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Structural cellular materials in nature, such as wood, trabecular bone, corals, and dentin combine complex biological functions with structural roles, such as skeletal support and impact protection1,2. They feature complex structural…
Diffusion in living tissues governs essential physiological processes and is well studied within cells. Yet how extracellular molecular motion emerges from the structural complexity of tissues remains unresolved. In the brain, molecules…
The growth of a crystal is usually determined by its surface. Many factors influence the growth dynamics. Energy barriers associated with the presence of steps most often decide about the emerging pattern. The height and type of…
The Voronoi-based cellular model is highly successful in describing the motion of two-dimensional confluent cell tissues. In the homogeneous version of this model, the energy of each cell is determined solely by its geometric shape and…
During development, highly ordered structures emerge as cells collectively coordinate with each other. While recent advances have clarified how individual cells process and respond to external signals, understanding collective cellular…
Adhesive cell-substrate interactions are crucial for cell motility and are responsible for the necessary traction that propels cells. These interactions can also change the shape of the cell, analogous to liquid droplet wetting on adhesive…
Cells use temporal dynamical patterns to transmit information via signaling pathways. As optimality with respect to the environment plays a fundamental role in biological systems, organisms have evolved optimal ways to transmit information.…
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…
Biological cells are able to adapt their behaviour in response to environmental cues. Durotaxis is a phenomenon in which cells adjust their migration depending on the mechanical properties of a surrounding substrate. Although durotaxis has…
Intracellular protein patterns regulate many vital cellular functions, such as the processing of spatiotemporal information or the control of shape deformations. To do so, pattern-forming systems can be sensitive to the cell geometry by…
Voronoi tessellations of scale-invariant fractal sets are characterized by topological and metrical properties that are significantly different from those of natural cellular structures. As an example we analyze Voronoi diagrams of…
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…
Detachment and fracture are central to many tissue-level processes, but they are challenging to simulate with Voronoi-type models that typically assume a confluent tissue. Here we analyze the finite Voronoi model, a nonconfluent extension…
Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with pseudopodia extended from other cells, and animals that move based on their vision of…
Open cellular solids usually possess random microstructures that may contain a characteristic length scale, such as the cell size. This gives rise to size dependent mechanical properties where large systems behave differently from small…
As an effective method to deliver external materials into biological cells, microinjection has been widely applied in the biomedical field. However, the cognition of cell mechanical property is still inadequate, which greatly limits the…
We present results on tagged particle diffusion in a meso-scale lattice model for sheared amorphous material in athermal quasi-static conditions. We find a short time diffusive regime and a long time diffusive regime whose diffusion…
Cells exhibit qualitatively different behaviors on substrates with different rigidities. The fact that cells are more polarized on the stiffer substrate motivates us to construct a two-dimensional cell with the distribution of focal…
Cellular patterns formed by self-organization of dislocations are a most conspicuous feature of dislocation microstructure evolution during plastic deformation. To elucidate the physical mechanisms underlying dislocation cell structure…
Within periodic materials and structures, wave scattering and dispersion occur across constituent material interfaces leading to a banded frequency response. In an earlier paper, the elastodynamics of one-dimensional periodic materials and…