We propose a PDE system intended to describe the earliest stages of the interactions between immune cells and tumor growth. The model is structured in size and space, and it takes into account the migration of the tumor antigen-specific cytotoxic effector cells towards the tumor micro-environment by a chemotactic mechanism. Remarkably, the model exhibits a possible control of the tumor growth by the immune response; nevertheless, the control is not complete in the sense that the asymptotic equilibrium states keep residual tumors and activated immune cells. We will discuss the mathematical modeling, numerical investigation and a few results on the analysis of the system.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: Workshop "Mathematical modeling in life and health sciences" (2024)

We introduce and study a new model for the progression of Alzheimer's disease incorporating the interactions of A_beta-monomers, oligomers, microglial cells and interleukins with neurons through different mechanisms such as protein polymerization, inflammation processes and neural stress reactions. In order to understand the complete interactions between these elements, we study a spatially-homogeneous simplified model that allows to determine the effect of key parameters such as degradation rates in the asymptotic behavior of the system and the stability of equilibriums. We observe that inflammation appears to be a crucial factor in the initiation and progression of Alzheimer's disease through a phenomenon of hysteresis, which means that there exists a critical threshold of initial concentration of interleukins that determines if the disease persists or not in the long term. These results give perspectives on possible anti-inflammatory treatments that could be applied to mitigate the progression of Alzheimer's disease. We also present numerical simulations that allow to observe the effect of initial inflammation and spatial dependence.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: Workshop "Mathematical modeling in life and health sciences" (2024)

We investigate the mean-field limits of large-scale networks of interacting biological neurons, represented by the so-called integrate-and-fire models. However, we do not assume any prior structure on the network but consider instead any connection weights that obey certain types of mean-field scaling. When the networks are dense, we are able to achieve a limit that resembles the widely recognized form of mean-field limit, through a graphon limit that tracks the role of individual neurons in the network. When the networks are potentially sparse, mathematically interpreting the role of individual neurons becomes increasingly difficult. Instead, we introduce novel statistical notions that directly describe the large-scale dynamics of networks. This is a joint work with P.-E. Jabin and V. Schmutz.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: Workshop "Mathematical modeling in life and health sciences" (2024)

Volume exclusion interactions play a key role in many biological systems. In particular, it seems to be the key to explaining spontaneous alignment of anisotropic particles, for example, alignment of myxobacteria or fibers in a network. Most individual-based models impose this type of alignment in their equations. Here we do not wish to impose this type of alignment, but to investigate how it might emerge from volume exclusion interactions. To carry this out, volume exclusion interactions will be modelled via a soft anisotropic repulsion potential (which are vastly used in the literature of liquid crystals). We will present an individual-based model based on this potential and derive the corresponding kinetic and macroscopic equations. This approach allows us to understand how alignment emerges from volume exclusion and how it also affects not only the orientation of the particles, but also their positions.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: Workshop "Mathematical modeling in life and health sciences" (2024)

Cell migration is a complex biological phenomenon playing an important role in many processes such as embryogenesis, but also in the development of pathologies such as cancer. The main driver of the motility is the actin network, the dynamics of which is regulated by many proteins. Mathematical models have been developped in the last decades to better understand this complexity. One of the difficulty leads on the representation of this moving domain. Several approaches have been proposed: Lagrangian Markers Cells [Edelstein-Kechet et al.(2011)], Level-set methods [Tesson et al.(2020)] or phase fields models [Ziebert-Aronson (2011)]. We propose in this talk to illustrate these methods with two biological issues. In the first one, we will model the impact of the microtubules on the process using the level set method. In the second one, we will use phase field models to explain atypical cases of adhesive haptotaxis [Luo et al (2020)], [Seveau Phd (2022)].

