Special Session 180: Individual and Collective Cells Dynamics in Medicine and Biology

Optimal Control of Cell Plasticity in GBM Cells via Levy-Driven Microscopic Dynamics

Sandesh Athni Hiremath Rhinelandpfalz Technical University Germany Co-Author(s):

Abstract: Glioblastoma (GBM) is a highly aggressive brain tumor characterized by extensive cellular heterogeneity and plasticity, which underlie its resistance to therapy and poor prognosis. Understanding and predicting the dynamic trajectories of GBM cell states is crucial for designing effective interventions. We propose a low-dimensional microscopic model driven by Levy noise that aims to capture the dynamics of gene regulation and transitions between phenotypic cell states. By formulating a stochastic optimal-control problem, we aim to find a suitable profile for the cell transcription factors that can drive cell-state transitions towards a particular desired state. Following this, we establish a macroscopic model for the system and propose a framework for integrating high-throughput single-cell data, thus offering a powerful tool for understanding GBM dynamics and guiding therapeutic development.

Beyond Differential Expression: A Robust ML Framework for Keloid Biomarker Discovery

Ali R Daher Marie and Louis Pasteur University France Co-Author(s):    Ali Daher, Fareeha Afzal, Raluca Eftimie

Abstract: Keloids are fibroproliferative skin disorders that arise following injury and extend beyond the original wound margins. Despite their clinical burden, their pathogenesis remains poorly understood, and current treatments are associated with high recurrence rates. Identifying biomarkers that uniquely distinguish keloids from other skin/scar types may provide insight into their underlying etiology and guide targeted therapeutic strategies. Previous studies have investigated candidate biomarkers; however, they are often limited by small sample sizes, restricted comparisons (e.g., keloid vs. hypertrophic scars), cross-platform inconsistencies, and reliance on conventional metrics such as fold-change, which may not capture the keloid uniquely distinguishing features. We present a rigorous, multi-layered machine learning framework to identify robust biomarkers that distinguish keloid from non-keloid samples. We curated and harmonized transcriptomic datasets (81 samples, 13 studies) across four tissue types: normal skin, normal scar, hypertrophic scar, and keloids, accounting for batch and technical variability. Using multiple classification algorithms with study-aware cross-validation, feature selection, stability analysis, and bootstrapping, we identified a minimal set of highly consistent genes with strong discriminatory power. Gene enrichment analysis of the five upregulated and three downregulated genes highlights increased lipid metabolism and decreased extracellular matrix organization as the dominant pathways affected, offering potential avenues for targeted treatment.

Computational investigation into the formation of nodules and cords during the evolution of the fibroproliferative Dupuytren Disorder

Raluca EFTIMIE University Marie and Louis Pasteur France Co-Author(s):    Georgiana Eftimie

Abstract: Dupuytren Disorder (DD) is a fibro-proliferative disorder characterised by fibrosis of palmar and digital fascia that leads to finger flexion deformities. It starts with a nodule in the palm, that can evolve into fibrous cords. Here, we present a simple mathematical model that can reproduce the main tissue-level patterns of DD: nodules, nodular cords and non-nodular cords. We investigate the parameters that have the most impact on cord contraction, and confirm that the fibroblast-to-myofibroblast transition is one of these parameters. Also, the amount of the injury signal required to trigger this transition seem to be important in Dupuytren contraction, pointing towards a potential link to individual genetics.

Data-driven modeling for Alzheimer`s disease

Wenrui Hao Penn State University USA Co-Author(s):

Abstract: Alzheimer`s disease (AD) is highly heterogeneous, with patients showing different biomarker trajectories, progression rates, and treatment responses. Traditional models offer insight but miss individual variability. We integrate machine learning with mechanistic mathematical modeling to build patient digital twins that simulate disease progression and test personalized therapies. This framework deepens understanding of the biomarker cascade and supports precision medicine, with potential to reduce clinical trial cost and accelerate therapeutic development.

