Organized by: Tharana Yosprakob (University of Alberta)

1. Michael Hendzel University of Alberta
   "Nuclear Microenvironments and Intranuclear Transport"
There is a poorly-defined transition in the size-dependent transport properties of molecules in the nucleoplasm. The most studied molecules, proteins and protein complexes, are small enough to diffuse freely through the nucleoplasm. That is not true of larger molecules but the transition between these two states and the underlying reason is poorly understood. Of particular interest is pre-mRNA and mRNA, which are significantly larger than most protein/protein complexes and must be trafficked to the nuclear pore for export. We have been studying size-dependent transport of small molecules, RNA, and particles of defined diameters to define the transport properties of the nucleoplasm and nuclear compartments. We confirm that mRNA transport is discontinuous and that mRNAs frequently become transiently trapped within the nucleoplasm. These transport properties are very similar to what is observed with 40 nm fluorescent particles microinjected into nuclei suggesting that this reflects a sharp size- dependent transition to obstructed diffusion characterized by transient caging. In comparing two cell lines, one cancer (U2OS) and a normal cell line from mouse (C2C12). These differ in their spatial organization and local densities of chromatin and, remarkably, show an order of magnitude difference in both the confinement volumes and the diffusion coefficients observed between the two cell lines. The cancer cell line showed much more rapid transport properties. Since most transport studies have been performed in cancer cell lines, this raises the possibility that find dramatic differences in the transport of both mRNAs and fluorescent beads. In this presentation, I will review the transport properties of molecules through the nucleoplasm and its compartments and discuss our new results that suggest a surprising range of biophysical properties of the nucleoplasm across cell types.
2. Kelsey Gasior University of Notre Dame
   "Molecular Interactions and Intracellular Phase Separation"
Found in both the nucleus and the cytoplasm, intracellular phase separation allows for the formation of liquidlike droplets that localize molecules, such as proteins and RNAs. Many RNA- binding proteins interact with different RNA species to create compartments necessary for cellular function, such as polarity and nuclear division. Additionally, the proteins that promote phase separation are frequently coupled to multiple RNA binding domains and several RNAs can interact with a single protein, leading to a large number of potential multivalent interactions. This work focuses on a multiphase, Cahn-Hilliard (CH) diffuse interface model to examine the RNA- protein interactions and competition driving intracellular phase separation. By combining the CH approach with a Flory-Huggins free energy scheme, biologically-relevant mass action kinetics, and phase-dependent diffusion, this model explores how molecular dynamics control droplet- scale phenomena. In-depth analysis using numerical simulations and combined sensitivity techniques, such as Morris Method Screening and Sobol’, shows the depth of complications underlying even the simplest droplet field properties, such as the time of separation and composition of the droplet field. These results show that while specific mathematical parameters can be set to push a system to phase separate, it shares control of the droplet field with the rates at which the protein and RNA can interact. Ultimately, this targeted and thorough approach to intracellular condensates begins to peel back the layers of complex molecular dynamics governing the formation and evolution of these droplets that contribute to cellular function.
3. Justin Knechtel Cross Cancer Institute, University of Alberta
   "Single Molecule Tracking of KMT5C in Chromatin Compartments"
Our genome is packaged into chromatin, a dynamic DNA-protein complex organized into distinct functional states defined by epigenetic modifications. These states give rise to spatially segregated chromatin compartments, such as euchromatin and heterochromatin, which differ in molecular composition and biophysical properties. KMT5C, a histone lysine methyltransferase that specifically targets histone H4 lysine 20 (H4K20), shows a striking pattern of chromatin compartmentalization: while it is both highly enriched and mobile within heterochromatin, it exhibits minimal exchange with the neighboring euchromatin. To investigate this behavior, we performed single particle tracking of KMT5C in living cells and quantitatively characterized its kinetic properties within and between chromatin compartments. We applied Hidden Markov Modeling to resolve discrete states of motion and leveraged our tracking data as a microrheological tool to assess the physical state of chromatin. These findings provide new insight into how the material properties and molecular organization of chromatin regulate protein dynamics within the nucleus.
4. Tharana Yosprakob University of Alberta
   "Spatial Organization and Dynamics of Nuclear Proteins"
The protein KMT5C regulates gene transcription and maintains genome integrity. It interacts with CBX5 proteins and is enriched within chromocenters, which are distinct regions in the nucleus where chromatin serves as an organizing scaffold. Although both proteins are similar in size and co-localize in chromocenters, fluorescence recovery after photobleaching (FRAP) reveals different mobility characteristics: CBX5 moves freely within and between chromocenters, whereas KMT5C is limited to movement within chromocenters. To understand these differences, we developed a reaction-diffusion model that incorporates diffusion and binding/unbinding dynamics between KMT5C, CBX5, and chromatin. Using multiple-timescale analysis, we show that the correct diffusion equation for this situation differs from Fick’s Law and predicts a non-uniform steady state concentration, which results in regions of condensation rather than a uniform distribution. Simulated bleaching experiment using this model is consistent with experimental FRAP result, indicating that differential enrichment of KMT5C and CBX5 arises primarily from their binding and unbinding interactions.

Organized by: Laura Wadkin (Newcastle University), Patrick Parkinson (Newcastle University)

1. Laura Wadkin Newcastle University
   "Optimising stem cell therapies for corneal damage: insights from clinical trial image analysis"
Limbal stem cell deficiency (LSCD) is an ocular disease characterized by a loss or deficiency of the stem cells in the limbus, which are vital for ensuring homeostasis of the corneal epithelium. When these stem cells are lost, the corneal epithelium breaks down becoming scarred and chronically inflamed, resulting in vision loss, chronic pain and photophobia. Treatment of LSCD takes the form of an ex-vivo cultured limbal stem cell (LSC) transplant into the affected eye. Although proven effective at restoring vision, much remains to be understood about the mechanics of corneal epithelium recovery following the LSC transplant. Our research aims to utilise the power of statistical image analysis and mathematical modelling to answer fundamental questions about the condition of the corneal epithelium in an LSCD affected eye, the proliferation and behaviours of LSCs following transplant, and how these behaviours result in the complete restoration of the corneal epithelium. Here, we analyse IVCM images from patients with total unilateral LSCD, taken before and after LSC transplant, to explore potential quantitative diagnostic and monitoring measures of the corneal recovery process.
2. Joel Vanin Biocomplexity Institute/Indiana University Bloomington
   "V-Cornea: A Multiscale Virtual Tissue Approach to Modeling Corneal Biology"
V-Cornea addresses key limitations in ocular irritation assessment methods through a computational framework for predicting corneal epithelial response to injury. Implemented in CompuCell3D, this agent-based model successfully simulates corneal epithelial homeostasis and recovery patterns following trauma or toxicant exposure. The model incorporates biologically-inspired rules governing cell behaviors (proliferation, differentiation, death) and critical signaling pathways including Epidermal Growth Factor (EGF). Our simulations accurately reproduce normal corneal architecture and predict healing timeframes of 3-5 days for slight and mild injuries, consistent with experimental observations. For moderate injuries involving basement membrane disruption, the model demonstrates extended recovery times and emergent structural disorganization that mimics recurrent corneal erosions. Our current work explores supplementary approaches to understand cellular responses to IL-1 signaling, particularly how contextual factors in the extracellular matrix influence diverse outcomes like death, proliferation, and differentiation. We're also investigating how barrier function loss in superficial cells relates to early corneal opacity through a dedicated hydration model. To make these computational tools accessible to non-programmers, we've developed a user-friendly graphical interface (GUI) that facilitates model parameter adjustment, simulation execution, and results visualization. This virtual-tissue approach, now more accessible through the GUI, shows promise for toxicological assessments and therapy optimization by providing a platform to test interventions across various injury scenarios.
3. Patricia Lamirande University of Oxford
   "Mathematical modelling of ocular drug delivery using mean first passage time"
Wet age-related macular degeneration is a progressive disease that can lead to severe visual impairment. Standard treatment involves repeated intraocular drug injections, typically administered monthly, highlighting the need to understand factors influencing drug retention and clearance. Mathematical modelling provides a powerful approach to studying these processes and can offer insights into the development of longer-lasting treatments. In this work, we present a mean first passage time (MFPT) modelling framework to investigate ocular pharmacokinetics and scaling relationships, examining the effects of injection location and anatomical variability. The MFPT quantifies the average time for a randomly diffusing particle to reach a target, making it well-suited for assessing drug distribution and clearance. We formulate a partial differential equation system describing the MFPT of a particle diffusing in a 3D finite domain, modelling the diffusion of ocular pharmaceutics in the eye. Our model quantifies how physiological and anatomical parameters influence the protein therapeutics kinetics (like vitreous half-life), compares interspecies and intraspecies variability, and evaluates the impact of injection site. We validate the modelling framework by comparing its predictions to detailed 3D anatomical scans of rabbit eyes and in vivo pharmacokinetics data from the same eyes, assessing its ability to capture key features of ocular drug transport.

Organized by: Keisha Cook, Anna Nelson (Clemson University), Alessandra Bonfanti (Politecnico di Milano) Giulia Celora (University of Oxford) Kelsey Gasior (University of Notre Dame) Qixuan Wang (University of California, Riverside)

Note: this minisymposia has multiple sessions. The other session is: and Part-2.

