Related papers: Physical Schemata Underlying Biological Pattern Fo…
Nature uses elongated shapes and filaments to build stable structures, generate motion, and allow complex geometric interactions. In this Review, we examine the role of biological filaments across different length scales. From the molecular…
Biological systems perform an astonishing array of dynamical processes -- including development and repair, regulation, behavior and motor control, sensing and signaling, and adaptation, among others. Powered by the transduction of stored…
Equations of motion that recognize biochemical patterns are described. The equations are partial differential equations in a continuous multiple component system in which adequate initial and boundary conditions are given. The biochemical…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…
The concept of evolutionary development of structures constituted a \emph{real} revolution in biology: it was possible to understand how the very complex structures of life can arise in an out-of-equilibrium system. The investigation of…
We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological…
Colonies of bacteria grown on thin agar plate exhibit fractal patterns as a result of adaptation to their environments. The bacterial colony pattern formation is regulated crucially by chemotaxis, the movement of cells along a chemical…
Bacterial communities such as biofilms are widely recognised as being important for survival and persistence of bacteria in harsh environments. Mechanistic models of biofilm growth indicate that the way in which the surface is seeded can…
Biological cells are able to generate intricate structures and respond to external stimuli, sculpting their membrane from within. Simplified biomimetic systems can aid in understanding the principles which govern these shape changes and…
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…
Throughout the evolution of biological species on Earth, cells and organs have developed many complex structures and processes to ensure their interactions with individual chemical molecules (small and macromolecular) and nanoscale objects…
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…
We study pattern formation in a chemotaxis model of bacteria and soil carbon dynamics as an example system where transient dynamics can give rise to pattern formation outside of Turing unstable regimes. We use a detailed analysis of the…
Rhythmic and sequential segmentation of the embryonic body plan is a vital developmental patterning process in all vertebrate species. However, a theoretical framework capturing the emergence of dynamic patterns of gene expression from the…
The rheological properties of biological tissues are core to processes such as cancer metastasis, wound healing and embryo development. The emergence of tissue and organ structures during morphogenesis requires the precise formation of…
We consider a reaction-diffusion system with discontinuous reaction terms modeled by non-ideal relays. The system is motivated by an epigenetic population model of evolution of two-phenotype bacteria which switch phenotype in response to…
Turing's theory of pattern formation has been used to describe the formation of self-organised periodic patterns in many biological, chemical and physical systems. However, the use of such models is hindered by our inability to predict, in…
Chemotactic bacteria have been observed to congregate into highly regular patterns. When the bacteria are placed in the center of a dish, a wave of bacteria can travel outward, leaving a regular pattern of spots or stripes in its wake.…
The present view of biological phenomena is based on a biochemical paradigm that development of living organisms is defined by information stored in a molecular form as some genetic code. However, new discoveries indicate that biological…
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…