Abstracts

Abstract: Understanding how living systems dynamically self-organise across spatial and temporal scales is a fundamental problem in biology; from the study of embryo development to the regulation of cellular physiology. In this talk, I will discuss how we can use mathematical modelling to uncover the role of microscale physical interactions in cellular self-organisation. I will illustrate this by presenting two seemingly unrelated problems: environmental-driven compartmentalisation of the intracellular space, and self-organisation during collective migration of multicellular communities. Our results reveal hidden connections between these two processes, hinting at the general role that chemical regulation of physical interactions plays in controlling self-organisation across scales in living matter.

Abstract: Tumour microenvironment is characterised by heterogeneity at various scales: from various cell populations (immune cells, cancer cells, ...) and various molecules secreted by cells (cytokines, growth factors, …); to phenotype heterogeneity inside the same cell population (e.g., immune cells with different phenotypes and different functions); as well as temporal and spatial heterogeneity of cells and molecules inside the microenvironment. In this talk we present some mathematical models developed over the past few years to investigate various aspects related to the phenotypic heterogeneity and plasticity of a particular immune cell population very important in certain solid tumours : the macrophages. The focus will be on single-scale vs. multi-scale models, and their parameterisation with data (if/when such data is available).

Abstract: Cellular adhesion is a fundamental mechanism underlying diverse collective cell behaviours, from tissue self-organisation in developmental biology to the formation of directional queues that guide cell migration. Modelling such interactions has also proven mathematically rich, motivating the use of continuum partial differential equation models that capture adhesion through nonlocal interaction kernels. These models can, for instance, reproduce classical cell-sorting patterns arising from differential adhesion in mixtures of cell populations. In this talk, we briefly review such models and explain how a local approximation of nonlocal aggregation–diffusion equations can be derived in the limit of short-range interactions. We then discuss recent advances in the field and highlight new results on pattern formation driven by adhesive interactions in migrating and proliferating cell populations, as well as in systems of nonreciprocally interacting cells.

Abstract: In this talk we introduce a new class of kinetic models, which overcome the standard assumption in kinetic transport theory that collision processes happen instantaneously. In particular, this modelling approach is interesting for applications in life-science, where the interaction-time between biological agents cannot meaningfully be neglected. On the level of the underlining stochastic processes this results in replacing the jump-process, which are defining the collisions, with continuous stochastic processes. As an example, we will investigate a kinetic model with non-instantaneous alignment collisions between particles. The collisions are described by a transport process in the joint state space of the colliding particles, where the states of the particles approach their midpoint. Moreover, we will elaborate on the question, which model can be used as an accurate first order non-instantaneous correction in the regime where the collision time is very small, implying that the collisions are almost instantaneous. Last, the instantaneous limit will be considered, where the latter leads to standard collisional kinetic models of Boltzmann type.

This is joint work with Carmela Moschella, Christian Schmeiser and Veronica Tora.

Abstract: In this talk, PDE models for the growth of heterogeneous cell populations will be considered. Both models with discrete phenotype states, which consist of coupled systems of nonlinear PDEs, and models wherein the phenotype enters as a continuous structuring variable, which are formulated as non-local PDEs, will be examined. Focusing on scenarios where cells with different phenotypes are spatially segregated across invading fronts, travelling wave solutions that exhibit sharp interfaces, for the first class of models, and concentration phenomena, for the second class of models, will be studied. Moreover, connections between such continuum models and underlying agent-based models will be addressed. 

Abstract: Viscoelasticity, i.e., the time-dependent mechanical response that combines viscous and elastic behaviour, plays a fundamental role in biological systems at all scales. At the cellular level, viscoelastic properties govern critical processes including mechanosensing, reorientation, and force generation. At the tissue scale, the interplay between elasticity and viscosity determines functional mechanical response to physiological loads. Modelling viscoelasticity in these contexts poses significant mathematical challenges, since they often exhibit nonlinear, anisotropic, and rate-dependent responses to external mechanical stimuli. In this talk, we present recent results in the mathematical modelling of viscoelasticity both for cells and for tissues. First, we examine viscoelastic effects on cell reorientation under cyclic stretching, showing how the frequency of applied deformation influences cytoskeletal alignment. Next, we explore the role of viscoelasticity in cell-substrate adhesion dynamics, focusing on how the interaction between integrins and the substrate’s dissipative properties regulates the frequency-dependent response of focal adhesions. Finally, we present a nonlinear viscoelastic model for biological tissues reinforced by distributed fibres, demonstrating how it captures the time-dependent mechanics of reproductive tissues.