1. Khanh Dao Duc University of British Columbia
   "Optimal Transport based metrics and statistics for quantifying cell shape heterogeneity"
Recent advances in experimental methodologies and community efforts have led to a surge in large cell image datasets, that require the developments of new methods to analyze them and extract meaningful information. In this context, I will describe our recent efforts to leverage optimal transport theory, with the introduction of metrics inspired by Wasserstein/Gromov-Wasserstein distances for 2D and 3D cell shapes, that are efficient to compute and can be used for a variety of tasks, including Dimensionality reduction, statistical testing and machine learning. Real data applications will focus on analyzing 2D contour of cancer cells, and 3D images of nucleus and cell shapes under different stages of development.
2. Peijie Zhou Peking University
   "Towards AI Virtual Cell Through Dynamical Generative Modeling of Single-cell Omics Data"
Reconstructing continuous cellular dynamics from sparse, high-dimensional single-cell omics data remains a fundamental challenge in systems biology. Recently, a paradigm shift has been witnessed by leveraging artificial intelligence—specifically, dynamical generative modeling—to develop an AI virtual cell, a predictive digital twin capable of simulating cellular behavior across time and space. In this talk, we introduce our recent attempts that integrate flow-based generative models with partial differential equations (PDEs) to infer latent dynamics from scRNA-seq data. For spatial transcriptomics data, we extend this method with stVCR, a generative model that aligns transcriptomic snapshots across biological replicates and temporal stages. To further infer stochastic dynamics from static data, we explore a regularized unbalanced optimal transport (RUOT) formulation and its theoretical connections to the Schrödinger Bridge and diffusion models. I will also introduce a generative deep-learning solver designed for this problem.Together, these works suggest how generative AI could have the potential to unify dynamical modeling, spatial reconstruction, and stochastic inference—transforming fragmented omics data into a predictive virtual cell.
3. Amanda Alexander University of Houston
   "Persistence of plasmid DNA in spatially organized bacterial populations"
Bacterial cells contain extrachromosomal DNA molecules called plasmids. In nature, plasmids often confer antibiotic resistance. Cells commonly have no mechanism for evenly partitioning plasmids during cell division, and thus there is some probability that one of two daughter cells does not inherit any plasmids. On the population scale, what factors influence the persistence of plasmid DNA over generations? Mathematical modeling is useful in answering this question, as it is difficult to experimentally resolve new plasmid loss from replication of previously plasmid-free cells over long time periods. We introduce a spatial Moran-like model of a finite cell population undergoing plasmid loss, because biologists frequently observe cell populations in spatially constrained microfluidic traps. We explore how properties of single cells impact the dynamics of the cell population in different trap geometries. This analysis reveals that the persistence of plasmid DNA in cell populations has a complex dependence on both spatial geometry and assumptions on single cell properties such as cell division age.
4. Grace McLaughlin University of North Carolina, Chapel Hill
   "Modeling Asynchronous Nuclear Division in Fungal Cells"
Multinucleate cells are common in biology, with examples including muscle cells, placenta, and fungi. Despite this, many aspects of their cell biology are not well understood. Nuclei within these large cells can undergo division, and their cell cycles are governed by biochemical oscillators. Dividing nuclei residing in a common cytosol would be expected to synchronize, as the oscillating levels of cell cycle regulators from each nucleus should in theory entrain neighbors. However, in the multinucleate fungus Ashbya gossypii, spatially neighboring nuclei have been observed to divide out of sync. Despite this apparent nuclear autonomy, nuclear density is controlled within a whole cell, suggesting cell cycles are coupled with cell growth. Does nuclear asynchrony play a role in regulating nuclear density? How do nuclei maintain asynchrony while coordinating their cell cycles on the whole-cell level? And how do nuclei achieve local asynchrony while sharing a common cytosol and originating from the same initial nucleus? To answer these questions, we model Ashbya nuclei as a dynamically growing system of coupled phase oscillators residing within a network-like cell. We find that robust control of nuclear density requires regulation of both cell morphology and cell cycle length. Furthermore, we show that even if cell cycles are coupled to changing nuclear density, it is still possible for them to stay asynchronous as long as this coupling is sufficiently weak. Finally, focusing on interactions between individual nuclei, we find that asymmetric coupling from mitotic nuclei towards younger nuclei can promote asynchrony. All together, these results show how asynchrony can persist in Ashbya, and how these cells achieve a balance between local autonomy with global coordination.

Organized by: Fabian Spill (University of Birmingham), Anotida Madzvamuse, University of British Columbia

Note: this minisymposia has multiple sessions. The other session is: and Part-2.

1. Alex Grigas Syracuse University
   "Modeling fluidity in stellate mesenchymal tissues"
In many developmental and disease processes, tissues shift from solid-like to fluid-like mechanical behavior to enable large-scale tissue flows. A key unresolved question is how different organisms regulate this transition by controlling cell-scale properties. In both zebrafish and chick, a fluid-to-solid transition occurs in the presomitic mesoderm, the driving force behind posterior body axis elongation. In zebrafish, this transition is well explained by a soft particle model that undergoes a jamming/unjamming transition, driven by small changes in global volume fraction and active fluctuations, without considering cell shape or deformation. However, the tissue architecture in chick is distinct from zebrafish, with large extracellular gaps and stellate cells with distinct arm junctions, indicating that even closely related species may have evolved different mechanisms to cross a fluid/solid transition. Here, we develop a computational model to understand the essential features needed to predict the unique properties of low density, but highly connected, stellate tissues, which tissue rounding experiments demonstrate are fluid-like on long timescale. We compare short-time retraction velocities and tissue relaxation due to laser ablation between experiment and simulation to determine whether the mesenchyme is under tension. Additionally, we propose novel glassy dynamics can be controlled not via density changes but instead by cell-cell adhesion unbinding kinetics coupled with contact inhibition of locomotion, and propose new experiments to test these ideas.
2. Sharon Minsuk Indiana U., Bloomington
   "The Role of Embryo, Tissue, and Cell Shape in Morphogenesis: Modeling the Cellular Dynamics of Tissue Deformation"
Morphogenesis of embryonic tissues involves complex and extreme deformations in response to intra- and intercellular forces; and is profoundly dependent on the geometry not only of the deforming tissue itself, but of the environment in which that tissue finds itself. Epiboly in zebrafish, the spreading of an epithelial sheet in response to external tension, to cover and engulf the rest of the spherical embryo, requires deformation of a shallow spherical cap into a full sphere, without tearing or buckling, accommodated by cell rearrangement as well as cell shape change. We built a computational model of epiboly. Rearrangement of mechanically coupled model cells is achieved by allowing those couplings to dynamically break and re-form; broken couplings in a tissue under tension risk tearing, which we prevent by adding a constraint on cell packing geometry. The straightening of the leading edge of the expanding tissue, as observed in living embryos, arises emergently and robustly from our model, and is associated with rapid cell rearrangement (tissue fluidization). Changes in cell shape and packing geometry have been implicated in promoting fluidization, suggesting they may play a role in facilitating both tissue deformation and edge straightening. I will briefly describe and demonstrate the model, with special emphasis on the interplay between embryo, tissue, and cell geometry, and the dynamics of morphological transformation.
3. Margherita De Marzio Harvard Medical School and Brigham and Women’s Hospital
   "Understanding the Role of Surface Curvature on Epithelial Plasticity"
To heal, remodel, or invade, the epithelial tissue transitions from a state that is sedentary and quiescent to one that is strikingly migratory and dynamic. This phenotypic switch is known as the epithelial unjamming transition (UJT). Previous theoretical models have characterized the UJT in flat epithelial layers. By contrast, the epithelium in vivo often resides on highly curved structures like pulmonary alveoli, airways, and intestines. How surface curvature, and the resulting topological defects and out-of-plane forces, impact epithelial plasticity remains poorly understood. In this talk, I will present our recent findings on the role of geometry on the migratory phenotype in vivo. Using a 2D spherical vertex model, we investigated the UJT within physiological ranges of cell density and surface curvature. I will show that increasing curvature promotes tissue fluidization and migration. At higher curvatures, cell rearrangements become energetically advantageous, leading to cellular configurations that are more malleable and migratory. I will demonstrate that this effect is not due to changes in the local mechanism of cell intercalation, which is independent of curvature. Instead, it stems from changes in the global structure of the cell-junction network, which becomes less tensed as curvature increases. Together, these results reveal curvature-induced unjamming as a novel mechanism of epithelial fluidization, offering insights into how surface geometry drives tissue malleability, remodeling, and stabilization.
4. Padmini Rangamani UCSD
   "Nanoscale curvature of the plasma membrane regulates mechanoadaptation through nuclear deformation and rupture"
Nuclear translocation of the transcription regulatory proteins YAP and TAZ is a critical readout of cellular mechanotransduction. Recent experiments have demonstrated that cells on substrates with well-defined nanotopographies demonstrate mechanoadaptation through a multitude of effects - increased integrin endocytosis as a function of nanopillar curvature, increased local actin assembly on nanopillars but decreased global cytoskeletal stiffness, and enhanced nuclear deformation. How do cells respond to local nanotopo-graphical cues and integrate their responses across multiple length scales? This question is addressed using a biophysical model that incorporates plasma membrane (PM) curvature-dependent endocytosis, PM curvature-sensitive actin assembly, and stretch-induced opening of nuclear pore complexes (NPCs) in the nuclear envelope (NE). This model recapitulates lower levels of global cytoskeletal assembly on nanopillar substrates, which can be partially compensated for by local actin assembly and NE indentation, leading to enhanced YAP/TAZ transport through stretched NPCs. Using cell shapes informed by electron micrographs and fluorescence images, the model predicts lamin A and F-actin localization around nanopillars, in good agreement with experimental measurements. Finally, simulations predict nuclear accumulation of YAP/TAZ following rupture of the NE and this is validated by experiments. Overall, this study indicates that nanotopography tunes mechanoadaptation through both positive and negative feedback on mechanotransduction.

Organized by: Jared Barber (Indiana University Indianapolis), Luoding Zhu

Note: this minisymposia has multiple sessions. The other session is: and Part-2.

1. Calina Copos Northeastern University
   "Migration modes of small cell groups: which forces govern their emergent movement?"
Collective cell migration is essential to many physiological and pathological processes, yet its classification remains incomplete. Focusing on cohesive cell pairs migrating on flat substrates, we identified two motility modes: the individual contributor (IC) mode, where each cell generates its own traction force dipole, and the supracellular (S) mode, characterized by a single dipole across the pair. Amoeboid Dictyostelium discoideum (Dd) cells predominantly adopt the IC mode, while mesenchymal Madin-Darby canine kidney (MDCK) cells favor the S mode. A two-dimensional biophysical model incorporating cell-cell and cell-matrix adhesions, along with boundary contractility, recapitulated these patterns. The IC mode emerged in Dd-like cells with balanced traction, whereas S mode dominated in asymmetric or MDCK-like pairs, often driven from the rear. Increasing cell-matrix adhesion promoted the IC mode in amoeboid chains but favored the S mode in MDCK-like cells. The model, extended to longer chains, offers a novel theoretical framework to study diverse collective migration behaviors.
2. Yuehui Xu Indiana University Indianapolis
   "A 3D Viscoelastic Model of Cell Migration with Mechanical and Adhesive Forces"
Gaining a deeper understanding of cell migration can aid in the development of treatments for a wide range of diseases in which it plays a major role, including infection and cancer. To investigate the mechanisms of cell migration and identify key factors that influence migratory behavior, we developed a three-dimensional mathematical model of an HEK 293 cell migrating unidirectionally on a flat substrate. The cell is represented as a network of viscoelastic elements, while focal adhesions are modeled as points on the cell membrane that connect to the substrate using elastic fibers. The model includes forward pushing forces that are typically generated by actin filaments and cause the cell to protrude in the migratory direction. It also includes an internal interconnected set of elements that represent the internal cell structure. We share how our approach is capable of producing results that agree qualitatively with experiment and vary simulation parameters to examine how the cell responds to changes in membrane stiffness, substrate stiffness, internal element elasticity, the number of focal adhesions, and frictional forces. Results suggest the model can be used to consider more physiologically relevant questions in the future such as the effects of different component properties on overall cell migration and forces.
3. John Dallon Brigham Young University
   "Modeling differential cell motion in the Dictyostelium discoideum slug"
Differential cell motion plays an important role in the front to back pattern formed during the slug stage of the organism Dictyostelium discoideum (Dd). The slug has at least two cell types: prespore cells and prestalk cells. As the slug moves the prestalk cells aggregate to the front of the moving slug while the prespore cells aggregate to the rear. In this talk I will discuss a force based mathematical model where cells attach and detach to one another via discrete adhesions with stochastic dynamics. Using simulations, different strategies that cells could employ are explored which cause differential cell motion leading to this front to back pattern.