Behavioral Feedback and Perceived Prevalence: Reconciling Epidemic Dynamics in a Classic Boarding School Outbreak

Harsh Jain University of Minnesota Duluth USA Co-Author(s):

Abstract: Mathematical models of infectious disease transmission increasingly support public health decision-making, yet observed epidemic dynamics reflect not only pathogen biology but also adaptive human behavior. Behavioral responses to perceived risk can alter contact patterns and transmission. When such feedbacks are ignored or absorbed into constant parameters, models may reproduce epidemic trajectories while implying unrealistic outbreak sizes. In this talk, we revisit the well-known 1978 influenza outbreak in a British boys boarding school. Standard SIR models fitted to the infection time series typically fail to explain the large fraction of students who remained uninfected. We show that this discrepancy reflects a structural limitation of constant-transmission models rather than a parameter estimation issue. We then infer a time-varying transmission rate and introduce perceived prevalence, a short-term memory of recent infections that approximates how severe the outbreak appears to the population. Incorporating this behavioral driver allows a minimal SIR model to match both the infection time course and the final outbreak size. We then translate these inferred dynamics into an agent-based model to examine whether the behavioral response reflects reduced contact rates or changes in per-contact transmission probability, while allowing heterogeneity in susceptibility through innate immunity among the students.

Modeling Collective Pattern Formation in Biological Reaction-Diffusion Systems Using Moving Mesh Methods

Darae Jeong Kangwon National University Korea Co-Author(s):

Abstract: Collective pattern formation arises in many biological systems, including cell aggregation, tissue organization, animal skin patterns, and interacting populations. Reaction-diffusion models provide an effective framework for describing the emergence and evolution of such spatial structures, but numerical simulation becomes challenging when solutions develop localized patterns, sharp gradients, and multiscale features. In this talk, I present moving mesh methods as an efficient computational approach for biological reaction-diffusion systems. The main idea is to adaptively redistribute mesh points according to the evolving solution profile, so that computational effort is concentrated near regions with significant spatial variation while unnecessary resolution is avoided elsewhere. I will discuss the basic idea and implementation of the moving mesh framework combined with finite difference discretizations, and illustrate its performance through examples exhibiting spike-type patterns, transition layers, and self-organized structures. These results show that moving mesh methods provide a practical and accurate tool for analyzing complex pattern formation phenomena in mathematical biology.

Mathematical modeling of glioblastoma dynamics and development of anti-cancer therapy in brain: Trojan neutrophils

Yangjin Kim Konkuk University/Brown University Korea Co-Author(s):    Haneol Cho, Junho Lee, Sean Lawler

Abstract: Glioblastoma multiforme (GBM) is the most aggressive form of brain cancer with the very poor survival and high recurrence rate. Tumor-associated neutrophils (TANs) play a pivotal role in regulation of the tumor microenvironment. In this study, we developed a new multi-scale model of the critical GBM-TAN interaction in the heterogeneous brain tissue. The model reveals that the dual and complex role of TANs (either anti-tumorigenic N1 and the pro-tumorigenic N2 type) regulates the phenotypic trajectory of the evolution of tumor growth and the invasive patterns in white and gray matter via mediators such as IFN-beta and TGF-beta. We investigated the effect of normalizing the immune environment on glioma growth by applying a therapeutic antibody and developed several strategies for eradication of tumor cells by neutrophil-mediated transport of nanoparticles. We also developed a strategy of combination therapy (surgery + Trojan neutrophils) for effective control of the infiltration of the glioma cells in one hemisphere before crossing the corpus callosum (CC) in order to prevent recurrence in the other hemisphere. This alternative approach compared to the extended resection of the glioma including CC or butterfly GBM may provide the greater anti-tumor efficacy and reduce side effects such as cognitive impairment.

