Mathematical Biology

The impact of social, economic, environmental factors and public health measures on the dynamics of COVID-19

Speaker: 
Jude Kong
Date: 
2021
Location: 
Zoom
Online
PIMS, University of British Columbia
Conference: 
Mathematical Biology Seminar
CRG: 
Abstract: 

The COVID-19 pandemic has passed its initial peak in most countries in the world, making it ripe to assess whether the basic reproduction number (R0) is different across countries and what demographic, social, and environmental factors other than interventions characterize vulnerability to the virus. In this talk, I will show the association (linear and non-linear) between COVID-19 R0 across countries and 17 demographic, social and environmental variables obtained using a generalized additive model. Moreover, I will present a mathematical model of COVID-19 that we designed and used to explore the effects of adopting various vaccination and relaxation strategies on the COVID-19 epidemiological long-term projections in Ontario. Our findings are able to provide public health bodies with important insights on the effect of adopting various mitigation strategies, thereby guiding them in the decision-making process.

Class: 

Stochastic Organization in the Mitotic Spindle

Speaker: 
Christopher Miles
Date: 
2021
Location: 
Zoom
Online
PIMS, University of British Columbia
Conference: 
Mathematical Biology Seminar
CRG: 
Abstract: 

For cells to divide, they must undergo mitosis: the process of spatially organizing their copied DNA (chromosomes) to precise locations in the cell. This procedure is carried out by stochastic components that manage to accomplish the task with astonishing speed and accuracy. New advances from our collaborators in the New York Dept of Health provide 3D spatial trajectories of every chromosome in a cell during mitosis. Can these trajectories tell us anything about the mechanisms driving them? The structure and context of this cutting-edge data makes utilizing classical tools from data science or particle tracking challenging. I will discuss my progress with Alex Mogilner on developing analysis for this data and mathematical modeling of emergent phenomena.

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Optimal curvature in long-range cell-cell communication

Speaker: 
Jun Allard
Date: 
2021
Location: 
Zoom
Online
PIMS, University of British Columbia
Conference: 
Mathematical Biology Seminar
CRG: 
Abstract: 

Cells in tissue can communicate short-range via direct contact, and long-range via diffusive signals. In addition, another class of cell-cell communication is by long, thin cellular protrusions that are ~100 microns in length and ~100 nanometers in width. These so-called non-canonical protrusions include cytonemes, nanotubes, and airinemes. But, before establishing communication, they must find their target cell. Here we demonstrate airinemes in zebrafish are consistent with a finite persistent random walk model. We study this model by stochastic simulation, and by numerically solving the survival probability equation using Strang splitting. The probability of contacting the target cell is maximized for a balance between ballistic search (straight) and diffusive (highly curved, random) search. We find that the curvature of airinemes in zebrafish, extracted from live cell microscopy, is approximately the same value as the optimum in the simple persistent random walk model. We also explore the ability of the target cell to infer direction of the airineme’s source, finding the experimentally observed parameters to be at a Pareto optimum balancing directional sensing with contact initiation.

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Cell symmetry breaking for movement through a mechanochemical mechanism

Speaker: 
Calina Copos
Date: 
2021
Location: 
Zoom
Online
PIMS, University of British Columbia
Conference: 
Mathematical Biology Seminar
CRG: 
Abstract: 

To initiate movement, cells need to form a well-defined "front" and "rear" through the process of cellular polarization. Polarization is a crucial process involved in embryonic development and cell motility and it is not yet well understood. Mathematical models that have been developed to study the onset of polarization have explored either biochemical or mechanical pathways, yet few have proposed a combined mechano-chemical mechanism. However, experimental evidence suggests that most motile cells rely on both biochemical and mechanical components to break symmetry. I will describe a mechano-chemical mathematical model for emergent organization driven by both cytoskeletal dynamics and biochemical reactions. We have identified one of the simplest quantitative frameworks for a possible mechanism for spontaneous symmetry breaking for initiation of cell movement. The framework relies on local, linear coupling between minimal biochemical stochastic and mechanical deterministic systems; this coupling between mechanics and biochemistry has been speculated biologically, yet through our model, we demonstrate it is a necessary and sufficient condition for a cell to achieve a polarized state.