The talk is based on joint works with C. Giverso and L. Preziosi (Politecnico di Torino), J. Ciambella and P. Nardinocchi (Sapienza University of Rome), C. Gimenez and R. De Vita (Virginia Tech). 

Abstract: Motivated by the modeling of bacteria microcolony morphogenesis across multiple scales, we explore in this talk models for a spatial population of interacting, growing and dividing particles. Starting from a microscopic stochastic model, we first write the corresponding stochastic differential equation satisfied by the empirical measure, and rigorously derive its mesoscopic (mean-field) limit. We then take an interest in the so-called localization limit, to reach a macroscopic (large-scale) model. The scaling consists in assuming that the range of interaction between individuals is very small compared to the size of the domain. In proving the localization limit using compactness arguments, the difficulties are twofold: first, growth and division render the system non-conservative, preventing the use of energy estimates. Second, the size of the particles, being a continuous trait, leads to new difficulties in obtaining compactness estimates. We first show rigorously the localization limit in the case without growth and fragmentation, under smoothness and symmetry assumptions for the interaction kernel. We then perform a thorough numerical study in order to compare the three modeling scales and study the different limits in situations not covered by the theory yet. These work provide a better understanding of the link between the micro- meso- and macro- scales for interacting particle systems.

       Abstract:

Abstract: Heterogeneity in individual cell behaviour may have a big impact in the emergent dynamics at the population level, and thus play an important role in cancer progression. The phenotype of cell, i.e. the ensemble of its observable characteristics determining its behaviour, can be quantified by the level of expression of certain proteins in the cell, which are typically measured on a continuum. For this reason, PDEs describing the evolutionary and spatiotemporal dynamics of phenotype-structured cancer cell populations at the macroscale have become increasingly popular in the mathematical community. In this talk we will discuss their link with microscale dynamics and calibration with single-cell proteomic data, as well as their analysis, from exact solutions to formal asymptotic behaviour in well-mixed and spatially-explicit models. 

Abstract: 

Abstract:  Ion transport across cellular membranes is a fundamental mechanism in many biological processes and is often modeled through Poisson–Nernst–Planck (PNP) systems. In this talk, we propose and analyze a Multiscale PNP (MPNP) model aimed at describing the correlated motion of positive and negative ions in the presence of surface traps, which can be interpreted as localized interactions at the membrane level. We focus on traps whose attraction range, of characteristic length δ, is much smaller than the macroscopic scale of the system. The physical setting is motivated by ion diffusion around a membrane-like interface, modeled here as an anchored gas bubble surrounded by a flow of charged surfactants. When ions reach the trap surface, they are reversibly adsorbed, mimicking ion-membrane interactions observed in biological systems. Following our previous works [1, 2, 3, 4, 5], the effect of short-range attractive potentials is incorporated through effective boundary conditions derived via asymptotic analysis and mass conservation. A key feature of the model is the simultaneous treatment of positive and negative ions [6], which is often neglected in approaches that consider each species independently.

In the second part of the talk, we address the numerical approximation of the system in regimes characterized by strong Coulomb interactions. In the limit of very short Debye length, the model converges to a quasi-neutral regime, leading to a reduced diffusion description. To accurately capture both the full PNP dynamics and the quasi-neutral limit, we develop an Asymptotic Preserving (AP) numerical scheme that remains stable without time-step restrictions as the Debye length tends to zero. Moreover, the proposed scheme is also Asymptotic Accurate (AA), ensuring uniform accuracy in the quasi-neutral limit, and independent of the initial conditions [7].

