Mathematical Cell Biology Symposium

Schedule

Part I: Invited talks by visitors (25 min + 5 min Q)

10:30 Coffee, tea & cookies; (intro’s and tech set-up)

11:00 Carsten Beta, (U Potsdam) Composite active matter – how motile cells move passive micro-cargo

11: 30 Arik Yochelis (Ben Gurion U) Versatile Patterns in the Actin Cortex of Motile Cells

12:00-12:10 Bio-Break

II: Participant talks (15 min + 5 min Q’s)

12:10-12:30 Eric Cytrynbaum (UBC): Mechanisms that determine dentition patterns in the gecko

12:30 Pizza lunch arrives.. Break for self-service

1:10 – 1:30 Anotida Madzvamuse (UBC): Developing mechanobiochemical models for 3D cell migration.

1:30-1:45 Bio-Break

Part III: Short talks by students (~10 min each+5 min Q’s)

1:45 Jack Hughes: PDE bifurcation analysis of actin waves models (PhD student with L Keshet)

2:00 Katie Faulkner: Modeling the onset of diabetes (PhD student with E Cytrynbaum)

2:15 Tim Tian: Dynamics of plant cell microtubules (PhD student with E Cytrynbaum)

2:30 Liam Yih: Virus capture by cells (PhD student with D Coombs)

2:45 Nitya Gadhiwala, Sharvaj Kubal, Elias Ventre [alphabetical order] (graduate students and PDF with Geoffrey Schiebinger)

3:00-3:15 End of formal program

Abstracts

Carsten Beta: Composite active matter – how motile cells move passive micro-cargo

Biohybrid micro-transport ­– the movement of micron-sized cargo particles by motile cells – is one of the most prominent applications in the emerging field of biohybrid systems. While many details of cellular locomotion have been studied in detail, only little is known about how the motility of cells is affected by the presence of passive micron-sized objects. Here, we demonstrate that motile amoeboid cells can act as efficient and versatile transport agents. Their transport properties result from the mechanical interactions with the passive cargo particle and reveal an optimal cargo size that enhances the locomotion of the load-carrying cells, even exceeding their motility in the absence of cargo. The experimental findings are rationalized in terms of an active particle model that describes the observed cell-cargo dynamics and enables us to derive the long-time diffusive transport of amoeboid microcarriers. As amoeboid locomotion is commonly observed for mammalian cells such as leukocytes, we expect that our results will provide a blueprint to study the transport performance of other medically relevant cell types, while at the same time stimulating more fundamental work towards an understanding of this type of composite active matter systems.

Arik Yochelis: Versatile Patterns in the Actin Cortex of Motile Cells

Self-organized patterns in the actin cytoskeleton are essential for eukaryotic cellular life. They are the building blocks of many functional structures that often operate simultaneously to facilitate, for example, nutrient uptake and movement of cells. Firstly, I will overview the challenges of intracellular actin waves and then show how using a mass-conserved reaction-diffusion model and bifurcation analysis, it is possible to demonstrate distinct coexisting actin wave patterns in the cortex of living cells. 

Selected references: [1] Beta, Gov, & Yochelis (2020) Why a large scale mode can be essential for understanding intracellular actin waves, Cells 9, 1533. [2] Yochelis, Flemming, & Beta (2022) Versatile patterns in the actin cortex of motile cells: Self-organized pulses can coexist with macropinocytic ring-shaped waves, Physical Review Letters 129, 088101.

Eric Cytrynbaum (UBC): How the lizard gets its smile: mechanisms that determine dentition patterns in the gecko

For over a century, the development and replacement of reptile teeth has been of interest originally for its value in comparative anatomy and evolutionary biology due to the prevalence of teeth in the fossil record and more recently as a model system for understanding spatiotemporal patterning in developmental biology. In collaboration with the Richman Lab (Joy Richman, UBC Dentistry), we are using the Leopard Gecko as a model organism to address the question of the mechanisms underlying the regular and long-lasting spatiotemporal patterns of tooth replacement seen in many polyphyodonts. In this talk, I will describe the data and our implementation and analysis of several mechanisms/models that have been proposed (but not implemented in mathematical form) in the past to explain the observations. Finding shortcomings in these models, we propose a new model, the Phase Inhibition Model, which does better at explaining the data. I will conclude by discussing ideas for how this model might be integrated with existing reaction-diffusion models of early development of dentition in reptiles.

