Mathematical Biology

Topological Data Analysis of Collective Behavior

Speaker: 
Dhananjay Bhaskar
Date: 
Wed, Sep 29, 2021
Location: 
PIMS, University of British Columbia
Online
Zoom
Conference: 
Mathematical Biology Seminar
Abstract: 

Active matter systems, ranging from liquid crystals to populations of cells and animals, exhibit complex collective behavior characterized by pattern formation and dynamic phase transitions. However, quantitative classification is challenging for heterogeneous populations of varying size, and typically requires manual supervision. In this talk, I will demonstrate that a combination of topological data analysis (TDA) and machine learning can uniquely identify the spatial arrangement of agents by keeping track of clusters, loops, and voids at multiple scales. To validate the approach, I will present 3 case studies: (1) data-driven modeling and analysis of epithelial-mesenchymal transition (EMT) in mammary epithelia, (2) unsupervised classification of cell sorting, and self-assembly patterns in co-cultures, and (3) parameter recovery from animal swarming trajectories.

Class: 

Sialic Acids in Membrane Organization and Receptor Function: Integrins and CD22

Speaker: 
Christopher Cairo
Date: 
Mon, Jun 28, 2021 to Tue, Jun 29, 2021
Location: 
Online
Conference: 
2021 Frontiers in Biophysics
Abstract: 

The plasma membrane contains a wide array of glycans and glycolipids, many of which are capped by sialic acids (also called neuraminic acid). As a result, sialic acids are front-line mediators of interactions between the extracellular surface and the external environment. Examples include host-pathogen interactions (e.g. influenza) and the recognition of host cells by leukocytes (white blood cells). Thus, the composition of sialosides in the membrane can influence receptor-receptor interactions critical to immunity and cellular function. Our group is investigating the influence of sialic acid on the function of adhesion and immune receptors through the development of tools that alter catabolism of membrane sialosides. The human neuraminidases (NEU) are a family of four isoenzymes (NEU1, NEU2, NEU3, and NEU4) which have a range of substrate preferences as well as cellular and tissue localization. Our group has developed a panel of selective inhibitors, many with nanomolar potency, are being used to investigate how degradation of sialosides influences the function of cellular receptors. We use fluorescence microscopy to measure the size of receptor clusters and lateral mobility of receptors. These biophysical methods provide critical insight into the influence of NEU activity on membrane receptor organization. We have examined the role of NEU enzymes on the function and organization of leukocyte adhesion receptors. We find that specific NEU enzymes can modulate integrin adhesion and affect leukocyte transmigration. In related work, we have examined the influence of synthetic glycoconjugates and inhibitors of NEU on the organization of the CD22 receptor of B cells. We propose that understanding the specific roles of NEU isoenzymes will identify new therapeutic strategies for autoimmunity, inflammation, and cancer.

Class: 

Nutations in Growing Plant Shoots: Endogenous and Exogenous Factors in the Presence of Elastic Deformations

Speaker: 
Daniele Agostinelli
Date: 
Mon, Jun 28, 2021 to Tue, Jun 29, 2021
Location: 
Online
Conference: 
2021 Frontiers in Biophysics
Abstract: 

Growing plant shoots exhibit circumnutations, namely, oscillations that draw three-dimensional trajectories, whose projections on the horizontal plane generate pendular, elliptical, or circular orbits. A large body of literature has followed the seminal work by Charles Darwin in 1880, but the nature of this phenomena is still uncertain and a long-lasting debate produced three main theories: the endogenous oscillator, the exogenous feedback oscillator, and the two-oscillator model. After briefly reviewing the three existing hypotheses, I will discuss a possible interpretation of these spontaneous oscillations as a Hopf-like bifurcation in a growing morphoelastic rod.

Class: 

Misfolding-Associated Exposure of Natively Buried Residues in Mutant SOD1 Facilitates Binding to TRAF6

Speaker: 
Pranav garg
Date: 
Mon, Jun 28, 2021 to Tue, Jun 29, 2021
Location: 
Online
Conference: 
2021 Frontiers in Biophysics
Abstract: 

Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disease primarily impacting motor neurons. Mutations in superoxide dismutase 1 (SOD1) are the second most common cause of familial ALS. Several of these mutations lead to misfolding or toxic gain of function in the SOD1 protein. Recently, we reported that misfolded SOD1 interacts with TNF receptor-associated factor 6 (TRAF6) in the SOD1-G93A rat model of ALS. Further, we showed in cultured cells that several mutant SOD1 proteins, but not wild type SOD1 protein, interact with TRAF6 via the MATH domain. Here, we sought to uncover the structural details of this interaction through molecular dynamics (MD) simulations of a dimeric model system, coarse grained using the AWSEM force field. We used direct MD simulations to identify buried residues, and predict binding poses by clustering frames from the trajectories. Metadynamics simulations were also used to deduce preferred binding regions on the protein surfaces from the potential of the mean force in orientation space. Well-folded SOD1 was found to bind TRAF6 via co-option of its native homodimer interface. However, if loops IV and VII of SOD1 were disordered, as typically occurs in the absence of stabilizing Zn2+ ion binding, these disordered loops now participated in novel interactions with TRAF6. On TRAF6, multiple interaction hot-spots were distributed around the equatorial region of the MATH domain beta barrel. Expression of TRAF6 variants with mutations in this region in cultured cells demonstrated that TRAF6 residue T475 facilitates interaction with different SOD1 mutants. These findings contribute to our understanding of the disease mechanism and uncover potential targets for the development of therapeutics.

