Mathematical Biology

The past decade has seen a rapid development of data-driven plant breeding strategies based on the two significant technological developments. First, the use of high throughput DNA sequencing technology to identify millions of genetic markers on that characterize the available genetic diversity captured by the thousands of available accessions in each major crop species. Second, the development of high throughput imaging platforms for estimating quantitative traits associated with easily accessible above-ground structures such as shoots, leaves and flowers. These data-driven breeding strategies are widely viewed as the basis for rapid development of crops capable of providing stable yields in the face of global climate change. Roots and other below-ground structures are much more difficult to study yet play essential roles in adaptation to climate change including as uptake of water and nutrients. Estimation of quantitative traits from images remains a significant technical and scientific bottleneck for both above and below-ground structures. The focus of this talk, inspired by the analytical results of Kac, van den Berg and many others in the area of spectral geometry, is to describe a computational and statistical methodology that employs stochastic processes as quantitative measurement tools suitable for characterizing images of multi-scale dendritic structures such as plant root systems. The substrate for statistical analyses in Wasserstein space are hitting distributions obtained by simulation. The practical utility of this approach is demonstrated using 2D images of sorghum roots of different genetic backgrounds and grown in different environments.

Malaria is a leading cause of death in many low-income countries despite being preventable, treatable and curable. One of the major roadblocks to malaria elimination is the emergence and spread of antimalarial drug resistance, which evolves when malaria parasites are exposed to a drug for prolonged periods. In this talk, I will introduce several statistical and mathematical models for monitoring the emergence and spread of antimalarial drug resistance. Results will be presented from a Bayesian geostatistical model that have generated spatio-temporal predictions of resistance based on prevalence data available only at discrete study locations and times. In this way, the model output provides insight into the spatiotemporal spread of resistance that the discrete data points alone cannot provide. I will discuss how the results of these models have been used to update public health policy.

The first response of epithelial cells to local wounds is a dramatic increase in cytosolic calcium. This increase occurs quickly – calcium floods into damaged cells within 0.1 s, moves into adjacent cells over ~20 s, and appears in a much larger set of surrounding cells via a delayed second expansion over 40-300 s – but calcium is nonetheless a reporter: cells must detect wounds even earlier. Using the calcium response as a proxy for wound detection, we have identified an upstream G-protein-coupled-receptor (GPCR) signaling pathway, including the receptor and its chemokine ligand. We present experimental and computational evidence that multiple proteases released during cell lysis/wounding serve as the instructive signal, proteolytically liberating active ligand to diffuse to GPCRs on surrounding epithelial cells. Epithelial wounds are thus detected by the activation of a protease bait. We will discuss the experimental evidence and a corresponding computational model developed to test the plausibility of these hypothesized mechanisms. The model includes calcium currents between each cell’s cytosol and its endoplasmic reticulum (ER), between cytosol and extracellular space, and between the cytosol of neighboring cells. These calcium currents are initiated in the model by cavitation-induced microtears in the plasma membranes of cells near the wound (initial influx), by flow through gap junctions into adjacent cells (first expansion), and by the activation of GPCRs via a proteolytically activated diffusible ligand (second expansion). We will discuss how the model matches experimental observations and makes experimentally testable predictions.

Supported by NIH Grant 1R01GM130130.

We assess Ontario’s reopening plans, taking into account the healthcare system capacity and uncertainties in contact rates during different reopening phases. Using stochastic programming and a disease transmission model, we find the optimal timing for each reopening phase that maximizes the relaxation of social contacts under uncertainties, while not overwhelming the health system capacity by an expected arrival time of a SARS-CoV-2 vaccine/drug.

* Written with Michael Chen and LIAM De-escalation Group

A panel session was heard after the morning session of the third day of this conference. The panelists were the speakers from the 4 preceeding talks.

1. The immune response to SARS-CoV-2: Friend or Foe? - Penelope Morel
2. Modelling the systemic and tissue-level immune response to SARS-CoV-2 - Adrianne Jenner
3. Models for immune system interaction and evolution - Jane Heffernan
4. A Quantitative Systems Pharmacology Model of the Immune Response to SARS-COV-2 - Wei Dai, Rohit Rao