References

[1] A. Raudino, A. Grassi, G. Lombardo, G. Russo, C. Astuto and M. Corti, Anomalous Sorption Kinetics of Self-Interacting Particles by a Spherical Trap, Communications in Computational Physics, 2022

[2] C. Astuto, A. Raudino and G. Russo, Multiscale modeling of sorption kinetics, Multiscale Modeling & Simulation, 2023

[3] C. Astuto, A. Coco and G. Russo, A finite-difference ghost-point multigrid method for multi-scale modelling of sorption kinetics of a surfactant past an oscillating bubble, Journal of Computational Physics, 2023

[4] C. Astuto, M. Lemou and G. Russo, Time multiscale modeling of sorption kinetics I: uniformly accurate schemes for highly oscillatory advection-diffusion equation, Multiscale Modeling & Simulations, 2025

[5] C. Astuto, High order multiscale methods for advection-diffusion equation in highly oscillatory regimes: application to surfactant diffusion and generalization to arbitrary domains, Communications in Computational Physics, 2025

[6] C. Astuto and G. Russo, Asymptotic Preserving and Accurate scheme for Multiscale Poisson-Nernst-Planck (MPNP) system, arXiv preprint arXiv:2507.01402, 2025

[7] C. Astuto, Standard versus Asymptotic Preserving Time Discretizations for the Poisson-Nernst-Planck System in the Quasi-Neutral Limit, arXiv preprint arXiv:2511.07964, 2025

Abstract: I will discuss recent results on the long-time behavior of Fokker-Planck models for Lotka-Volterra-type interactions, showing how to exploit the regularity of solutions to prove their convergence to equilibrium in relative entropy.

Abstract: Particle therapy (PT) features highly localized energy deposition patterns that differ substantially from conventional photon radiotherapy. While treatment plan evaluation commonly relies on Tumor Control Probability (TCP) and Normal Tissue Complication Probability (NTCP) models, most existing approaches are phenomenological, developed for photons, and based on in-vitro biological effectiveness. These models often neglect key radiation-induced stochastic effects and tissue heterogeneities, such as variations in dose, oxygenation, radiosensitivity, and cell cycle. The aim of our work is to develop a mechanistic, biophysically grounded TCP/NTCP framework for particle therapy, spanning from single-cell responses to whole-organ endpoints.

Methods
We developed a GPU-accelerated, mechanistic agent-based model based on microdosimetry and the Generalized Stochastic Microdosimetric Model (GSM2), which computes energy deposition, DNA damage formation and repair, cell division, and repopulation at single-cell resolution. The model explicitly accounts for stochastic energy deposition, radiation quality, oxygenation, and cellular heterogeneity. By integrating GSM2 into an extended Relative Seriality Model, we derived mechanistic TCP and NTCP formulations capable of describing different organ volume effects, partial irradiation, oxygen gradients, and fractionation schemes.

Results
The GSM2-driven TCP/NTCP model successfully reproduces experimental NTCP data for different particles, including protons, helium, and carbon ions, across multiple fractionation schemes, such as rat spinal cord and lung injury models. The framework enables systematic investigation of the impact of radiation quality, LET, dose, irradiated volume, tissue architecture, and oxygen distribution - from uniform conditions to gradients in multicellular spheroids - on both microscopic (DNA damage, cell survival) and macroscopic (TCP/NTCP) endpoints.

Conclusions
Our work presents a fast, mechanistic, single-cell–resolved TCP/NTCP model for particle therapy that accounts for physical, chemical, and biological heterogeneities and stochastic effects. By moving beyond purely dosimetric and phenomenological approaches, the model provides a robust tool for biologically informed treatment plan evaluation and optimization in particle therapy.

Abstract: In this talk, we study a parabolic PDE system modeling the interaction between a biological species and a lethal chemical substance that induces negative chemotaxis. The model is motivated by the dynamics of E. coli bacteria and hydrogen peroxide, which is self-produced by the bacteria while simultaneously acting as a lethal chemorepellent. Under different external supply regimes of the substance, we will analyze qualitative properties of solutions. For constant supplies, stability and convergence toward spatially homogeneous steady states will be established, showing how the balance between the logistic growth rate and the chemical supply governs the long-term dynamics. For supplies with persistent periodic behavior, threshold conditions will be identified, under which solutions asymptotically inherit the periodicity. Numerical simulations illustrating the analytical results and additional dynamical behaviors will also be discussed.

