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Mathematical modeling of infectious diseases can help public health officials to make decisions related to the mitigation of epidemic outbreaks. However, over or under estimations of the morbidity of any infectious disease can be problematic. Therefore, public health officials can always make use of better models to study the potential implication of their decisions and strategies prior to their implementation. Previous work focuses on the mechanisms underlying the different epidemic waves observed in Mexico during the novel swine origin influenza H1N1 pandemic of 2009 and showed extensions of classical models in epidemiology by adding temporal variations in different parameters that are likely to change during the time course of an epidemic, such as, the influence of media, social distancing, school closures, and how vaccination policies may affect different aspects of the dynamics of an epidemic. This current work further examines the influence of different factors considering the randomness of events by adding stochastic processes to meta-population models. I present three different approaches to compare different stochastic methods by considering discrete and continuous time. For the continuous time stochastic modeling approach I consider the continuous-time Markov chain process using forward Kolmogorov equations, for the discrete time stochastic modeling I consider stochastic differential equations using Wiener's increment and Poisson point increments, and also I consider the discrete-time Markov chain process. These first two stochastic modeling approaches will be presented in a one city and two city epidemic models using, as a base, our deterministic model. The last one will be discussed briefly on a one city SIS and SIR-type model.
ContributorsCruz-Aponte, Maytee (Author) / Wirkus, Stephen A. (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Camacho, Erika T. (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
There has been important progress in understanding ecological dynamics through the development of the theory of ecological stoichiometry. This fast growing theory provides new constraints and mechanisms that can be formulated into mathematical models. Stoichiometric models incorporate the effects of both food quantity and food quality into a single framework that produce rich dynamics. While the effects of nutrient deficiency on consumer growth are well understood, recent discoveries in ecological stoichiometry suggest that consumer dynamics are not only affected by insufficient food nutrient content (low phosphorus (P): carbon (C) ratio) but also by excess food nutrient content (high P:C). This phenomenon, known as the stoichiometric knife edge, in which animal growth is reduced not only by food with low P content but also by food with high P content, needs to be incorporated into mathematical models. Here we present Lotka-Volterra type models to investigate the growth response of Daphnia to algae of varying P:C ratios. Using a nonsmooth system of two ordinary differential equations (ODEs), we formulate the first model to incorporate the phenomenon of the stoichiometric knife edge. We then extend this stoichiometric model by mechanistically deriving and tracking free P in the environment. This resulting full knife edge model is a nonsmooth system of three ODEs. Bifurcation analysis and numerical simulations of the full model, that explicitly tracks phosphorus, leads to quantitatively different predictions than previous models that neglect to track free nutrients. The full model shows that the grazer population is sensitive to excess nutrient concentrations as a dynamical free nutrient pool induces extreme grazer population density changes. These modeling efforts provide insight on the effects of excess nutrient content on grazer dynamics and deepen our understanding of the effects of stoichiometry on the mechanisms governing population dynamics and the interactions between trophic levels.
ContributorsPeace, Angela (Author) / Kuang, Yang (Thesis advisor) / Elser, James J (Committee member) / Baer, Steven (Committee member) / Tang, Wenbo (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
In 1968, phycologist M.R. Droop published his famous discovery on the functional relationship between growth rate and internal nutrient status of algae in chemostat culture. The simple notion that growth is directly dependent on intracellular nutrient concentration is useful for understanding the dynamics in many ecological systems. The cell quota in particular lends itself to ecological stoichiometry, which is a powerful framework for mathematical ecology. Three models are developed based on the cell quota principal in order to demonstrate its applications beyond chemostat culture.
First, a data-driven model is derived for neutral lipid synthesis in green microalgae with respect to nitrogen limitation. This model synthesizes several established frameworks in phycology and ecological stoichiometry. The model demonstrates how the cell quota is a useful abstraction for understanding the metabolic shift to neutral lipid production that is observed in certain oleaginous species.