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: Workshop "Mathematical modeling in life and health sciences" (2024)

The study of collective dynamics is attracting the interest of different research fields, both due to their wide range of applications and to their ability to model self-organization. The emergence of global patterns from local interactions can be easily observed in flock of birds, schools of fish, human crowds, but also cells exhibit collective behaviors in different biological processes characterizing the human body (e.g. in embryogenesis, wound healing, immune response, tumor growth). The main feature of collective cells migration is that the emergent behavior is also driven by chemical stimuli, and not only by mechanical interactions. In this talk I will present a general class of hybrid ODE-PDE models, gathering the advantages of multiscale descriptions. In this context, cells are modeled as discrete entities and their dynamics is given described by a system of second-order ODEs, while the chemical signal influencing the motion is modelled as a continuous signal solving a diffusive equation. The particular coupling of the two scales raises some issues that have been analytically investigated over the last years. Concerning applications, I will present recent advancements on a hybrid mathematical model inspired by Cancer-on-chip experiments, where tumor cells are treated with chemotherapy drug and secrete chemical signals in the environment, thus stimulating immune response.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: Workshop "Mathematical modeling in life and health sciences" (2024)

The adoption of hybrid models for self-organization dynamics allows to provide an accurate description of cell motion in tissues or organs. From a numerical point of view, the proposed approach may have drawbacks in terms of computational cost, if the number of cells involved significantly increases. In this perspective, the idea is to introduce a fully macroscopic mathematical model, in which cells are treated as a continuous cellular density. Starting from a class of hybrid ODE-PDE models, a new pressureless nonlocal Euler-type model with chemotaxis has been rigorously derived in [1], under the assumption of monokinetic initial data. Outside the monokinetic case, a numerical study has been performed in the one-dimensional case [2]. In this talk I will present some advancements in the numerical approximation of this model in the multidimensional case, to understand the role of different effects in the dynamics. Finally, parameter estimation of the macroscopic model is performed, in order to find the optimal parameters and to provide realistic numerical simulations. I will show different scenarios, comparing the nonlocal Euler-type model with chemotaxis models existing in the literature. This talk is based on an ongoing work with Marta Menci and Roberto Natalini.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: Workshop "Mathematical modeling in life and health sciences" (2024)

In this talk, I will review some questions that arise around the classical Vicsek model - which is a model for collective dynamics where agents move at a constant speed while trying to adopt the averaged orientation of their neighbours, up to some noise. I will discuss the emergence of bifurcations leading to disordered and ordered motion, depending on the local density of the agents. This is a very interesting phenomenon: it showcases how two completely different observed behaviours can appear simultaneously from agents that interact following the same rules.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: Workshop "Mathematical modeling in life and health sciences" (2024)

Microbial communities form complex ecosystems that provide beneficial services to humans in a variety of contexts, such as food fermentation, crop protection, bioprocessing or health and well-being. The complexity of microbial interactions makes it difficult to decipher the drivers of community dynamics and functions. Building digital twins of microbial communities could provide insights into their functioning, and strategies for improving the services they provide. In this talk, I will present genome-based models of microbial communities that predict functions and dynamics, and thus represent good candidates for digital twins. However, they induce a high numerical load, especially when coupled with PDE models of microbial populations. A surrogate modeling strategy will be used to provide fast approximations of the genome-based model, in order to overcome this difficulty.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: Workshop "Mathematical modeling in life and health sciences" (2024)

In this talk I am going to consider a Boltzmann-type equation for the description of a collision dynamic which is not instantaneous. This new class of kinetic equations has been introduced by Kanzler, Schmeiser, and Tora to model ensembles of living agents, where the changes of state are the result of complicated internal processes, and not simple mechanical interactions. We extend their work introducing a first-order approximation to the instantaneous equation, where non-binary collisions are included. This is motivated by the fact that during an extended collision period there is a positive probability that a colliding pair is joined by additional particles. The interaction kernel is of alignment type, where the states of the particles approach each other. For this spatially homogeneous approximation, we check that the formal properties of the system are kept. Furthermore, existence and uniqueness of solutions and instantaneous limit are examined.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: Workshop "Mathematical modeling in life and health sciences" (2024)