Abstract:

Abstract: 

Abstract: A wide range of physical, chemical, and biological systems exhibit a dynamical behaviour characterised by the emergence of travelling waves that propagate from a stable phase into an unstable one. At the deterministic level, such behaviour is typically described by the Fisher--Kolmogorov--Petrovsky--Piscunov (FKPP) equation, but finite-size effects or external noise can significantly alter the dynamics. Finite-size effects arise from small particle numbers, leading to density cut-offs and internal fluctuations, while external noise originates from random environmental perturbations. Although finite-size effects have been widely investigated in the literature, existing models -- usually formulated as extensions of the FKPP equation -- are often phenomenological or based on theoretically inconsistent derivations. In this work, we employ a well-established stochastic procedure to derive a family of stochastic differential equations from a class of interacting-particle models, encompassing hard-core and point-like particles. This framework allows us to determine corrections to the FKPP equation, compare them with the literature, establish a criterion for the relevance of stochastic fluctuations, and analyse the impact of internal and external noise on the wave propagation speed.

Abstract:

Abstract: 

Abstract:

Abstract: In this work, we are interested in the mathematical modeling of the impact of apoptosis on the dynamics of cellular tissues, and in particular on cell tissue fluidity. Indeed, cell apoptosis corresponds to the programmed cell death: when they leave the tissue, they induce local contractions but also enable cells rearrangements.

We first propose an individual-based model that provides the dynamics of the positions, velocities and polarities of the cells, idealized as hard spheres. Cells interact with each other through contact forces, smooth attraction, and polarity alignment. The model also involves a microscopic description of apoptotic and proliferation events. The present work is an extension of the model proposed in [3] and validated by experiments on cellular rings. Numerical simulations are performed and several indicators of fluidity are analyzed.

Next, we derive a macroscopic description, following the methodology proposed in [1], [2]. We start from a mean-field dynamics of the kinetic distribution function in phase-space (position, polarity, radius), where contact forces have been replaced with repulsion forces. We then introduce a specific time and space rescaling and identify the equilibria distribution functions, which are parameterized by two macroscopic quantities: the density and the mean polarity. Based on the Generalized Collision Invariant (GCI) method [2], we are then able to identify their dynamics: the resulting description can be seen as a modified Self-Organized Hydrodynamics (SOH) model. We finally discuss the obtained model and highlight the effect of the apoptotic events on the dynamics.

This is a joint work with Laurent Navoret (Université de Strasbourg) and Marcela Szopos (Université Paris Cité). It has also been carried out in collaboration with Romain Levayer (Institut Pasteur) and Daniel Riveline (IGBMC, Université de Strasbourg) in the context of the ANR project MAPEFLU.

References

[1] Degond, P., Dimarco, G., Mac, T. B. N., and Wang, N. Macroscopic models of collective motion with repulsion. Communications in Mathematical Sciences, 13(6), 1615–1638 (2015).

[2] Degond, P., and Motsch, S. Continuum limit of self-driven particles with orientation interaction. Mathematical Models and Methods in Applied Sciences, 18(supp01), 1193–1215 (2008).

[3] Vecchio, S. L., Pertz, O., Szopos, M., Navoret, L., and Riveline, D. Spontaneous rotations in epithelia as an interplay between cell polarity and boundaries. Nature Physics (2024).

Abstract: Metastatic spread, i.e. the spread of cancer cells to other organs, encompasses multiple temporal and spatial scales, is affected by both collective as well as rare events, and is governed by genetic evolution processes. In this talk, I will present a time-continuous spatial branching process that captures both the genetic lineages relating cancer cells to each other, while simultaneously keeping track of their spatial position when leaving a primary tumour and surviving to form metastases. Our results reveal interesting mathematical properties of this global branching mechanism which can be used to provide a connection between larger scale population genetics-based modelling of metastatic spread and local-scale continuum models of tumour growth.