A critical step in mounting an immune response is antigen recognition by T cells. This step proceeds by productive interactions between T cell receptors (TCR) on the surface of T cells and foreign antigen, in the form of peptide-major-histocompatibility-complexes (pMHC), on the surface of antigen-presenting-cells (APC). Antigen recognition is exceedingly difficult to understand because the vast majority of pMHC on APCs are derived from self-proteins. Nevertheless, T cells have been shown to be exquisitely sensitive, responding to as few as 10 antigenic pMHC in an ocean of tens of thousands of self pMHC. In addition, T cells are extremely specific and respond only to a small subset of pMHC by virtue of their specific TCR. To explain the sensitivity of T cells to pMHC it has been proposed that a single pMHC may serially bind multiple TCRs. Integrating present knowledge on the spatial-temporal dynamics of TCR/pMHC in the T cell-APC contact interface, we have constructed mathematical models to investigate the degree of TCR serial engagements by pMHC. In addition to reactions within clusters, the models capture the formation and mobility of TCR clusters. We find that a single pMHC serially binds a substantial number of TCRs in a TCR cluster only if the TCR/pMHC bond is stabilized by coreceptors and/or pMHC dimerization. In a separate study we propose that serial engagements can explain T cell specificity. Using Monte Carlo simulations, we show that the stochastic nature of TCR/pMHC interactions means that multiple binding events are needed for accurate detection of foreign pMHC. Critical to our studies are estimates of TCR/pMHC reaction rates and mobilities. In the second half of the thesis, we show that Fluorescence Recovery After Photobleaching (FRAP) experiments can reveal effective diffusion coefficients. We then show, using asymptotic analysis and model fitting, that FRAP experiments can be used to estimate reaction rates between cell surface proteins, like TCR/pMHC. Lastly, we use FRAP experiments to investigate how the actin cytoskeleton modulates TCR mobility and report effective reaction rates between TCR and the cytoskeleton. / Science, Faculty of / Mathematics, Department of / Graduate

archives@tulane.edu / 1 / Owen Richfield

Bacillus subtilis capable of producing surfactin was cultured to evaluate effects of microbial cell mass on natural gas hydrate formation, dissociation, and stability characteristics. The direct molecular influences of microbial cell wall polymers inhibited gas hydrate formation significantly, decreased hydrate formation rates, and increased dissociation rates. Upon the introduction of bentonite, significant synergy was observed in the system in the form of a catalytic effect. Microbes cultured from seafloor seawater-saturated sediments collected from Mississippi Canyon 118 (MC-118) produced similar effects and generalized the observed trends. MC-118 cultures also produced biosurfactant in several culture media, which was shown to catalyze natural gas hydrate formation in porous media. Microorganisms inhabit gas hydrate macrostructures and consume hydrocarbons and other substrates from within. Sulfate reduction and anaerobic hydrocarbon oxidation occurred within gas hydrate during incubations with MC-118 indigenous consortia. A mathematical model was developed to explore the diffusion-reaction implications in massive seafloor gas hydrates.

For many years bovine brucellosis was a zoonosis endemic in large parts of the world. While it is still endemic in some parts, such as the Middle East or India, several countries such as Australia and Canada have successfully eradicated brucellosis in cattle by applying vaccines, improving the hygienic standards in cattle breeding, and slaughtering or quarantining infected animals. The large economical impact of bovine brucellosis and its virulence for humans, coming in direct contact to fluid discharges from infected animals, makes the eradication of bovine brucellosis important to achieve. To achieve this goal several vaccines have been developed in the past decades. Today the two most commonly used vaccines are Brucella abortus vaccine strain 19 and strain RB51. Both vaccines have been shown to be effective, but the mechanisms of immune responses following vaccination with either of the vaccines are not understood yet. In this thesis we analyze the immunological data obtained through vaccination with the two strains using mathematical modeling. We first design a measure that allows us to separate the subjects into good and bad responders. Then we investigate differences in the immune responses following vaccination with strain 19 or strain RB51 and boosting with strain RB51. We develop a mathematical model of immune responses that accounts for formation of antagonistic pro and anti-inflammatory and memory cells. We show that different characteristics of pro-inflammatory cell development and activity have an impact on the number of memory cells obtained after vaccination. / Master of Science