Despite significant advances in the in silico modeling of human physiology, understanding the complex behavior of fluids in the eye and identifying the main factors that influence their dynamics is still a very challenging field. On the one hand, the description requires a multi-scale characterization, since these phenomena encompass a wide range of spatial and temporal scales, from the molecular level to networks of a few meters, between a one-second heartbeat and a lifetime. On the other hand, the fluid dynamics is influenced by the interaction with surrounding tissues and their temperature, which calls for a multi-physics approach. In addition, the geometric representation can be very complex and the availability of real data is scarce. In this challenging context, the aim of this talk is to present our continuous efforts from a modeling and numerical viewpoint to develop a powerful and flexible mathematical and computational framework called the Ocular Mathematical Virtual Simulator. The combined effects of ocular blood flow and different ocular tissues are described by a coupled hemodynamics and biomechanics model. The multi-scale aspect, essential to properly account for systemic effects of the blood circulation coupled with local effects on the tissues of interest, is represented by a coupled partial and ordinary differential equations for fluid flow. The PDE/ODE coupling is handled via (i) operator splitting for the time discretization, which provides modularity of the solution algorithm while preserving the physical energy at the discrete level; and (ii) Hybridizable Discontinuous Galerkin (HDG) method for the PDE discretization, which ensures conservation of fluxes of mass and linear momentum at the discrete level. A special interest is devoted to the issues of verification, validation and treatment of inherent uncertainties. Finally, we discuss some specific applications related to glaucoma, a leading cause of irreversible blindness worldwide, that currently lacks cure and for which existing treatments focus on managing the condition and slowing its progression.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: Workshop "Mathematical modeling in life and health sciences" (2024)

The pancreatic innervation undergoes dynamic remodeling during the development of pancreatic ductal adenocarcinoma (PDAC). Denervation experiments have shown that different types of axons can exert either pro- or anti-tumor effects, but conflicting results exist in the literature, leaving the overall influence of the nervous system on PDAC incompletely understood. To address this gap, we propose a continuous mathematical model of nerve-tumor interactions that allows in silico simulation of denervation at different phases of tumor development. This model takes into account the pro- or anti-tumor properties of different types of axons (sympathetic or sensory) and their distinct remodeling dynamics during PDAC development. We observe a “shift effect” where an initial pro-tumor effect of sympathetic axon denervation is later outweighed by the anti-tumor effect of sensory axon denervation, leading to a transition from an overall protective to a deleterious role of the nervous system on PDAC tumorigenesis. Our model also highlights the importance of the impact of sympathetic axon remodeling dynamics on tumor progression. These findings may guide strategies targeting the nervous system to improve PDAC treatment.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: Workshop "Mathematical modeling in life and health sciences" (2024)

In this talk, I’ll be present some recent advancement in the modelling of the size dynamics of adipose cells. Adipose cells or adipocytes are the specialized cells composing the adipose tissue in a variety of species. Their role is the storage of energy in the form of a lipid droplet inside their membrane. Based on the amount of lipid they contain, one can consider the distribution of adipocyte per amount of lipid and observe a peculiar feature : the resulting distribution is bimodal, thus having two local maxima. The aim of this talk is to introduce a model built from the Lifshitz-Slyozov equations that is able to replicate this bimodale feature. I also introduce a microscopic scale model build from the Becker-Döring equations and show a new convergence result toward the Lifshitz-Slyozov-inspired model, which provides a rate of convergence. I will also present some extension to stochastic models, which support some extension of the deterministic model to better approximate data. Regarding the data, I’ll present some parameter estimation on measures from rats.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: Workshop "Mathematical modeling in life and health sciences" (2024)