Organized by: Andreas Buttenschoen (University of Massachusetts Amherst), Calina Copos (Northeastern University)

1. Jupiter Algorta University of British Columbia
   "A Data-Driven Model of Polarity Reversal in Migrating Cells"
We study how motile cells can reverse their polarity when exposed to changing stimuli, using mathematical modeling alongside extensive experimental data from optogenetic assays carried out by our collaborators in the Orion Weiner lab (UCSF). These experiments revealed an unexpected phenomenon: when a localized input is followed by a global stimulus, cells often reverse their direction of turning. To explain this, our collaborators hypothesized the existence of a slow-acting, locally produced inhibitor downstream of Rac, a signaling molecule known to promote actin assembly and front-edge protrusion. We test this idea by adapting an existing reaction diffusion model that, under certain conditions, produces a stable spatial pattern: a polarized distribution with a clear front and back. This modeling framework, often referred to as wave-pinning, has not previously been fitted directly to experimental data. Here, we calibrate the model’s reaction terms to time-dependent Rac activity data, introducing a novel approach that embraces cellular heterogeneity by fitting a distribution of parameters across multiple cells. While the Rac-inhibitor circuit captures several key features of the response, it fails to reproduce reversal. Incorporating PIP3, an upstream regulator of Rac, allows the model to recover reversal dynamics and reproduce the full range of observed behaviours. In this presentation, we will show the development of our modeling framework from its earliest steps, including how data fitting informed model refinement. Our results validate the experimental hypothesis and yield new predictions about the molecular timing and feedback logic underlying flexible polarity control.
2. Mariya Savinov New York University
   "Modeling mechanically driven tumor cluster coattraction on ECM"
Authors: Mariya Savinov (1), Jeremy Garcia (2), Alex Mogilner (1,2), Carlos Carmona-Fontaine (2) (1): Courant Institute of Mathematical Sciences, New York University, New York, NY. (2): Department of Biology, New York University, New York, NY Collective cell migration is essential for morphogenesis, playing a key role in processes such as embryonic development and cancer metastasis. The ability of cells to collectively migrate in a directional manner depends on coordination cues, both local between cells and extracellular (e.g. chemotaxis). How cells in cancer clusters coordinate their movements, particularly in early metastasis, is still not well understood. Here we tackle this question using a combined experimental and modeling approach. Our experimental efforts employed a model system of multicellular tumor structures, which we refer to as cell clusters, on extracellular matrix (ECM). We found that when two cell groups are within a threshold distance, they “coattractâ€, spontaneously migrating collectively towards each other. Surprisingly, the tumor cell clusters also detect and then migrate toward biologically inert beads, suggesting that the coattraction is a consequence of a mechanical cue of the ECM. To uncover the mechanisms underlying the robust coattraction threshold, we developed a mathematical model of the ECM as a 2D deformable elastic, cable-network material. As experiments have shown that cell clusters pull and concentrate the ECM, the model ECM is subjected to isotropic contractile stresses by the tumor cell clusters. Through analysis and numerical simulation, our model reveals how the mechanical force distribution of the underlying ECM acts as a symmetry-breaking cue to initiate cell cluster coattraction. We reproduce key experimental results and, notably, our model predicts a lower coattraction threshold between a single cluster and bead as compared to a pair of cell clusters. This work demonstrates how mechanical forces in the ECM can efficiently guide tumor cell cluster migration, and has broad implications regarding the survival of tumor cells during the metastatic journey.
3. Wei Wang Johns Hopkins University
   "Statistics of fracture in collective cell migration"
When cells migrate collectively, individual cells or small groups can detach from the main body. These fracture events play an important role in cancer invasion and other biological processes, but their statistics and physical control mechanisms remain unclear. We present a theoretical and experimental study that quantifies the statistics of fracture events in collectively migrating tissues and connects them to physical models of active matter with growth and breakup. We analyze experiments where human carcinoma cells migrate along chemotactic gradients in microchannels and sometimes rupture away from the invading strand. Most rupture events involve single cells, but larger clusters also occur. The rupture probability shows little dependence on the degree of geometric confinement. To understand these observations, we construct a phase-field model of deformable cells that incorporates chemotaxis, heterogeneous cell states (followers, guided cells, and leader cells), and cell-cell and cell-wall adhesion. This model recapitulates key features of the experiments, including the distribution of rupture sizes and times. Our results show that cell-channel adhesion is necessary for cells in narrow channels to invade, and strong cell-cell adhesion leads to fewer but larger ruptures. Chemotaxis also influences the rupture behavior: Strong chemotaxis strength leads to larger and faster ruptures. We also examine the connection between biological jamming transitions and fracture. Our results suggest unjamming is necessary but not sufficient to create ruptures. To generalize this picture, we study how cell groups control their cluster sizes using a one-dimensional active particle model of growing and fragmenting chains. In this model, rupture is driven by random cell motility, and cluster size is set by the balance between growth and breakup. We compute the rupture rate analytically and solve for the exact steady-state size distributions. We show that these statistics depend only on the ratio of break to division rates, and that size variability can be reduced by restricting division to cluster edges or localizing rupture to the interior. Our theory also suggests that the observed drop in fracture rate in experiments can be explained by relatively small changes in cell motility. Together, these results provide a physical framework for understanding the statistics of fracture in collective migration, with implications for both tissue size regulation and cancer cell metastasis.
4. Eric Cytrynbaum University of British Columbia
   " A model for root zone regulation by brassinosteroid and CLASP"
The root apical meristem of the plant A. thaliana is organized into distinct zones, each of which plays an important developmental role. The plant hormone brassinosteroid and the protein CLASP influence the size and dynamics of the elongation and division zones thereby controlling the rate of root growth. This regulation allows plant growth to be responsive to environmental conditions. In this talk, I will describe a model for a mechanism by which brassinosteroid and CLASP modulate cell elongation and cell division. The model is able to match measured root growth data for wild type and two mutants under the condition that CLASP has a biphasic influence on the rate of cell cycle progression, with a maximum cell division rate for intermediate levels of CLASP. This result suggests that CLASP, a regulator of microtubule dynamics, must be finely tuned to allow microtubules to efficiently relocalize through the cell cycle.

Organized by: Keisha Cook, Anna Nelson (Clemson University), Alessandra Bonfanti (Politecnico di Milano) Giulia Celora (University of Oxford) Kelsey Gasior (University of Notre Dame) Qixuan Wang (University of California, Riverside)

Note: this minisymposia has multiple sessions. The other session is: and Part-1.

1. Merlin Pelz University of Minnesota
   "Effect of compartmentalization: synchronization and symmetry-breaking of diffusively coupled cells in 2-D and 3-D"
The Kuramoto model has been used in the last decades to gain insight into the behaviour of coupled discrete oscillators, as it is simple enough to be analyzed and exhibits a breadth of possible behaviours, such as synchronization, oscillation quenching, and chaos. However, the question arises how one can derive precise coupling terms between spatially localized oscillators, e.g., cells, that interact through a time-dependent diffusion field. We focus on a compartmental-reaction diffusion system with nonlinear intracellular kinetics of two species inside each small and well-separated cell with reactive boundary conditions. For the case of one bulk-diffusing species in ℝ² and ℝ³, we derive new memory-dependent integro-ODE systems that characterize how intracellular oscillations in the collection of cells are coupled through the PDE bulk-diffusion field. By using a fast numerical approach relying on the ``sum-of-exponentials'' method to derive a time-marching scheme for this nonlocal system, diffusion induced synchrony (in-phase, anti-phase, mixed-mode etc.) is examined for various spatial arrangements of cells. This theoretical modelling framework, relevant when spatially localized nonlinear oscillators are coupled through a PDE diffusion field, is distinct from the traditional Kuramoto paradigm for studying oscillator synchronization on networks or graphs. It opens up new avenues for characterizing synchronization phenomena associated with various discrete oscillatory systems in the sciences, such as quorum-sensing behaviour. Allowing for two bulk-diffusing species, our systems show that cell group symmetry-breaking can be achieved due to an exceeding cell membrane permeability ratio of the two species while their diffusivities in the bulk are on the same order. This behaviour cannot be obtained with standard two-species reaction-diffusion systems that were mentioned first in Turing's pioneering work on morphogenesis. Our systems expose a simple way through which cell specialization may emerge robustly. (This is joint work with Michael J. Ward.)
2. Sharon Lubkin North Carolina State University
   "Geometry, pattern, and mechanics of notochords"
Chordocytes, in early zebrafish and other teleost notochords, have been shown to pack in a small number of stereotyped patterns. Mutations or treatments which disrupt the typical patterning are associated with developmental defects, including scoliosis. The dominant WT “staircase” pattern is the only regular pattern displaying transverse eccentricity. Morphometry and pattern analysis have established a length ratio governing which patterns will be observed. Physical models of cell packing in the notochord have established relationships between this geometric ratio, a mechanical tension ratio, the transverse aspect ratio, pattern, pressure, and taper. Since a major function of the early notochord is to act as both a column and a beam, we aim to understand the overall resistance to compression and bending in terms of these mesoscale cell/tissue properties. To frame the relationships between these properties, we have developed a model of the notochord as an elastic closed-cell foam, packed in either the “staircase” or “bamboo” pattern. A pressure study reveals a surprising lack of shape change as internal notochord pressure is varied, and determines the tension ratio between different surfaces in the notochord in terms of the relative stiffnesses and internal pressure. A bending study reveals that deformations of the model notochords are well described by classical beam theory, and determines the flexural rigidity of the model notochords in terms of relative stiffnesses and pressure. We find that the staircase pattern is more than twice as stiff as the bamboo pattern. Moreover, the staircase pattern is more than twice as stiff in lateral bending as in dorsoventral bending. This biomechanical difference may provide a specific developmental advantage to regulating the cell packing pattern in early-stage notochords. Partially funded by Simons Foundation grant 524764.
3. Anna Nelson University of New Mexico
   "Modeling mechanisms of microtubule growth and nucleation in living neurons"
The stability and polarity of the microtubule cytoskeleton is required for long-range, sustained transport within neuronal cells. 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 up-regulated. 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 growth 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.
4. Julio Belmonte North Carolina State University
   "Brillouin Microscopy and Physical Modelling Reveal the Role of Dynamic Changes in Cell Material Properties During Gastrulation"
During animal development, the acquisition of three-dimensional morphology is a direct consequence of the dynamic interaction between cellular forces and cell/tissue compliance. While the generation and transmission of cellular forces has been widely explored, less is known about cell material properties, which are often assumed to be uniform and constant during morphogenesis. Using line-scan Brillouin microscopy we found that cells in the Drosophila embryo undergo rapid and spatially varying changes in their material properties along their apical-basal axis during gastrulation. We identify microtubules as potential effectors of cell mechanics in this system, which show progressive enrichment and alignment along the apical-basal axis of central mesodermal cells during furrow formation. We corroborate our experimental findings with a novel agent-based physical model of gastrulation using the Cellular Potts model. Our model highlights for the first time the importance of cell's longitudinal (apical-basal) stiffness in translating actin-driven apical constriction into cell shape changes; shows that only variation in cells' sub-apical compartment stiffness contributes to furrow formation; and predicts that, while stiffer mesoderm correlates with deeper furrows, better outcomes are achieved if cells are initially softer and stiffen over time, as seen in our Brillouin measurements. Our work provides the first spatio-temporal description of the rapidly evolving material properties of cell populations during morphogenesis, highlights the potential of Brillouin microscopy in studying the dynamic changes in cell material properties, and suggests a new role for microtubules during gastrulation.