Thesis (PhD)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: In Uganda, cattle are an important reservoir of Trypanosoma brucei rhodesiense, a parasite that causes human African trypanosomiasis or sleeping sickness. We developed mathematical models to examine the transmission of T. b. rhodesiense by tsetse vector species, Glossina fuscipes fuscipes in a host population that consists of humans, domestic and wild mammals, and reptiles. The models were developed and analysed based on the situation in Tororo district in Southeastern Uganda, where sleeping sickness is endemic and which has a cattle and human population of 40, 000 and 500, 000, respectively. Assuming populations of cattle and humans only, the impact of mass chemoprophylaxis and vector control through insecticide-treated cattle (ITC) is evaluated. Keeping 12% or 82% of the cattle population on insecticides that have an insecticidal killing effect of 100% at all times or trypanocides that have 100% efficacy, respectively, can lead to the control of T. b. rhodesiense in both humans and cattle. Optimal control of T. b. rhodesiense is shown to be achieved through ITC alone or a combination of chemoprophylaxis and ITC, the former being the cheapest control strategy. Allowing for the waning effect of insecticides and including wildhosts, T. b. rhodesiense control can be achieved by keeping 21% or 27% of the cattle population on insecticides through whole-body or restricted application, respectively. Restricting the treatment of insecticides to adult cattle only would require 24% or 33% of the adult cattle population to be kept on insecticides through whole-body or restricted application, respectively, to control T. b. rhodesiense. A cost-effectiveness and benefit-cost analysis of using ITC to control T. b. rhodesiense show that restricted application of insecticides is a cheaper and more beneficial strategy compared to whole-body treatment. The results of the study show that the restricted application of insecticides on cattle provides a cheap, safe and farmer-based strategy for controlling tsetse and trypanosomiasis. / AFRIKAANSE OPSOMMING: In Uganda is beeste ’n belangrike reservoir van Trypanosoma brucei rhodesiense, ’n parasiet wat tripanosomiase of slaapsiekte in mense veroorsaak. Ons het wiskundige modelle ontwikkel wat die oordrag van T. b. Rhodesiense deur tesetse vektor spesies, Glossina fuscipes fuscipes in ’n draer populasie wat bestaan uit mense, mak en wilde diere en reptiele, ondersoek. Die modelle was ontwikkel en geanaliseer gebaseer op die oordrag situasie in die Tororo distrik in Suidoostelike Uganda, ’n gebied waar slaapsiekte endemies is en wat ’n populasie van 40, 000 beeste en 500, 000 mense het. Die impak van massa chemoprofilakse en vektor beheer deur insekdoder-behandelde beeste is gevalueer onder die aanname van bees en mens populasies alleenlik. Beheer oor T. b. Rhodesiense in beide mense en beeste kan verkry word deur of 12% van die bees populasie te behandel met ’n insekdoder wat 100% effektief is ten alle tye of 82% van die bees populasie te behandel met tripanosiedes wat 100% effektief is. Daar is aangetoon dat optimale beheer van T. b. Rhodesiense bereik kan word deur die gebruik van insekdoders alleenlik of ’n kombinasie van insekdoders en chemoprofilakse, hoewel eersgenoemde die goedkoopste strategie is. Wanneer die kwynende effek van insekdoders asook wilde diere as draers in ag geneem word, kan T. b. Rhodesiense beheer verkry word deur 21% van beeste se hele liggaam met insekdoders te behandel of 27% gedeeltelik te behandel. As slegs volwasse beeste met insekdoders behandel word, moet 24% se hele liggaam of 33% gedeeltelik behandel word vir beheer van T. b. Rhodesiense. ’n Koste-effektiwiteit en voordeel-koste analise van insekdoders as beheermaatstaf vir T. b. Rhodesiense toon aan dat gedeeltelike behandeling van die bees se liggaam die goedkoper en meer voordelige strategie is in vergelyking met behandeling van die hele liggaam. Die resultate van die studie wys dat gedeeltelike behandeling van beeste met insekdoders ’n goedkoop, veilige en landbouer-gebaseerde strategie is om tsetse en tripanosomiase te beheer.

