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Collective cell motions underlie structure formation during embryonic development. Tissues exhibit emergent multicellular characteristics such as jamming, rigidity transitions, and glassy dynamics, but there remain questions about how those…
Biological tissues are complex structures composed of many elements which make light-based tissue diagnostics challenging. Over the past decades, Monte Carlo technique has been used as a fundamental and versatile approach toward modeling…
A two-dimensional mathematical model for cells migrating without adhesion capabilities is presented and analyzed. Cells are represented by their cortex, which is modelled as an elastic curve, subject to an internal pressure force. Net…
Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular…
A simple model is proposed that describes the various morphodynamic principles of migrating cells from polar to amoeboidal motions. The model equation is derived using competing internal cellular compass variables and symmetries of the…
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.…
Morphogenesis involves complex shape changes of biological tissues. Yet, tissue shape changes depend on tissue rheology, which in turn arises from the interplay of large numbers of cells. Here, we link cell- and tissue-scale mechanics by…
In this work we approach cell migration under a large-scale assumption, so that the system reduces to a particle in motion. Unlike classical particle models, the cell displacement results from its internal activity: the cell velocity is a…
Living cells respond to mechanical changes in the matrix surrounding them by applying contractile forces that are in turn transmitted to distant cells. We calculate the mechanical work that each cell performs in order to deform the matrix,…
Morphogenesis, the process by which an adult organism emerges from a single cell, has fascinated humans for a long time. Modelling this process can provide novel insights into development and the principles that orchestrate the…
A mathematical model is proposed for shape evolution and locomotion of fish epidermal keratocytes on elastic substrates. The model is based on mechanosensing concepts: cells apply contractile forces onto the elastic substrate, while cell…
Tumor cells invade individually or in groups, mediated by mechanical interactions between cells and their surrounding matrix. These multicellular dynamics are reminiscent of leader-follower coordination and epithelial-mesenchymal…
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,…
The process of morphogenesis, which can be defined as an evolution of the form of an organism, is one of the most intriguing mysteries in the life sciences. It is clear, that gene expression patterns cannot explain the development of the…
Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…
The hydrodynamic theory of active nematics has been often used to describe the spatio-temporal dynamics of cell flows and motile topological defects within soft confluent tissues. Those theories, however, often rely on the assumption that…
Constructing physical models of living cells and tissues is an extremely challenging task because of the high complexities of both intra- and intercellular processes. In addition, the force that a single cell generates vanishes in total due…
During epithelial wound healing, cell morphology near the healed wound and the healing rate vary strongly among different developmental stages even for a single species like \textit{Drosophila}. We develop deformable particle (DP) model…
Cell type (e.g. pluripotent cell, fibroblast) is the end result of many complex processes that unfold due to evolutionary, developmental, and transformational stimuli. A cell's phenotype and the discrete, a priori states that define various…
Equations for dislocation evolution bridge the gap between dislocation properties and continuum descriptions of plastic behavior of crystalline materials. Computer simulations can help us verify these evolution equations and find their…