Organized by: Fabian Spill (University of Birmingham), Anotida Madzvamuse, University of British Columbia

Note: this minisymposia has multiple sessions. The other session is: and Part-1.

1. Gulsemay Yigit The University of British Columbia
   "Reaction-Diffusion Systems in Bilayer Geometries with Variable Width"
In this talk, we study reaction-diffusion systems when the width of the bilayer geometry is varied. Our aim is to understand the influence of bilayer geometries, and their role in pattern formation. Bilayer geometries are fundamental in cellular and developmental biology; bilayer structures of the cytosol-cortex mechanism significantly affect the diffusion and reaction rates of molecules which are essential in cell signaling. As the width of the thin layer geometries becomes smaller and smaller, the Laplace operator representing classical planar diffusion becomes the Laplace-Beltrami operator representing surface diffusion. Furthermore, we exploit the thin-layer approximation to explore and understand conditions for the diffusion-driven instabilities. Finally, we present bulk- and surface-finite element simulations of the reaction-diffusion systems on bilayer geometries with variable width sizes.
2. Maryam Parvizi University of Birmingham
   "A Mathematical Energy-Based Framework for Modeling Single-Cell Epithelial Migration"
We propose a comprehensive energy-based mathematical framework for modeling singlecell epithelial migration, integrating key intracellular mechanisms that drive motility. This model unifies the dynamic interactions among endoplasmic reticulum (ER) morphology, cytoskeletal architecture, cell shape regulation, and migratory polarization. Specifically, our framework accounts for (i) structural transitions in the ER between sheet-like and tubular states, (ii) stochastic polymerization and depolymerization of actin filaments and microtubules, and (iii) the establishment and maintenance of front–rear polarity. These transitions are represented as metastable states within a global free-energy landscape, where mechanical coupling between the ER and cytoskeleton governs intracellular force distribution, organelle positioning, and shape adaptation. Central to this model is an extension of the Ginzburg–Landau theory , which we apply to describe key biophysical transitions: actin filament polymerization and depolymerization, microtubule instability, structural shifts in ER morphology (tubules versus sheets), and the establishment of spatial polarity. These phenomena are treated as transitions between metastable states governed by a global free energy functional. The ER–cytoskeleton interaction is modeled as a mechanically coupled system that influences force generation, intracellular trafficking, and front–rear organization.
3. Stephanie Portet University of Manitoba
   "Transport of intermediate filaments in cells"
Intermediate filaments are key components of the cytoskeleton, playing essential roles in cell mechanics, signalling and migration. Their organization into networks is a major determinant of their cellular functions. The spatiotemporal organization of intermediate filaments results from the interplay between assembly and disassembly processes, along with various modes of intracellular transport. In this talk, I will provide an overview of mathematical models used to investigate different aspects of the intracellular transport mechanisms of intermediate filaments. Co-authors – John C. Dallon (Department of Mathematics, Brigham Young University, Provo, Utha, USA) Sandrine Etienne-Manneville (CPMC, Institut Pasteur, Paris, France) and Youngmin Park (Department of Mathematics, University of Florida, Gainesville, Florida, USA)
4. Vijay Rajagopal The University of Melbourne
   "MitoMimics: Synthetic microscopy timelapse data for zero-annotation AI segmentation and tracking of mitochondrial dynamics"
Mitochondrial dynamics—the motion, fusion, division, and turnover of mitochondria—govern their capacity to produce energy and execute signaling roles. The growing interest in live imaging and tracking of these dynamics is hampered by current mitochondrial segmentation methods, which show limited accuracy, especially with low signal-to-noise ratio data. To address this challenge, we introduce MitoMimics, a software program that generates synthetic time-lapse movies of mitochondrial dynamics. AI models trained on MitoMimics-generated data outperform existing methods in mitochondria image segmentation. Furthermore, MitoMimics offers advanced capabilities: it segments individual mitochondria, tracks fusion and fission events, and maps emergent mitochondrial network dynamics by automated graph network construction and analysis.

Organized by: Jared Barber (Indiana University Indianapolis), Luoding Zhu

Note: this minisymposia has multiple sessions. The other session is: and Part-1.

1. Anotida Madzvamuse University of British Columbia
   "A geometric bulk-surface PDE approach for modelling single and collective cell migration"
In this talk, I will present a geometric bulk-surface PDE approach for modelling single cell migration. First, I will discuss a geometric-surface PDE approach where cell migration is described by a force balance equation posed only on the cell plasma membrane, under a sharp interface formulation. The evolution law for the cell plasma membrane is discribed through forces acting at each material point, in the normal direction. These forces include (but are not limited to): actomyosin forces for cell polarisation, driven by molecular species resident on the plasma membrane and these obey a surface reaction-diffusion system; forces describing the energetic nature of the plasma membrane (e.g. surface tension, bending energy, etc); forces associated with volume constraint and external forces (including cell-to-cell interactions, cell-to-obstacle interactions), and so forth. By introducing bulk dynamics associated with the bulk-surface wave-pinning model, we will demonstrate the generalisation to a geometric bulk-surface modelling approach. To support the modelling approach, numerical examples will be exhibited based on evolving bulk-surface finite elements to model single and collective cell migration through stationary and deformable extracellular matrices as well as cell migration through confined spaces, reminiscent of microfluidic devices.
2. Jared Barber Indiana University Indianapolis
   "Admissible behaviors for a model of actin filaments pushing the cell forward"
During cell migration across a 2D surface, cells develop a flat protrusive structure called a lamellipodium (“sheet-like foot”). Actin (protein) filaments form inside of this structure and push at the leading edge of the cell in order to propel the cell forward. While there are various complexities associated in this process, in this talk, we explore a simple version of the “Filament-Based Lamellipodium Model (FBLM)”. In this version, filaments are represented by multiple line segments that are relatively short, parallel to each other, and perpendicular to the front of the cell/lamellipodium. The model includes frictional forces as well as forces that tend to keep the filaments approximately equally spaced from each other, the front of the cell, and the side of the lamellipodium. Such forces are derived by defining corresponding energies and then using variational techniques. We study this system near equilibrium to better understand what solutions are admissible and share numerical representations of such solutions. Such information informs us about the variation that may arise when actin filament networks act to push forward the lamellipodium during cell migration.
3. Jianda Du University of Florida
   "Effect of Curvature in a Cell Migration Model"
Cell migration is essential for processes such as tissue development, wound healing, and cancer metastasis. For instance, during gastrulation—an early stage of embryonic development—cell migration is crucial for the formation of germ layers that eventually develop into tissues and organs. We extend a previously established continuum mechanical model of cell migration by introducing curvature as a key factor. We investigate how curvature influences cell migration in spreading embryonic tissues of two species: the aquatic frog Xenopus laevis and the axolotl salamander Ambystoma mexicanum. Simulations are conducted with various initial tissue shapes to assess the impact of curvature. Sensitivity analysis and approximate Bayesian computation with sequential Monte Carlo (ABC-SMC) are used to evaluate the importance of incorporating curvature and to additionally determine the form of curvature dependence that best reflects the experimental data.
4. David Odde University of Minnesota
   "Modeling the mechanics of glioblastoma progression and treatment."
Effector CD8+ T cells must make cell-to-cell contacts (TCR-MHC-antigenic-peptide-complex) to identify and eliminate cancer cells selectively. This requirement could become a make-or-break factor in the clearance of solid tumors such as glioma, which we focus on in this study, where T cells have to actively search for the cancer cells in the tissue. Several immunotherapies, such as checkpoint blockade and adoptive T cell therapy, have been proposed; however, all of these essentially aim to make T cells better killers, not migrators. In this study, we recognize an equally important factor crucial for their success, i.e., their migration in the tissue. T cells have been assumed to be optimal navigators based on evolutionary reasons, an idea we challenge in this study. Using a combination of ex vivo brain tissue and in vitro assays, we found that T cells, on average, migrated slower than reported in the literature (0.5-2 μm/min, 0.1-1 μm/min vs 6-10 μm/min, 10-30 μm/min) and only modestly faster than cancer cells in a similar setting (0.1-0.2 μm/min), suggesting the need for improvement for effective immune response and immunotherapy. Strikingly, for T cells, the best description was not a single, homogeneous population of superdiffusive walks as previously found but a mix of comparable numbers of sub, normal, and superdiffusive walks, especially at longer time scales. This heterogeneity is advantageous for finding targets of a range of sizes but worse than the single superdiffusive population for finding a fixed target such as a glioma. We investigated the reason for such slow migration. Our T cells, consistent with previous studies, showed evidence of a 'stop-and-go' pattern. We found that hyper adhesive interactions with the perivascular space of blood vessels, the entry point of T cells into the brain, microglia, a major antigen-presenting cell in the brain, and hyaluronic acid, a major ECM protein in the brain, all could explain many, but not all, of the 'stops”. Reducing these 'stops' could increase net T cell migration, potentially an improvement enough to stop the inevitable GBM recurrence under current standard therapy regimens. Next, we used drug-perturbation experiments and high-resolution imaging to unravel the biomechanics of CD8+ T cell migration. We discovered that these T cells are capable of using multiple modes, highlighting their adaptive nature, but often use the familiar motor-clutch mode of cell migration usually reported for cancer cells, but with altered, faster protrusion and focal-adhesion dynamics. To capture these dynamics we developed a momentum-conserving model for hybrid bleb-adhesion-based rapid T cell migration. Together, these results advance our fundamental understanding of T cell migration in the brain, which may inspire better immunotherapies in the future that are focused on making T cells both powerful killers and adept at rapidly locating target cancer cells.