Next a producer-grazer model is developed based on the cell quota model and nutrient recycling. The model incorporates a novel feedback loop to account for animal toxicity due to accumulation of nitrogen waste. The model exhibits rich, complex dynamics which leave several open mathematical questions.
Lastly, disease dynamics in vivo are in many ways analogous to those of an ecosystem, giving natural extensions of the cell quota concept to disease modeling. Prostate cancer can be modeled within this framework, with androgen the limiting nutrient and the prostate and cancer cells as competing species. Here the cell quota model provides a useful abstraction for the dependence of cellular proliferation and apoptosis on androgen and the androgen receptor. Androgen ablation therapy is often used for patients in biochemical recurrence or late-stage disease progression and is in general initially effective. However, for many patients the cancer eventually develops resistance months to years after treatment begins. Understanding how and predicting when hormone therapy facilitates evolution of resistant phenotypes has immediate implications for treatment. Cell quota models for prostate cancer can be useful tools for this purpose and motivate applications to other diseases.
First, a data-driven model is derived for neutral lipid synthesis in green microalgae with respect to nitrogen limitation. This model synthesizes several established frameworks in phycology and ecological stoichiometry. The model demonstrates how the cell quota is a useful abstraction for understanding the metabolic shift to neutral lipid production that is observed in certain oleaginous species.
Next a producer-grazer model is developed based on the cell quota model and nutrient recycling. The model incorporates a novel feedback loop to account for animal toxicity due to accumulation of nitrogen waste. The model exhibits rich, complex dynamics which leave several open mathematical questions.
Lastly, disease dynamics in vivo are in many ways analogous to those of an ecosystem, giving natural extensions of the cell quota concept to disease modeling. Prostate cancer can be modeled within this framework, with androgen the limiting nutrient and the prostate and cancer cells as competing species. Here the cell quota model provides a useful abstraction for the dependence of cellular proliferation and apoptosis on androgen and the androgen receptor. Androgen ablation therapy is often used for patients in biochemical recurrence or late-stage disease progression and is in general initially effective. However, for many patients the cancer eventually develops resistance months to years after treatment begins. Understanding how and predicting when hormone therapy facilitates evolution of resistant phenotypes has immediate implications for treatment. Cell quota models for prostate cancer can be useful tools for this purpose and motivate applications to other diseases.
ContributorsPacker, Aaron (Author) / Kuang, Yang (Thesis advisor) / Nagy, John (Committee member) / Smith, Hal (Committee member) / Kostelich, Eric (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
The portability of genetic tools from one organism to another is a cornerstone of synthetic biology. The shared biological language of DNA-to-RNA-to-protein allows for expression of polypeptide chains in phylogenetically distant organisms with little modification. The tools and contexts are diverse, ranging from catalytic RNAs in cell-free systems to bacterial proteins expressed in human cell lines, yet they exhibit an organizing principle: that genes and proteins may be treated as modular units that can be moved from their native organism to a novel one. However, protein behavior is always unpredictable; drop-in functionality is not guaranteed.
My work characterizes how two different classes of tools behave in new contexts and explores methods to improve their functionality: 1. CRISPR/Cas9 in human cells and 2. quorum sensing networks in Escherichia coli.
1. The genome-editing tool CRISPR/Cas9 has facilitated easily targeted, effective, high throughput genome editing. However, Cas9 is a bacterially derived protein and its behavior in the complex microenvironment of the eukaryotic nucleus is not well understood. Using transgenic human cell lines, I found that gene-silencing heterochromatin impacts Cas9’s ability to bind and cut DNA in a site-specific manner and I investigated ways to improve CRISPR/Cas9 function in heterochromatin.
2. Bacteria use quorum sensing to monitor population density and regulate group behaviors such as virulence, motility, and biofilm formation. Homoserine lactone (HSL) quorum sensing networks are of particular interest to synthetic biologists because they can function as “wires” to connect multiple genetic circuits. However, only four of these networks have been widely implemented in engineered systems. I selected ten quorum sensing networks based on their HSL production profiles and confirmed their functionality in E. coli, significantly expanding the quorum sensing toolset available to synthetic biologists.