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Stochasticity in an ecological model of the microbiome influences the efficacy of simulated bacteriotherapies

Speaker: 
Eric Jones
Date: 
2021
Location: 
Zoom
Online
PIMS, Simon Fraser University
Conference: 
Emergent Research: The PIMS Postdoctoral Fellow Seminar
Abstract: 

We consider a stochastic bistable two-species generalized Lotka-Volterra model of the microbiome and use it as a testbed to analytically and numerically explore the role of direct (e.g., fecal microbiota transplantation) and indirect (e.g., changes in diet) bacteriotherapies. Two types of noise are included in this model, representing the immigration of bacteria into and within the gut (additive noise) and variations in growth rate associated with the spatially inhomogeneous distribution of resources (multiplicative noise). The efficacy of a bacteriotherapy is determined by comparing the mean first-passage times (the average time required for the system to transition from one basin of attraction to the other) with and without the intervention. Concepts from transition path theory are used to investigate how the role of noise affects these bacteriotherapies.

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Feedback onto cellular polarization from paxillin, implications for migrating cells

Speaker: 
Laurent MacKay
Date: 
2021
Location: 
Zoom
Online
PIMS, University of British Columbia
Conference: 
Mathematical Biology Seminar
CRG: 
Abstract: 

Cellular polarization plays a critical during cellular differentiation, development, and cellular migration through the establishment of a long-lived cell-front and cell-rear. Although mechanisms of polarization vary across cells types, some common biochemical players have emerged, namely the RhoGTPases Rac and Rho. The low diffusion coefficient of the active form of these molecules combined with their mutual inhibitory interaction dynamics have led to a prototypical pattern-formation system that can polarizes cell through a non-Turing pattern formation mechanism termed wave-pinning. We investigate the effects of paxillin, a master regulator of adhesion dynamics, on the Rac-Rho system through a positive feedback loop that amplifies Rac activation. We find that paxillin feedback onto the Rac-Rho system produces cells that (i) self-polarize in the absence of any input signal (i.e., paxllin feedback causes a Turing instability) and (ii) become arrested due to the development of multiple protrusive regions. The former effect is a positive finding that can be related to certain cell-types, while the latter outcome is likely an artefact of the model. In order to minimize the effects of this artefact and produce cells that can both self-polarize as well as migrate for extended periods of time, we revisit some of model's parameter values and use lessons from previous models of polarization. This approach allows us to draw conclusions about the biophysical properties and spatiotemporal dynamics of molecular systems required for autonomous decision making during cellular migration.

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Extrinsic and intrinsic controls of cortical flow regulate C. elegans embryogenesis

Speaker: 
Kenji Sugioka
Date: 
2021
Location: 
Zoom
Online
PIMS, University of British Columbia
Conference: 
Mathematical Biology Seminar
CRG: 
Abstract: 

Cell division is a vital mechanism for cell proliferation, but it often breaks its symmetry during animal development. Symmetry-breaking of cell division, such as the orientation of the cell division axis and asymmetry of daughter cell sizes, regulates morphogenesis and cell fate decision during embryogenesis, organogenesis, and stem cell division in a range of organisms. Despite its significance in development and disease, the mechanisms of symmetry-breaking of cell division remain unclear. Previous studies heavily focused on the mechanism of symmetry-breaking at metaphase of mitosis, wherein a localized microtubule-motor protein activity pulls the mitotic spindle. Recent studies found that cortical flow, the collective migration of the cell surface actin-myosin network, plays an independent role in the symmetry-breaking of cell division after anaphase. Using nematode C. elegans embryos, we identified extrinsic and intrinsic cues that pattern cortical flow during early embryogenesis. Each cue specifies distinct cellular arrangements and is involved in a critical developmental event such as the establishment of the left-right body axis, the dorsal-ventral body axis, and the formation of endoderm. Our research started to uncover the regulatory mechanisms underlying the cortical flow patterning during early embryogenesis.

Class: 

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

Speaker: 
David Schneider
Date: 
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.

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

Speaker: 
David Earn
Jonathan Dushoff
Date: 
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.

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Mathematical modelling of the emergence and spread of antimalarial drug resistance

Speaker: 
Jennifer Flegg
Date: 
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.

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