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Collective cell migration governs a range of physiological and pathological processes, from tissue morphogenesis to cancer invasion, in which topological defects arise as an inevitable consequence of frequent cellular rearrangement and…
Despite the fundamental importance of solid-solid transformations in many technologies, the microscopic mechanisms remain poorly understood. Here, we explore the atomistic mechanisms at the migrating interface during solid-solid phase…
We consider a partial differential equation model for the growth of heterogeneous cell populations subdivided into multiple distinct discrete phenotypes. In this model, cells preferentially move towards regions where they feel less…
We develop an agent-based model of the motion and pattern formation of vesicles. These intracellular particles can be found in four different modes of (undirected and directed) motion and can fuse with other vesicles. While the size of…
Cell motility is one of the most fundamental phenomena underlying biological processes that maintain living organisms alive. Here we introduce a simple model to describe the motility of cells which include not only time-correlated internal…
Collective cell migration plays a crucial role in numerous biological processes, including tumour growth, wound healing, and the immune response. Often, the migrating population consists of cells with various different phenotypes. This…
For the first time the phenomenon of cellular structure coarsening are consistently analysed from the positions of kinetic, hydrodynamic and stochastodynamic theories of nonequilibrium statistical systems. Thereby micro-, meso- and…
Movement of cell clusters along extracellular matrices (ECM) during tissue development, wound healing, and early stage of cancer invasion involve various inter-connected migration modes such as: (1) cell movement within clusters, (2)…
There is increasing interest in the analysis of biological tissue, its organization and its dynamics with the help of mathematical models. In the ideal case emergent properties on the tissue scale can be derived from the cellular scale.…
Cell shape is determined by a balance of intrinsic properties of the cell as well as its mechanochemical environment. Inhomogeneous shape changes underly many morphogenetic events and involve spatial gradients in active cellular forces…
The migratory dynamics of cells in physiological processes, ranging from wound healing to cancer metastasis, rely on contact-mediated cell-cell interactions. These interactions play a key role in shaping the stochastic trajectories of…
We present a general theoretical framework to discuss mechanisms of morphogen transport and gradient formation in a cell layer. Trafficking events on the cellular scale lead to transport on larger scales. We discuss in particular the case…
The skin forms an efficient barrier against the environment, and rapid cutaneous wound healing after injury is therefore essential. Healing of the uppermost layer of the skin, the epidermis, involves collective migration of keratinocytes,…
Multicellular collective migration is a ubiquitous strategy of cells to translocate spatially in diverse tissue environments to accomplish a wide variety of biological phenomena, viz. embryonic development, wound healing, and tumor…
In this paper, we introduce a three-dimensional mathematical model of collagen contraction with microbuckling based on the two-dimensional model previously developed by the authors. The model both qualitatively and quantitatively replicates…
Cell migration is crucial to many physiological and pathological processes. During migration, a cell adapts its morphology, including the overall morphology and nucleus morphology, in response to various cues in complex microenvironments,…
The origin of the dramatic slowdown of dynamics near the glass transition temperature (Tg) remains a long-standing fundamental and unresolved issue in soft condensed matter. While single-molecule (SM) experiments using fluorescent probes…
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…
We propose a theoretical model which relies on the generalized Langevin equation and may account for various dynamical features of the thermal motion of organelles, vesicles or macromolecules in viscoelastic media such as polymer networks.…
Most cancers in humans are large, measuring centimeters in diameter, composed of many billions of cells. An equivalent mass of normal cells would be highly heterogeneous as a result of the mutations that occur during each cell division.…