# Mathematical Biology Seminar - Fall 2024

Seminars are typically held on Wednesdays from 1:00 - 2:00 PM as hybrid talks unless otherwise noted. The in-person presentation will take place in CULM 505 with a Zoom option for virtual attendees.

For questions about the seminar schedule, please contact James MacLaurin.

### September 11

**Bryan Currie**, NJIT

**Maximum Increase in Widths and Algebra with Quintet Information**

Mathematical phylogenists are interested in improving models for evolution, and our current models tend to spit out trees that seem more balanced than trees we infer from data. As tree balance is ambiguous, there are several tree balance indices which capture different notions of balance. One less-understood tree balance index is maximum increase in widths when limited to binary trees. We partially fill in a gap in the literature by describing the structure and size of maximal trees for leaf numbers that are not powers of two.

As for the quintets, it is well-known that data of unrooted quartets among taxa can determine the unrooted tree topology under the multispecies coalescent model of evolution. However, these data cannot determine the root of the tree, and so biologists have resorted to including an outgroupspecies, which is significantly less related to the others in the study that split off from a common ancestor of the entire relevant clade. While a reasonable idea, this leads to problems if the outgroup chosen is too closely or too distantly related. Unrooted quintet data had already been shown to identify the root for a binary tree, but we used an algebraic approach to reprove this and also show that quintet data can also detect network features invisible to quartet data, such as rooting in some cases and 2-cycles in some cases.

### September 18

**James MacLaurin**, NJIT

**An Introduction to the Coupling Method (for deriving Fokker-Planck population density PDEs from particle systems)**

Mathematical phylogenists are interested in improving models for evolution, and our current models tend to spit out trees that seem more balanced than trees we infer from data. As tree balance is ambiguous, there are several tree balance indices which capture different notions of balance. One less-understood tree balance index is maximum increase in widths when limited to binary trees. We partially fill in a gap in the literature by describing the structure and size of maximal trees for leaf numbers that are not powers of two.

As for the quintets, it is well-known that data of unrooted quartets among taxa can determine the unrooted tree topology under the multispecies coalescent model of evolution. However, these data cannot determine the root of the tree, and so biologists have resorted to including an outgroupspecies, which is significantly less related to the others in the study that split off from a common ancestor of the entire relevant clade. While a reasonable idea, this leads to problems if the outgroup chosen is too closely or too distantly related. Unrooted quintet data had already been shown to identify the root for a binary tree, but we used an algebraic approach to reprove this and also show that quintet data can also detect network features invisible to quartet data, such as rooting in some cases and 2-cycles in some cases.

### September 25

**Shahriar Afkhami**, NJIT

**Numerical simulations and physics-informed neural networks for magnetic drug delivery**

Magnetic drug delivery is a promising method for non-invasive, targeted treatment for certain diseases, including cancer, particularly for targeting specific, hard-to-reach sites in the body, resulting in reducing side effects by lowering dosages. This is achieved by injecting superparamagnetic iron oxide nanoparticles containing therapeutic drugs into the bloodstream and using an external magnet to guide these nanoparticles to the tumor site. I will present a computational model consisting of a stochastic ordinary differential equation model to simulate nanoparticle trajectories in blood flow and to determine the optimal conditions for magnetic drug delivery. I will also present a physics-informed neural network approach as an efficient machine learning method for solving the governing initial value differential equation.

### October 9

**Andrew White**, NJIT

**Role of calcium buffers in synaptic neurotransmitter release and its short-term modulation**

Neurotransmitter release is caused by a series of biological steps. It starts with an action potential traveling down the axon and inducing the voltage gated calcium ion channels to open and induces an influx of calcium ions into the pre-synaptic terminal. Following this, calcium ions bind to sensor proteins signaling the vesicles to fuse with the inner pre-synaptic membrane which release their contents into the synaptic cleft. The efficiency of neurotransmitter release is not constant, but changes from pulse to pulse and it can either increase (short term facilitation or STF) or decrease (short term depression or STD). Collectively, these behaviors are referred to as short-term synaptic plasticity (STSP).

Our aim is to understand how the properties of intracellular calcium-binding molecules called calcium buffers affect STSP. To address this question, we solve the corresponding system of reaction-diffusion PDEs numerically (via a Crank-Nicholson scheme) and explore interesting STSP behaviors elicited in different parameter regimes. In our research we are focusing on calcium buffers that have two calcium ion binding sites per buffer molecule. To find optimal buffering properties associated with each specific STSP behavior that we observe, we employ a differential evolution optimization algorithm. Finally, we discuss possible extensions of this work to the study of other calcium dependent mechanisms such as intracellular calcium waves caused by calcium-induced calcium release, known to be strongly dependent on buffering properties.

### October 23

**Joshua McGinnis**, University of Pennsylvania (UPenn)

**Title/Abstract Forthcoming**

### October 30

**Mark Van Den Bosch**, Leiden University

**Multidemensional Stability of Planar Travelling Waves for Stochastically Perturbed Reaction-Diffusion Systems**

*Abstract Forthcoming*

### November 6

**Rik Westdorp**, Leiden University

**Long timescale soliton dynamics in the Korteweg -de Vries equation with multiplicative translation-invariant noise**

*Abstract Forthcoming*

### November 13

**Rainer Engelken**, Columbia University

**Title/Abstract Forthcoming**

### November 20

**Allison Edgar**, NJIT

**Title/Abstract Forthcoming**