Asthma-mediated control of optic glioma growth via T cell-microglia interactions: A mathematical model

Donggu Lee Konkuk University Korea Co-Author(s):    Sean Lawler, Yangjin Kim

Abstract: Optic glioma, a slow-growing tumor, is associated with Neurofibromatosis type 1 (NF1) mutations and increased midkine (MDK) production. A connection between asthma and optic glioma has previously been observed, but the mechanisms are unclear. To elucidate the role of asthma in the regulation of glioma formation, we investigated the role of T cells and the subsequent pathways in the regulation of microglia, a key player in the glioma tumor microenvironment (TME). While asthma is often linked to chronic inflammation, our mathematical analysis and experimental evidence suggest that inflammation can play a key role in suppressing the proliferation of optic glioma cells via immune reprogramming of T cells and the delicate control of signaling networks in microglia. Our mathematical model unveils the complex interactions between tumor and immune cells in optic glioma. Our results indicate that asthma-induced T cell reprogramming inhibits tumor growth by promoting the release of decorin and a subsequent suppression of CCR8 and the intercellular binding kinetics in microglia, followed by blocking of CCL5 production in TME via suppression of NFkB. We developed anti-cancer strategies by leveraging this asthma-induced immune regulation.

Beyond homogeneity: Assessing the validity of the Michaelis-Menten rate law in spatially heterogeneous environments

Seunggyu Lee Korea University Korea Co-Author(s):

Abstract: The Michaelis-Menten (MM) rate law has been a fundamental tool in describing enzyme-catalyzed reactions for over a century. When substrates and enzymes are homogeneously distributed, the validity of the MM rate law can be easily assessed based on relative concentrations: the substrate is in large excess over the enzyme-substrate complex. However, the applicability of this conventional criterion remains unclear when species exhibit spatial heterogeneity, a prevailing scenario in biological systems. Here, we explore the MM rate law`s applicability under spatial heterogeneity by using partial differential equations. In this study, molecules diffuse very slowly, allowing them to locally reach quasi-steady states. We find that the conventional criterion for the validity of the MM rate law cannot be readily extended to heterogeneous environments solely through spatial averages of molecular concentrations. That is, even when the conventional criterion for the spatial averages is satisfied, the MM rate law fails to capture the enzyme catalytic rate under spatial heterogeneity. In contrast, a slightly modified form of the MM rate law, based on the total quasi-steady state approximation (tQSSA), is accurate. Specifically, the tQSSA-based modified form, but not the original MM rate law, accurately predicts the drug clearance via cytochrome P450 enzymes and the ultrasensitive phosphorylation in heterogeneous environments. Our findings shed light on how to simplify spatiotemporal models for enzyme-catalyzed reactions in the right context, ensuring accurate conclusions and avoiding misinterpretations in in silico simulations.

An Age-Structured and Renewal Perspective on Metastatic Growth

GEORGIOS LOLAS INCELLIA Greece Co-Author(s):    Lolas, Georgios, Gavriliadis, Panagiotis, & Matsoukas, Themis

Abstract: \begin{abstract} We revisit the classical Iwata--Kawasaki--Shigesada model of metastatic dissemination by reformulating it in terms of lesion age rather than tumor size. Whereas the original framework classifies metastases according to size, size alone does not fully capture the biological history of a lesion: tumors of similar size may differ markedly in their age, growth trajectory, and capacity to generate further metastatic spread. By taking lesion age as the principal structuring variable, we obtain a formulation that is both mathematically more tractable and biologically more informative. This shift in perspective transforms the original size-structured transport equation into an age-structured model with a simpler and more transparent structure. The resulting formulation preserves the behavior of the classical model over clinically relevant time scales, while improving computational efficiency and interpretability. In particular, it clarifies how metastatic burden accumulates over time, how newly seeded lesions contribute to the evolving population, and how a relatively small number of clinically visible metastases may coexist with a much larger, occult population of microscopic disease. We further prove that the age-structured formulation is exactly equivalent to a renewal equation governing the production of new metastases. This equivalence makes the system amenable to direct analytical treatment. In the case of Gompertzian growth and power-law metastatic emission, the model yields explicit results for the asymptotic expansion of the metastatic population and provides a natural framework for the analysis of long-time behavior and detection thresholds. Overall, the age-based reformulation offers a transparent, biologically meaningful, and computationally efficient framework linking primary tumor growth, metastatic seeding, and the emergence of clinically detectable disease. \end{abstract}

