Mathematical Biology Seminar - Fall 2022

September 14

Joon Ha, Howard University

Location: WebEx

A Reduced-Mathematical Model Derived by Data, Not Mathematical Methods Enhances Diabetes Research

Diabetes is a progressive disease that is associated with multiple organs and tissues. The complex pathophysiology of the disease requires mathematical models to understand underlying mechanism. A common form of diabetes, type 2 diabetes is a failure of insulin-secreting pancreatic beta-cells to increase insulin to the level demanded by the body to maintain normal blood glucose. Clinical studies have shown that glucose concentration sharply rises at the onset of the disease, and in turn, diabetes complication rates also rapidly increase at the tipping point. Thus, it is desired to find early biomarkers of onset of T2D before the tipping point at which the loss of beta-cell function becomes nearly irreversible. Estimation of the secretory capacity of beta-cells is crucial to prevent and intervene in the disease. Oral glucose tolerance tests (OGTT) are currently used together with math models to estimate insulin requirements termed insulin sensitivity and insulin secretion capacity termed beta-cell function. During OGTTs, glucose and insulin measurements are required as inputs to estimate two metabolic parameters, insulin sensitivity and beta-cell function. In this talk, we show that; 1) our novel model (Ha and Sherman, AJP 2020) outperforms conventional methods to estimate metabolic parameters; 2) A model simplified by data rather than mathematical methods saves cost of diabetes research; 3) Further, the model predicts progression to diabetes.

September 28

Megan Owen, Lehman College

Location: CULM 505

Continuous Phylogenetic Tree Space: Algorithms and Applications

A continuous phylogenetic tree space is a geometric space whose points correspond to phylogenetic (evolutionary) trees with branch lengths.  Such a space provides a framework for analyzing both the tree topology and branch lengths together, which is important for processes such as the multi-species coalescent which depend on tree branch lengths.  The most well-known such space is the Billera-Holmes-Vogtmann (BHV) treespace, which I will introduce.  I will then discuss some recent work on algorithms and applications, including visualizing phylogenetic landscapes and detecting bias in phylogenetic inference.

October 5

Katherine St. John, TBA

Location: CULM 505

Analyzing Phylogenetic Treespace

This talk focuses on intriguing results about assembling, summarizing, and visualizing the space of phylogenetic trees. Evolutionary histories, or phylogenies, form an integral part of much work in biology. In addition to the intrinsic interest in the interrelationships between species, phylogenies are used for drug design, multiple sequence alignment, and even as evidence in a recent criminal trial. A simple representation for a phylogeny is a rooted, binary tree, where the leaves represent the species, and internal nodes represent their hypothetical ancestors. For even this simple way to represent evolution, finding the optima for bimolecular sequences for a fixed set of species is NP-hard. This talk will highlight  some of the elegant questions that arise from improving search and visualizing the results in this highly structured space. This talk assumes no background in biology and all are welcome.

November 2

Daniel Gomez, University of Pennsylvania

Location: CULM 505

Spike Solutions to the Singularly Perturbed Fractional Gierer-Meinhardt System

The singularly perturbed Gierer-Meinhardt system is a model reaction-diffusion system used to study the effects of short-range activation and long-range inhibition in biological systems. In the singularly perturbed limit the activator has an asymptotically small diffusivity and this conspires with the longer range of the inhibitor to form localized spike solutions. In this talk I will discuss recent work on the formal asymptotic analysis of spike solutions in one-dimensional domains when both the activator and inhibitor exhibit Lévy flights. Mathematically this leads to a fractional reaction-diffusion system in which the classical Laplacian is replaced with the fractional Laplacian. The singular behaviour of the corresponding fractional Green's function plays a crucial role in the asymptotic analysis of spike solutions and, depending on the fractional order, this leads to direct analogies with spike solutions to the classical Gierer-Meinhardt system in one-, two-, and three-dimensional domains.

November 9

Mareike Fischer, University of Greifswald

Location: CULM 505

How Far is My Network From Being Edge-Based? Proximity Measures for Edge-Basedness of Unrooted Phylogenetic Networks

Phylogenetic networks which are, as opposed to trees, suitable to describe processes like hybridization and horizontal gene transfer, play a substantial role in evolutionary research. However, while non-treelike events need to be taken into account, they are relatively rare, which implies that biologically relevant networks are often assumed to be similar to trees in the sense that they can be obtained by taking a tree and adding some additional edges. This observation led to the concept of so-called tree-based networks, which recently gained substantial interest in the literature. Unfortunately, though, identifying such networks in the unrooted case is an NP-complete problem. Therefore, classes of networks for which tree-basedness can be guaranteed are of the utmost interest. 

The most prominent such class is formed by so-called edge-based networks, which have a close relationship to generalized series parallel graphs known from graph theory. They can be identified in linear time and are in some regards biologically more plausible than general tree-based networks. While concerning the latter proximity measures for general networks have already been introduced, such measures are not yet available for edge-basedness. This means that for an arbitrary unrooted network, the "distance" to the nearest edge-based network could so far not be determined. In my talk, I will fill this gap by introducing two classes of proximity measures for edge-basedness.

This project is joint work with Tom Hamann and Kristina Wicke.

November 30

Xinxin Du, Flatiron Institute

Location: CULM 505

Modeling Epithelial Tissue as a 3D, Self-Sculpting, Viscoelastic Slab with Active Surfaces

Morphogenesis occurs during an animal's embryonic development; it is a process in which many cells and tissues change the way they are shaped and organized.  Epithelia are cell monolayers that actively alter their shape to create future body parts of the animal; this makes the epithelia one of the most active and critical structures in early animal development.  Even though epithelial cells exist and move in three dimensions, mathematical models frequently describe them as merely two-dimensional.  However, recent imaging technology has begun to reveal pertinent dynamics in the third dimension of the tissue.  With the importance of the third dimension in mind, we developed a self-sculpting, three-dimensional, computational model of epithelia whose dynamics are driven by active forces on its surface.  We present an initial, fundamental study for a reduced version of an epithelia that investigates how surface forces alter its internal dynamics.  Our model captures the 3D slab-like geometry of epithelia, viscoelasticity of tissue response, fluid surroundings, and driving from active surface forces.  We represent epithelial tissue as a thick slab, a 3D continuum comprised of a viscous Newtonian fluid with an extra viscoelastic stress.  Employing this model, we simulate and make quantitative predictions about 3D cell dynamics and cell shape deformations as they respond to surface forces in common morphological contexts.  In particular, we will discuss the initiation of ventral furrow invagination and T1 transitions in Drosophila embryogenesis.