CDEV Subgroup Contributed Talks

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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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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Somdatta Sinha

Indian Institute of Science Education Research

"using networks for modelling three-dimensional structures of proteins"

Proteins are macromolecules in the cell performing most of the metabolic processes. The protein is made up of a linear chain of amino-acids (primary structure) synthesized, through transcription and translation of the corresponding gene/DNA sequence inside the cell. The functional protein is a three-dimensional structure that is formed due to spontaneous or assisted folding of the linear chain decided by the physicochemical forces exerted due to the size, charge and chemical nature of the amino acids. The 3D structure essentially determines the function of the protein - known as the 'Structure-Function paradigm' in molecular biophysics. We have modelled the 3-dimensional structure of proteins using the network/graph theory, where the amino acids are the nodes, and links are the physicochemical forces that hold any two amino acids together. I will show how the network approach can clearly explain the large functional differences in proteins and their mutants, having insignificant structural variations, not easily identifiable using standard structural biology methods, and thereby questioning the universality of the 'Structure-Function paradigm'.

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Nathan Smyers

University of North Carolina at Chapel Hill

"From Data to Dynamics: Uncovering Cell Signaling Networks with Physics-Informed Machine Learning"

Cell signaling is governed by complex networks of biochemical interactions. These networks are critical for a wide range of cellular functions, including detecting environmental changes and cellular motility. Modeling these processes with reaction-diffusion equations (RDEs) requires prior knowledge of protein-protein interactions for constructing the underlying network. The complex nature of signaling pathways means many relevant interactions may be unknown. To address this challenge, we developed a deep learning-based method to infer reaction networks from data. By integrating a physics-informed neural network (PINN) with a neural network for symbolic regression, this method learns interpretable RDE models from spatiotemporal data, effectively learning the biochemical reactions driving dynamics. To develop and validate our approach, we applied it to data generated from a model of cell polarity establishment. This approach has the potential to overcome limitations from incomplete knowledge of protein-protein interactions, serving as a powerful tool for uncovering how cells regulate complex behaviors.

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Anna Nelson

University of New Mexico

"Modeling mechanisms of microtubule dynamics and polarity in neurons"

The stability and polarity of the microtubule cytoskeleton is required for long-range, sustained transport within neuronal cellsl. In particular, the healthy microtubule cytoskeleton is comprised of tubulin protein and is stable with a particular orientation. However, when injured, these microtubules are dynamic, rearrange their orientation, and the appearance of microtubules is upregulated. It is unknown what mechanisms are involved in this balance between dynamic rearrangement and sustained function. Using a stochastic mathematical model that incorporates experimental data, we seek to understand how nucleation can impact microtubule dynamics in dendrites of fruit fly neurons. In the stochastic model, we assume two mechanisms limit microtubule growth: limited tubulin availability and the dependence of shrinking events on microtubule length. To better understand our stochastic model, we develop a partial differential equation (PDE) model that describes microtubule growth and nucleation dynamics, and we compare analytical results to results from the complex stochastic model. Insights from these models can then be used to understand what mechanisms are used organize into polarized structures in neurons, and how microtubule dynamics, like nucleation, may impact cargo localization post-injury.

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Dietmar Oelz

The University of Queensland

"Mechanochemical pattern formation in Hydra"

Tissue morphogenesis involves the self-organized creation of patterns and shapes. In many cases details of underlying mechanisms are elusive, yet an increasing amount of experimental data suggests that chemical morphogens and mechanical processes are strongly coupled. Here, we develop and simulate a minimal model for the emergence of asymmetry in aggregates of the Hydra polyp based on mechanochemical coupling of surface stiffness and a morphogen concentration. We contrast this model with the classical morphogen patterning mechanisms based on Turing type reaction diffusion systems. In analogy to this classical mechnism, we carry out the stability analysis of the lower dimensional toy model and identify minimal conditions for symmetry breaking. Our results suggest that mechanochemical pattern formation underlies symmetry breaking in Hydra.

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