Myxococcus xanthus, a social bacterium, exhibits intriguing collective behavior, characterized by coordinated group movement and the ability of each bacterium to change its movement direction by reversing its body axis. This behavior results in the formation of interesting patterns, such as rippling, where cells self-organize into colliding counter-propagating waves, and swarming, where cells align and move together in large groups. The complex nature of this behavior has captured the attention of biologists, physicists, and mathematicians, driving extensive research efforts. This talk has two main goals. First, we present new biological data on Myxococcus xanthus, featuring high-resolution movies of their collective movements. Using advanced algorithms, we segment these movies, track cell trajectories, and analyze reversals. From these observations, we propose a kinetic model explaining the emergence of rippling patterns. Second, we develop a 2D agent-based model where bacterial reversals are closely linked to congestion, a hypothesis confirmed by our data. This model accurately replicates the rippling and swarming dynamics and highlights the crucial role of background anisotropy in the formation and persistence of these patterns. It also shows that the emergence of both rippling and swarming can be explained by the same rules at the individual level. This project is in collaboration with Vincent Calvez (Laboratoire de Mathématiques de Bretagne Atlantique), Tâm Mignot (Laboratoire de Chimie Bactérienne - Marseille) and Jean-Baptiste Saulnier (Laboratoire de Chimie Bactérienne).

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: Workshop "Mathematical modeling in life and health sciences" (2024)

The analysis of equations arising in neuroscience raises many challenging questions that always require the development of new tools to answer them. In this presentation we will illustrate two exponential convergence results obtained using the two different techniques of Relative Entropy with Poincaré-type inequality on the one hand and Harris theory on the other. In particular, the presentation will be motivated by the case study of the Integrate and Fire model with random discharge used in mathematical neuroscience to describe the spiking activity of neurons [1, 2]. This study will be an opportunity to highlight some peculiar differences between the two techniques mentioned above [3]. The results we present are an ongoing collaboration with Professor J. A. Canizo and Professor M. J. Caceres from University of Granada, Professor D. Salort from Sorbonne University and Doctor A. Lora-Ramos from University of Granada.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: Workshop "Mathematical modeling in life and health sciences" (2024)

In this talk, mathematical models for the spatial spread and evolutionary dynamics of heterogeneous cell populations will be considered. In these models, which are formulated as partial differential equations, a continuous structuring variable captures intercellular heterogeneity in cell proliferation and migration rates. Analytical and numerical results summarising the behaviour of the solutions to the model equations will be presented, and the main biological insights generated by these results will be discussed.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: 7th Workshop "Mathematics for Medicine (against Cancer)" (2024)

Hormone-responsive breast cancer is among the most prevalent tumor types in women. While adjuvant endocrine therapy, targeting non-mutated estrogen receptor alpha (Er-alpha), represents a highly efficient option for these patients, three percent of them relapse each year, often with metastasis. Genetic alterations that might drive relapse could be previously identified only in a fraction of these tumors, suggesting the need to identify alternative scenarios for the evolution of therapy resistant tumors. These include non-genetic sources of cell intrinsic tolerance to therapies, as well as of adaptability and plasticity. While intra-tumor heterogeneity is a recognized hallmark of cancer, the mechanisms that generate such heterogeneity, which in turn increases the chances of the cancer cell population to evolve when challenged, are currently less understood. By combining single-cell technologies, perturbation screens, and computational modeling, we aim at dissecting the evolvability of hormone-responsive breast cancer cells. While increasing our knowledge on the evolution of breast cancer, our study could provide insights into potentially new combinatorial therapies, that might limit tumor evolution and increase the efficacy of the current standard of care.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: 7th Workshop "Mathematics for Medicine (against Cancer)" (2024)

