Quantitative Descriptors of Particulate Dynamics in Biological Systems

Menssen, Rebecca

doi:https://doi.org/10.21985/n2-s254-w347

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Quantitative Descriptors of Particulate Dynamics in Biological Systems

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This dissertation presents two projects with the goal of understanding how to quantitatively describe biological data, particularly data that is highly dynamic. The first study presents an improved quantitative tool for the analysis of particulate trajectories. Particulate trajectory data appears in several different biological contexts, and the majority of analyses performed on particulate trajectory data have been limited to mean squared displacement (MSD) analysis, which has multiple pitfalls. The jump distance distribution (JDD) is presented as an alternative to MSD analysis, and addresses many issues and is especially advantageous in the data-poor limit. In this thesis, we construct and validate a derivation of the JDD for different transportation modes and dimensions and implement a parameter estimation and model selection scheme. This scheme is validated, and direct improvements over MSD analysis are shown. Through an analysis of bacterial chemotaxis data, we highlight the JDD's ability to extract parameters at a variety of time scales, as well as extract underlying biological features of interest. The second study presented in this dissertation takes its inspiration from pulsatile actomyosin dynamics in the early C. elegans zygote. Pulsatile systems are pervasive in biology but many systems have not be examined in a mathematical context due to their complexity. Utilizing a toy model for a pulsatile system allows for mathematical tools to be applied to a system where the ground truth is known. This aids in understanding how to interpret the same analysis as performed on experimental data. This is the approach taken in this dissertation, with a simple model with fluid flows is used to understand how flows change a pulsatile systems. Basic mathematical analysis is then performed to understand these flows, as well as how to interpret data. The same mathematical tools are then taken to C. elegans image data, showing clear differences between mutants, and showing that with biological data, one cannot decouple the chemistry from mechanics (flows). Examining the two together allows for a deeper level of analysis and clearer delineation of differences between phenotypes. As this project is just the beginning of a larger study, much discussion is given to general implications of this work, and how one would extend and improve upon it.

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