A cell-based mathematical model for meniscus tissue regeneration

Nishith NM Mohan RPTU Kaiserslautern-Landau Germany Co-Author(s):    Shimi Chettiparambil Mohanan, Nishith Mohan and Christina Surulescu

Abstract: We propose and analyze a haptotaxis model for mensicus tissue regeneration, obtained by parabolic upscaling from kinetic transport equations written for the mesoscopic densities of mesenchymal stem cells and chondrocytes, which evolve in an artificial scaffold impregnated with hyaluron. We establish global existence of classical solutions to the coupled macroscopic system and investigate the qualitative behavior of solutions through stability and bifurcation analysis. They reveal that haptotaxis mechanisms primarily drive the emergence of spatial patterns. Numerical simulations further illustrate the influence of varying tactic sensitivities and initial configurations on the spatio-temporal evolution of the system.

Decoding Genetically Encoded Wiring Principles of the Brain from Connectome and Spatial Transcriptome Data

Honda Naoki Nagoya University Japan Co-Author(s):    Honda Naoki and Jigen Koike

Abstract: How genetically encoded molecular patterns shape brain-wide neural wiring remains a fundamental question in neuroscience. To address this, we developed SPERRFY (Spatial Positional Encoding for Reconstructing Rules of axonal Fiber connectivitY), a data-driven framework that integrates connectome data with spatial transcriptome data to infer latent positional gradients underlying neural connectivity. Using mouse brain data from the Allen Brain Atlas, SPERRFY analyzes paired gene-expression profiles at the source and target regions of anatomical projections by canonical correlation analysis. This approach identifies multiple gradient pairs that explain major features of the connectome, spanning both global and local organization. Neural connectivity reconstructed from the inferred gradients shows strong predictive performance and substantially outperforms reconstruction based on physical distance alone. Comparison with null models further supports the biological relevance of the extracted structure. By linking the inferred gradients to individual genes, SPERRFY also provides candidate molecular determinants of wiring specificity. These results extend the classical chemoaffinity concept from topographic circuits to whole-brain connectivity and provide a general framework for decoding genetically encoded design principles of brain architecture.

Towards Data-Driven Modeling of Cell Cycle and Wound Closure Processes

Qiyao (Alice) Q Peng Lancaster University England Co-Author(s):    Erik Blom, Leah Pomfret, Richard Mort and Stefan Engblom

Abstract: Effective wound repair treatments rely on a clear picture of how cell proliferation and migration are coordinated during tissue restoration. Fibroblasts are key contributors to tissue restoration in the dermis, and modern imaging tools allow their cell-cycle progression to be observed directly, enabling comparison between experiments and computational models. Here we investigate how different stages of the cell cycle influence fibroblast-driven wound closure using the Discrete Laplacian Cell Mechanics (DLCM) framework driven by time-lapse microscopy data. In vitro assays provide cell positions, migration behaviour, and cycle-stage information, and we show that incorporating proliferation, migration, and cell cycle arrest allows the computational model to reproduce the essential experimental trends. The results reveal that arrest in the G1 phase notably impacts the cell cycle dynamics and that the initial spatial arrangement of cycle states significantly affects wound closure. By linking single-cell cycle dynamics with emergent tissue behaviour this work establishes a quantitative approach for exploring how intracellular processes shape repair processes. More broadly, it demonstrates the value of integrating high-resolution data with cell-based mechanical models and provides a foundation for systematic in silico evaluation of therapeutic interventions.

