Biomat 2023: Multiscale Methods at the Frontier Between Data and Mathematical Models

Reproduction of complex life hinges on the reliable translation of the linear information that is contained in our DNA into complex 3D shapes and functions. In this course, I will present chemical and biophysical principles that enable this reliable self-organisation. While there is only a limited number of candidate mechanisms and at times it may be difficult to uncover any candidate mechanism, often more than one mechanism can, in principle, explain the same biological phenomenon. Careful data-based mathematical modelling is therefore important to distinguish between candidate mechanisms. In the last part, I will discuss approaches for data-based modelling and model selection.

The course discusses some aspects of cell motility both at the individual cell level and at the collective level. The presentation is theoretical but the problems studied will be motivated by biological questions. One of the main aspects of the course is to treat the cell itself and at a larger cell an assembly of cells as active matter and to discuss cell motility within the framework of active matter theory.

1-Introduction to cell motility: The first lecture gives a general introduction to single cell motility in two and three dimensions. It discusses the large scale motion of cells as a persistent random walk and introduces briefly taxis phenomena. The final part discusses the general physical principles of cell motion on a solid substrate

2-Keratocyte motion: Keratocytes are one of the most studied models of cell motility. They have a very flat shape containing mostly the actin-myosin cytoskeleton that can be considered as an active gel. This second lecture presents very simple models of keratocyte motions emphasizing in particular the relative roles of actin turn-over and of acto-myosin contractility. It also discusses the shape of moving cells.

3-Spontaneous cell motion in cell monolayers: The third lecture considers collective cell motion in a confluent layer of elongated cells on a solid substrate. The cell layer is considered as an active nematic fluid. The lecture introduces the hydrodynamic theory of active nematics and shows how spontaneous flows can occur in the absence of imposed pressure gradients. If the activity is very large the layer reaches an active turbulent state.

4-Collective cell migration in an elastic matrix: During metastasis cancer cells migrate collectively through conjonctive tissues that can be considered as elastic media. Experiments in particular by P. Friedl have shown that there exist several types of migration patterns. The lectures presents a hydrodynamic theory of the cells migration in an elastic medium by considering them as an active polar fluid permeating through an elastic gel, and discusss the stability of a unifomly moving pattern. It also presents a more microscopic model where the cells remodel the matrix both by secreting and degrading it.

In this mini-course we will link together two sides of the recent progresses in higher-order systems.

On the one hand, we will describe recent advances in dynamical systems with interactions among groups of nodes (higher-order interactions) and the novel phenomenologies that stem from them.

On the other one, we will see how recent tools from algebraic topology and multivariate information theory characterise these behaviours in real-world data.
Finally, we will describe the current attempts to infer or reconstruct the original underlying higher-order models from data.

A fundamental question in neuroscience is how structure and function of neural systems are related. We study this interplay by combining a familiar auto-associative neural network with an evolving mechanism for the birth and death of synapses. A feedback loop then arises leading to two qualitatively different behaviours. In one, the network structure becomes heterogeneous and dissasortative and the system displays good memory performance. In the other, the structure remains homogeneous and incapable of pattern retrieval. These findings are compatible with experimental results on early brain development, and provide an explanation for the existence of synaptic pruning. Other evolving networks, such as those of protein interaction, might share the basic ingredients for this feedback loop, and indeed many of their structural features are as predicted by our model.

Epithelial sheets form specialized 3D structures suited to their physiological roles, such as branched alveoli in the lungs, tubes in the kidney, and villi in the intestine. To generate and maintain these structures, epithelia must undergo complex 3D deformations across length and time scales. How epithelial shape arises from active stresses, viscoelasticity and luminal pressure remains poorly understood. I will present different approaches to study the mechanobiology of epithelial shape from the bottom up. I will discuss new technologies to design epithelia of arbitrary size and geometry and to subject them to controlled mechanical deformations in 3D. I will show that monolayers exhibit superelastic behavior when stretch is applied and that they readily buckle when tension is released. We use this phenomenology and a 3D vertex model to rationally direct spontaneous pattern formation, and hence engineer tissue folding. I will also present our recent advances to understand the mechanobiology of intestinal organoids. We show that these organoids exhibit a non-monotonic stress distribution that defines mechanical and functional compartments. From these experiments we conclude that the stem cell compartment folds through apical constriction and that cells are pulled out of the crypt along a gradient of increasing tension, rather than pushed by a compressive stress downstream of mitotic pressure as previously assumed. This experimental and theoretical work unveils how patterned forces enable folding and collective migration in the intestinal crypt.