Dynamics of a linearly-perturbed May-Leonard competition model The May-Leonard model was introduced to examine the behavior of three competing populations where rich dynamics, such as limit cycles and nonperiodic cyclic solutions, arise. In this talk, we will discuss an extended May-Leonard model, where the system is perturbed by adding the capability of global mutations, allowing …
Optimization of Immunotherapy Treatment Regimen for Glioblastoma The most common and aggressive primary brain cancer, Glioblastoma multiforme (GBM), exhibits a highly immune-suppressed tumor microenvironment. Monotherapy with anti-PD-1—a common immunotherapy which targets the PD-L1/PD-1 axis—has proved to be unsuccessful likely due to added layers of immune suppression. Murine experiments show that CCR2+ myeloid cells are chemo-kinetically …
Immunotherapy: Using math to help the immune system fight cancer In recent years, immunotherapy has been taking a central role in cancer therapies. In this talk we will provide an overview of some of our recent works in mathematical modeling of immunotherapy. Among the topics we will discuss are engineered T cell therapy, transforming growth …
Production and Modeling of DNA Toroidal Condensates Via Liquid Crystal Theory Genomic organization conformations are widely studied in all cells, and bacteriophages offer simpler systems to study genomic packing. Experimental studies on phage capsids have found encapsidated toroidal DNA condensates. In vitro DNA condensation into toroids is the simplest condensation system allowing analysis on toroidal …
Registration Problems and Applications to Biomathematics I will discuss some mathematical approaches to various registration problems, where one seeks to align points from different spaces. These include matching points between different metric spaces or registering graphs or hypergraphs with different node sets. Along the way, I'll talk about motivating problems that come from biology, such …
Stochastic switching of delayed feedback suppresses oscillations in genetic regulatory systems Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates the effect of delayed feedback. To do so, we consider a hybrid model …
Deconstructing the Integrated Oscillator Model for Pancreatic Beta-Cells Electrical bursting oscillations in the beta-cells of pancreatic islets have been a focus of investigation for more than fifty years. This has been aided by mathematical models, which are descendants of the pioneering Chay-Keizer model that was published 40 years ago. This presentation describes the key biophysical …
Trait-shift induced interaction modification and unusual consequences onecosystem dynamics Ecosystems are traditionally modeled by networks of species with constant interaction strengths between them. However, it has been increasingly recognized that there is substantial intraspecific variation in ecologically important traits. The distribution of such traits within a species can shift in response to environmental change or …
Controlling Pattern Formation in Active-Ordered Fluids Active fluids comprised of reconstituted biopolymers and motor proteins are self-driven materials that exhibit rich spatiotemporal dynamics. These dynamics are characterized by buckling instabilities and the proliferation of topological defects in orientational order. These defects drive material flows and give the system its striking, characteristic texture and dynamics. One …
A stochastic first-order reaction gene translation and nuclear-to-cell ratio homeostasis model Cell size varies between different cell types, and between different growth and osmotic conditions. However, the nuclear-to-cell volume ratio (N/C ratio) is largely maintained. In this presentation, I will first introduce an osmotic pressure balance model of N/C ratio determination, which relates the N/C …