Organized by: James Holehouse (The Santa Fe Institute), Kaan Öcal (University of Melbourne) and Augustinas Sukys (University of Melbourne)

1. Daniel Muratore Santa Fe Institute
   "Cellular Macromolecular Dynamics Induce Emergent Viral Biogeography in the Pacific Ocean"
Viruses are the most numerically abundant biological entity in the ocean, and the success of viral infection is determined by the capacity of their microbial hosts to provide necessary macromolecular machinery to synthesize viral progeny. Stochastic processes governing the relative balance of the nucleic acid and protein production in the infected ‘virocell’ can disrupt viral replication and lead to the production of viral particles packaged with host, as opposed to viral, genomes. This talk will discuss a stochastic process model of viral infection informed by light availability (cellular energy input) that determine cell macromolecular production. We identify regimes under which different viral infection strategies prevail and compare them with known population distributions of marine bacteriophages. Latitudinal shifts in seasonality and average day length unveil a regime shift in viral infection efficacy that corresponds to a rapid restructuring of viral fitnesses, suggesting the sub cellular environment informs global-scale biogeographic trends in microbial pathogens in the ocean.
2. Anish Pandya UT Austin
   "Transcriptional noise tunes correlations between stages of the mRNA lifecycle"
Gene expression is a key process conserved in life. A central goal is to understand complex intracellular processes through construction of gene regulatory networks from biophysical mechanisms. Many models of Eukaryotic gene expression represent biophysical processes such as (multi-)promoter binding, post-transcriptional modifications, and product degradation as transitions between states in a Markov Chain. A key step is from correlations in co-expression data to inferring molecular mechanisms. We demonstrate the converse— deducing the expected Pearson correlation and squared coefficient of variation of mRNA waiting time distributions a priori from models—can pose indistinguishability problems. In particular, if the mRNA waiting time distribution contains combinations of reversible or (effectively) irreversible transitions and or the transcriptional reaction network contains cycles. We characterize the dependence of the mRNA Pearson correlation coefficients and the coefficient of variation on causal properties of transcriptional reaction graphs. With the linear noise approximation, we exactly calculate the expected properties of the covariance, Pearson correlation coefficient, and coefficient of variation. In addition, we investigate the degeneracy of transcriptional waiting time distributions to correlative measurements of post-transcriptional mRNA with few transcriptional gene states. In these models, we show causal relationships do not necessarily entail correlative relationships. To potentially mitigate spurious correlations, we discuss methods to potentially distinguish between causal generating mechanisms based on correlations between post-transcriptional products.
3. Ethan Levien Dartmouth College
   "Gene expression following abrupt antibiotic exposure"
Single-cell mother machine experiments have revealed that genetically homogeneous bacterial populations can exhibit divergent cell fates following abrupt antibiotic exposure. The mechanisms underlying this divergence remain unclear, particularly the respective roles of intrinsic and extrinsic factors. Here, we propose a simple model of single-cell gene expression and growth dynamics following sudden drug exposure, grounded in established scaling relations between proteome allocation and growth rate. In this model, resources allocated to the transcription of resistance genes behave analogously to generalized momenta, and their initial variation predicts eventual cell fate. Without parameter fitting, the model recapitulates key experimental observations, including the emergence of distinct phenotypic outcomes and the existence of a critical threshold in TetR production velocity that determines survival. We further derive a scaling law for the critical velocity as a function of external drug concentration, yielding a testable prediction for future experiments.
4. Lucy Ham University of Melbourne
   "Cell fate control in space and time: fundamental limits on spatial organisation in multicellular systems"
Genetically identical cells develop and maintain distinct identities over time, despite fluctuations in intracellular and extracellular conditions. This talk examines the mechanisms behind cell fate determination and spatial patterning in multicellular systems. Using spatial stochastic models, we investigate how gene regulatory networks interact with cell-to-cell communication to control cell fate decisions. Our results show that feedback loops and paracrine signalling act as biological switches that trigger transitions from temporary to stable cellular states. We provide mathematical expressions that predict the signalling thresholds needed for these transitions and identify a key physical constraint: the mean size of phenotypic regions scales with the cubic root of signalling strength. This relationship reveals why maintaining large, stable domains requires disproportionately high signalling costs. This work highlights the fundamental trade-offs between pattern stability and signalling efficiency that organisms must balance during development. Our findings contribute to a deeper understanding of the principles governing tissue organisation and multicellular patterning in biological systems.

Organized by: Eric Cytrynbaum (University of British Columbia), Tim Tian (University of British Columbia)

1. Hannah Scanlon Duke University
   "Mechanisms of Microtubule Polarity Regulation in Neuronal Regeneration"
Across many organisms, neurons in the peripheral nervous system (PNS) can regenerate injured axons while neurons in the central nervous system cannot. Experimentalists have identified responses in polarized, cytoskeletal filaments called microtubules which are key to facilitating axon regeneration in injured PNS neurons. In a healthy neuron, microtubules maintain a strict polarity distribution over the lifetime of the cell. In response to axon injury in the PNS, microtubules rearrange dramatically to facilitate axonal regeneration. While several mechanisms have been hypothesized to regulate microtubule polarity organization, they are difficult to verify experimentally. Motivated by experiments in fruit flies, we use multi-scale mathematical modeling to investigate mechanisms related to microtubule polarity regulation. This work seeks to assess the efficacy of hypothesized mechanisms at producing the microtubule polarity observed in healthy neurons and in response to axon injury.
2. Taeyoon Kim Purdue University
   "Reconstituting the Mechanical and Dynamic Behaviors of the Actin Cytoskeleton"
Actin cytoskeleton is a dynamic structural scaffold used by eukaryotic cells to provide mechanical integrity and resistance to deformation, while simultaneously remodeling itself and adapting to diverse extracellular stimuli. The actin cytoskeleton utilizes these properties to play crucial roles in essential cellular processes such as cell migration and division. However, despite its known mechanical role in cell behaviors, a clear understanding of the mechanical properties of actin cytoskeleton and the molecular origin of these properties still lacks, partly due to experimental limitations. Computer simulations can access time and length scales inaccessible by experiments, and thus aid in creating a descriptive model of the molecular interactions that evolve into the mechanical properties observed on cellular scales. To this end, we have developed a cutting-edge computational model which is designed to reproduce the mechanical and dynamic behaviors of actin cytoskeleton within cells. Guided by explicit experimental data, we systematically explored, via simulation, how the mechanics and dynamics of actins and actin-binding proteins determine the deformation, flow, and stiffness of the passive actin cytoskeleton. We also investigated how interactions between the passive cytoskeletal constituents and active molecular motors lead to force generation, contraction, and morphological changes in the active actin cytoskeleton. In this talk, we will briefly introduce our foundational works and discuss our recent studies designed to illuminate the mechanisms of various cellular phenomena, including the pulsed contraction of cell cortex, actin retrograde flow in the lamellipodia, and cell blebbing.
3. Calina Copos Northeastern University
   "Modeling insights into actin cytoskeleton regulation with external size changes"
Actin is one of the most abundant proteins in eukaryotic cells and a fundamental component of the cytoskeleton, playing a critical role in maintaining cell structure and enabling motility. A compelling preliminary experimental observation underpins our work: in micropatterned epithelial cells of increasing sizes, the mechanical energy does not scale linearly with size. Instead, an optimal force is generated at a critical cell size, suggesting a force response that combines both passive and active mechanical components. To explore this phenomenon, we present a mechanical model of the actin cytoskeleton in an adherent cell that captures the observed biphasic response in force production, arising from an underlying scaling law in cytoskeletal mechanical properties. Complementing this, we develop an agent-based model that simulates the microscopic dynamics of actin filament formation, incorporating crosslinkers and myosin motors. Within this framework, we test various hypotheses — such as the impact of limited resources — that could give rise to the scaling law identified in the macroscopic model. Together, these efforts constitute a multiscale approach aimed at uncovering the mechanisms by which cell size regulates cytoskeletal force generation.
4. Tim Y.Y. Tian University of British Columbia
   "Organization of Plant Cortical Microtubules"
The self-organization of cortical microtubule arrays within plant cells is an emergent phenomenon with important consequences for the synthesis of the cell wall, cell shape, and subsequently the structure of plants. Mathematical modelling and experiments have elucidated the underlying processes involved. However, the mechanical influence of membrane curvature on these elastic filaments has largely been ignored. We previously proposed a model to describe how the anchoring process may control the deflection of individual microtubules seeking to minimize bending on a cylindrical cell. We implement this process into a model of interacting microtubules and find the cell curvature influence should be significant: the array favours orientations parallel to the direction of elongation rather than the expected transverse direction. Even without elasticity, the geometry of large cells hinders robust microtubule organization. These results suggest the necessity of additional processes to overcome these factors. Alongside this, there has been growing interest in modelling the influence of various other processes such as nucleation and membrane tension. We present ongoing efforts in piecing together our results with others from increasingly complex models, with the goal of better understanding the bigger picture of microtubule organization.

