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- All Subjects: Mathematics
- All Subjects: Synthetic Biology
- Creators: School of Mathematical and Statistical Sciences
- Creators: Wang, Xiao
Description
Recombinases are powerful tools for genome engineering and synthetic biology, however recombinases are limited by a lack of user-programmability and often require complex directed-evolution experiments to retarget specificity. Conversely, CRISPR systems have extreme versatility yet can induce off-target mutations and karyotypic destabilization. To address these constraints we developed an RNA-guided recombinase protein by fusing a hyperactive mutant resolvase from transposon TN3 to catalytically inactive Cas9. We validated recombinase-Cas9 (rCas9) function in model eukaryote Saccharomyces cerevisiae using a chromosomally integrated fluorescent reporter. Moreover, we demonstrated cooperative targeting by CRISPR RNAs at spacings of 22 or 40bps is necessary for directing recombination. Using PCR and Sanger sequencing, we confirmed rCas9 targets DNA recombination. With further development we envision rCas9 becoming useful in the development of RNA-programmed genetic circuitry as well as high-specificity genome engineering.
ContributorsStandage-Beier, Kylie S (Author) / Wang, Xiao (Thesis advisor) / Brafman, David A (Committee member) / Tian, Xiao-jun (Committee member) / Arizona State University (Publisher)
Created2018
Description
Synthetic biology is an emerging field which melds genetics, molecular biology, network theory, and mathematical systems to understand, build, and predict gene network behavior. As an engineering discipline, developing a mathematical understanding of the genetic circuits being studied is of fundamental importance. In this dissertation, mathematical concepts for understanding, predicting, and controlling gene transcriptional networks are presented and applied to two synthetic gene network contexts. First, this engineering approach is used to improve the function of the guide ribonucleic acid (gRNA)-targeted, dCas9-regulated transcriptional cascades through analysis and targeted modification of the RNA transcript. In so doing, a fluorescent guide RNA (fgRNA) is developed to more clearly observe gRNA dynamics and aid design. It is shown that through careful optimization, RNA Polymerase II (Pol II) driven gRNA transcripts can be strong enough to exhibit measurable cascading behavior, previously only shown in RNA Polymerase III (Pol III) circuits. Second, inherent gene expression noise is used to achieve precise fractional differentiation of a population. Mathematical methods are employed to predict and understand the observed behavior, and metrics for analyzing and quantifying similar differentiation kinetics are presented. Through careful mathematical analysis and simulation, coupled with experimental data, two methods for achieving ratio control are presented, with the optimal schema for any application being dependent on the noisiness of the system under study. Together, these studies push the boundaries of gene network control, with potential applications in stem cell differentiation, therapeutics, and bio-production.
ContributorsMenn, David J (Author) / Wang, Xiao (Thesis advisor) / Kiani, Samira (Committee member) / Haynes, Karmella (Committee member) / Nielsen, David (Committee member) / Marshall, Pamela (Committee member) / Arizona State University (Publisher)
Created2018
Description
A semi-implicit, fourth-order time-filtered leapfrog numerical scheme is investigated for accuracy and stability, and applied to several test cases, including one-dimensional advection and diffusion, the anelastic equations to simulate the Kelvin-Helmholtz instability, and the global shallow water spectral model to simulate the nonlinear evolution of twin tropical cyclones. The leapfrog scheme leads to computational modes in the solutions to highly nonlinear systems, and time-filters are often used to damp these modes. The proposed filter damps the computational modes without appreciably degrading the physical mode. Its performance in these metrics is superior to the second-order time-filtered leapfrog scheme developed by Robert and Asselin.
ContributorsBurke, Lee Matthew Moore (Author) / Moustaoui, Mohamed (Thesis director) / Kostelich, Eric (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Honey bees (Apis mellifera) are responsible for pollinating nearly 80\% of all pollinated plants, meaning humans depend on honey bees to pollinate many staple crops. The success or failure of a colony is vital to global food production. There are various complex factors that can contribute to a colony's failure, including pesticides. Neonicotoids are a popular pesticide that have been used in recent times. In this study we concern ourselves with pesticides and its impact on honey bee colonies. Previous investigations that we draw significant inspiration from include Khoury et Al's \emph{A Quantitative Model of Honey Bee Colony Population Dynamics}, Henry et Al's \emph{A Common Pesticide Decreases Foraging Success and Survival in Honey Bees}, and Brown's \emph{ Mathematical Models of Honey Bee Populations: Rapid Population Decline}. In this project we extend a mathematical model to investigate the impact of pesticides on a honey bee colony, with birth rates and death rates being dependent on pesticides, and we see how these death rates influence the growth of a colony. Our studies have found an equilibrium point that depends on pesticides. Trace amounts of pesticide are detrimental as they not only affect death rates, but birth rates as well.
ContributorsSalinas, Armando (Author) / Vaz, Paul (Thesis director) / Jones, Donald (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of International Letters and Cultures (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
A Guide to Financial Mathematics is a comprehensive and easy-to-use study guide for students studying for the one of the first actuarial exams, Exam FM. While there are many resources available to students to study for these exams, this study is free to the students and offers an approach to the material similar to that of which is presented in class at ASU. The guide is available to students and professors in the new Actuarial Science degree program offered by ASU. There are twelve chapters, including financial calculator tips, detailed notes, examples, and practice exercises. Included at the end of the guide is a list of referenced material.
