized colloidal suspensions. In the case of interfaces the new theory allows us to quantitatively calculate surface tensions, surface potentials, and the ionic density profiles both for the water-air and the water-oil interfaces. For the hydrophobic colloidal suspensions, the theory allows us to calculate the critical coagulation concentrations (CCC) for various electrolyte solutions. The theoretical results are found to be in excellent agreement with the experimental data. The ionic interaction with the interfaces is found to be related to the classification of ions into chatropes and kosmotropes. The theory, therefore, sheds new light on the Hofmeister series which governs the stability of protein solutions. For colloidal suspensions, we also study the role of electrostatic correlations on the distribution of multivalent ions near the colloidal surface. A new theory is introduced which allows us to include the interionic correlations as a renormalized boundary condition for the Poisson-Boltzmann equation. The calculated ionic density profiles are then compared with the Monte Carlo simulations, showing a good agreement. Finally, we explore the role of colloidal polarizability on the ionic distribution. We find that polarizability causes the counterion repulsion from the surface and can affect the electrophoretic mobility of colloidal particles.