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Yes / The coupling of thermal (Multi Stage Flash, MSF) and membrane processes (Reverse Osmosis, RO) in desalination systems has been widely presented in the literature to achieve an improvement of performance compared to an individual process. However, very little study has been made to the combined Multi Effect Distillation (MED) and Reverse Osmosis (RO) processes. Therefore, this research investigates several design options of MED with thermal vapor compression (MED_TVC) coupled with RO system. To achieve this aim, detailed mathematical models for the two processes are developed, which are independently validated against the literature. Then, the integrated model is used to investigate the performance of several configurations of the MED_TVC and RO processes in the hybrid system. The performance indicators include the fresh water productivity, energy consumption, fresh water purity, and recovery ratio. Basically, the sensitivity analysis for each configuration is conducted with respect to seawater conditions and steam supply variation. Most importantly, placing the RO membrane process upstream in the hybrid system generates the overall best configuration in terms of the quantity and quality of fresh water produced. This is attributed to acquiring the best recovery ratio and lower energy consumption over a wide range of seawater salinity.

The quorum sensing signaling system based on intercellular exchange of N-acyl-homoserine lactones is used by many proteobacteria to regulate the transcription of essential genes in a signal density-dependent manner. It is involved in a number of processes including the development of highly organized bacterial communities, e.g., biofilms, the regulation of expression of virulence factors, production of antibiotics, and bioluminescence. The extensive genetic and biochemical data available on the quorum sensing system in Vibrio fischeri allows the development of a systems biology approach to undertake a spatial and dynamical analysis of the regulation throughout the population. The quorum sensing regulated lux genes are organized in two divergent transcriptional units: luxR and luxICDABEG. The latter contains the genes required for luminescence and the luxI gene necessary for synthesis of an N-acyl-homoserine lactone commonly called autoinducer (AI). The luxR gene codes for a transcriptional regulatory protein that activates the transcription of both operons at a threshold concentration of AI. The positive feedback loop induces a rapid increase of transcription level of the lux genes when a critical population density is reached (reflected by the concentration of AI in the environment). With a combination of molecular biology tools, physiological analysis, and mathematical modeling we identified critical characteristics of the system and expect to assign parameter values in order to achieve a comprehensive understanding of the dynamics. An ordinary differential equation mathematical model is used to investigate the dynamics of the system and derive parameter values. In parallel a novel microfluidic cell culture experimental set-up is used to carefully control environmental parameters as well as to achieve chemostatic conditions for high-density cell populations. An unstable variant of the green fluorescent protein was used as a reporter to follow the time response at a single cell level. Thus spatial organization and noise across the population can be analyzed. Plasmids carrying different genetic constructs were transformed in a recombinant Escherichia coli strain to specifically identify genetic and biochemical elements involved in the regulation of the lux genes under diverse conditions. Then the quantitative data extracted from batch culture and microfluidic assays were used to assign parameter values in the models. The particular question being investigated first is the nature of the regulation to increasing concentration of the signal. The hypothesis tested is that the regulation of the production of the signal by individual cells is biphasic and, therefore, quorum sensing should be robust to global and local variations in cell density. / Master of Science

Mathematical models have long been used to describe complex biological interactions with the aim of predicting mechanistic interactions hard to distinguish from data. This dissertation uses modeling, mathematical analyses, and data fitting techniques to provide hypotheses on the mechanisms of immune response formation and function. The immune system, comprised of the innate and adaptive immune responses, is responsible for protecting the body against invading pathogens, with disease or vaccine induced immune memory leading to fast responses to subsequent infections. While there is some agreement about the underlying mechanisms of adaptive immune memory, innate immune memory is poorly understood. Stimulation with lipopolysaccharide induces differential phenotypes in innate immune cells depending on the strength of the stimulus, such that a secondary lipopolysaccharide encounter of a constant dose results in either strong or weak inflammatory cytokine expression. We model the biochemical kinetics of three molecules involved in macrophages responses to lipopolysaccharide and find that once a macrophage is programed to show a weak inflammatory response this cannot be reverted. Contrarily, a secondary lipopolysaccharide stimulus of a very high dose or