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Item Quantifying robustness of the gap gene network(Montana State University - Bozeman, College of Letters & Science, 2024) Andreas, Elizabeth Anne; Chairperson, Graduate Committee: Tomas Gedeon; Bree Cummins (co-chair)Early development of Drosophila melanogaster (fruit fly) facilitated by the gap gene network has been shown to be incredibly robust, and the same patterns emerge even when the process is seriously disrupted. We investigate this robustness using a previously developed computational framework called DSGRN (Dynamic Signatures Generated by Regulatory Networks). Our mathematical innovations include the conceptual extension of this established modeling technique to enable modeling of spatially monotone environmental effects, as well as the development of a collection of graph theoretic robustness scores for network models. This allows us to rank order the robustness of network models of cellular systems where each cell contains the same genetic network topology but operates under a parameter regime that changes continuously from cell to cell. We demonstrate the power of this method by comparing the robustness of two previously introduced network models of gap gene expression along the anterior-posterior axis of the fruit fly embryo, both to each other and to a random sample of networks with same number of nodes and edges. We observe that there is a substantial difference in robustness scores between the two models. Our biological insight is that random network topologies are in general capable of reproducing complex patterns of expression, but that using measures of robustness to rank order networks permits a large reduction in hypothesis space for highly conserved systems such as developmental networks.Item Comparing network models of gap gene interaction during Drosophila melanogaster development(Montana State University - Bozeman, College of Letters & Science, 2021) Andreas, Elizabeth Anne; Chairperson, Graduate Committee: Tomas GedeonEarly development of Drosophila melanogaster (fruit fly) facilitated by the gap gene network has been shown to be incredibly robust, and the same patterns emerge even when the process is seriously disrupted. In this thesis we plan to investigate this robustness using a previously developed computational framework called Dynamic Signatures Generated by Regulatory Networks (DSGRN). The principal result of this research has been in extending DSGRN to study how tissue-scale behavior arises from network behavior in individual cells, such as gap gene expression along the anterior-posterior (A-P) axis of the Drosophila embryo. Essentially, we extend DSGRN to study cellular systems where each cell contains the same network structure but operates under a parameter regime that changes continuously from cell to cell. We then use this extension to study the robustness of two different models of the gap gene network by looking at the number of paths in each network that can produce the observed gap gene expression. While we found that both networks are capable or replicating the data, we hypothesize that one network is a better fit than the other. This is significant in two ways; finding paths shows us that the spatial data can be replicated using a single network with different parameters along the A-P axis, and that we may be able to use this extension of DSGRN to rank network models.