CDEV-01 Contributed Talks

Chongming Li

Queen's University Department of Mathematics and Statistics

"Well-Posedness and Stability Analysis of a PDE-ODE Model for the Evolution of Bacterial Persisters"

Most antibiotics kill bacteria by disrupting cell wall formation during mitosis. Bacterial persisters are individuals within a population that avoid this fate by not replicating. We use a parabolic PDE to model the phenotypic switch between normal, active bacteria and persisters along with a nonlocal birth-jump process that captures epigenetic inheritance. In addition, we relate bacterial population development to resource dynamics in order to depict a more realistic bacterial growth limit. Mathematically, the model consists of a non-local PDE coupled to an ODE. We prove the well-posedness of the model using semi-group theory and the Banach fixed point theorem. We then examine the evolutionarily stable strategies of persister cells by conducting a global invasion analysis with an appropriately chosen Lyapunov functional.

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Neda Khodabakhsh Joniani

University of Sydney

"A Voronoi Cell-Based model for Corneal epithelial cells"

The cornea represents the outermost transparent layer of the eye and is structured in multiple layers. The corneal epithelium, which forms the exterior surface of the cornea, is distinct from many other epithelial tissues in that it consists of 5 to 7 layers, rather than a single layer. This stratification process involves the upward movement of cells from the basal layer to the upper layers, a mechanism known as cell delamination. Additionally, the integrity of the corneal epithelium is maintained through the migration of new basal cells from the periphery toward the centre of the cornea. Despite its crucial role in maintaining corneal function, the regulatory mechanisms governing this process, as well as how it adapts to cell loss during wound healing, remain poorly understood. Our research aims to explore the regulation of corneal cell behavior through the use of a Voronoi cell-based model, which links local cellular interactions to the emergent dynamics observed in the stratified epithelium.

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Shikun Nie

UBC

"Estimating Rate Parameters in Super-Resolution Imaging via Hidden Continuous Markov Chains with Discretized Emissions"

In this talk, I will illustrate how to model the dynamics of the fluorophores used in single-molecule localization microscopy (SMLM) as a hidden Markov chain with discretized emissions. I will generalize the proposed models in literature into a simple framework model. With the 3-state model as a particular example of our general formulation, I will show the process to obtain the transmission matrix by constructing a system of linear inhomogeneous transport partial differential equations (PDEs), which is solved by repeated Laplace-Inverse Laplace transforms. To demonstrate the usefulness of the transmission matrix, we designed two simple algorithms to solve the inference problem of the transition rates. In conclusion, the general formation is widely applicable to various techniques in SMLM, representative of the SMLM camera and adaptable to solve other active research problems such as molecule counting problems.

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Holly Huber

University of Southern California

"Multiscale Probabilistic Modeling - A Bayesian Approach to Augment Mechanistic Models of Cell Signaling with Machine-Learning Predictions of Binding Affinity"

Recently, the Nobel Prize winning machine learning (ML) model, AlphaFold, expanded its protein structure prediction capabilities from monomers to multimers with AlphaFold3. Here, we investigate this expanded utility in the novel context of mechanistic models of cell signaling. These models describe cell signaling events, such as binding, amongst a network of molecules, mostly proteins, and have been applied to answer both clinical and fundamental biology questions. For example, cell signaling models have been used to propose improvements to CAR-T cell therapies and to elucidate cellular ‘decision making’. Use of these models is oftentimes limited by a sparsity of data for parameterization. Thus, in this work, we introduce a Bayesian framework that incorporates information about protein structure to guide parameter inference for mechanistic models. Rather than searching all plausible parameter values, we can refine our search by considering information that is specific to the proteins involved in the signaling event. Excitingly, we find augmenting mechanistic models of signaling to be uniquely compatible with established ML models. We test our approach on two signaling models. In both cases, our approach improves parameter estimates—however, these improvements do not significantly change prediction performance on test data for either model. We find that this is due to a lack of sensitivity between the informed parameters and the test outputs. In contrast, when we examine an output that is sensitive to the changed parameters, we see a clear change in the predicted dynamics. We note that our proposed approach is limited to parameters of reversible, bimolecular binding reactions. Yet, excitingly, mechanistic models of cell signaling are often comprised of such reactions, ensuring the relatively wide applicability of our inference approach in this context.

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