Matching Items (20)
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- All Subjects: Applied Mathematics
- Creators: Ringhofer, Christian
Description
Signaling cascades transduce signals received on the cell membrane to the nucleus. While noise filtering, ultra-sensitive switches, and signal amplification have all been shown to be features of such signaling cascades, it is not understood why cascades typically show three or four layers. Using singular perturbation theory, Michaelis-Menten type equations are derived for open enzymatic systems. When these equations are organized into a cascade, it is demonstrated that the output signal as a function of time becomes sigmoidal with the addition of more layers. Furthermore, it is shown that the activation time will speed up to a point, after which more layers become superfluous. It is shown that three layers create a reliable sigmoidal response progress curve from a wide variety of time-dependent signaling inputs arriving at the cell membrane, suggesting that natural selection may have favored signaling cascades as a parsimonious solution to the problem of generating switch-like behavior in a noisy environment.
ContributorsYoung, Jonathan Trinity (Author) / Armbruster, Dieter (Thesis advisor) / Platte, Rodrigo (Committee member) / Nagy, John (Committee member) / Baer, Steven (Committee member) / Taylor, Jesse (Committee member) / Arizona State University (Publisher)
Created2013
Description
A general continuum model for simulating the flow of ions in the salt baths that surround and fill excitable neurons is developed and presented. The ion densities and electric potential are computed using the drift-diffusion equations. In addition, a detailed model is given for handling the electrical dynamics on interior membrane boundaries, including a model for ion channels in the membranes that facilitate the transfer of ions in and out of cells. The model is applied to the triad synapse found in the outer plexiform layer of the retina in most species. Experimental evidence suggests the existence of a negative feedback pathway between horizontal cells and cone photoreceptors that modulates the flow of calcium ions into the synaptic terminals of cones. However, the underlying mechanism for this feedback is controversial and there are currently three competing hypotheses: the ephaptic hypothesis, the pH hypothesis and the GABA hypothesis. The goal of this work is to test some features of the ephaptic hypothesis using detailed simulations that employ rigorous numerical methods. The model is first applied in a simple rectangular geometry to demonstrate the effects of feedback for different extracellular gap widths. The model is then applied to a more complex and realistic geometry to demonstrate the existence of strictly electrical feedback, as predicted by the ephaptic hypothesis. Lastly, the effects of electrical feedback in regards to the behavior of the bipolar cell membrane potential is explored. Figures for the ion densities and electric potential are presented to verify key features of the model. The computed steady state IV curves for several cases are presented, which can be compared to experimental data. The results provide convincing evidence in favor of the ephaptic hypothesis since the existence of feedback that is strictly electrical in nature is shown, without any dependence on pH effects or chemical transmitters.
ContributorsJones, Jeremiah (Author) / Gardner, Carl (Committee member) / Baer, Steven (Committee member) / Crook, Sharon (Committee member) / Kostelich, Eric (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2013
Description
In vertebrate outer retina, changes in the membrane potential of horizontal cells affect the calcium influx and glutamate release of cone photoreceptors via a negative feedback. This feedback has a number of important physiological consequences. One is called background-induced flicker enhancement (BIFE) in which the onset of dim background enhances the center flicker response of horizontal cells. The underlying mechanism for the feedback is still unclear but competing hypotheses have been proposed. One is the GABA hypothesis, which states that the feedback is mediated by gamma-aminobutyric acid (GABA), an inhibitory neurotransmitter released from horizontal cells. Another is the ephaptic hypothesis, which contends that the feedback is non-GABAergic and is achieved through the modulation of electrical potential in the intersynaptic cleft between cones and horizontal cells. In this study, a continuum spine model of the cone-horizontal cell synaptic circuitry is formulated. This model, a partial differential equation system, incorporates both the GABA and ephaptic feedback mechanisms. Simulation results, in comparison with experiments, indicate that the ephaptic mechanism is necessary in order for the model to capture the major spatial and temporal dynamics of the BIFE effect. In addition, simulations indicate that the GABA mechanism may play some minor modulation role.