Data driven mathematical modeling of immune cells interactions in tissues

Leili Shahriyari University of Massachusetts Amherst USA Co-Author(s):

Abstract: In this talk, I present a computational approach to precision oncology that combines mechanistic modeling with modern machine learning to build predictive digital twins; patient- and subgroup-specific models that forecast tumor progression and response to therapy. Our foundation is quantitative systems pharmacology (QSP) modeling, where tumor immune dynamics are represented as systems of differential equations. We parameterize these models using patient observations and introduce a clustered inference strategy that stratifies individuals by immune profiles and estimates mechanistic parameters within each cluster. This reduces heterogeneity, improves identifiability, and yields interpretable subgroup phenotypes that link immune state to dynamical behavior. A distinguishing aspect of our evaluation is out-of-treatment generalization: we calibrate tumor growth and immune dynamics without fitting treatment response data, then use the resulting mechanistic parameters to predict outcomes under therapy. This design sharpens the scientific test of the model and targets the real-world challenge of predicting under new regimens. I then describe a digital twin platform that operationalizes this pipeline.

Modeling Tumor-Immune Interactions in the Glioblastoma Microenvironment

Tracy Stepien University of Florida USA Co-Author(s):    Lucy Allan, Gillian Carr, Gregory P. Takacs, Jeffrey K. Harrison

Abstract: Glioblastoma (GBM) is an aggressive brain tumor that is extremely fatal with no current treatment options available that can achieve remission. One potential explanation for minimally effective treatments is due to the characteristically high immune-suppressive glioma microenvironment. We develop an agent-based model to simulate the interactions of glioma cells, T cells, and myeloid-derived suppressor cells (MDSCs) and the effects of oxygen, a T cell chemoattractant, and an MDSC chemoattractant. To validate our model and quantify cell clustering patterns in GBM, we use spatial statistics comparing simulations to data extracted from cross-sectional tumor images of cellular biomarkers.

Novel 3D multiscale advancements in modelling Glioblastoma invasion and relapse

Dumitru Trucu University of Dundee Scotland Co-Author(s):

Abstract: Recognising that the complexity of Glioblastoma (GBM) progression requires ever more sophisticated cross-scale interlinked processes to be considered in our modelling approaches, in this work we propose three novel advancements of the multiscale moving boundary framework introduced and established in Trucu et al. 2013 (https://doi.org/10.1137/110839011) and further developed in Robyn and Trucu 2019 (https://doi.org/10.1007/s11538-019-00598-w) and Szabolcs Suveges et al. 2021 (https://doi.org/10.3390/math9182214) by which the presence of the extracellular matrix fibres present at the interface is accounted for alongside with the availability of nutrients within sensing regions of the GBM cells. These will not only enable us to determine more realistic laws for the tumour boundary movement, but also to explore non-local go-or-grow collective cell motility behaviours arising within the bulk of the tumour, as well as to formulate mathematical the emergence of isotropic-to-anisotropic transition within the GBM cell population transport during the invasion of the surrounding brain tissue. These framework developments allow us to explore the emergence of cellular stress caused by both hypoxic behaviour and GBM treatment that lead to acquiring resistance and result in GBM relapse. This further addressed by considering the impact that key metabolic components have over the GBM progression and relapse in the presence treatment.

Mathematical Issues in Mechanical Models for Cells and TIssues

Fred Vermolen University of Hasselt Belgium Co-Author(s):

Abstract: Some cells like muscle cells, cancer cells, fibroblasts and myofibroblasts exert forces on their direct environment. Cells exert these forces because of rapid wound closure, to contract muscles or to migrate to other part of the body. Therefore, it is important to consider elastic effects in the tissue surrounding the cells. In this talk, we consider various formalisms for the impact of cellular forces in terms of the immerse interface method, as well as various constitutive equations that involve visco-elastiic effects that are combined with microstructural changes.