Title: Traditional Applied Math, and then, Working with High Dimensional Biological Data Abstract: I will give an overview of my interests in two parts. The first part will be on passive tracer problems – with the goal of finding formulas of descriptive statistics (mean, variance, skewness) for a solute distribution advected by a smooth flow in a tube with arbitrary cross-section. We found explicit formulas which predict these statistics relying ultimately only on the cross-section of the tube, and see…

Title: Circadian Rhythms in Multinucleate Cells Abstract: Circadian rhythms are among the most researched cellular processes, but limited work has been done on how these rhythms are coordinated between nuclei in multinucleate cells. I'll analyze a mathematical model for circadian oscillations in a multinucleate cell, motivated by mRNA and protein data from the filamentous fungus Neurospora crassa. Stochastic simulations of this model illuminate the importance of mRNA-protein phase separation, in which mRNAs are kept close to the nucleus in which they were transcribed, while proteins can diffuse…

Title: A Recommendation Systems Approach for Detecting Epistasis Abstract: There are a variety of methods used to understand and interpret an organism’s phenotype, the physical expression of one or more genes. Epistasis, the phenomenon of one mutation affecting the resulting quantitative or qualitative phenotype, is used to assess gene variation in an attempt to find a combination of single nucleotide polymorphisms (SNPs) that contribute to a certain phenotype. Since one SNP rarely completely describes an organism’s phenotype, detecting these groups,…

Title: Exploring Phage Treatment for Bacterial Infections with Mathematical Modeling Abstract: Antimicrobial resistance (AMR) is a serious threat to global health today. A renewed interest in phage therapy – the use of bacteriophages to treat pathogenic bacterial infections – has emerged given the spread of AMR and lack of new drug classes in the antibiotic pipeline. This talk will feature mathematical models from an ongoing research project that began in 2019 during the Collaborative Workshop for Women in Mathematical Biology…

Title: Understanding Complex Social Systems using Minimal Mathematical Models Abstract: Minimal mathematical models are used to understand complex phenomena in the physical, biological, and social sciences. This modeling philosophy never claims, nor even attempts, to fully capture the mechanisms underlying the phenomena, and instead offers insights and predictions not otherwise possible. Here, we explore minimal dynamical systems models to understand several complex social phenomena, including the profit-driven abandonment of restaurant tipping, the public health tradeoffs of e-cigarettes, and the progression…

Title:  Collective motion in the mitotic spindle Abstract:  Math models of interacting individuals moving as a collective have been profoundly successful in describing physical and social phenomena ranging from swarming insects to human crowds. Especially in molecular biology, recent advances in machine-learning-based automated tracking have led to droves of new data of collective motion. I’ll discuss two related projects, both studying chromosomes (DNA) moving during mitosis (cell division). The first project will hopefully convince you that modeling this system as a collective is…