T cells are a subset of white blood cells that can be protective by controlling infections and tumors on one side, but that can also be deleterious by triggering autoimmunity and autoinflammation. A central quest of my research activity as a cellular immunologist is to elucidate how T cell responses are calibrated to ensure enough protection against infectious agents and tumors, while avoiding inflicting damages to healthy tissues. Calibration of T cell responses occurs through various molecular switches that tune the abilities of T cells to explore their environment, to establish tight contacts with potential target cells and to deliver bioactive molecules such as lytic granules that can kill target cells. How calibration operates from the molecular scale up to the functional output of T cell populations remains poorly understood. To first provide a background on this topic, I will briefly present recent projects in which collaboration with computational scientists has been decisive to grasp some of the calibration mechanisms at play in T cells. This includes: • the digital activation of individual nanoclusters of an adhesive receptor to allow graded adhesion. • a share of labor mechanism accounting for the efficacy of T cells at eliminating target cells. • the emergence of collective migratory behaviors in cell populations facing chemoattractant gradients. I will also present ongoing applications of machine learning approaches to extract refined signatures from T cell image datasets. Such applications include: • the discrimination of T cell alterations in patients with highly related genetic defects • the prediction of the efficacy of therapeutic antibodies for the treatment of autoimmune diseases. To further stimulate interdisciplinary exchange, I will expose some of the most advanced experimental approaches in the field of cellular immunology and explain the nature of the generated datasets. I will then formulate a series of unsolved questions around the topic of T cell response calibration, for which mathematical modeling or analytical approaches are expected to provide solutions.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: 7th Workshop "Mathematics for Medicine (against Cancer)" (2024)

Tumors are typically comprised of heterogeneous cell populations exhibiting diverse phenotypes. This heterogeneity, which is correlated with tumor aggressiveness and treatment-failure, confounds current drug screening efforts to identify effective candidate therapies for individual tumors. In the first part of the talk I will present a modeling-driven statistical framework that enables the deconvolution of tumor samples into individual subcomponents exhibiting differential drug-response, using standard bulk drug-screen measurements. In the second part of the talk I will present some efforts towards obtaining insights about tumor evolution from standard genomic data. In particular, we analyze the site frequency spectrum (SFS), a population summary statistic of genomic data, for exponentially growing tumor populations, and we demonstrate how these results can in principle be used to gain insights into tumor evolutionary parameters.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: 7th Workshop "Mathematics for Medicine (against Cancer)" (2024)

T lymphocytes are key cellular components of the immune system since they can eliminate virusinfected cells and tumor cells. T cells recognize target cells by forming tight contacts known as immunological synapses (IS). The mechanisms and parameters responsible for the assembly and the spatial patterning of the IS are still poorly understood. In particular the mechanism leading to the segregation between the T-cell receptor (TCR) recognizing the foreign antigens and the LFA-1 integrin responsible of cell adhesion is subject to debate. In this work we propose an analytical and numerical modeling of the IS, with the hypothesis that the TCR-LFA-1 segregation is driven by the difference of height between the TCR-pMHC ligandreceptor couple on the one hand, and the LFA1-ICAM1 ligand-receptor couple on the other hand, together with an inhomogeneous pressure field exerted by the cortical actin cytoskeleton. Our numerical mesoscale simulation is based on the Dynamically Triangulated Surface (DTS) modeling, using Monte Carlo Metropolis algorithm. It validates qualitatively our hypothesis. However, to quantitatively validate this mechanism, we need to know the true pressure field driven by the cortical actin cytoskeleton that the lymphocyte exerts on its target cell. We propose an analytical approach based on elasticity theory to determine the single solution of the 3D force field exerted by the lymphocyte while knowing only the one- dimensional height deformation measured by traction-force microscopy (TFM) experiments, compensating the lack of information by minimizing the residual force on the lymphocyte-free region. This approach will be used in a near future to extract pressure field from TFM experiments. This is a joint work with Loïc Dupré and Nicolas Destainville.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: 7th Workshop "Mathematics for Medicine (against Cancer)" (2024)