Anotida Madzvamuse: Developing mechanobiochemical models for 3D cell migration

In this talk, I will review mechanobiochemical models for single cell migration starting with the work by Lewis and Murray in 1991. Recent advances include generalisations of this work to include more biophysical properties that drive single cell migration and these include modelling stress tensors associated with cell polarisation, cell contraction, volume constraint, hydrostatic pressure driven by actomyosin concentrations and the formulation of systems of reaction-diffusion equations to describe actomyosin force generation. The resulting models are coupled viscoelastic continuum mechanics whose displacements (also velocity) are driven by the molecular species that are modelled by reaction-diffusion systems. The complex nonlinear coupled systems of partial differential equations are then solved by use of bulk-surface finite elements on 2- and 3-D deforming domains. I will conclude by illustrating different scenarios of cell polarisation and migration given appropriate choices of model parameters.

Jack Hughes: A student’s perspective on generating bifurcation diagrams for mass-conserved reaction-diffusion systems (PDE bifurcation analysis)

Here I will discuss a student’s perspective on generating the bifurcation diagram given in Prof Arik Yochelis' presentation. This will include a discussion on why the problem is difficult and how I overcame the challenges required to produce the diagram. I will discuss five different solution branches on the bifurcation diagram, including spatially homogeneous solutions, travelling waves and fronts, excitable pulses, and stationary solutions. I will also discuss the challenges faced in computing the stability of these solutions, and the results I found.

Katie Faukner: Modeling Type II Diabetes Progression

As an individual moves from healthy to pre-diabetic to diabetic, there are many physiological changes that occur, but it is not known which of these changes drive the progression to type II diabetes. In this talk I will describe a simple model for glucose regulation and how modeling can help determine which physiological changes are capable of pushing an individual from healthy to diseased. By framing this problem in terms of bifurcations, we can find models that create qualitative changes to the system that allow for movement between healthy and diseased states. We will examine a model that includes the toxicity of lipids in the pancreas, and find a bifurcation that describes the progression to diabetes type II.

Liam Yih: The Mechanisms of Influenza Movement on Cell Surfaces

Influenza A virus (IAV), one of the viruses responsible for the seasonal flu, has been shown in the past to move around on cell surfaces. It does this by utilising two of its primary receptors: hemagglutinin (HA) and neuraminidase (NA). HA functions by binding to sialic acid (SA) groups found on glycoproteins on cell surfaces while NA acts as a cleaver, cleaving sialic acid groups from glycoproteins. By taking advantage of a HA-NA binding-cleaving cycle, IAV can roll around on cell surfaces to reach its target destination. However, it has also been shown that IAV can move around on surfaces by simple thermal diffusion of glycoproteins. Here, I talk about the interactions between these two modes of movement and how their interplay will be investigated through the use of simulations. 

Tim Tian: Dynamics of Plant Cell Microtubules

The self-organization of ordered cortical microtubule arrays plays an important role in the development of plant cells. This is observed to emerge from a combination of various factors such as microtubule-microtubule interactions, nucleation, and localization of microtubule-associated proteins. Distilling this process into the interaction of one-dimensional bodies on the two-dimensional cortex, quantitative models have been proposed to emulate array formation. Modelling microtubules as thin elastic rods constrained on a surface, it has been found that microtubule shapes resulting from curvature minimization may differ significantly from the previously assumed geodesic paths. We implement this in an event-driven simulation, and based on some preliminary work, we find that this curvature mechanics provides a strong influence for directional alignment. This simulation provides the opportunity for further exploration into mechanical influences on array formation and their regulation through microtubule-associated proteins.

Nitya Gadhiwala, Sharvaj Kubal, Elias Ventre [alphabetical order], and Geoffrey Schiebinger: Improved single-cell data analysis using spatial transcriptomics and lineage tracing.

Measurement technologies like single-cell RNA sequencing, by allowing to obtain gene expression levels at the single cell level, have significantly improved the understanding of the mechanisms underlying cell differentiation over the last few decades. The recent advent of technologies providing datasets with a joint information between cells along with their expression levels should allow similar advances. In this talk, we focus on the analysis of two types of such data:

1) Spatial transcriptomics goes one step beyond single-cell RNA sequencing, yielding high-dimensional images of gene expression in a tissue, which offer the prospect of understanding cell signaling. As sequencing all RNA molecules over large spatial areas is prohibitively expensive, reducing the number of RNAs sequenced while controlling the resulting technical noise is crucial. For this sake, we have developed denoising algorithms based on low rank matrix recovery, that also leverage the spatial smoothness of gene expression images. Our method is backed by theoretical recovery guarantees, as well as tests on real data which suggest that it is possible to reduce the number of RNAs sequenced by more than 10-fold, without significantly increasing recovery error.

2) The recent development of CRISPR-based measurement methods allows to reconstruct the lineage tree of a population of cells together with their gene expression profiles. We show how a specific information contained in such tree allows to reconstruct the distribution of the underlying probabilistic process without branching, and then to extend a theory of trajectory inference, developed in the case of probabilistic Markov processes, to the case of branching processes with similar guarantees. 

The organizers are grateful to PIMS and to CAIMS for seed fund that supported this event, and for help with the logistics.