ContributorsDougher, Caroline Marie (Author) / Milovanovic, Jelena (Thesis director) / Boggess, May (Committee member) / Barrett, The Honors College (Contributor) / Department of Information Systems (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
Covering subsequences with sets of permutations arises in many applications, including event-sequence testing. Given a set of subsequences to cover, one is often interested in knowing the fewest number of permutations required to cover each subsequence, and in finding an explicit construction of such a set of permutations that has size close to or equal to the minimum possible. The construction of such permutation coverings has proven to be computationally difficult. While many examples for permutations of small length have been found, and strong asymptotic behavior is known, there are few explicit constructions for permutations of intermediate lengths. Most of these are generated from scratch using greedy algorithms. We explore a different approach here. Starting with a set of permutations with the desired coverage properties, we compute local changes to individual permutations that retain the total coverage of the set. By choosing these local changes so as to make one permutation less "essential" in maintaining the coverage of the set, our method attempts to make a permutation completely non-essential, so it can be removed without sacrificing total coverage. We develop a post-optimization method to do this and present results on sequence covering arrays and other types of permutation covering problems demonstrating that it is surprisingly effective.
ContributorsMurray, Patrick Charles (Author) / Colbourn, Charles (Thesis director) / Czygrinow, Andrzej (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Physics (Contributor)
Created2014-12
Description
Deconvolution of noisy data is an ill-posed problem, and requires some form of regularization to stabilize its solution. Tikhonov regularization is the most common method used, but it depends on the choice of a regularization parameter λ which must generally be estimated using one of several common methods. These methods can be computationally intensive, so I consider their behavior when only a portion of the sampled data is used. I show that the results of these methods converge as the sampling resolution increases, and use this to suggest a method of downsampling to estimate λ. I then present numerical results showing that this method can be feasible, and propose future avenues of inquiry.
ContributorsHansen, Jakob Kristian (Author) / Renaut, Rosemary (Thesis director) / Cochran, Douglas (Committee member) / Barrett, The Honors College (Contributor) / School of Music (Contributor) / Economics Program in CLAS (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
This paper focuses on the Szemerédi regularity lemma, a result in the field of extremal graph theory. The lemma says that every graph can be partitioned into bounded equal parts such that most edges of the graph span these partitions, and these edges are distributed in a fairly uniform way. Definitions and notation will be established, leading to explorations of three proofs of the regularity lemma. These are a version of the original proof, a Pythagoras proof utilizing elemental geometry, and a proof utilizing concepts of spectral graph theory. This paper is intended to supplement the proofs with background information about the concepts utilized. Furthermore, it is the hope that this paper will serve as another resource for students and others to begin study of the regularity lemma.
ContributorsByrne, Michael John (Author) / Czygrinow, Andrzej (Thesis director) / Kierstead, Hal (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Chemistry and Biochemistry (Contributor)
Created2015-05
Description
Lights Out is a puzzle game where the goal is to turn off all the lights on a nxn board starting from a random configuration. In order to find the solution of a configuration, the game is constructed using a matrix basis in the span of the field Z mod 2.This the game can be modeled by the system Ap=s which will be the center of the investigation when determining the solvability for any n×n board since A is not always invertable leading to some interesting cases. The goal of this thesis was to construct a model that will allow the player to solve for the pushes to attain the zero-state for an nxn system. Constructing the model gave a procedure that will allow to solve the puzzle game. The procedure presented here first uses a simple clearing technique (valid for any board size) to turn off all the lights except in the last row, which we call the standard-clear. The heart of the technique, is to give a way to use the information about which lights remain lit in the last row to determine which switches in the first row need to be pushed before the standard-clear. This part of the solution algorithm we call the first row adjustment, and it depends heavily on the specific board size n of the problem. Finally, after these first row pushes are made, the standard clear will now turn off all the lights including (seemingly magically) the last row. Thus the solution to the Lights Out puzzle of a given size is reduced to finding a first row adjustment for that size. (Please refer to the actual thesis for the full abstract)
ContributorsBarraza, Jay Romeo (Author) / Vaz, Paul (Thesis director) / Paupert, Julien (Committee member) / Civil, Environmental and Sustainable Engineering Programs (Contributor) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
Currently in synthetic biology only the Las, Lux, and Rhl quorum sensing pathways have been adapted for broad engineering use. Quorum sensing allows a means of cell to cell communication in which a designated sender cell produces quorum sensing molecules that modify gene expression of a designated receiver cell. While useful, these three quorum sensing pathways exhibit a nontrivial level of crosstalk, hindering robust engineering and leading to unexpected effects in a given design. To address the lack of orthogonality among these three quorum sensing pathways, previous scientists have attempted to perform directed evolution on components of the quorum sensing pathway. While a powerful tool, directed evolution is limited by the subspace that is defined by the protein. For this reason, we take an evolutionary biology approach to identify new orthogonal quorum sensing networks and test these networks for cross-talk with currently-used networks. By charting characteristics of acyl homoserine lactone (AHL) molecules used across quorum sensing pathways in nature, we have identified favorable candidate pathways likely to display orthogonality. These include Aub, Bja, Bra, Cer, Esa, Las, Lux, Rhl, Rpa, and Sin, which we have begun constructing and testing. Our synthetic circuits express GFP in response to a quorum sensing molecule, allowing quantitative measurement of orthogonality between pairs. By determining orthogonal quorum sensing pairs, we hope to identify and adapt novel quorum sensing pathways for robust use in higher-order genetic circuits.
ContributorsMuller, Ryan (Author) / Haynes, Karmella (Thesis director) / Wang, Xiao (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Chemistry and Biochemistry (Contributor) / School of Life Sciences (Contributor)
Created2015-05