Master of Science / Department of Grain Science and Industry / Sajid Alavi / Extrusion is a popular technology for production of expanded products. However, variability in multiple input parameters can lead to significant variations in the end product which becomes a concern for process control and efficiency in industries. This study was focused on understanding the uncertainty in input parameters during extrusion and their impact on variability in output. A mechanistic model was developed for bubble growth dynamics in starch based melts at microscopic and macroscopic levels using heat, mass and momentum transfer equations. This model was used for uncertainty simulations using the Monte-Carlo method by integrating it with a stochastic interface for input of randomly generated process data based on experimentally obtained distributions and output of simulated distributions of end-product properties such as expansion ratio (ER). A pilot-scale twin screw extruder was used for processing of corn-based expanded products, which was used as a model system for experimental validation of the mathematical model. A 4x2 factorial design was used with different in-barrel moisture contents (19, 23, 28 and 33% dry basis) and extruder screw speeds (250 and 350 rpm) to measure process data (such as moisture injection rate and T[subscript]d[subscript]i[subscript]e) and product characteristics (such as ER). Average experimental ER ranged from 2.33-10.88 and simulated ER ranged from 1.16-12.86, where both had similar trends with respect to in-barrel moisture (MC) and die temperature (T[subscript]d[subscript]i[subscript]e = 108.8-145.4˚C) although conditions for optimum expansion differed possibly due to non-correspondence of material properties. Experimental coefficient of variation (CV) for MC (0.6-1.6%) and T[subscript]d[subscript]i[subscript]e (0.29-0.91%) and an assumed CV of 2% for a material constant (k[subscript]f) that controls the consistency index of starch-based melt were used for simulations. The stochastic model was used to carry out sensitivity analysis for CV of ER with respect to CV of MC, T[subscript]d[subscript]i[subscript]e and k[subscript]f. Variability in ER was impacted the most by variation in T[subscript]d[subscript]i[subscript]e, followed by MC with k[subscript]f having relatively lower impact on it. Since there are fundamental flaws in modeling approach as reflected by the thermodynamically infeasible parameter dynamics, the results from these mechanistic or stochastic simulations cannot be used as a basis for scientific analysis.