Class: 

Cytoplasmic Streaming and the Swirling Instability of the Microtubule Cytoskeleton

Speaker: 
Raymond Goldstein
Date: 
Mon, Jun 28, 2021 to Tue, Jun 29, 2021
Location: 
Online
Conference: 
2021 Frontiers in Biophysics
Abstract: 

Cytoplasmic streaming is the persistent circulation of the fluid contents of large eukaryotic cells, driven by the action of molecular motors moving along cytoskeletal filaments, entraining fluid. Discovered in 1774 by Bonaventura Corti, it is now recognized as a common phenomenon in a very broad range of model organisms, from plants to flies and worms. This talk will discuss physical approaches to understanding this phenomenon through a combination of experiments (on aquatic plants, Drosophila, and other active matter systems), theory, and computation. A particular focus will be on streaming in the Drosophilaoocyte, for which I will describe a recently discovered "swirling instability" of the microtubule cytoskeleton.

Class: 

Nutations in Growing Plant Shoots: Endogenous and Exogenous Factors in the Presence of Elastic Deformations

Speaker: 
Daniele Agostinelli
Date: 
Wed, Aug 4, 2021
Location: 
Zoom
Online
Conference: 
Mathematical Biology Seminar
Abstract: 

Growing plant shoots exhibit circumnutations, namely, oscillations that draw three-dimensional trajectories, whose projections on the horizontal plane generate pendular, elliptical, or circular orbits. A large body of literature has followed the seminal work by Charles Darwin in 1880, but the nature of this phenomena is still uncertain and a long-lasting debate produced three main theories: the endogenous oscillator, the exogenous feedback oscillator, and the two-oscillator model. After briefly reviewing the three existing hypotheses, I will discuss a possible interpretation of these spontaneous oscillations as a Hopf-like bifurcation in a growing morphoelastic rod.

Class: 

Environmental Escape from the Prisoner's Dilemma

Speaker: 
Jaye Sudweeks
Date: 
Wed, Jul 28, 2021
Location: 
Zoom
Online
Conference: 
Mathematical Biology Seminar
Abstract: 

During reproduction, viruses manufacture products that diffuse within the host cell. Because a virus does not have exclusive access to its own gene products, coinfection of multiple viruses allows for strategies of cooperation and defection— cooperators produce large amounts of gene product while defectors produce less product but specialize in appropriating a larger share of the common pool. Experimental data shows that, under conditions where coinfection is common, bacteriophage $\Phi$6 becomes trapped in a Prisoner’s dilemma, with defectors spreading to fixation, causing lowered population fitness. However, these experiments did not allow for fluctuation in the density of the external viral population. Here, I’ll discuss a model formulated to see if environmental feedback can free $\Phi$6 from the Prisoner’s dilemma. I’ll also discuss the concept of the Effective Game, which incorporates the frequency and density of different viral types in the environment.

Class: 

Dynamic Self Organization and Microscale Fluid Properties of Nucleoplasm

Speaker: 
Jay Newby
Date: 
Wed, Jul 21, 2021
Location: 
Zoom
Online
Conference: 
Mathematical Biology Seminar
Abstract: 

The principal function of the nucleus is to facilitate storage, retrieval, and maintenance of the genetic information encoded into DNA and RNA sequences. A unique feature of nucleoplasm—the fluid of the nucleus—is that it contains chromatin (DNA) and RNA.

In contrast to other important biological polymer hydrogels, such as mucus and extracellular matrix, the nucleic acid polymers have a sequence. Recent experiments have shown that during the growth phase of the cell cycle, chromatin condenses in a sequence specific manner into regions within the nucleoplasm, possibly so that functionally related genes are grouped together spatially even though they might be far apart in terms of sequence distance.

At the same time, we are becoming increasingly aware of the role of liquid-liquid phase separation (LLPS) in cellular processes in the nucleus and the cytoplasm. Complex molecular interactions over a wide range of timescales can cause large biopolymers (RNA, protein, etc) to phase separate from the surrounding nucleoplasm into distinct biocondensates (spherical droplets in the simplest cases).

I will discuss recent work modelling the role of nuclear biocondensates in neurodegenerative disease and several ongoing projects related to
modelling and microscopy image analysis.

Class: 

Epidemic arrivals and Antibiotic Calenders

Speaker: 
Alastair Jamieson-Lane
Date: 
Wed, Jul 7, 2021
Location: 
Zoom
Online
PIMS, University of British Columbia
Conference: 
Mathematical Biology Seminar
Abstract: 

Here I give two tiny talks on some of my research from the past couple years. In the first half of the talk I re-examine some popular heuristics for epidemic "time of spread" through the world airline network, and use hitting times and branching processes to explore the mathematical underpinnings of these observations. In the second half of the talk, we zoom in to exploring how antibiotics spreads through a single hospital, the various models and their conflicting recommendations. Mostly just some straightforward dynamical systems, with the opportunity for some cute asymptotic arguments on the side.

Class: 

Dynamical inference for biological processes through the lens of optimal transport

Speaker: 
Stephen Zhang
Date: 
Wed, Jun 30, 2021
Location: 
Zoom
Online
Conference: 
Mathematical Biology Seminar
Abstract: 

Understanding how cells change their identity and behaviour over time in living systems is a key question in many fields of biology. Measurement of cell states is inherently destructive, and so the relationship of the current state of a cell to some future state, or ‘fate’, cannot be observed experimentally. Trajectory inference refers to the general problem of trying to estimate various aspects of the state-fate relationship. We discuss optimal transport as a useful analytical tool for trajectory inference, and we develop a mathematical framework for recovering trajectories in both non-equilibrium as well as equilibrium systems.

Class: 

Pages