ContributorsChang, Shaojie (Author) / Baer, Steven M. (Thesis advisor) / Gardner, Carl L (Thesis advisor) / Crook, Sharon M (Committee member) / Kuang, Yang (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2012
Description
The retina is the lining in the back of the eye responsible for vision. When light photons hits the retina, the photoreceptors within the retina respond by sending impulses to the optic nerve, which connects to the brain. If there is injury to the eye or heredity retinal problems, this part can become detached. Detachment leads to loss of nutrients, such as oxygen and glucose, to the cells in the eye and causes cell death. Sometimes the retina is able to be surgically reattached. If the photoreceptor cells have not died and the reattachment is successful, then these cells are able to regenerate their outer segments (OS) which are essential for their functionality and vitality. In this work we will explore how the regrowth of the photoreceptor cells in a healthy eye after retinal detachment can lead to a deeper understanding of how eye cells take up nutrients and regenerate. This work uses a mathematical model for a healthy eye in conjunction with data for photoreceptors' regrowth and decay. The parameters for the healthy eye model are estimated from the data and the ranges of these parameter values are centered +/- 10\% away from these values are used for sensitivity analysis. Using parameter estimation and sensitivity analysis we can better understand how certain processes represented by these parameters change within the model as a result of retinal detachment. Having a deeper understanding for any sort of photoreceptor death and growth can be used by the greater scientific community to help with these currently irreversible conditions that lead to blindness, such as retinal detachment. The analysis in this work shows that maximizing the carrying capacity of the trophic pool and the rate of RDCVF, as well as minimizing nutrient withdrawal of the rods and the cones from the trophic pool results in both the most regrowth and least cell death in retinal detachment.
ContributorsGoldman, Miriam Ayla (Author) / Camacho, Erikia (Thesis director) / Wirkus, Stephen (Committee member) / School of Mathematical and Natural Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
Description
Research shows that the subject of mathematics, although revered, remains a source of trepidation for many individuals, as they find it difficult to form a connection between the work they do on paper and their work's practical applications. This research study describes the impact of teaching a challenging introductive applied mathematics course on high school students' skills and attitudes towards mathematics in a college Summer Program. In the analysis of my research data, I identified several emerging changes in skills and attitudes towards mathematics, skills that high-school students needed or developed when taking the mathematical modeling course. Results indicated that the applied mathematics course had a positive impact on several students' attitudes, in general, such as, self-confidence, meanings of what mathematics is, and their perceptions of what solutions are. It also had a positive impact on several skills, such as translating real-life situations to mathematics via flow diagrams, translating the models' solutions back from mathematics to the real world, and interpreting graphs. Students showed positive results when the context of their problems was applied or graphical, and fewer improvement on problems that were not. Research also indicated some negatives outcomes, a decrease in confidence for certain students, and persistent negative ways of thinking about graphs. Based on these findings, I make recommendations for teaching similar mathematical modeling at the pre-university level, to encourage the development of young students through educational, research and similar mentorship activities, to increase their inspiration and interest in mathematics, and possibly consider a variety of sciences, technology, engineering and mathematics-related (STEM) fields and careers.
Contributorsagoune, linda (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Castillo-Garsow, Carlos W (Thesis advisor) / Mubayi, Anuj (Committee member) / Arizona State University (Publisher)
Created2020
Description
Factory production is stochastic in nature with time varying input and output processes that are non-stationary stochastic processes. Hence, the principle quantities of interest are random variables. Typical modeling of such behavior involves numerical simulation and statistical analysis. A deterministic closure model leading to a second order model for the product density and product speed has previously been proposed. The resulting partial differential equations (PDE) are compared to discrete event simulations (DES) that simulate factory production as a time dependent M/M/1 queuing system. Three fundamental scenarios for the time dependent influx are studied: An instant step up/down of the mean arrival rate; an exponential step up/down of the mean arrival rate; and periodic variation of the mean arrival rate. It is shown that the second order model, in general, yields significant improvement over current first order models. Specifically, the agreement between the DES and the PDE for the step up and for periodic forcing that is not too rapid is very good. Adding diffusion to the PDE further improves the agreement. The analysis also points to fundamental open issues regarding the deterministic modeling of low signal-to-noise ratio for some stochastic processes and the possibility of resonance in deterministic models that is not present in the original stochastic process.
ContributorsWienke, Matthew (Author) / Armbruster, Dieter (Thesis advisor) / Jones, Donald (Committee member) / Platte, Rodrigo (Committee member) / Gardner, Carl (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2015
Description
Combination therapy has shown to improve success for cancer treatment. Oncolytic virotherapy is cancer treatment that uses engineered viruses to specifically infect and kill cancer cells, without harming healthy cells. Immunotherapy boosts the body's natural defenses towards cancer. The combination of oncolytic virotherapy and immunotherapy is explored through deterministic systems of nonlinear differential equations, constructed to match experimental data for murine melanoma. Mathematical analysis was done in order to gain insight on the relationship between cancer, viruses and immune response. One extension of the model focuses on clinical needs, with the underlying goal to seek optimal treatment regimens; for both frequency and dose quantity. The models in this work were first used to estimate parameters from preclinical experimental data, to identify biologically realistic parameter values. Insight gained from the mathematical analysis in the first model, allowed for numerical analysis to explore optimal treatment regimens of combination oncolytic virotherapy and dendritic vaccinations. Permutations accounting for treatment scheduled were done to find regimens that reduce tumor size. Observations from the produced data lead to in silico exploration of immune-viral interactions. Results suggest under optimal settings, combination treatment works better than monotherapy of either type. The most optimal result suggests treatment over a longer period of time, with fractioned doses, while reducing the total dendritic vaccination quantity, and maintaining the maximum virotherapy used in the experimental work.