My work characterizes how two different classes of tools behave in new contexts and explores methods to improve their functionality: 1. CRISPR/Cas9 in human cells and 2. quorum sensing networks in Escherichia coli.
1. The genome-editing tool CRISPR/Cas9 has facilitated easily targeted, effective, high throughput genome editing. However, Cas9 is a bacterially derived protein and its behavior in the complex microenvironment of the eukaryotic nucleus is not well understood. Using transgenic human cell lines, I found that gene-silencing heterochromatin impacts Cas9’s ability to bind and cut DNA in a site-specific manner and I investigated ways to improve CRISPR/Cas9 function in heterochromatin.
2. Bacteria use quorum sensing to monitor population density and regulate group behaviors such as virulence, motility, and biofilm formation. Homoserine lactone (HSL) quorum sensing networks are of particular interest to synthetic biologists because they can function as “wires” to connect multiple genetic circuits. However, only four of these networks have been widely implemented in engineered systems. I selected ten quorum sensing networks based on their HSL production profiles and confirmed their functionality in E. coli, significantly expanding the quorum sensing toolset available to synthetic biologists.
ContributorsDaer, René (Author) / Haynes, Karmella (Thesis advisor) / Brafman, David (Committee member) / Nielsen, David (Committee member) / Kiani, Samira (Committee member) / Arizona State University (Publisher)
Created2017
Description
Lignocellulosic biomass represents a renewable domestic feedstock that can support large-scale biochemical production processes for fuels and specialty chemicals. However, cost-effective conversion of lignocellulosic sugars into valuable chemicals by microorganisms still remains a challenge. Biomass recalcitrance to saccharification, microbial substrate utilization, bioproduct titer toxicity, and toxic chemicals associated with chemical pretreatments are at the center of the bottlenecks limiting further commercialization of lignocellulose conversion. Genetic and metabolic engineering has allowed researchers to manipulate microorganisms to overcome some of these challenges, but new innovative approaches are needed to make the process more commercially viable. Transport proteins represent an underexplored target in genetic engineering that can potentially help to control the input of lignocellulosic substrate and output of products/toxins in microbial biocatalysts. In this work, I characterize and explore the use of transport systems to increase substrate utilization, conserve energy, increase tolerance, and enhance biocatalyst performance.
ContributorsKurgan, Gavin (Author) / Wang, Xuan (Thesis advisor) / Nielsen, David (Committee member) / Misra, Rajeev (Committee member) / Nannenga, Brent (Committee member) / Arizona State University (Publisher)
Created2018
Description
The most advanced social insects, the eusocial insects, form often large societies in which there is reproductive division of labor, queens and workers, have overlapping generations, and cooperative brood care where daughter workers remain in the nest with their queen mother and care for their siblings. The eusocial insects are composed of representative species of bees and wasps, and all species of ants and termites. Much is known about their organizational structure, but remains to be discovered.
The success of social insects is dependent upon cooperative behavior and adaptive strategies shaped by natural selection that respond to internal or external conditions. The objective of my research was to investigate specific mechanisms that have helped shaped the structure of division of labor observed in social insect colonies, including age polyethism and nutrition, and phenomena known to increase colony survival such as egg cannibalism. I developed various Ordinary Differential Equation (ODE) models in which I applied dynamical, bifurcation, and sensitivity analysis to carefully study and visualize biological outcomes in social organisms to answer questions regarding the conditions under which a colony can survive. First, I investigated how the population and evolutionary dynamics of egg cannibalism and division of labor can promote colony survival. I then introduced a model of social conflict behavior to study the inclusion of different response functions that explore the benefits of cannibalistic behavior and how it contributes to age polyethism, the change in behavior of workers as they age, and its biological relevance. Finally, I introduced a model to investigate the importance of pollen nutritional status in a honeybee colony, how it affects population growth and influences division of labor within the worker caste. My results first reveal that both cannibalism and division of labor are adaptive strategies that increase the size of the worker population, and therefore, the persistence of the colony. I show the importance of food collection, consumption, and processing rates to promote good colony nutrition leading to the coexistence of brood and adult workers. Lastly, I show how taking into account seasonality for pollen collection improves the prediction of long term consequences.