applied prior to waning of the effects of the primary stimulus can induce a phenotype switch in macrophages initially programed to show strong inflammatory responses. Some pathogens, such as the hepatitis B virus, have developed strategies that hinder an efficient innate immune response. Hepatitis B virus infection is a worldwide pandemic with approximately 257 million chronically infected people. One beneficial event in disease progression is the seroclearance of hepatitis B e antigen often in combination with hepatitis B antibody formation. We propose mathematical models of within-host interactions and use them to predict that hepatitis B e antibody formation causes hepatitis B e antigen seroclearance and the subsequent reactivation of cytotoxic T cell immune responses. We use the model to quantify the time between antibody formation and antigen clearance and the average monthly hepatocyte turnover during that time. We further expand the study of hepatitis B infection, by investigating the kinetics of the virus under an experimental drug administered during a clinical trial. Available drugs usually fail to induce hepatitis B s antigen clearance, defined as the functional cure point of chronic hepatitis B infections. Drug therapy clinical trials that combined RNA interference drug ARC-520 with entecavir have shown promising results in reducing hepatitis B s antigen titers. We develop pharmacokinetic-pharmacodynamic models describing the mechanistic interactions of the drugs, hepatitis B virus DNA, and virus proteins. We fit the model to clinical trial data and predict that ARC-520 alone is responsible for the reduction of hepatitis B s and e antigens, while entecavir is the driving force behind viral reduction. This work was supported by Simons Foundation, Grant No. 427115, and National Science Foundation, Grant No. 1813011. / Doctor of Philosophy / Mathematical models have long been used to describe complex biological interactions with the aim of predicting interactions that explain observed data and informing new experiments. This dissertation uses modeling, mathematical analyses, and data fitting techniques to provide hypotheses on the mechanisms of immune response formation and function. The immune system, comprised of the innate and adaptive immune responses, is responsible for protecting the body against invading pathogens, such as viruses, bacteria, or fungi. If an immune response to a secondary pathogen encounter differs from the response when the body first encounters the specific pathogen, this is called immune memory. The mechanisms underlying the memory of immune responses are well understood in the context of adaptive immune responses, but less so for innate immune responses. Stimulation with lipopolysaccharide, a cell wall component of many bacteria, programs innate immune cells, such as macrophages, to be in one of two states, called phenotypes, depending on the strength of the stimulus. Based on their phenotype the macrophages show either a weak or strong inflammatory response upon a secondary lipopolysaccharide encounter of a constant dose. We model the biochemical kinetics of three molecules involved in macrophages responses to lipopolysaccharide. We find that once a macrophage is programed to show a weak inflammatory response this cannot be reverted. Contrarily, a secondary lipopolysaccharide stimulus that is either of a very high dose or applied before the effects of the primary stimulus have waned, can induce a phenotype switch in macrophages initially programed to show strong inflammatory responses. Some pathogens, such as the hepatitis B virus, have developed strategies that hinder an efficient innate immune response. Hepatitis B virus infection is a worldwide pandemic with approximately 257 million chronically infected people. Hepatitis B e antigen is a protein that infected liver cells release into blood and that impairs adaptive immune responses. It is considered a beneficial event in disease progression, and called hepatitis B e antigen clearance, when hepatitis B e antigen becomes indetectable in a patient's blood. We propose mathematical models of interactions between liver cells, the virus, hepatitis B e antigens and hepatitis B e antibodies, which neutralize the antigens. We predict that antibody formation causes antigen clearance and a reactivation of immune responses. We furthermore use the model to quantify the time between antibody formation and antigen clearance and the average number of liver cells killed during that time. We further expand the study of hepatitis B infection, by investigating the kinetics of the virus under an experimental drug administered during a clinical trial. Available drugs rarely induce hepatitis B s antigen clearance, but clinical trials that combined a novel drug, called ARC-520, with the commonly used drug entecavir have shown promising results in reducing hepatitis B s antigen titers in the blood of infected patients. Following the clearance of hepatitis B s antigen, a protein that is released by infected cells and impairs adaptive immunity, the body usually has the capability to control the infection without medication. We develop mathematical models describing the interactions of the drugs, hepatitis B virus, and virus proteins. We fit the model to clinical trial data and predict that ARC-520 alone is responsible for the reduction of hepatitis B s and e antigens, while entecavir is the driving force behind viral reduction.

