Mathematical modeling of Drosophila larvae crawling
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The fruit ﬂy Drosophila melanogaster is a widely used model organism for development and gene-based diseases. The ﬂies’ genetic homology to humans, tractable genetics and straightforward manipulability make them well suitable for studies of neurologic disorders and neural degeneration. Due to the close relation between the latter and the musculoskeletal system, locomotive impairment and behavioral changes can be used diagnostically for screening and characterization of such disease models. For this purpose, advanced methods to quantify behavioral phenotypes are crucial. Given the complications arising with studying adult ﬂies on a population level as well as the lethality of some mutations before adulthood, studies at the larval stage are more suitable. However, a quantitative mathematical model of the crawling pattern has been lacking so far. In this thesis work I show that the development of such a model and appropriate analysis techniques enable quantiﬁcation of the crawling behavior and extraction of intricate details that were previously missed. In my studies, Drosophila larvae were found to follow a bimodal persistent random walk pattern, switching between an actual forward crawling phase and events where the larvae rest and reorient. This enabled quantifying the larval behavior using a set of parameters within the framework of this mathematical model. I further used the analysis I developed to study larval model systems of Alzheimer’s disease and Fragile X mental retardation, which allowed identifying diﬀerences in the modes of locomotion that were previously missed. The novel ability to sensitively and robustly quantify behavior, as described in this work, opens up the possibility to employ these methods for future drug and genetic screens. Finally, I show that starting from the analysis of a small sample of crawling larvae we can robustly simulate the mutant-speciﬁc crawling in its quantitative and qualitative aspects. Using these simulations, predictions can be made on the feasibility of experiments that may require an impractically large number of individuals to reach statistical signiﬁcance, and the outcome of laborious experiments can be pre-estimated by simulations.