The anticancer ruthenium complex KP1339 (BOLD-100), globally evaluated currently in clinical phase II studies, was developed for improved tumor-targeting and to reduce chemotherapyassociated side effects. Mechanistically, BOLD-100 is delivered to malignant tissue bound to serum albumin. Intratumorally, BOLD-100 induces endoplasmic reticulum (ER) stress via chaperone GRP78 inhibition, leading to unfolded protein response and apoptosis induction. Resistance acquisition presents a major limitation for effective cancer therapy. Additionally, treatment success is often regulated by tumor microenvironmental cells. Thus, dissection of these aspects is essential for promoting (pre)clinical development of BOLD-100. Here we report on the identification of BOLD-100 as a multi-faceted onco-metabolism-regulating compound by targeting several aspects of cancer cell metabolism. BOLD-100 massively interfered with cancer cell glycolysis, inducing downregulation of cellular pyruvate and citrate contents. This, in turn, impacted on lipid metabolism – specifically, de novo fatty acid synthesis and beta-oxidation - translating into epigenetic gene expression deregulation via depletion of acetyl-coenzyme A. Alterations in glycolysis-driven lipid processing also contributed to BOLD-100 resistance acquisition. Distinct lipid metabolism routes were identified as vulnerabilities of BOLD-100-resistant in vitro and in vivo models. Additionally, the anti-Warburg compound BOLD-100 significantly reduced release of the immunosuppressive metabolite lactate. Despite increased glycose uptake, lactate secretion was diminished in the resistant subline linked to loss of monocarboxylate transporter 1 (MCT1) expression, based on a frame-shift mutation in the MCT1 chaperone basigin (CD147). Preliminary data suggest that BOLD-100 also decreases lactate production in cancer-associated fibroblasts, associated with altered expression of MCT-1 and CD147. This suggests an impact of BOLD-100 on the metabolic crosstalk between cancer cells and the immune microenvironment. Summarizing, we uncover novel modes of action of BOLD-100 and unravel molecular mechanisms driving resistance acquisition. BOLD-100-induced lactate reduction indicates a potential to overcome the immune-suppressive environment of solid tumors. The impact on metabolic cross-talks between cancer cells and the components of the microenvironment are currently evaluated. This is a joint work with Dina Baier, Theresa Mendrina, Mate Rusz, Christine Pirker, Samuel Meier-Menches, Gunda Koellensperger, and Bernhard K. Keppler.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: 7th Workshop "Mathematics for Medicine (against Cancer)" (2024)

This talk is devoted to the mathematical modelling of a glioblastoma tumour dynamics structured by a cellular hierarchy. The work is motivated by recent experimental data and their analysis, which indicate the impact of the cellular structure of tumour cell populations on disease dynamics and patient prognosis. We propose new mechanistic mathematical models that allow linking the observed cellular patterns to the key parameters of different cell populations, which in turn characterise their dynamics and allow predictions. The results are discussed in the context of tumour evolution, but also from the perspective of mathematical challenges arising in coupling spatial and structured dynamics. We discuss different modelling and data analysis approaches.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: 7th Workshop "Mathematics for Medicine (against Cancer)" (2024)

Chronic kidney diseases imply an ongoing need to remove toxins, with hemodialysis as the preferred treatment modality. We investigate and find expressions for phosphate clearance during dialysis based on the single pass (SP) model corresponding to a standard clinical hemodialysis and the multi pass (MP) model, where dialysate is recycled and therefore makes a smaller clinical setting possible such as a novel transportable dialysis suitcase. For both cases we find that the convective contribution to the dialysate is negligible for the phosphate kinetics. The SP and MP models are calibrated to clinical data of ten patients showing consistency between the models and provide estimates of the kinetic parameters. Immediately after dialysis a rebound effect in the phosphate level is observed. We give a simple formula describing this effect which is valid both posterior to SP or MP dialysis. The analytical formulas provide explanations to observations of previous clinical studies. The work is based on an interdisciplinary collaboration between mathematicians and a nephrologist and I will touch upon the benefits and challenges of such a collaboration.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: 7th Workshop "Mathematics for Medicine (against Cancer)" (2024)