Circadian rhythms in mammals are self-sustained repeating activities driven by the circadian gene expression in cells, which is regulated at both transcriptional and posttranscriptional stages. In this work, we first used mathematical modeling to investigate the transcriptional regulation of circadian gene expression, with a focus on the mechanisms of robust genetic oscillations in the mammalian circadian core clock. Secondly, we built a coarse-grained model to study the post-transcriptional regulation of the rhythmicities of poly(A) tail length observed in hundreds of mRNAs in mouse liver. Lastly, we examined the application of Sobol indices, which is a global sensitivity analysis method, to mathematical models of biological oscillation systems, and proposed two methods tailored for the calculation of circular Sobol indices. In the first project, we modified the core negative feedback loop in a mathematical model of the mammalian genetic oscillator so that the unrealistic tight binding between the repressor PER and the activator BMAL1 is relaxed for robust oscillations. By studying the modified extended models, we found that the auxiliary positive feedback loop, rather than the auxiliary negative feedback loop, makes the oscillations more robust, yet they are similar when accounting for circadian rhythms (~24h period). In the second project, we investigated the regulation of rhythmicities in poly(A) tail length by four coupled rhythmic processes, which are transcription, deadenylation, polyadenylation, and degradation. We found that rhythmic deadenylation is the strongest contributor to the rhythmicity in poly(A) tail length and the rhythmicity in the abundance of the mRNA subpopulation with long poly(A) tails. In line with this finding, the model further showed that the experimentally observed distinct peak phases in the expression of deadenylases, regardless of other rhythmic controls, can robustly cluster the rhythmic mRNAs by their peak phases in poly(A) tail length and abundance of the long-tailed subpopulation. In the last project, we reviewed the theoretical basis of Sobol indices and identified potential problems when it is applied to mathematical models of biological oscillation systems. Based on circular statistics, we proposed two methods for the calculation of circular Sobol indices and compared their performance with the original Sobol indices in several models. We found that though the relative rankings of the contribution from parameters are the same across three methods, circular Sobol indices can better quantitatively distinguish the contribution of individual parameters. Through this work, we showed that mathematical modeling combined with sensitivity analysis can help us understand the mechanisms underlying the circadian gene expression in mammalian cells. Also, testable predictions are made for future experiments and new ideas are provided that can enable potential chronopharmacology research. / Doctor of Philosophy / Circadian rhythms are repeating biological activities with ~24h period observed in most living organisms. Disruption of circadian rhythms in humans has been found to be promote cancer, metabolic diseases, cognitive degeneration etc. In this work, we first used mathematical modeling to study the mechanisms of robust oscillations in the mammalian circadian core clock, which is a molecular regulatory network that drives circadian gene expression at transcriptional stage. Secondly, we built a coarse-grained model to investigate the post-transcriptional regulation of the rhythmicities in poly(A) tail length, which are observed in hundreds of mRNAs in mouse liver. Lastly, we examined the application of Sobol indices, which is a global sensitivity analysis method, to mathematical models of biological oscillation systems, and proposed two methods tailored for the calculation of circular Sobol indices. In the first project, we modified a previous mathematical model of the mammalian genetic oscillator so that it sustains robust oscillation with more realistic parameter values. Our analysis of the model further showed that the auxiliary positive feedback loop, rather than the auxiliary negative feedback loop, makes the oscillations more robust. In the second project, we found that rhythmic deadenylation, among the coupled transcription, polyadenylation, and degradation processes, mostly controls the rhythmicity of poly(A) tail length and mRNA subpopulation with long poly(A) tails. Lastly, we reviewed the theoretical basis of Sobol indices and found potential problems when it is applied to mathematical models of biological oscillation systems. Based on circular statistics, we proposed two circular Sobol indices, which can better distinguish the contribution of individual parameters to model outputs than the original Sobol indices. Altogether, we used mathematical modeling and sensitivity analysis to investigate the regulation of circadian gene expression in mammalian cells, providing testable predictions and new ideas for future experiments and chronopharmacology research.