The success of social insects is dependent upon cooperative behavior and adaptive strategies shaped by natural selection that respond to internal or external conditions. The objective of my research was to investigate specific mechanisms that have helped shaped the structure of division of labor observed in social insect colonies, including age polyethism and nutrition, and phenomena known to increase colony survival such as egg cannibalism. I developed various Ordinary Differential Equation (ODE) models in which I applied dynamical, bifurcation, and sensitivity analysis to carefully study and visualize biological outcomes in social organisms to answer questions regarding the conditions under which a colony can survive. First, I investigated how the population and evolutionary dynamics of egg cannibalism and division of labor can promote colony survival. I then introduced a model of social conflict behavior to study the inclusion of different response functions that explore the benefits of cannibalistic behavior and how it contributes to age polyethism, the change in behavior of workers as they age, and its biological relevance. Finally, I introduced a model to investigate the importance of pollen nutritional status in a honeybee colony, how it affects population growth and influences division of labor within the worker caste. My results first reveal that both cannibalism and division of labor are adaptive strategies that increase the size of the worker population, and therefore, the persistence of the colony. I show the importance of food collection, consumption, and processing rates to promote good colony nutrition leading to the coexistence of brood and adult workers. Lastly, I show how taking into account seasonality for pollen collection improves the prediction of long term consequences.
ContributorsRodríguez Messan, Marisabel (Author) / Kang, Yun (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Kuang, Yang (Committee member) / Page Jr., Robert E (Committee member) / Gardner, Carl (Committee member) / Arizona State University (Publisher)
Created2018
Description
In our modern world the source of for many chemicals is to acquire and refine oil. This process is becoming an expensive to the environment and to human health. Alternative processes for acquiring the final product have been developed but still need work. One product that is valuable is butanol. The normal process for butanol production is very intensive but there is a method to produce butanol from bacteria. This process is better because it is more environmentally safe than using oil. One problem however is that when the bacteria produce too much butanol it reaches the toxicity limit and stops the production of butanol. In order to keep butanol from reaching the toxicity limit an adsorbent is used to remove the butanol without harming the bacteria. The adsorbent is a mesoporous carbon powder that allows the butanol to be adsorbed on it. This thesis explores different designs for a magnetic separation process to extract the carbon powder from the culture.
ContributorsChabra, Rohin (Author) / Nielsen, David (Thesis director) / Torres, Cesar (Committee member) / Barrett, The Honors College (Contributor) / Chemical Engineering Program (Contributor)
Created2015-05
Description
For colonies of ponerine ant species, sterility regulation after a founding queen's death is not totally achieved in the worker caste, and the possibility of sexual reproduction is opened to workers. The persisting survival of these colonies is dependent on capturing the optimal reproductive ratio; yet, an informational gap bounds the mechanisms detailing the selection of new reproductives and the suppression of ovarian development in rejected reproductives. We investigated the mechanisms of worker policing, one of the primary methods of ovarian suppression, through continuous video observation for a period of five days at the start of colony instability. Observations suggest policing in H. saltator is performed by a majority of a colony, including potential reproductives, and requires multiple events to fully discourage ovarian growth.
ContributorsChien, Jeffrey (Co-author) / Barat Ali, Fatima (Co-author) / Kang, Yun (Thesis director) / Liebig, Juergen (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2018-12
Description
Division of Labor among social insects is frequently discussed in regards to the colony's worker population. However, before a colony achieves a worker population, a queen is required to perform all of the tasks necessary for her survival: foraging, building the colony, and brood care. A simple ODE model was developed through the use of a framework of replicator equations in dynamical environments to investigate how queen ants perform and distribute all of the tasks necessary for her and her colony's survival by incorporating individual internal thresholds and environmental stimulus. Modi�cations to the internal threshold, risk of performing the task, and the rate of increase of the environmental stimulus were also explored. Because of the simplicity of the model, it could also be used to measure the task performance of larger populations of social insects. However, the model has only been applied to the data collected from Pogonomyrmex barbatus single queen ants.