How a cell organizes its organelles is fundamental to its function. I will focus on the nucleus, a cell’s central organ, and its properties, such as number, size and position. I will discuss nuclear positioning and size scaling in multi-nucleated muscle cells. Mispositioned nuclei are associated with muscle disease. Using coarse, deterministic, as well as detailed, stochastic models, we use data from drosophila larval muscles to identify the most plausible model. This model assumes repulsive forces created by microtubules between nuclei and the cell sides and correctly reproduces and predicts bifurcating nuclear positioning patterns and nuclear shapes. Finally, we show that nuclear size scaling is driven by nuclear positioning, evidenced in the data and predicted by a partialdifferential- equations size sensing model. This creates a plausible link between mispositioned nuclei and muscle disease.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: 7th Workshop "Mathematics for Medicine (against Cancer)" (2024)

One of the most prevalent forms of central nervous system tumors, diffuse low grade gliomas (LGG) have distinct clinical outcomes and require different treatment strategies based on their clinicopathological characteristics. In contrast to extraaxial or extracranial tumors, LGG diffusely infiltrate the brain parenchyma and can extend well beyond the original tumor mass detectable by standard radiological means. Although a comprehensive neuropsychological evaluation reveals abnormalities in the majority of patients at the time of diagnosis, subjective and clinical symptoms are typically subtle. LGG are thus diagnosed at various stages, depending on the size, location, and growth kinetics of the tumor. Feasible total onco-functional resection of LGG within the brain is often deemed impossible due to its extent or location. Understanding tumor infiltration patterns can thus be of paramount importance to maximize tumor resection and improve patient outcome. In this talk, I will discuss our current project, in collaboration with the Department of Neurosurgery of the Kepler University Klinikum in Linz, aiming at understanding which role do the brain fibers (assessed by DTI data) have on the low grade glioma progression, and whether they have any.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: 7th Workshop "Mathematics for Medicine (against Cancer)" (2024)

How various processes combine to enable cancer cells to invade tissue is still an open question. We have been using non-linear partial differential equation models to investigate how different processes can enhance cancer cell invasion. Here, I shall investigate the impact of the Allee effect on one cancer cell type invading, and then consider how different specialised cancer cell phenotypes can co-operate to overcome the obstacles that normal cells and extracellular matrix provide, and determine if this is more efficient than invasion by a single generalist cell type.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: 7th Workshop "Mathematics for Medicine (against Cancer)" (2024)

Evolutionary dynamics permeates life and life-like systems. Mathematical methods can be used to study evolutionary processes, such as selection, mutation, and drift, and to make sense of many phenomena in the life sciences. How likely is a single mutant to take over a population of individuals? What is the speed of evolution, if things have to get worse before they can get better (aka, fitness valley crossing)? Can cooperation, hierarchical relationships between individuals, spatial interactions, or randomness influence the speed or direction of evolution? Applications to biomedicine will be discussed.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: 7th Workshop "Mathematics for Medicine (against Cancer)" (2024)

Virtually all processes in health and disease rely on the careful orchestration of a large number of diverse individual components ranging from molecules to cells and entire organs. Networks provide a powerful framework for describing and understanding these complex systems in a holistic fashion. They offer a unique combination of a highly intuitive, qualitative description, and a plethora of analytical, quantitative tools. In my presentation, I will first review how molecular networks can be understood as maps for elucidating the relation between molecular-level perturbations and their phenotypic manifestations. I will then sketch out a number of challenges in the areas of network biology and network medicine, as well as recent efforts of my group to address them. These efforts range from methodological work on the visualization and interpretation of large biomedical data combining artificial intelligence with virtual reality technology, to translational efforts towards concrete clinical applications in rare diseases and drug repurposing.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: 7th Workshop "Mathematics for Medicine (against Cancer)" (2024)