ContributorsSummer, Ilyssa Aimee (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Nagy, John (Thesis advisor) / Mubayi, Anuj (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2016
Description
The Mathematical and Theoretical Biology Institute (MTBI) is a summer research program for undergraduate students, largely from underrepresented minority groups. Founded in 1996, it serves as a 'life-long' mentorship program, providing continuous support for its students and alumni. This study investigates how MTBI supports student development in applied mathematical research. This includes identifying of motivational factors to pursue and develop capacity to complete higher education.
The theoretical lens of developmental psychologists Lev Vygotsky (1978, 1987) and Lois Holzman (2010) that sees learning and development as a social process is used. From this view student development in MTBI is attributed to the collaborative and creative way students co-create the process of becoming scientists. This results in building a continuing network of academic and professional relationships among peers and mentors, in which around three quarters of MTBI PhD graduates come from underrepresented groups.
The extent to which MTBI creates a Vygotskian learning environment is explored from the perspectives of participants who earned doctoral degrees. Previously hypothesized factors (Castillo-Garsow, Castillo-Chavez and Woodley, 2013) that affect participants’ educational and professional development are expanded on.
Factors identified by participants are a passion for the mathematical sciences; desire to grow; enriching collaborative and peer-like interactions; and discovering career options. The self-recognition that they had the ability to be successful, key element of the Vygotskian-Holzman theoretical framework, was a commonly identified theme for their educational development and professional growth.
Participants characterize the collaborative and creative aspects of MTBI. They reported that collaborative dynamics with peers were strengthened as they co-created a learning environment that facilitated and accelerated their understanding of the mathematics needed to address their research. The dynamics of collaboration allowed them to complete complex homework assignments, and helped them formulate and complete their projects. Participants identified the creative environments of their research projects as where creativity emerged in the dynamics of the program.
These data-driven findings characterize for the first time a summer program in the mathematical sciences as a Vygotskian-Holzman environment, that is, a `place’ where participants are seen as capable applied mathematicians, where the dynamics of collaboration and creativity are fundamental components.
The theoretical lens of developmental psychologists Lev Vygotsky (1978, 1987) and Lois Holzman (2010) that sees learning and development as a social process is used. From this view student development in MTBI is attributed to the collaborative and creative way students co-create the process of becoming scientists. This results in building a continuing network of academic and professional relationships among peers and mentors, in which around three quarters of MTBI PhD graduates come from underrepresented groups.
The extent to which MTBI creates a Vygotskian learning environment is explored from the perspectives of participants who earned doctoral degrees. Previously hypothesized factors (Castillo-Garsow, Castillo-Chavez and Woodley, 2013) that affect participants’ educational and professional development are expanded on.
Factors identified by participants are a passion for the mathematical sciences; desire to grow; enriching collaborative and peer-like interactions; and discovering career options. The self-recognition that they had the ability to be successful, key element of the Vygotskian-Holzman theoretical framework, was a commonly identified theme for their educational development and professional growth.
Participants characterize the collaborative and creative aspects of MTBI. They reported that collaborative dynamics with peers were strengthened as they co-created a learning environment that facilitated and accelerated their understanding of the mathematics needed to address their research. The dynamics of collaboration allowed them to complete complex homework assignments, and helped them formulate and complete their projects. Participants identified the creative environments of their research projects as where creativity emerged in the dynamics of the program.
These data-driven findings characterize for the first time a summer program in the mathematical sciences as a Vygotskian-Holzman environment, that is, a `place’ where participants are seen as capable applied mathematicians, where the dynamics of collaboration and creativity are fundamental components.
ContributorsEvangelista, Arlene Morales (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Holmes, Raquell M. (Committee member) / Mubayi, Anuj (Committee member) / Arizona State University (Publisher)
Created2015
Description
The 2009-10 influenza and the 2014-15 Ebola pandemics brought once again urgency to an old question: What are the limits on prediction and what can be proposed that is useful in the face of an epidemic outbreak?
This thesis looks first at the impact that limited access to vaccine stockpiles may have on a single influenza outbreak. The purpose is to highlight the challenges faced by populations embedded in inadequate health systems and to identify and assess ways of ameliorating the impact of resource limitations on public health policy.