1. 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.
2. 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.
3. neda khodabakhsh joniani Mrs She
   "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.
4. 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.
5. somdata sina INDIAN INSTITUTE OF SCIENCE EDUCATION RESEARCH (IISER) KOLKATA, INDIA
   "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'.
6. 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.
7. 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.
8. 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.
9. Katrin Schröder Goethe University
   "mRNA Translation Stalling in Single-Codon Resolution Monte-Carlo Ribosome Flow Model Simulations"
Ribosomal stalling during translation of mRNA can result for example from oxidative conditions surrounding the site of translation. It impacts the cellular protein production machinery and therefore decrease cell proliferation. Accordingly, the rate of protein synthesis (R) can be considered as a hallmark of ribosomal stalling. In vivo experiments can determine protein content of a cell and differences in ribosomal density for different stalling scenarios. We employ the Ribosome Flow Model (RFM) coupled with Monte Carlo simulations to quantitatively establish the implications of three stalling patterns motivated by biological processes: We consider (1) the overall frequency of stalling sides as defined by harmful mRNA modification, (2) the degree of the reduction of the translocation rate λ reflecting the severity of mRNA transcriptional impairments, as well as (3) the effect of clustering, chain and gap impairments, as well as cluster locality of these anomalies. Each of these stalling patterns impacts protein synthesis rate and ribosomal density differently. We show how quantitative prediction of the impact of each and combinations of these patterns can be used as to study and predict mRNA stalling. Major findings of our analysis are, that for a given severity of mRNA damage, the equilibrium rate of protein synthesis R* does not depend on impairment locality, and is not related to the ribosomal density. In contrast, ribosomal density is strongly dependent on the locality of impairment clustering.
10. Adriana Zanca The University of Melbourne
    "Cell fate through the lens of random dynamical systems"
How pluripotent cells give rise to progressively more specialised cells over multiple cell divisions, known as cell fate, remains one of the mysteries of systems biology. During development, it is of the utmost importance that cells uphold certain division regimes for an organism to survive and thrive. Beyond development, cell fate perturbations can result in cancer and other pathological conditions. The theoretical and mathematical biology community has been making contributions to our understanding of cell fate including by quantifying Waddington’s seminal landscape using dynamical systems, performing statistical trajectory inference on single-cell sequencing data, or considering geometric and algebraic approaches to cell fate. In this talk, I will present a random dynamical systems interpretation of cell fate. This approach is, arguably, a generalisation of existing models of cell fate that may be able to provide new perspectives into cell fate.
11. Supriya Bidanta Indiana University
    "Understanding the role of hydration in aging of skin epidermis through a modeling cell-cell communication"
Advances in cell type and gene expression mapping have significantly enhanced our understanding of the human body. However, comprehending interactions at cellular and tissue levels is equally critical for unveiling mechanisms underlying health and aging. This project leverages data from the Human BioMolecular Atlas Program (HuBMAP) and Human Cell Atlas (HCA) to explore cellular functionality within functional tissue units (FTUs) of the skin epidermis. Using HuBMAP and HCA single-cell RNA sequencing (scRNA-seq) and transcriptomics data, we identify key cell types acting as chemical secretors (ligands) and receivers (receptors) in healthy and diseased tissue. We employ PhysiCell, an agent-based modeling platform, to construct a 3D computational cellular environment. The workflow involves preprocessing the transcriptomics data into a machine-readable format and generating chemical communication graphs that capture th ofe dynamic interplay signaling molecules between secretor and receiver cells. By combining biological data with multiscale ABM, we aim to visually and quantitatively model the chemical interactions within the epidermal FTUs of human skin tissue. The overarching goal is to develop a mathematical model elucidating how hydration-mediated cellular communication impacts tissue homeostasis and delays aging processes. This research has the potential to provide new insights into the mechanisms of skin aging and inform strategies for promoting tissue health through hydration management.
12. Samuel Johnson University of Oxford
    "Mathematical Optimisation of Actin-Driven Protrusion Formation in Eukaryotic Chemotaxis"
In eukaryotic chemotaxis, cells extend and retract transient actin-driven protrusions at their membrane. These protrusions facilitate both the detection of external chemical gradients and directional movement via the formation of focal adhesions with the extracellular matrix. While extensive experimental work has characterised how protrusive activity varies with a range of environmental parameters, the mechanistic principles governing these relationships remain poorly understood. Here, we model the extension of actin-based protrusions in chemotaxis mathematically as an optimisation problem, wherein cells must balance the detection of external chemical gradients with the energetic cost of protrusion formation. The model highlights energetic efficiency in movement as a major predictor of phenotypic variation amongst motile cell populations, successfully reproducing experimentally observed but previously non-understood patterns of protrusive activity across a range of biological systems. Additionally, we leverage the model to generate novel predictions regarding cellular responses to environmental perturbations, providing testable hypotheses for future experimental work.

1. 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.
2. 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.
3. 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.
4. Katrin Schröder Goethe University
   "mRNA Translation Stalling in Single-Codon Resolution Monte-Carlo Ribosome Flow Model Simulations"
Ribosomal stalling during translation of mRNA can result for example from oxidative conditions surrounding the site of translation. It impacts the cellular protein production machinery and therefore decrease cell proliferation. Accordingly, the rate of protein synthesis (R) can be considered as a hallmark of ribosomal stalling. In vivo experiments can determine protein content of a cell and differences in ribosomal density for different stalling scenarios. We employ the Ribosome Flow Model (RFM) coupled with Monte Carlo simulations to quantitatively establish the implications of three stalling patterns motivated by biological processes: We consider (1) the overall frequency of stalling sides as defined by harmful mRNA modification, (2) the degree of the reduction of the translocation rate λ reflecting the severity of mRNA transcriptional impairments, as well as (3) the effect of clustering, chain and gap impairments, as well as cluster locality of these anomalies. Each of these stalling patterns impacts protein synthesis rate and ribosomal density differently. We show how quantitative prediction of the impact of each and combinations of these patterns can be used as to study and predict mRNA stalling. Major findings of our analysis are, that for a given severity of mRNA damage, the equilibrium rate of protein synthesis R* does not depend on impairment locality, and is not related to the ribosomal density. In contrast, ribosomal density is strongly dependent on the locality of impairment clustering.
5. Adriana Zanca The University of Melbourne
   "Cell fate through the lens of random dynamical systems"
How pluripotent cells give rise to progressively more specialised cells over multiple cell divisions, known as cell fate, remains one of the mysteries of systems biology. During development, it is of the utmost importance that cells uphold certain division regimes for an organism to survive and thrive. Beyond development, cell fate perturbations can result in cancer and other pathological conditions. The theoretical and mathematical biology community has been making contributions to our understanding of cell fate including by quantifying Waddington’s seminal landscape using dynamical systems, performing statistical trajectory inference on single-cell sequencing data, or considering geometric and algebraic approaches to cell fate. In this talk, I will present a random dynamical systems interpretation of cell fate. This approach is, arguably, a generalisation of existing models of cell fate that may be able to provide new perspectives into cell fate.

1. Supriya Bidanta Indiana University
   "Understanding the role of hydration in aging of skin epidermis through a modeling cell-cell communication"
Advances in cell type and gene expression mapping have significantly enhanced our understanding of the human body. However, comprehending interactions at cellular and tissue levels is equally critical for unveiling mechanisms underlying health and aging. This project leverages data from the Human BioMolecular Atlas Program (HuBMAP) and Human Cell Atlas (HCA) to explore cellular functionality within functional tissue units (FTUs) of the skin epidermis. Using HuBMAP and HCA single-cell RNA sequencing (scRNA-seq) and transcriptomics data, we identify key cell types acting as chemical secretors (ligands) and receivers (receptors) in healthy and diseased tissue. We employ PhysiCell, an agent-based modeling platform, to construct a 3D computational cellular environment. The workflow involves preprocessing the transcriptomics data into a machine-readable format and generating chemical communication graphs that capture th ofe dynamic interplay signaling molecules between secretor and receiver cells. By combining biological data with multiscale ABM, we aim to visually and quantitatively model the chemical interactions within the epidermal FTUs of human skin tissue. The overarching goal is to develop a mathematical model elucidating how hydration-mediated cellular communication impacts tissue homeostasis and delays aging processes. This research has the potential to provide new insights into the mechanisms of skin aging and inform strategies for promoting tissue health through hydration management.
2. Samuel Johnson University of Oxford
   "Mathematical Optimisation of Actin-Driven Protrusion Formation in Eukaryotic Chemotaxis"
In eukaryotic chemotaxis, cells extend and retract transient actin-driven protrusions at their membrane. These protrusions facilitate both the detection of external chemical gradients and directional movement via the formation of focal adhesions with the extracellular matrix. While extensive experimental work has characterised how protrusive activity varies with a range of environmental parameters, the mechanistic principles governing these relationships remain poorly understood. Here, we model the extension of actin-based protrusions in chemotaxis mathematically as an optimisation problem, wherein cells must balance the detection of external chemical gradients with the energetic cost of protrusion formation. The model highlights energetic efficiency in movement as a major predictor of phenotypic variation amongst motile cell populations, successfully reproducing experimentally observed but previously non-understood patterns of protrusive activity across a range of biological systems. Additionally, we leverage the model to generate novel predictions regarding cellular responses to environmental perturbations, providing testable hypotheses for future experimental work.