The expansion of pre-malignant, i.e., mutated but not yet malignant cells is an important prerequisite for cancer. It is well accepted that the frequency of pre-malignant stem cells increases with age. However, the underlying mechanisms are not well understood. Potential explanations include immune dysfunction, increase of chronic inflammation and age-related accumulation of mutations. A detailed understanding of pre-malignant stem cell dynamics is crucial to identify patients with a high risk of cancer. Since pre-malignant cells do not cause symptoms, it is challenging to study them in humans. A suitable scenario to invest their dynamics under stress conditions is hematopoietic stem cell transplantation (bone marrow transplantation), a curative treatment for many diseases of the blood forming (hematopoietic) system. In case of allogeneic stem cell transplantation, the stem cells are harvested from a donor who might, as a significant proportion of healthy individuals, harbor pre-malignant cells. Before the transplantation, the recipient’s marrow is eradicated using high dose chemotherapy or radio-chemotherapy. Therefore, the donor cells are exposed to strong proliferative stimuli in the host environment, which potentially unmask differences between healthy and pre-malignant stem cells. We propose quantitative non-linear ordinary differential equation models to investigate the dynamics of pre-malignant hematopoietic stem cells. The models account for key mechanisms mediating clonal expansion, such as mutationrelated changes of stem cell proliferation & self-renewal, aberrant response of mutated cells to systemic signals and chronic inflammation. Combining model simulations, longitudinal patient data and in silico clinical trials, we address the following questions: (i) Why do pre-malignant cells expand in some individuals but not in others? (ii) How do pre-malignant cells respond to systemic cues such as chronic inflammation & physiological feedbacks? (iii) How do cell-intrinsic and host-specific factors contribute to cell expansion? (iv) What does stem cell transplantation data tell us about the differences between healthy and pre-malignant stem cells?

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: 7th Workshop "Mathematics for Medicine (against Cancer)" (2024)

My research combines experimental biology (robotic high-throughput immunoassays) with data science (machine learning, bioinformatics) to gain a holistic view of interactions between microbes and the immune system. Our current conception of these immune responses is mostly based on DNA sequencing of antibody genes, whereas the actual functional consequences thereof (the molecular structures “antigens” recognized) are vastly unknown. I strive to unravel the functional capacity of these enormous immune repertoires targeting microbes and to shed light on their role in human health. Here, I will be giving and brief overview of the experimental methods we are using to generate large datasets, and then discuss machine learning and bioinformatics approaches we are using to interpret this data.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: 7th Workshop "Mathematics for Medicine (against Cancer)" (2024)

About 30% of breast cancer patients develop metastases and eventually succumb to the disease. Tumor cell adaptations to distant microenvironments during the multistep process of metastasis contribute to the heterogeneity of metastatic tumors and the remodeling of tumor-promoting metastatic niches. This inherent complexity challenges the development of effective metastatic treatment strategies. To gain a holistic view of the metastatic process we profile tumor and immune cells in breast cancer metastasis on single-cell resolution. We dissect the tumor heterogeneity contributing to metastasis progression and describe the dynamic changes in the metastatic immune niche. Ultimately, we aim to develop novel immuno-oncology strategies in metastasis.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: 7th Workshop "Mathematics for Medicine (against Cancer)" (2024)

The maintenance of the hematopoietic system is a complex and highly dynamic process where cell division, self-renewal, and differentiation events are regulated by homeostatic control networks. An evolutionary mathematical model with feedback control that is parameterized with data from label propagation experiments in mice predicts the existence of major invasion barriers for advantageous mutants (such as TET2 or DNMT3A mutants) in short term stem cell and multipotent progenitor cell compartments. It further provides an evolutionary explanation or why mutant invasion can become more likely with age, and suggests that evolutionary niche construction dynamics, based on mutant-induced inflammation, could be central to mutant emergence. The mathematical analysis further provides new interpretations of experimentally estimated rates of cellular self-renewal and differentiation.

• Thematic program: Mathematics for Biology and Medicine (2024/2025)
• Event: 7th Workshop "Mathematics for Medicine (against Cancer)" (2024)