Age-specific per capita constraint rates play an important role on the dynamics of communicable diseases and, influenza is, of course, no exception. Yet the challenges associated with estimating age-specific contact rates have not been decisively met. And so, this thesis attempts to connect contact theory with age-specific contact data in the context of influenza outbreaks in practical ways. In mathematical epidemiology, proportionate mixing is used as the preferred theoretical mixing structure and so, the frame of discussion of this dissertation follows this specific theoretical framework. The questions that drive this dissertation, in the context of influenza dynamics, proportionate mixing, and control, are:
I. What is the role of age-aggregation on the dynamics of a single outbreak? Or simply speaking, does the number and length of the age-classes used to model a population make a significant difference on quantitative predictions?
II. What would the age-specific optimal influenza vaccination policies be? Or, what are the age-specific vaccination policies needed to control an outbreak in the presence of limited or unlimited vaccine stockpiles?
Intertwined with the above questions are issues of resilience and uncertainty including, whether or not data collected on mixing (by social scientists) can be used effectively to address both questions in the context of influenza and proportionate mixing. The objective is to provide answers to these questions by assessing the role of aggregation (number and length of age classes) and model robustness (does the aggregation scheme selected makes a difference on influenza dynamics and control) via comparisons between purely data-driven model and proportionate mixing models.
This thesis looks first at the impact that limited access to vaccine stockpiles may have on a single influenza outbreak. The purpose is to highlight the challenges faced by populations embedded in inadequate health systems and to identify and assess ways of ameliorating the impact of resource limitations on public health policy.
Age-specific per capita constraint rates play an important role on the dynamics of communicable diseases and, influenza is, of course, no exception. Yet the challenges associated with estimating age-specific contact rates have not been decisively met. And so, this thesis attempts to connect contact theory with age-specific contact data in the context of influenza outbreaks in practical ways. In mathematical epidemiology, proportionate mixing is used as the preferred theoretical mixing structure and so, the frame of discussion of this dissertation follows this specific theoretical framework. The questions that drive this dissertation, in the context of influenza dynamics, proportionate mixing, and control, are:
I. What is the role of age-aggregation on the dynamics of a single outbreak? Or simply speaking, does the number and length of the age-classes used to model a population make a significant difference on quantitative predictions?
II. What would the age-specific optimal influenza vaccination policies be? Or, what are the age-specific vaccination policies needed to control an outbreak in the presence of limited or unlimited vaccine stockpiles?
Intertwined with the above questions are issues of resilience and uncertainty including, whether or not data collected on mixing (by social scientists) can be used effectively to address both questions in the context of influenza and proportionate mixing. The objective is to provide answers to these questions by assessing the role of aggregation (number and length of age classes) and model robustness (does the aggregation scheme selected makes a difference on influenza dynamics and control) via comparisons between purely data-driven model and proportionate mixing models.
ContributorsMorales, Romarie (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Mubayi, Anuj (Thesis advisor) / Towers, Sherry (Committee member) / Arizona State University (Publisher)
Created2016
Description
The Visceral Leishmaniasis (VL) is primarily endemic in five countries, with India and Sudan having the highest burden. The risk factors associated with VL are either unknown in some regions or vary drastically among empirical studies. Here, a dynamical model, motivated and informed by field data from the literature, is analyzed and employed to identify and quantify the impact of region dependent risks on the VL transmission dynamics. Parameter estimation procedures were developed using model-derived quantities and empirical data from multiple resources. The dynamics of VL depend on the estimates of the control reproductive number, RC, interpreted as the average number of secondary infections generated by a single infectious individual during the infectious period. The distribution of RC was estimated for both India (with mean 2.1 ± 1.1) and Sudan (with mean 1.45 ± 0.57). This suggests that VL can be established in naive regions of India more easily than in naive regions of Sudan. The parameter sensitivity analysis on RC suggests that the average biting rate and transmission probabilities between host and vector are among the most sensitive parameters for both countries. The comparative assessment of VL transmission dynamics in both India and Sudan was carried out by parameter sensitivity analysis on VL-related prevalences (such as prevalences of asymptomatic hosts, symptomatic hosts, and infected vectors). The results identify that the treatment and symptoms’ developmental rates are parameters that are highly sensitive to VL symptomatic and asymptomatic host prevalence, respectively, for both countries. It is found that the estimates of transmission probability are significantly different between India (from human to sandflies with mean of 0.39 ± 0.12; from sandflies to human with mean 0.0005 ± 0.0002) and Sudan (from human to sandflies with mean 0.26 ± 0.07; from sandflies to human with mean 0.0002 ± 0.0001). The results have significant implications for elimination. An increasing focus on elimination requires a review of priorities within the VL control agenda. The development of systematic implementation of control programs based on identified risk factors (such as monitoring of asymptomatically infected individuals) has a high transmission-blocking potential.
ContributorsBarley, Kamal K (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Mubayi, Anuj (Thesis advisor) / Safan, Muntaser (Committee member) / Arizona State University (Publisher)
Created2016