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Collagen is the most abundant extracellular-matrix protein in mammals and the main structural and load-bearing element of connective tissues. Collagen networks show remarkable strain-stiffening properties which tune the mechanical functions…
Actin flow in the cortical cytoskeleton underneath the cell membrane generates mechanical stresses that shape the cell surface. We study this mechanism using a hydrodynamic model of a compressible active gel polymerizing at the membrane and…
The vertex model is widely used to describe the dynamics of epithelial tissues, because of its simplicity and versatility and the direct inclusion of biophysical parameters. Here, it is shown that quite generally, when cells modify their…
Epithelial-Mesenchymal Transition (EMT), and the corresponding reverse process, Mesenchymal-Epithelial Transition (MET), are dynamic and reversible cellular programs orchestrated by many changes at biochemical and morphological levels. A…
Active nematic models explain the topological defects and flow patterns observed in epithelial tissues, but the nature of active stress-whether it is extensile or contractile, a key parameter of the theory-is not well established…
Optimal transport has become part of the standard quantitative economics toolbox. It is the framework of choice to describe models of matching with transfers, but beyond that, it allows to: extend quantile regression; identify discrete…
Active cellular transport is a fundamental mechanism for protein and vesicle delivery, cell cycle and molecular degradation. Viruses can hijack the transport system and use it to reach the nucleus. Most transport processes consist of…
In this paper we introduce the optimal control of a kinetic model describing agents who migrate on a graph and interact within its nodes exchanging a physical quantity. As a prototype model, we consider the spread of an infectious disease…
Gradual transformation of the epidermal stem cells to corneocytes involves a chain of chronologically well-arranged events that mostly stimulated locally by their neighbors. Cell diversity that observed during the differentiation through…
Migration of animal cells is based on the interplay between actin polymerization at the front, adhesion along the cell-substrate interface, and actomyosin contractility at the back. Active gel theory has been used before to demonstrate that…
Cell alignment often forms nematic order, which can lead to anomalous collective cell flow due to the so-called active force. Although it is appreciated that cell migration is driven by traction force, a quantitative evaluation of the…
In this survey we report some recent results in the mathematical modeling of epidemic phenomena through the use of kinetic equations. We initially consider models of interaction between agents in which social characteristics play a key role…
The migration behavior of colliding cells is critically determined by transient contact-interactions. During these interactions, the motility machinery, including the front-rear polarization of the cell, dynamically responds to surface…
Healthy cartilage is a remarkable tissue, able to withstand tens of millions of loading cycles with minimal damage. While much is known about the structural origins of its compressive mechanics, how composition determines its mechanical…
Mathematical modelling has a long history in the context of collective cell migration, with applications throughout development, disease and regenerative medicine. The aim of modelling in this context is to provide a framework in which to…
Properties of transport of molecular motors are investigated. A simplified model based on the concept of Brownian ratchets is applied. We analyze a stochastic equation of motion by means of numerical methods. The transport is systematically…
There are numerous scenarios in which populations of cells migrate in crowded environments. Typical examples include wound healing, cancer growth and embryo development. In these crowded environments cells are able to interact with each…
Eukaryote cells have a flexible shape, which dynamically changes according to the function performed by the cell. One mechanism for deforming the cell membrane into the desired shape is through the expression of curved membrane proteins.…
Intracellular transport is an essential function in eucaryotic cells, facilitated by motor proteins - proteins converting chemical energy into kinetic energy. It is known that motor proteins work in teams enabling unidirectional and…
Cell migration is closely linked to cell shape, yet cell size is often assumed to remain constant. This assumption is challenged by recent experiments showing that cells undergo volume loss during spreading and swelling upon activation,…