1. Devi Prasad Panigrahi University College London
   "Intermittent attractions lead to emergent material properties in migrating cell aggregates"
Cells migrate in response to gradients in extra-cellular chemical signals in a process known as chemotaxis. Recent experiments on the model microorganism Dictyostelium discoideum have shown that dense aggregates of cells collectively undergoing chemotaxis exhibit emergent fluid-like properties such as viscosity and surface tension. In this work, we use simulations to explain how active interactions between cells give rise to these emergent phenomena. We propose an agent-based model for intermittent cell-cell attachments and show that it gives rise to emergent fluid-like behavior for an aggregate of cells. We generalize this model to include cell-surface attachments, and show that surface-associated aggregates display properties similar to a liquid droplet resting on a surface. Furthermore, we study the situation where cells self-generate and respond to a chemical gradient by consuming an externally supplied chemoattractant. Our simulations reveal how individual cells move inside the swarm as the cells move as a collective. Finally, we predict some of the key cellular processes that are responsible for this collective behavior, and provide hypotheses to be tested in future experimental studies.
2. Wesley Ridgway University of Oxford
   "Motility-Induced Patterning in Signalling Bacteria"
Chemical signaling, or quorum sensing (QS), promotes collective behaviour in bacteria, from biofilm formation to swarming. By coupling QS systems with genes that control motility, bacteria can be engineered to generate tunable spatio-temporal patterns in vitro. However, it is not well-understood in general how the type of gene-regulatory network affects emergent population-level patterning. In this talk, we investigate the effect of the gene-regulatory network on emergent patterning in a population of motile bacteria that interact via QS. By formally upscaling a cell-level model in a biologically relevant scaling regime, we derive a continuum model that explicitly accounts for genetic regulation of motility and signal production through chemical structuring. Using a WKBJ-like framework, we derive criteria for the onset of two types of emergent patterning for a canonical QS circuit. We also uncover a new route to the well-known phenomenon of motility-induced phase separation (MIPS) through genetic regulation of tumbling frequency. Lastly, we discuss generalisations of our WKBJ-like analysis to more complex gene-regulatory networks that exhibit bistability.
3. Connor Shrader University of Utah
   "Quantifying the roles of drift and selection in spermatogonial stem cell dynamics"
Stem cells maintain and repair our tissues, but not all stem cells are identical. As organisms age, distinct stem cell 'clones' can begin to dominate the cell population. While this behavior has been observed across multiple species and organs, the mechanisms and consequences of stem cell clonality are still poorly understood. We have developed a novel experimental approach using a CRISPR-Cas9 system to uniquely “barcode” spermatogonial stem cell clones in the testes of male zebrafish. Once these fish reach sexual maturity, we sample sperm each month to determine the contribution of each stem cell clone to the sperm pool over time. The observed clonal dynamics may be driven by factors such as genetic drift, selection, or sampling error. We hypothesize that a small number of clones are under positive selection, resulting in their eventual dominance in the sperm pool. To bridge the gap between theory and data, we have developed stochastic models of stem cell dynamics in the testis. These models are formulated as hidden Markov models that describe rules for the division and differentiation of stem cells within the testis. We first evaluate our ability to estimate model parameters on simulated data. Then, we apply our model to the experimental data to quantify evidence for genetic drift and selection. Our models provide insight into how individual stem cell behavior can lead to population-level clonality.
4. Marwa Akao Nagoya university
   "Quantitative understanding of bone loss mechanism in mice using mathematical analysis"
Osteoporosis is a disease that affects more than 200 million people all over the world. Although its underlying mechanisms are gradually being revealed, effective treatments or preventive measures have not been established yet. This study focused on age-related osteoporosis by measuring bone mass and bone metabolism markers in mice from 4 to 52 weeks of age. We developed mathematical models describing bone metabolism and analyzed experimental data. From the result of data analysis, we quantitatively elucidated the mechanisms of bone loss. Furthermore, we conducted treatment intervention simulations by changing parameter values in mathematical models to identify effective bone metabolism pathways for increasing bone mass and new potential therapeutic strategies.
5. William Annan Clarkson University
   "Studying Retinal Detachment Progression Using an Immersed Boundary Method"
Retinal detachment occurs when the neurosensory retina separates from the retinal pigment epithelium (RPE), disrupting the nutrient supply to photoreceptor cells. There are three types of retinal detachment: exudative (ERD), tractional (TRD), and rhegmatogenous (RRD), with RRD being the most common. RRD develops when a retinal tear or hole allows vitreous humor to enter the subretinal space, causing the neurosensory retina to detach from the RPE. If left untreated, this condition can lead to irreversible vision loss. Although ophthalmological tools can detect RRD, its rate of progression—particularly due to continuous eye movement—remains poorly understood. This study develops a fluid-structure interaction model to examine how various factors, including retinal thickness, elasticity, adhesion strength between the retina and RPE, vitreous humor density and viscosity, and eye rotation speed, influence detachment progression. By quantifying detachment rates under different conditions, this research aims to enhance our understanding of RRD dynamics and refine estimates of effective treatment timelines to prevent permanent visual impairment. Student: William Ebo Annan Advisors: Prof. Diana White & Prof. Emmanuel O.A. Asamani

1. Lucy Ham The University of Melbourne
   "Cell fate control in space and time"
Genetically identical cells can adopt distinct, stable states, playing a crucial role in development and tissue organisation. This talk explores the mechanisms driving cell fate decisions, focusing on the interplay between gene regulatory networks and cell-to-cell communication. Using spatial stochastic models that capture fine-scale regulatory dynamics, we demonstrate how feedback loops and paracrine signalling function as switch-like controllers of cell fate, enabling transitions from transient to stable states. We derive mathematical expressions predicting the threshold signalling strength required to trigger phase transitions and establish a fundamental limit on the spatial spread of phenotypic regions. Specifically, we show that the mean region size scales proportionally to the cubic root of the signalling strength, implying that large, stable domains are prohibitively costly to maintain. This trade-off between robustness and signalling precision highlights the constraints organisms must navigate during development to maintain spatial organisation. Our findings provide key insights into the principles governing multicellular patterning and the regulation of tissue structure.
2. Molly Brennan University College London
   "An asymptotic upscaling of transport across bacterial membranes"
Multiscale problems are prevalent in many real world scenarios, especially in biology, where the behaviour of a single microorganism can have considerable impact over lengthscales much larger than its own. In this work we consider the effect of the membrane microstructure of a bacterial cell on the behaviour of concentration profiles of relevant molecules on bacterial and bacterial colony lengthscales. Transport through the outer membrane of gram-negative bacteria is restricted to specific channels and non-specific porins. These provide a size-restricted passageway for small molecules through an otherwise impermeable membrane. The effects of these channels are important, for example, antibiotics must cross the outer membrane in order to effectively target gram-negative bacteria, and quorum sensing molecules must cross the membrane to allow bacterial colonies to coordinate mass phenotypic changes such as the production of virulence factors. In mathematical models this limiting transport mechanism across the membrane is often represented via phenomenological constitutive boundary conditions. In this work, we systematically derive the correct effective boundary conditions to impose across a bacterial membrane in terms of physical channel and porin properties. We use a hybrid mathematical approach, combining multiscale methodology such as asymptotic homogenisation and boundary layer theory with numerical simulations. More broadly, because we consider a generic membrane geometry and do not impose a specific outer problem, the results that we derive have a wide scope of potential applications beyond bacterial membranes, for example, to model water vapour or heat loss through fabrics, or mass transfer through surface coatings in chemical engineering.
3. Augustinas Sukys The University of Melbourne
   "Cell-cycle dependence of bursty gene expression: insights from fitting mechanistic models to single-cell RNA-seq data"
Many genes are expressed in bursts of transcription, associated with alternating active and inactive promoter states. Such transcriptional bursting is characterised by the burst frequency and burst size, which describe how often a burst occurs and how many transcripts are produced per burst. These two burst parameters offer a simple, intuitive and practical quantitative description of bursty gene expression dynamics. However, a transcriptome-wide picture of how the burst frequency and size are modulated due to gene replication and other cell-cycle dependent factors remains missing. To address this, we fit mechanistic models of gene expression to mRNA count data for thousands of mouse genes, obtained by sequencing of single cells whose cell-cycle position has been inferred previously. Although we observe substantial heterogeneity in transcriptional regulation, we find that upon DNA replication, the genome-wide median burst frequency approximately halves, while the median burst size remains mostly unchanged, thus shedding light on the effect of gene dosage compensation. We show that to accurately estimate the bursting kinetics from sequencing data, mechanistic models must explicitly account for gene copy number variation and extrinsic noise due to factors varying across the cell cycle, whereas correcting for technical noise due to imperfect mRNA capture is less critical.
4. Elizabeth Trofimenkoff University of Lethbridge
   "Mathematical modeling of transcription-independent splicing events in human gene expression"
Pre-mRNA often contains introns, which are non-coding sequences that need to be cut out or spliced before translation occurs. The spliceosome, an essential catalyst composed of several proteins with specific sequence affinities, is required for this process. Very long introns must be removed in pieces, a process known as recursive splicing. The experimental literature on the time it takes for the splicing process to occur is inconsistent. Splicing was traditionally believed to be a slow process that could take anywhere from one to tens of minutes per splicing event. However, recent reports suggest that some splicing events occur within a few tens of seconds. We developed the chemical master equation corresponding to the biochemical mechanism of splicing, allowing us to derive the system’s probability distribution, and perform a stability analysis on two conditions based on an unknown association constant parameter associated with the binding step of the scaffolding complex. We also concluded that the distribution of splice times for a single event ranges from a few tens of seconds to a few tens of minutes. Through sensitivity analyses, we have found that the mean splicing time and distribution are almost entirely dependent on the rate at which the spliceosome is activated in the assembly process—i.e. when the U1 and U4 splicing factors dissociate—which confirms that this is the rate limiting step in the catalytic process. Finally, we have examined the distributions of recursive splicing up to six events, and derived analytic solutions for these recursive splicing events in the case where the scaffolding complex strongly binds to the pre-mRNA complex (the condition thought to favor recursive binding), thus providing a model that can be fit to experimental data to in order to evaluate the number of recursive splicing events occurring.
5. Stéphanie Abo University of Oxford
   "Travelling waves in age-structured collective cell migration"
This work examines the interplay between age-structure and migration dynamics in collective cell behaviour. We focus on the integration of cell cycle dynamics with spatial migration, particularly examining the 'go-or-grow' hypothesis in the context of age-dependent processes. Our framework extends classical travelling wave theory to account for the age structure of cell populations, offering new insights into how cell cycle phases influence moving fronts and invasion dynamics. We analyse wave speed characteristics and front dynamics in age-structured systems, addressing a significant gap in current mathematical biology literature. The research provides a novel theoretical foundation for understanding how cell-cycle dependent proliferation and migration behaviours contribute to collective cell dynamics.
6. Gordon R. McNicol University of Waterloo
   "Mechanotransducing structures promote self-driven cell surface patterning"
Cells respond to their local environment through mechanotransduction, converting mechanical signals into a biological response (e.g. cell growth, proliferation or differentiation). The cell cytoskeleton, particularly actomyosin stress fibres (SFs), and focal adhesions (FAs), which bind the cytoskeleton to the extra-cellular matrix (ECM), are central to this process, activating intracellular signalling cascades in response to deformation. We present a novel two-dimensional bio-chemo-mechanical model to describe the development of these structures, coupled through a positive feedback loop, and the associated cell deformation. Building on our previous one-dimensional approach, we similarly employ reaction-diffusion-advection equations to describe the evolution of key scaffolding and signalling proteins, and connect their concentrations to a viscoelastic description of the cell cytoplasm, ECM and adhesions. Further, we now incorporate other key mechanotransducing structures including the stiff cell nucleus, and plasma and cortical membranes. Working in an axisymmetric framework, we employ this model to explain how, dependent upon the mechanical properties of the surrounding ECM, non-uniform patterns of cell striation develop, leading to FA and SF localisation at the cell periphery. Moreover, a linear stability analysis reveals the stability of the axisymmetric configuration to various normal modes of deformation. By identifying non-axisymmetric modes with positive growth rates our model demonstrates a possible mechanism for self-driven surface patterning of cells in vitro.
7. Marc Roussel University of Lethbridge
   "The bacterial dimeric transcription factor NsrR: a case study of a regulatory protein with a large number of states"
In a number of bacteria, nitric oxide (NO) is converted to nitrate by an enzyme called Hmp. In emph{Streptomyces coelicolor}, synthesis of Hmp is in turn controlled by an iron-sulfur protein called NsrR. NsrR represses the transcription of two copies of the emph{hmp} gene in the emph{S. coelicolor} genome, but reaction of NsrR's iron-sulfur cluster with NO causes NsrR to dissociate from the emph{hmp} promoter, thus allowing Hmp to be expressed. While this is a straightforward control mechanism, NsrR is a dimer, and the iron-sulfur cluster in each monomer of NsrR can react with NO several times. Eventually, a repair system restores the NO-damaged iron-sulfur clusters of the dimers. But given that a single reaction with NO is sufficient to cause the NsrR dimer to dissociate from the emph{hmp} promoter, do we need to model the complex chemistry of the dimer, or is a highly simplified model that considers a single NsrR unit and its iron-sulfur cluster sufficient to capture the dynamics of this control system?
8. Paco Castaneda Ruan The University of Auckland
   "Exploring the role of Ca2+ influx in controlling competing oscillatory mechanisms in T cells using ODEs"
Across the spectrum of cell types, the concentration of calcium controls a wide array of cellular functions. These calcium signals, usually in the form of periodic oscillations, play a paramount role in correct cellular activity. T cells are fundamental to the correct behaviour of the immune system. These cells have recently been shown to exhibit two competing oscillatory mechanisms, depending on the influx of extracellular Ca2+. Ca2+ influx is controlled by two molecules, STIM1 and STIM2. When both STIMs are present, T cells showcase sinusoidal Ca2+ oscillations on a raised baseline, but when one of them is absent the nature of the oscillation changes to a mix of Ca2+ spikes and bursting periods. In this talk, we will present an ODE that attempts to explain how these two molecules control the nature of these oscillations in T cells
9. Lynne Cherchia University of Southern California
   "A tale of trafficking: On prolactin receptor localization in pancreatic β-cells"
The prolactin receptor (PRLR) is a single-pass transmembrane receptor driving pancreatic β-cell proliferation via JAK/STAT signaling activation. This signal transduction pathway enables insulin-secreting β-cells to adapt to metabolic stress; however, the precise mechanisms underlying the pathway’s proliferative effect remain ill-defined. Here we implement a pipeline that uses live-cell fluorescence imaging, reconstitution approaches, and fluorescence correlation spectroscopy (FCS) to inform a mathematical model of PRLR signaling in β-cells and build a quantitative, mechanistic understanding of the signaling network. PRLR signaling is dynamic, involving changes in the spatial organization of signaling molecules. We have observed PRLR undergoing rapid internalization, a behavior that has been shown and modeled in other signaling pathways but has not been considered in a mathematical model of PRLR signaling. Such a model is useful for predicting strategies to modulate β-cell function. PRLR internalization is observed in both our minimal engineered PRLR expression system and in native pancreatic tissue, while FCS and chemigenetic labeling with SNAP-tag confirm the presence of a low concentration plasma membrane pool of PRLR. Our imaging data are used to integrate PRLR trafficking dynamics into an ordinary differential equation (ODE) model of PRLR signaling. We employ the ODE model to test hypotheses targeting how the spatial heterogeneity of PRLR signaling dynamics affects downstream signaling outcomes. Our data underscore the versatility of building a generalizable modeling-imaging framework to quantitatively understand signal transduction in and beyond β-cells.
10. Rebecca Crossley University of Oxford
    "Travelling waves of phenotypically structured cell populations migrating into extracellular matrix"
Collective cell migration plays a crucial role in numerous biological processes, including cancer growth, wound healing, and the immune response. Often, the migrating population consists of cells with various different phenotypes. This study derives a general mathematical framework for modelling cell migration into the micro-environment, which is coarse-grained from an underlying individual-based model that captures some of the dynamics of cell migration that are influenced by the phenotype of the cell, such as: random movement, proliferation, phenotypic transitions, and interactions with the external environment. The resulting model provides a continuum, macroscopic description of cell invasion, which represents the phenotype of the cell as a continuous variable and is much more amenable to simulation and analysis than its individual-based counterpart when considering a large number of phenotypes. The results highlight how phenotypic structuring impacts the spatial and temporal dynamics of cell populations, demonstrating that different environmental pressures and phenotypic transition mechanisms significantly influence invasion patterns.

