Mathematical Biology

Kac goes to work: Stochastic processes as probes of the architecture of plant root systems

Speaker: 
David Schneider
Date: 
Fri, Jan 29, 2021
Location: 
Zoom
Conference: 
PIHOT kick-off event
CRG: 
pihot
Abstract: 

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.

Class: 

From 1918 to 2020: Analyzing the past and forecasting the Future

Speaker: 
David Earn
Jonathan Dushoff
Date: 
Wed, Jul 8, 2020
Location: 
Zoom
PIMS, University of British Columbia
McMaster University
Conference: 
Mathematical Biology Seminar
CRG: 
Abstract: 

Comparisons are constantly being made between the 1918 influenza pandemic and the present COVID-19 pandemic. We will discuss our previous work on influenza pandemics, and the tools we have used to understand the temporal patterns of those outbreaks. Applying similar tools to the COVID-19 pandemic is easier in some respects and harder in others. We will describe our current approach to modelling the spread of COVID-19, and some of the challenges and limitations of epidemic forecasting.

Class: 

Mathematical modelling of the emergence and spread of antimalarial drug resistance

Speaker: 
Jennifer Flegg
Date: 
Wed, Jul 29, 2020
Location: 
Zoom
Conference: 
Mathematical Biology Seminar
CRG: 
Abstract: 

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.

Class: 

Micro-Pharmacology: Recognizing and Overcoming the Tissue Barriers to Drug Delivery

Speaker: 
Kasia Rejniak
Date: 
Wed, Jul 22, 2020
Location: 
Zoom
Conference: 
Mathematical Biology Seminar
Abstract: 

Systemic chemotherapy is one of the main anticancer treatments used for most kinds of clinically diagnosed tumors. However, the efficacy of these drugs can be hampered by the physical attributes of the tumor tissue, such as tortuous vasculature, dense and fibrous extracellular matrix, irregular cellular architecture, metabolic gradients, and non-uniform expression of the cell membrane receptors. This can impede the transport of therapeutic agents to tumor cells in quantities sufficient to exert the desired effect. In addition, tumor microenvironments undergo dynamic spatio-temporal changes during treatment, which can also obstruct the observed drug efficacy. To examine ways to improve drug delivery on a cell-to-tissue scale (single-cell pharmacology), we developed the microscale pharmacokinetics/pharmacodynamics modeling framework “microPKPD”. I will present how this framework can be used to design optimal schedules for various treatments and to investigate the development of drug-induced resistance.

Class: 

Something's wrong in the (cellular) neighborhood: Mechanisms of epithelial wound detection

Speaker: 
Shane Hutson
Date: 
Wed, Jul 15, 2020
Location: 
Zoom
Conference: 
Mathematical Biology Seminar
CRG: 
Abstract: 

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.

Class: 

Mathematical model, analysis and simulations of the COVID-19 pandemic with variable infection rate: Application to South Korea

Speaker: 
Meir Shillor
Date: 
Wed, Jun 24, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
CRG: 
Abstract: 

The talk describes a substantial extension of the Middle East Respiratory Syndrome (MERS) model constructed, analyzed and simulated in Al-Asuoad et. al. BIOMATH 5 (2016)1, Al-Asuoad, Oakland University Dissertation (2017), and Al-Asuoad and Shillor, BIOMATH 7(1)(2018)2 to the case of the current COVID-19 Respiratory Syndrome pandemic that is sweeping the globe. It is caused by the new SARS-CoV-2 coronavirus that has been identified in December 2019 and since then outbreaks have been reported in all parts of the world. To help predict the dynamics and possible controls of the pandemic we developed a mathematical model for the pandemic. The model has a compartmental structure similar but more complex to the SARS and MERS models. It is a coupled system of nonlinear ordinary differential equations (ODEs) and a differential inclusion for the contact rate parameter. The talk will describe the model in detail, mention some of its analysis, and describe our computer simulations of the pandemic in South Korea. The main modeling novelties are in taking into account the shelter-in-place directives, the rates at which the populations obey them and the observed changes in the infectiveness of ‘contact number’ of the SARS-CoV-2 virus. The model predictions are fitted to some of the data from the outbreak in South Korea. Since the DFE (in South Korea) is found to be asymptotically stable, the pandemic will eventually die out (as long as some control measures remain in place). And, indeed, the model simulations show that the COVID-19 will in the near future be contained. However, the containment time and the severity of the outbreak depend crucially on the contact coefficients and the isolation or shelter-in-place rate constant. The simulations show that when randomness is added to the model coefficients the model captures the pandemic dynamics very well. Finally, the model highlights the importance of isolation of infected individuals and may be used to assess other control measures. It is general and will be used to analyze outbreaks in other parts of the world.

*with Aycil Cesmelioglu and Anna M. Spagnuolo

1 http://dx.doi.org /10.11145/j.biomath.2016.12.141
2 http://dx.doi.org/10.11145/j.biomath.2018.02.277

Class: 

Scenario tree and adaptive decision making on optimal type and timing for intervention and social-economic activity changes

Speaker: 
MIchael Chen
Kyeongah Nah
Date: 
Wed, Jun 24, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
CRG: 
Abstract: 

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

Class: 

Law of mass action and saturation in SIR model with applications to coronavirus

Speaker: 
Theodore Kolokolnikov
Date: 
Wed, Jun 24, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
CRG: 
Abstract: 

It is common in SIR models to assume that the infection rate is proportional to the product S*I of susceptible and infected individuals. This form is motivated by the law of mass action from chemistry. While this assumption works at the onset of the outbreak, it needs to be modified at higher rates such as seen currently in much of the world (as of June 2020). We propose a physics-based model which leads to a simple saturation formula based on first principles incorporating the spread radius and population density. We then apply this modified SIR model to coronavirus and show that it fits much better than the ``classical'' law of mass action.

Class: 

CAIMS - PIMS Coronavirus Modelling Conference - Panel

Speaker: 
Penelope Morel
Adrianne Jenner
Jane Heffernan
Wei Dai
Rohit Rao
Date: 
Wed, Jun 24, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
Abstract: 

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
Class: 

A Quantitative Systems Pharmacology Model of the Immune Response to SARS-COV-2

Speaker: 
Wei Dai
Rohit Rao
Date: 
Wed, Jun 24, 2020
Location: 
Zoom
Conference: 
CAIMS - PIMS Coronavirus Modelling Conference
CRG: 
Abstract: 

Rapid development of a QSP model to support novel COVID-19 therapies. We intend to publish this model quickly to encourage community feedback. The simulated dynamics of immune response are modeled by describing viral activation of innate and adaptive immune processes involving both pro-inflammatory mediators regulating viral clearance and cell damage (e.g. neutrophils and cytotoxic lymphocytes) as well as counter-regulatory immune suppressive mediators (e.g. Treg cells and IL-10).

Class: 

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