The Influence of Multi-Scale Dynamics on Physical and Behavioral Cellular Patterns

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Physical, observable patterns and repeated patterns of behavior are vital for cellular function. Such patterns occur at scales ranging from the intracellular to the tissue level. Disruption or misuse of these patterns can have devastating consequences for human health as it can lead to amyotrophic lateral sclerosis (ALS), Alzheimer's, or metastatic cancer. The overarching aim of my research program is to leverage novel mathematical modeling, numerical simulations, sensitivity analysis, and an interdisciplinary approach to investigate how vitally important small- and large-scale interactions are for maintaining cellular patterns and function. In particular, I will examine the link between different scales in three unique biological settings. Liquid-liquid phase separation (LLPS) provides an excellent environment to mathematically study how the formation of membrane-less compartments alter the molecular dynamics that occur within the cellular environment. My work on the epithelial mesenchymal transition (EMT) will use an interdisciplinary approach to focus on how complicated single-molecule dynamics and intracellular signaling cascades are involved in changes to behavioral patterns, such as metastasis. While these two model systems are seemingly disparate, they actually provide the perfect environment to develop the novel mathematical tools and biological understanding necessary to explore multi-scale patterning dynamics in both embryogenesis and the tumor environment via the differential adhesion hypothesis (DAH). Proposed over 50 years ago, the DAH suggests that different cell populations de-mix from each other in a manner similar to liquid-like de-mixing to form new embryonic compartments. Research into LLPS will develop the mathematical tools necessary to understand how cells are rearranging themselves in the embryo while the study of intracellular dynamics with EMT will further the understanding of how transmembrane proteins that prevent cellular movement, such as E-cadherin, are affected during this liquid-like cellular movement. By coupling these novel mathematical approaches with biological experiments, my work exists at the cutting edge of biomathematics and provides a truly novel approach to understanding how multi-scale patterns emerge in the cellular environment and, potentially, how they are exploited by disease.