Schedule and 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.

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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.