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"In this work we consider an optimal design problem formulated on a two dimensional domain filled with two isotropic dielectric materials. The objective is to find a design that supports an electric field which is as close as possible to a target field, under a constraint on the amount of the better dielectric. In the case of a zero target field, the practical purpose of this problem is to avoid the so called dielectric breakdown of the material caused due to a relatively large electric field. In general, material layout problems of this type fail to have an optimal configuration of the two materials. Instead one must study the behavior of minimizing sequences of configurations. From a practical perspective, optimal or nearly optimal configurations of the two materials are of special interest since they provide the information needed for the manufacturing of optimal designs. Therefore in this work, we develop theoretical and numerical means to support a tractable method for the numerical computation of minimizing sequences of configurations and illustrate our approach through numerical examples. The same method applies if we were to replace the electric field by electric flux, in our objective functional. Similar optimization design problems can be formulated in the mathematically identical contexts of electrostatics and heat conduction."

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.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Vita. / Includes bibliographical references. / by Weng Cho Chew. / Ph.D.

Antibodies and antibody fragments are the largest class of biotherapeutics in development with many products already available in the clinic. Antibodies are promising due to their naturally high affinity and specificity for biological targets. A key stumbling block to biopharmaceutical development compared to small molecule drugs is the general requirement for a stable liquid formulation, which is often difficult to obtain due to issues with aggregation, phase separation, particle formation, and chemical instabilities. Aberrant solution behaviour limits the production, storage and delivery of the monoclonal antibody. Biopharmaceutical solution behaviour is determined by weak, transient protein-protein and protein-solvent interactions. An attractive interaction potential between proteins in solution can lead to association. Irreversible association occurs when proteins undergo large scale structural changes and aggregate. Reversible association is less severe, but can lead to undesirable solution properties such as high viscosity, phase separation and opalescence, which can lead to difficulties throughout the downstream processing and formulation steps. These problems can become exacerbated during formulation of antibodies when trying to achieve high protein concentrations often required for effective antibody dosage. Firstly, we studied the domains of the Fab fragment using statistical models and continuum electrostatic calculations and found that the CH1 domain is more soluble than the other domains and has properties of intrinsically disordered like proteins which is supported by observations in the literature. We then investigated the immunoglobulin superfamily and found 11 proteins which may have a similarly disordered nature. We present a new web server for predicting protein solubility from primary sequence using an in-house algorithm that weighs the contribution of various sequence properties for predicting solubility. Lastly, we conducted physical characterisation of an antibody and human serum albumin in pharmaceutically relevant buffers and found that the interaction potential can be modelled using spherical models from low to high protein concentration. We hope that the work outlined in this thesis will contribute to the theoretical understanding and modelling of protein solution behaviour.

Electrostatic interaction has long been proposed to be an important factor for stabilizing protein. Charge-charge interaction may especially be important to the thermostability of protein, as having more surface electrostatic interactions is one of the common structural features found in thermophilic proteins when compared to their mesophilic homologues. In order to quantitatively investigate the electrostatic contribution to protein stability, two complementary approaches, namely the double mutant cycle approach and pKa shift approach, were carried out. / In the double mutant cycle approach, the coupling free energies of two salt bridges (E6/R92 and K46/E62) and one a long range ion pair (E90/R92) were estimated by using circular dichroism, to find out the thermodynamic parameters of the protein model Thermococcus celer L30e and its charge-to-neutral mutants. It was found that the coupling free energy was temperature independent and was about 3 kJ mol-1 per salt bridge. By using a novel analysis of double mutant cycle of DeltaC p, it was also found that the interaction of salt bridge plays an important role in the reduction of DeltaCp. The temperature independency of coupling free energy and the effect of reducing DeltaCp could explain the general observation very well that thermophilic proteins have highly up-shifted protein stability curves is due to its elevated electrostatic interactions when compared with their mesophilic homologs. / In the pKa shift approach, the native state pKa values of acidic residues were obtained by fitting the side chain carboxyl 13C chemical shifts to microscopic model or global fitting of titrational event (GloFTE), whereas the denatured state pKa values were obtained by conventional pH titration of terminal protected 5-residue glycine-based model peptide. It was found that the surface charge-charge interactions, either attractive or repulsive, were strong and complicated because of the high surface charge density of T. celer L30e. However, the fact that most of the acidic residues have significantly downshifted native state pK a values indicated the surface charge distribution of T. celer L30e is optimized for stabilizing the protein. In addition, we have shown that temperature has negligible effect on pKa values in both native state and denatured state, therefore temperature can only marginally amplify the stabilizing effect in linear manner. / To overcome the unwanted crystallization problem of wild-type T. celer L30e in the low ionic strength neutral pH NMR conditions, which were essential for the pKa shift approach, a quintuple Arg-to-Lys variant was designed to dramatically improve the crystalline solubility, while the surface charges, as well as the structural, thermodynamic, and electrostatic properties, were conserved. It has also shown that electrostatic interaction played a critical role in crystallization at low ionic strength conditions, and arginine residue was especially important in crystal packing because of its high ability of forming salt bridges and hydrogen bonds. / Wild-type T. celer L30e has also shown to have no observable residual structure in the guanidine HC1-induced denatured state, indicating that denatured state of T. celer L30e should not have large effect on the overall protein stability. / Chan, Chi Ho. / Adviser: Kam Bo Wong. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 202-218). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

