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Item Reconstructing embedded graphs from persistence diagrams(2020-10) Belton, Robin Lynne; Fasy, Brittany T.; Mertz, Rostik; Micka, Samuel; Millman, David L.; Salinas, Daniel; Schenfisch, Anna; Schupbach, Jordan; Williams, LuciaThe persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space. Recent work has shown that well-chosen (finite) sets of PDs can differentiate between geometric simplicial complexes, providing a method for representing complex shapes using a finite set of descriptors. A related inverse problem is the following: given a set of PDs (or an oracle we can query for persistence diagrams), what is underlying geometric simplicial complex? In this paper, we present an algorithm for reconstructing embedded graphs in Rd (plane graphs in R2) with n vertices from n2 −n+d+1 directional (augmented) PDs. Additionally, we empirically validate the correctness and time-complexity of our algorithm in R2 on randomly generated plane graphs using our implementation, and explain the numerical limitations of implementing our algorithm.Item Physiological dynamic compression regulates central energy metabolism in primary human chondrocytes(2018-02) Salinas, Daniel; Mumey, Brendan M.; June, Ronald K.Chondrocytes use the pathways of central metabolism to synthesize molecular building blocks and energy for cartilage homeostasis. An interesting feature of the in vivo chondrocyte environment is the cyclical loading generated in various activities (e.g., walking). However, it is unknown whether central metabolism is altered by mechanical loading. We hypothesized that physiological dynamic compression alters central metabolism in chondrocytes to promote production of amino acid precursors for matrix synthesis. We measured the expression of central metabolites (e.g., glucose, its derivatives, and relevant co-factors) for primary human osteoarthritic chondrocytes in response to 0–30 minutes of compression. To analyze the data, we used principal components analysis and ANOVA-simultaneous components analysis, as well as metabolic flux analysis. Compression-induced metabolic responses consistent with our hypothesis. Additionally, these data show that chondrocyte samples from different patient donors exhibit different sensitivity to compression. Most importantly, we find that grade IV osteoarthritic chondrocytes are capable of synthesizing non-essential amino acids and precursors in response to mechanical loading. These results suggest that further advances in metabolic engineering of chondrocyte mechanotransduction may yield novel translational strategies for cartilage repair.Item Combining Targeted Metabolomic Data with a Model of Glucose Metabolism: Toward Progress in Chondrocyte Mechanotransduction(2016-01) Salinas, Daniel; Minor, Cody A.; Carlson, Ross P.; McCutchen, Carley N.; Mumey, Brendan M.; June, Ronald K.Osteoarthritis is a debilitating disease likely involving altered metabolism of the chondrocytes in articular cartilage. Chondrocytes can respond metabolically to mechanical loads via cellular mechanotransduction, and metabolic changes are significant because they produce the precursors to the tissue matrix necessary for cartilage health. However, a comprehensive understanding of how energy metabolism changes with loading remains elusive. To improve our understanding of chondrocyte mechanotransduction, we developed a computational model to calculate the rate of reactions (i.e. flux) across multiple components of central energy metabolism based on experimental data. We calculated average reaction flux profiles of central metabolism for SW1353 human chondrocytes subjected to dynamic compression for 30 minutes. The profiles were obtained solving a bounded variable linear least squares problem, representing the stoichiometry of human central energy metabolism. Compression synchronized chondrocyte energy metabolism. These data are consistent with dynamic compression inducing early time changes in central energy metabolism geared towards more active protein synthesis. Furthermore, this analysis demonstrates the utility of combining targeted metabolomic data with a computational model to enable rapid analysis of cellular energy utilization.Item An enumerative approach to computing cut sets in metabolic networks(Montana State University - Bozeman, College of Engineering, 2013) Salinas, Daniel; Chairperson, Graduate Committee: Brendan MumeyThe productivity of organisms used in biotechnology may be enhanced when certain parts of their metabolism are rendered inaccessible. This can be achieved with genetic modifications, but current techniques set a practical limit on number of modifications that can be applied. Taking advantage of this limit, we implement a brute force algorithm that can compute cut sets for any set of metabolites and reactions that is shown to perform better than alternative approaches. Also, an attempt is made to approximate a binary linear program with a quadratic program; this approximation is meant to be used when refining the growth model of organisms used in flux balance analysis. The approximation is shown to be less efficient that the original program. Finally, extensions to the brute force algorithm are proposed.