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Time delays, modelling the process of intracellular gene expression, have been shown to have important impacts on the dynamics of pattern formation in reaction-diffusion systems. In particular, past work has shown that such time delays can…
Biological cells can actively tune their intracellular architecture according to their overall shape. Here we explore the rheological implication of such coupling in a minimal model of a dense cellular material where each cell exerts an…
Biological systems are majorly dependent on their property of bistability in order to exhibit nongenetic heterogeneity in terms of cellular morphology and physiology. Spatial patterns of phenotypically heterogeneous cells, arising due to…
Since its foundations, more than one hundred years ago, the field of structural biology has strived to understand and analyze the properties of molecules and their interactions by studying the structure that they take in 3D space. However,…
Many animals have patterned fur, feathers, or scales, such as the stripes of a zebra. Turing models, or reaction-diffusion systems, are a class of mathematical models of interacting species that have been successfully used to generate…
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…
Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in cell biology, such as cell polarization. Coupled bulk-surface models naturally include compartmentalization of cytosolic and membrane-bound polarity…
Cell migration in confining physiological environments relies on the concerted dynamics of several cellular components, including protrusions, adhesions with the environment, and the cell nucleus. However, it remains poorly understood how…
Living cells employ excitable reaction-diffusion waves for internal cellular functions, in which curvature-inducing proteins are often involved. However, the role of their mechanochemical coupling is not well understood. Here, we report the…
The emergence of a spatially-organized population distribution depends on the dynamics of the population and mediators of interaction (activators and inhibitors). Two broad classes of models have been used to investigate when and how…
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic…
Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in ameliorating problems of pattern robustness and selection, in addition to more realistic…
Growth patterns generated by filamentous organisms (e.g. actinomycetes and fungi) involve spatial and temporal dynamics at different length scales. Several mathematical models have been proposed in the last thirty years to address these…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
Diffusion models have attained prominence for their ability to synthesize a probability distribution for a given dataset via a diffusion process, enabling the generation of new data points with high fidelity. However, diffusion processes…
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…
We propose a simple mathematical model to describe the mechanical relaxation of cells within a curved epithelial tissue layer represented by an arbitrary curve in two-dimensional space. This model generalises previous one-dimensional models…
Mechanical cues like the rigidity of the substrate are main determinants for the decision making of adherent cells. Here we use a mechano-chemical model to predict the cellular response to varying substrate stiffness. The model equations…
We propose a new model to describe diffusion processes within active deformable media. Our general theoretical framework is based on physical and mathematical considerations, and it suggests to use diffusion tensors directly coupled to…
Convergent extension of epithelial tissue is a key motif of animal morphogenesis. On a coarse scale, cell motion resembles laminar fluid flow; yet in contrast to a fluid, epithelial cells adhere to each other and maintain the tissue layer…