This paper deals with approximating an upper bound for the number of equilibrium points of a potential field produced by point charges in the plane. This is a simplified form of a problem posed by Maxwell [4], who considered spatial configurations of the point charges. Using algebraic techniques, we will give an upper bound for planar charges that is sharper than the bound given in [6] for most general configurations of charges. Then we will study an example of a configuration of charges that has exactly the number of equilibrium points that Maxwell's conjecture predicts, and we will look into the nature of the extremal points in this case. We will conclude with a solution to the twin problem for the logarithmic potential, followed by a discussion of the conditions necessary for a degenerate case in the plane.

In keeping with the goals of our laboratory, efforts in this thesis are directed towards improving our understanding, and therefore our ability to calculate, the energetics of protein-ligand interactions. Electrostatic contributions to protein-ligand binding events are poorly understood, and underrepresented in data sets used to parameterize the energetics of protein unfolding and binding. Therefore, the focus in this thesis is placed on ion-protein interactions as model systems that can give insight into the contribution of charge-charge interactions to the enthalpy, entropy, and heat capacity changes associated with binding. In order to measure the energetics of charge-charge interactions, both differential scanning calorimetry and isothermal titration calorimetry are employed. The use of linked equilibria to determine binding energetics for both extremely tight, and extremely weak binding events is described in the context of ligand binding linked to protein unfolding. The implications for drug screening methods based on protein unfolding are discussed. The theoretical development is then used to measure ion binding to proteins in two different systems that exhibit very different ion binding sites and system features. The first system involves anion binding to a protein-protein complex, in which the binding site is formed when the protein-protein complex is formed. Binding of phosphate and sulfate occur with the same energetics, indicating that net charge is not dominating the observed energetics. Further, no salt-dependence to the binding of anions is observed. In the second system ions bind to the active site of a ribonuclease. Again, phosphate and sulfate bind to the ribonuclease with the same energetics, however comparing the energetics of binding for these anions between systems reveals differences in the energetic profiles. Further, in the ribonuclease case, there is a strong salt-dependence observed for the binding of a nucleotide inhibitor. The apparent discrepancies in the observed energetics and salt-dependencies in these systems can be resolved by considering the role of desolvation upon binding as well as the binding site geometries. This analysis leads to important considerations for interpreting an observed salt-dependence to a binding event. Furthermore, it is indicated that the current structure-based energetics calculations underestimate the contributions arising from charge-charge interactions.

PhD / Electrostatics of aerosols for inhalation is a relatively new research area. Charge properties of these particles are largely unknown but electrostatic forces have been proposed to potentially influence lung deposition. Investigation on the relationship between formulation and aerosol charging is required to understand the fundamental mechanisms. A modified electrical low pressure impactor was employed to measure the particles generated from metered dose inhalers and dry powder inhalers. This equipment provides detailed size and charge information of the aerosols. The particles were sized by impaction onto thirteen stages. The net charges in twelve of the size fractions were detected and recorded by sensitive electrometers. The drug deposits were quantified by chemical assay. The aerosol charge profiles of commercial metered dose inhalers were product-dependent, which was due to differences in the drug, formulation, and valve stem material. The calculated number of elementary charges per drug particle of size ≤ 6.06 μm ranged from zero to several ten thousands. The high charge levels on particles may have a potential effect on the deposition of the aerosol particles in the lung when inhaled. New plastic spacers marketed for use with metered dose inhalers were found to possess high surface charges on the internal walls, which was successfully removed by detergent-coating. Detergent-coated spacer had higher drug output than the new ones due to the reduced electrostatic particle deposition inside the spacer. Particles delivered from spacers carried lower inherent charges than those directly from metered dose inhalers. Those with higher charges might be susceptible to electrostatic forces inside the spacers and were thus retained. The electrostatic low pressure impactor was further modified to disperse two commercial Tubuhaler® products at 60 L/min. The DPIs showed drug-specific responses to particle charging at different RHs. The difference in hygroscopicity of the drugs may play a major role. A dual mechanistic charging model was proposed to explain the charging behaviours. The charge levels on drug particles delivered from these inhalers were sufficiently high to potentially affect deposition in the airways when inhaled. Drug-free metered dose inhalers containing HFA-134a and 227 produced highly variable charge profiles but on average the puffs were negatively charged, which was thought to be due to the electronegative fluorine atoms in the HFA molecules. The charges of both HFAs shifted towards neutrality or positive polarity with increasing water content. The spiked water might have increased the electrical conductivity and/or decreased the electronegativity of the bulk propellant solution. The number of elementary charges per droplet decreased with decreasing droplet size. This trend was probably due to the redistribution of charges amongst small droplets following electrostatic fission of a bigger droplet when the Raleigh limit was reached.