Mathematical Biology

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: 

High-Order Accuracy Computation of Coupling Functions for Strongly Coupled Oscillators

Speaker: 
Youngmin Park
Date: 
Wed, Oct 13, 2021
Location: 
PIMS, University of Manitoba
Zoom
Online
Conference: 
Emergent Research: The PIMS Postdoctoral Fellow Seminar
Abstract: 

We develop a general framework for identifying phase reduced equations for finite populations of coupled oscillators that is valid far beyond the weak coupling approximation. This strategy represents a general extension of the theory from [Wilson and Ermentrout, Phys. Rev. Lett 123, 164101 (2019)] and yields coupling functions that are valid to higher-order accuracy in the coupling strength for arbitrary types of coupling (e.g., diffusive, gap-junction, chemical synaptic). These coupling functions can be used to understand the behavior of potentially high-dimensional, nonlinear oscillators in terms of their phase differences. The proposed formulation accurately replicates nonlinear bifurcations that emerge as the coupling strength increases and is valid in regimes well beyond those that can be considered using classic weak coupling assumptions. We demonstrate the performance of our approach through two examples. First, we use diffusively coupled complex Ginzburg-Landau (CGL) model and demonstrate that our theory accurately predicts bifurcations far beyond the range of existing coupling theory. Second, we use a realistic conductance-based model of a thalamic neuron and show that our theory correctly predicts asymptotic phase differences for non-weak synaptic coupling. In both examples, our theory accurately captures model behaviors that weak coupling theories can not.

Speaker Biography

Youngmin Park, Ph.D., is currently a PIMS Postdoc at the University of Manitoba under the supervision of Prof. Stéphanie Portet. He received his PhD in Mathematics from the University of Pittsburgh in 2018, where he applied dynamical systems methods to problems in neuroscience. His first postdoc involved auditory neuroscience research at the University of Pennsylvania in the Department of Otorhinolaryngology, before moving on to his next postdoc researching molecular motor dynamics in the Department of Mathematics at Brandeis University. He is now at Manitoba, continuing to apply dynamical systems methods to biological questions related to molecular motor transport and neural oscillators.

Class: 

Footnotes to Turing (1952): Some Modern Challenges in Pattern Formation

Speaker: 
Andrew Krause
Date: 
Wed, Oct 6, 2021
Location: 
PIMS, University of British Columbia
Online
Zoom
Conference: 
Mathematical Biology Seminar
Abstract: 

Motivated by recent work with biologists, I will showcase some mathematical results on Turing instabilities in complex domains. This is scientifically related to understanding developmental tuning in a variety of settings such as mouse whiskers, human fingerprints, bat teeth, and more generally pattern formation on multiple scales and evolving domains. Some of these problems are natural extensions of classical reaction-diffusion models, amenable to standard linear stability analysis, whereas others require the development of new tools and approaches. These approaches also help close the vast gap between the simple theory of diffusion-driven pattern formation, and the messy reality of biological development, though there is still much work to be done in validating even complex theories against the rich pattern dynamics observed in nature. I will emphasize throughout the role that Turing's 1952 paper had in these developments, and how much of our modern progress (and difficulties) were predicted in this paper. I will close by discussing a range of open questions, many of which fall well beyond the extensions I will discuss, but at least some of which were known to Turing.

Class: 

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