Mathematical Biology

Adventures with Partial Identification in Studies of Marked Individuals

Speaker: 
Simon Bonner
Date: 
Thu, Mar 17, 2022
Location: 
PIMS, University of Victoria
Online
Zoom
Conference: 
PIMS-UVic Distinguished Colloquium
Abstract: 

Monitoring marked individuals is a common strategy in studies of wild animals (referred to as mark-recapture or capture-recapture experiments) and hard to track human populations (referred to as multi-list methods or multiple-systems estimation). A standard assumption of these techniques is that individuals can be identified uniquely and without error, but this can be violated in many ways. In some cases, it may not be possible to identify individuals uniquely because of the study design or the choice of marks. Other times, errors may occur so that individuals are incorrectly identified. I will discuss work with my collaborators over the past 10 years developing methods to account for problems that arise when are only individuals are only partially identified. I will present theoretical aspects of this research, including an introduction to the latent multinomial model and algebraic statistics, and also describe applications to studies of species ranging from the golden mantella (an endangered frog endemic to Madagascar measuring only 20 mm) to the whale shark (the largest know species of fish, measuring up to 19m).

Class: 

Directional sensing and signal integration by immune cells

Speaker: 
Sean Collins
Date: 
Wed, Mar 23, 2022
Location: 
Zoom
Online
Conference: 
Mathematical Biology Seminar
Abstract: 

Human neutrophils and other immune cells sense chemical gradients to navigate to sites of injury, infection, and inflammation in the body. Impressively, these cells can detect gradients that differ by as little as about 1% in concentration across the length of the cell. Abstract models suggest that they may do this by integrating opposing local positive and long-range negative signals generated by receptors. However, the molecular basis for signal processing remains unclear. To investigate models of sensing, we developed experimental tools to control receptors with light while measuring downstream signaling responses with spatial resolution in single cells. We are directly measuring responses to both local and cell-wide receptor activation to determine the wiring of signal processing. While we do not see evidence for long-range negative signals, we do see a subcellular context-dependence of signal transmission. We propose that signal transmission from receptors happens locally, but cell-wide polarity biases sensing to maintain persistent migration and achieve temporal averaging to promote directional accuracy.

Class: 

Feelling Fundamental Principles of Bacterial Cell Physiology using Long-Term Time-Lapse Atomic Force Microscopy

Speaker: 
Haig Alexander Eskandarian
Date: 
Wed, Mar 16, 2022
Location: 
PIMS, University of British Columbia
Zoom
Online
Conference: 
Mathematical Biology Seminar
Abstract: 

Exposure of bacteria to cidal stresses typically select for the emergence of stress-tolerant cells refractory to killing. Stress tolerance has historically been attributed to the regulation of discrete molecular mechanisms, including though not limited to regulating pro-drug activation or pumps abrogating antibiotic accumulation. However, fractions of mycobacterial mutants lacking these molecular mechanisms still maintain the capacity to broadly tolerate stresses. We have sought to understand the nature of stress tolerance through a largely overlooked axis of mycobacterial-environmental interactions, namely microbial biomechanics. We developed Long-Term Time-Lapse Atomic Force Microscopy (LTTL-AFM) to dynamically characterize nanoscale surface mechanical properties that are otherwise unobservable using other established advanced imaging modalities. LTTL-AFM has allowed us to revisit and redefine fundamental biophysical principles underlying critical bacterial cell processes targeted by a variety of cidal stresses and for which no molecular mechanisms have previously been described. I aim to highlighting the disruptive power of LTTL-AFM to revisit dogmas of fundamental cell processes like cell growth, division, and death. Our studies aim to uncover new molecular paradigms for how mycobacteria physically adapt to stress and provide expanded avenues for the development of novel treatments of microbial infections.

Class: 

Humans Make Things Messy

Speaker: 
Shelby M. Scott
Date: 
Wed, Feb 16, 2022
Location: 
PIMS, University of British Columbia
Zoom
Online
Conference: 
Mathematical Biology Seminar
Abstract: 

Models become notably more complex when stochasticity is introduced. One of the best ways to add frustrating amounts of randomness to your model: incorporate humans. In this talk, I discuss three different ways in which humans have made things messy in my mathematical models, statistical models, and data science work. Despite the fact that humans do, indeed, make things messy, they also make our models so much more realistic, interesting, and intriguing. So while humans make things messy, it is so worth it to bring them into your work.

Class: 

Asymptotic analysis of the concentration difference due to diffusive fluxes across narrow windows

Speaker: 
Frédéric Paquin-Lefebvre
Date: 
Wed, Feb 9, 2022
Location: 
PIMS, University of British Columbia
Zoom
Online
Conference: 
Mathematical Biology Seminar
Abstract: 

How far inside a domain does a flux of Brownian particles perturb a background concentration when particles can escape through a neighboring window? What motivates this question is the dynamics of ions entering and exiting nanoregions of excitable cells through ionic membrane channels. Here this is explored using a simple diffusion model consisting of the Laplace's equation in a domain whose boundary is everywhere reflective except for a collection of narrow circular windows, where either flux or absorbing boundary conditions are prescribed. We derive asymptotic formulas revealing the role of the influx amplitude, the diffusion properties, and the geometry, on the concentration difference. Lastly, a length scale to estimate how deep inside a domain a local diffusion current can spread is introduced. This is joint work with David Holcman at ENS.