1. Gordon R. McNicol University of Waterloo
   "Mechanotransducing structures promote self-driven cell surface patterning"
Cells respond to their local environment through mechanotransduction, converting mechanical signals into a biological response (e.g. cell growth, proliferation or differentiation). The cell cytoskeleton, particularly actomyosin stress fibres (SFs), and focal adhesions (FAs), which bind the cytoskeleton to the extra-cellular matrix (ECM), are central to this process, activating intracellular signalling cascades in response to deformation. We present a novel two-dimensional bio-chemo-mechanical model to describe the development of these structures, coupled through a positive feedback loop, and the associated cell deformation. Building on our previous one-dimensional approach, we similarly employ reaction-diffusion-advection equations to describe the evolution of key scaffolding and signalling proteins, and connect their concentrations to a viscoelastic description of the cell cytoplasm, ECM and adhesions. Further, we now incorporate other key mechanotransducing structures including the stiff cell nucleus, and plasma and cortical membranes. Working in an axisymmetric framework, we employ this model to explain how, dependent upon the mechanical properties of the surrounding ECM, non-uniform patterns of cell striation develop, leading to FA and SF localisation at the cell periphery. Moreover, a linear stability analysis reveals the stability of the axisymmetric configuration to various normal modes of deformation. By identifying non-axisymmetric modes with positive growth rates our model demonstrates a possible mechanism for self-driven surface patterning of cells in vitro.
2. Marc Roussel University of Lethbridge
   "The bacterial dimeric transcription factor NsrR: a case study of a regulatory protein with a large number of states"
In a number of bacteria, nitric oxide (NO) is converted to nitrate by an enzyme called Hmp. In emph{Streptomyces coelicolor}, synthesis of Hmp is in turn controlled by an iron-sulfur protein called NsrR. NsrR represses the transcription of two copies of the emph{hmp} gene in the emph{S. coelicolor} genome, but reaction of NsrR's iron-sulfur cluster with NO causes NsrR to dissociate from the emph{hmp} promoter, thus allowing Hmp to be expressed. While this is a straightforward control mechanism, NsrR is a dimer, and the iron-sulfur cluster in each monomer of NsrR can react with NO several times. Eventually, a repair system restores the NO-damaged iron-sulfur clusters of the dimers. But given that a single reaction with NO is sufficient to cause the NsrR dimer to dissociate from the emph{hmp} promoter, do we need to model the complex chemistry of the dimer, or is a highly simplified model that considers a single NsrR unit and its iron-sulfur cluster sufficient to capture the dynamics of this control system?
3. Paco Castaneda Ruan The University of Auckland
   "Exploring the role of Ca2+ influx in controlling competing oscillatory mechanisms in T cells using ODEs"
Across the spectrum of cell types, the concentration of calcium controls a wide array of cellular functions. These calcium signals, usually in the form of periodic oscillations, play a paramount role in correct cellular activity. T cells are fundamental to the correct behaviour of the immune system. These cells have recently been shown to exhibit two competing oscillatory mechanisms, depending on the influx of extracellular Ca2+. Ca2+ influx is controlled by two molecules, STIM1 and STIM2. When both STIMs are present, T cells showcase sinusoidal Ca2+ oscillations on a raised baseline, but when one of them is absent the nature of the oscillation changes to a mix of Ca2+ spikes and bursting periods. In this talk, we will present an ODE that attempts to explain how these two molecules control the nature of these oscillations in T cells
4. Lynne Cherchia University of Southern California
   "A tale of trafficking: On prolactin receptor localization in pancreatic β-cells"
The prolactin receptor (PRLR) is a single-pass transmembrane receptor driving pancreatic β-cell proliferation via JAK/STAT signaling activation. This signal transduction pathway enables insulin-secreting β-cells to adapt to metabolic stress; however, the precise mechanisms underlying the pathway’s proliferative effect remain ill-defined. Here we implement a pipeline that uses live-cell fluorescence imaging, reconstitution approaches, and fluorescence correlation spectroscopy (FCS) to inform a mathematical model of PRLR signaling in β-cells and build a quantitative, mechanistic understanding of the signaling network. PRLR signaling is dynamic, involving changes in the spatial organization of signaling molecules. We have observed PRLR undergoing rapid internalization, a behavior that has been shown and modeled in other signaling pathways but has not been considered in a mathematical model of PRLR signaling. Such a model is useful for predicting strategies to modulate β-cell function. PRLR internalization is observed in both our minimal engineered PRLR expression system and in native pancreatic tissue, while FCS and chemigenetic labeling with SNAP-tag confirm the presence of a low concentration plasma membrane pool of PRLR. Our imaging data are used to integrate PRLR trafficking dynamics into an ordinary differential equation (ODE) model of PRLR signaling. We employ the ODE model to test hypotheses targeting how the spatial heterogeneity of PRLR signaling dynamics affects downstream signaling outcomes. Our data underscore the versatility of building a generalizable modeling-imaging framework to quantitatively understand signal transduction in and beyond β-cells.
5. Rebecca Crossley University of Oxford
   "Travelling waves of phenotypically structured cell populations migrating into extracellular matrix"
Collective cell migration plays a crucial role in numerous biological processes, including cancer growth, wound healing, and the immune response. Often, the migrating population consists of cells with various different phenotypes. This study derives a general mathematical framework for modelling cell migration into the micro-environment, which is coarse-grained from an underlying individual-based model that captures some of the dynamics of cell migration that are influenced by the phenotype of the cell, such as: random movement, proliferation, phenotypic transitions, and interactions with the external environment. The resulting model provides a continuum, macroscopic description of cell invasion, which represents the phenotype of the cell as a continuous variable and is much more amenable to simulation and analysis than its individual-based counterpart when considering a large number of phenotypes. The results highlight how phenotypic structuring impacts the spatial and temporal dynamics of cell populations, demonstrating that different environmental pressures and phenotypic transition mechanisms significantly influence invasion patterns.