As propriedades das peças produzidas por fundição dependem principalmente da macroestrutura final de grãos. A modelagem matemática da solidificação de ligas metálicas com o objetivo de prever a macroestrutura de grãos sofreu avanços muito importantes nas últimas décadas, porém os modelos matemáticos chamados de determinísticos até hoje não são capazes de modelar o crescimento individual dos grãos durante todos os estágios da solidificação. O objetivo do presente trabalho é desenvolver um modelo matemático multifásico e multigrãos capaz de simular a solidificação equiaxial de ligas binárias. As equações deste modelo foram construídas com base nas equações macroscópicas de conservação de massa, energia e espécies químicas. A característica que distingue o modelo implementado neste trabalho de outros modelos publicados na literatura é a consideração individual de grãos de diferentes tamanhos e a consideração do crescimento dendrítico ou globulítico. As equações macroscópicas de conservação de massa, energia e espécies químicas são resolvidas separadamente para cada classe de tamanhos de grão. Os resultados obtidos pelo presente modelo foram comparados com um modelo que considera os grãos individualmente, mas que só é capaz de simular os instantes iniciais da solidificação, em que a morfologia dos grãos é globulítica. Posteriormente foi realizada uma comparação com um modelo de solidificação equiaxial com muitas características semelhantes às do presente modelo, mas que não considera individualmente grãos de diferentes tamanhos. Foi realizada uma análise paramétrica do presente modelo, que posteriormente foi utilizado para tentar reproduzir resultados obtidos experimentalmente por diversos autores. Os resultados obtidos mostram que o modelo matemático proposto é capaz de simular todo o período de solidificação, incluindo a solidificação dendrítica ou globulítica, monitorando individualmente o crescimento de grãos com tamanhos diferentes. Os resultados obtidos pelo modelo implementado no presente trabalho reproduzem quase que exatamente as curvas de resfriamento e a previsão de tamanho de grão médio obtidas por um modelo que considera os grãos apenas de forma média. O modelo desenvolvido apresentou resultados próximos aos resultados experimentais para a previsão do tamanho de grão médio e para a distribuição de tamanhos de grão final em uma amostra de alumínio comercialmente puro inoculado com Al- 5%Ti-1%B. / Properties of components obtained by solidification processes depend strongly on the final grain structure. In the past few decades, there has been a significant breakthrough in the mathematical modeling of metallic alloy solidification to predict the grain macrostructure. Nevertheless, the so-called deterministic models are still not capable of modeling the individual growth of grains throughout the solidification time. The objective of the present work it to propose, implement, and evaluate a multiphase and multigrain mathematical model of equiaxed solidification in binary alloys. The equations of the model are based on the macroscopic conservation equations of mass, energy, and chemical species. The main feature that distinguishes the present model from other models available in the literature is the consideration of the growth of individual grains of different sizes, and of the dendritic or globulitic growth. The macroscopic conservation equations of mass, energy, and chemical species were applied separately to each class of grains of different sizes. The results obtained from the present model were compared with those from a model that also simulates the individual growth of grains, but was developed only for the early stages of solidification, during which there is globulitic growth. Next, the results were compared with those from a similar model, but which does not consider the individual growth of grains, following only a grain of average size. A parametric analysis was carried out with the present model, which was later used to simulate different experiments presented by several authors. The model was capable of simulating several phenomena, including the globulitic and dendritic growth for each class of grain, during the whole solidification time. The results obtained with the present model reproduce very accurately the cooling curves and the prediction of grain size obtained from a model that considers only a grain of average size. The present model results are in close agreement with measurements of average grain size and grain size distribution in an commercially pure Al with different additions of Al-5%Ti-1%B.

Many parts of the world are facing water crises due to the lack of clean drinking water. Growing industrialization in many areas and extensive use of chemicals for various concerns has increased the burden of deleterious contaminants in drinking water especially in developing countries. It is reported that nearly half of the population in developing countries suffers from health problems associated with lack of potable drinking water as well as the presence of microbiologically contaminated water [1] . Synthetic and natural organic contaminants are considered among the most undesirable contaminants found in water. Various treatment processes are applied for the removal of organic contaminants from water including reverse osmosis membranes, ion exchange, oxidation, nanofiltration, and adsorption. The adsorption process is a widely-used technology for the removal of organic compounds from water. In this work, the adsorption of chloroform and methyl tertiary butyl ether (MTBE) onto granular zeolites was investigated. Zeolites were specifically chosen because they have shown higher efficiency in removing certain organics from water than granular activated carbon (GAC). Batch adsorption experiments to evaluate the effectiveness of several granular zeolites for the removal of MTBE and chloroform from water were conducted and the results compared with GAC performance. Results of these batch equilibrium experiments showed that ZSM-5 was the granular zeolite adsorbent with the greatest removal capacity for MTBE and chloroform from water, and outperformed GAC. Fixed-bed adsorption experiments with MTBE and chloroform were performed using granular ZSM-5. Breakthrough curves obtained from these column experiments were used to understand and predict the dynamic behavior of fixed bed adsorbers with granular ZSM-5. The ii film pore and surface diffusion model (FPSDM) was fit to the breakthrough curve data obtained from the fixed bed adsorption experiments. The FPSDM model takes into account the effects of axial dispersion, film diffusion, and intraparticle diffusion mechanisms during fixed bed adsorption. Generally, good agreement was obtained between the FPSDM simulated results and experimental breakthrough profiles. This study demonstrated that film diffusion is the primary controlling mass transfer mechanism and therefore must be accurately determined for good breakthrough predictions.