Class: 

Emergence of diverse collective behaviors from local topological perception

Speaker: 
Jack Tisdell
Date: 
Fri, Dec 10, 2021
Location: 
PIMS, University of British Columbia
Zoom
Online
Conference: 
Mathematical Biology Seminar
Abstract: 

Modeling "social" interactions within a large population has proven to be a rich subject of study for a variety of scientific communities during the past few decades. Specifically, with the goal of predicting the macroscopic effects resulting from microscopic-scale endogenous as well as exogenous interactions, many emblematic models for the emergence of collective behaviors have been proposed. In this talk we present a dynamical model for generic crowds in which individual agents are aware of their local environment, i.e., neighboring agents and domain boundary features, and may seek static targets. Our model incorporates features common to many other "active matter'' models like collision avoidance, alignment among agents, and homing toward targets. However, it is novel in key respects: the model combines topological and metrical features in a natural manner based upon the local environment of the agent's Voronoi diagram. With only two parameters, it is shown to capture a wide range of collective behaviors that go beyond the more classical velocity consensus and group cohesion. The work presented here is joint with R. Choksi and J.C. Nave at McGill

Class: 

Single-molecule insights for DNA/RNA/protein interactions and drug discovery and development: the next level of resolution, for the next era of genetic medicines

Speaker: 
Sabrina Leslie
Date: 
Wed, Nov 3, 2021
Location: 
PIMS, University of British Columbia
Zoom
Online
Conference: 
Mathematical Biology Seminar
Abstract: 

Molecular interactions lie at the core of biochemistry and biology, and their understanding is crucial to the advancement of biotechnology, therapeutics, and diagnostics. Most existing tools make “ensemble” measurements and report a single result, typically averaged over millions of molecules or more. These measurements can miss rare events, averaging out the natural variations or sub-populations within biological samples, and consequently obscure insights into multi-step and multi-state reactions. The ability to make and connect robust and quantitative measurements on multiple scales - single molecules, cellular complexes, cells, tissues - is a critical unmet need. In this talk, I will introduce a general method called “CLiC” imaging to image molecular interactions one molecule at time with precision and control, and under cell-like conditions. CLiC works by mechanically confining molecules to the field of view in an optical microscope, isolating them in nanofabricated features, and eliminates the complexity and potential biases inherent to tethering molecules. By imaging the trajectories of many single molecules simultaneously and in a dynamic manner, CLiC allows us to investigate and discover the design rules and mechanisms which govern how therapeutic molecules or molecular probes interact with target sites on nucleic acids; and how molecular cargo is released inside cells from lipid nanoparticles. In this talk, I will discuss applications of our imaging platform to better understand DNA, RNA, protein interactions, as well as emerging classes of genetic medicines, gene editing and drug delivery systems. I will highlight current and potential future applications to connect our observations from the level of single molecule to single cells, and opportunities for collaboration as we set up our labs at UBC.

Class: 

The Tumor Growth Paradox

Speaker: 
Thomas Hillen
Date: 
Wed, Nov 10, 2021
Location: 
PIMS, University of Alberta
Zoom
Conference: 
Mathematical Biology Seminar
Abstract: 

The tumor invasion paradox relates to the artifact that a cancer that is exposed to increased cell death (for example through radiation), might spread and grow faster than before. The presence of cancer stem cells can convincingly explain this effect. In my talk I will use non-local and local reaction-diffusion type models to look at tumor growth and invasion speeds. We can show that in certain situations the invasion speed increases with increasing death rate - an invasion paradox (joint work with A. Shyntar and M. Rhodes).

Class: 

The Connection Between RDEs and PDEs

Speaker: 
Louigi Addario-Berry
Date: 
Thu, Oct 14, 2021
Location: 
PIMS, University of Victoria
Zoom
Online
Conference: 
PIMS-UVic Distinguished Lecture
Abstract: 

Recursive distributional equations (RDEs) are ubiquitous in probability. For example, the standard Gaussian distribution can be characterized as the unique fixed point of the following RDE

$$
X = (X_1 + X_2) / \sqrt{2}
$$

among the class of centered random variables with standard deviation of 1. (The equality in the equation is in distribution; the random variables and must all be identically distributed; and and must be independent.)

Recently, it has been discovered that the dynamics of certain recursive distributional equations can be solved using by using tools from numerical analysis, on the convergence of approximation schemes for PDEs. In particular, the framework for studying stability and convergence for viscosity solutions of nonlinear second order equations, due to Crandall-Lions, Barles-Souganidis, and others, can be used to prove distributional convergence for certain families of RDEs, which can be interpreted as tree- valued stochastic processes. I will survey some of these results, as well as the (current) limitations of the method, and our hope for further interplay between these two research areas.

Class: 

Programmable Human Organoids via Genetic Design and Engineering

Speaker: 
Mo Ebrahimkhani
Date: 
Wed, Oct 13, 2021
Location: 
PIMS, University of British Columbia
Zoom
Online
Conference: 
Mathematical Biology Seminar
Abstract: 

Synthetic biology offers bottom-up engineering strategies that intends to understand complex systems via design-build-test cycles. In development, gene regulatory networks emerge into collective cellular behaviors with multicellular forms and functions. Here, I will introduce a synthetic developmental biology approach for tissue engineering. It involves building developmental trajectories in stem cells via programmed gene circuits and network analysis. The outcome of our approach is decoding our own development and to create programmable organoids with both natural or artificial designs and augmented functions.

Class: 

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