ContributorsKincade, Katherine Margaret (Author) / Kang, Yun (Thesis director) / Fewell, Jennifer (Committee member) / Lanchier, Nicolas (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
Synthetic gene networks have evolved from simple proof-of-concept circuits to
complex therapy-oriented networks over the past fifteen years. This advancement has
greatly facilitated expansion of the emerging field of synthetic biology. Multistability is a
mechanism that cells use to achieve a discrete number of mutually exclusive states in
response to environmental inputs. However, complex contextual connections of gene
regulatory networks in natural settings often impede the experimental establishment of
the function and dynamics of each specific gene network.
In this work, diverse synthetic gene networks are rationally designed and
constructed using well-characterized biological components to approach the cell fate
determination and state transition dynamics in multistable systems. Results show that
unimodality and bimodality and trimodality can be achieved through manipulation of the
signal and promoter crosstalk in quorum-sensing systems, which enables bacterial cells to
communicate with each other.
Moreover, a synthetic quadrastable circuit is also built and experimentally
demonstrated to have four stable steady states. Experiments, guided by mathematical
modeling predictions, reveal that sequential inductions generate distinct cell fates by
changing the landscape in sequence and hence navigating cells to different final states.
Circuit function depends on the specific protein expression levels in the circuit.
We then establish a protein expression predictor taking into account adjacent
transcriptional regions’ features through construction of ~120 synthetic gene circuits
(operons) in Escherichia coli. The predictor’s utility is further demonstrated in evaluating genes’ relative expression levels in construction of logic gates and tuning gene expressions and nonlinear dynamics of bistable gene networks.
These combined results illustrate applications of synthetic gene networks to
understand the cell fate determination and state transition dynamics in multistable
systems. A protein-expression predictor is also developed to evaluate and tune circuit
dynamics.
complex therapy-oriented networks over the past fifteen years. This advancement has
greatly facilitated expansion of the emerging field of synthetic biology. Multistability is a
mechanism that cells use to achieve a discrete number of mutually exclusive states in
response to environmental inputs. However, complex contextual connections of gene
regulatory networks in natural settings often impede the experimental establishment of
the function and dynamics of each specific gene network.
In this work, diverse synthetic gene networks are rationally designed and
constructed using well-characterized biological components to approach the cell fate
determination and state transition dynamics in multistable systems. Results show that
unimodality and bimodality and trimodality can be achieved through manipulation of the
signal and promoter crosstalk in quorum-sensing systems, which enables bacterial cells to
communicate with each other.
Moreover, a synthetic quadrastable circuit is also built and experimentally
demonstrated to have four stable steady states. Experiments, guided by mathematical
modeling predictions, reveal that sequential inductions generate distinct cell fates by
changing the landscape in sequence and hence navigating cells to different final states.
Circuit function depends on the specific protein expression levels in the circuit.
We then establish a protein expression predictor taking into account adjacent
transcriptional regions’ features through construction of ~120 synthetic gene circuits
(operons) in Escherichia coli. The predictor’s utility is further demonstrated in evaluating genes’ relative expression levels in construction of logic gates and tuning gene expressions and nonlinear dynamics of bistable gene networks.
These combined results illustrate applications of synthetic gene networks to
understand the cell fate determination and state transition dynamics in multistable
systems. A protein-expression predictor is also developed to evaluate and tune circuit
dynamics.
ContributorsWu, Fuqing (Author) / Wang, Xiao (Thesis advisor) / Haynes, Karmella (Committee member) / Marshall, Pamela (Committee member) / Nielsen, David (Committee member) / Brafman, David (Committee member) / Arizona State University (Publisher)
Created2017