Magnetic nanoparticle (MNP) combined with biomolecules in a microfluidic system can be efficiently used in various applications such as mixing, pre-concentration, separation and detection. They can be either integrated for point-of care applications or used individually in the area of bio-defense, drug delivery, medical diagnostics, and pharmaceutical development. The interaction of magnetic fields with magnetic nanoparticles in microfluidic flows will allow simplifying the complexity of the present generation separation and detection systems. The ability to understand the dynamics of these interactions is a prerequisite for designing and developing more efficient systems. Therefore, in this work proof-of-concept experiments are combined with advanced numerical simulation to design, develop and optimize the magnetic microfluidic systems for mixing, separation and detection. Different strategies to combine magnetism with microfluidic technology are explored; a time-dependent magnetic actuation is used for efficiently mixing low volume of samples whereas tangential microfluidic channels were fabricated to demonstrate a simple low cost magnetic switching for continuous separation of biomolecules. A simple low cost generic microfluidic platform is developed using assembly of readily available permanent magnets and electromagnets. Microfluidic channels were fabricated at much lower cost and with a faster construction time using our in-house developed micromolding technique that does not require a clean room. Residence-time distribution (RTD) analysis obtained using dynamic light scattering data from samples was successfully used for the first time in microfluidic system to characterize the performance. Both advanced multiphysics finite element models and proof of concept experimentation demonstrates that MNPs when tagged with biomolecules can be easily manipulated within the microchannel. They can be precisely captured, separated or detected with high efficiency and ease of operation. Presence of MNPs together with time-dependent magnetic actuation also helps in mixing as well as tagging biomolecules on chip, which is useful for point-of-care applications. The advanced mathematical model that takes into account mass and momentum transport, convection & diffusion, magnetic body forces acting on magnetic nanoparticles further demonstrates that the performance of microfluidic surface-based bio-assay can be increased by incorporating the idea of magnetic actuation. The numerical simulations were helpful in testing and optimizing key design parameters and demonstrated that fluid flow rate, magnetic field strength, and magnetic nanoparticle size had dramatic impact on the performance of microfluidic systems studied. This work will also emphasize the importance of considering magnetic nanoparticles interactions for a complete design of magnetic nanoparticle-based Lab-on-a-chip system where all the laboratory unit operations can be easily integrated. The strategy demonstrated in this work will not only be easy to implement but also allows for versatile biochip design rules and provides a simple approach to integrate external elements for enhancing mixing, separation and detection of biomolecules. The vast applications of this novel concept studied in this work demonstrate its potential of to be applied to other kinds of on-chip immunoassays in future. We think that the possibility of integrating magnetism with microfluidic-based bioassay on a disposable chip is a very promising and versatile approach for point-of care diagnostics especially in resource-limited settings.

Modeling of brain activity is often seen as requiring great computing power. However in the special case of modeling scalp EEG it is possible to adopt a continuum approximation for the cortex, and then to use the techniques of wave physics to describe its consequent large-scale dynamics. The model incorporates the following critical components: two classes of neurons (excitatory and inhibitory), the typical number and strength of connections between these two classes, the corresponding connections within the thalamus and between the thalamus and cortex, the time constants and basic physiology of neurons, and the propagation of activity between neurons. Representing the immense intricacy of brain anatomy and physiology with suitable summary equations and average parameter values has meant that the model is able to capture the essential characteristics of EEG and ERPs, and to do so in a computationally manageable way.