Related papers: The biological frontier of pattern formation
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…
Mathematical models play an increasingly important role in the interpretation of biological experiments. Studies often present a model that generates the observations, connecting hypothesized process to an observed pattern. Such generative…
The properties of a front between two different phases in the presence of a smoothly inhomogeneous external field that takes its critical value at the crossing point is analyzed. Two generic scenarios are studied. In the first, the system…
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…
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…
Plant morphogenesis relies on dynamic growth deformations at the cell and tissue scales driven by osmotic fluxes. A mechanistic understanding of this phenomenon demands a physical framework that integrates cell imbibition, tissue mechanics,…
We show that very small-amplitude oscillations of a highly symmetric, spheric or cylindrical, interface (thin membrane) between two fluids can result in inhomogeneous instability and breaking of the interface symmetry: the frequency of the…
It is shown that physical fields are formed by physical structures, which in their properties are differential-geometrical structures. These results have been obtained due to using the mathematical apparatus of skew-symmetric differential…
A large variety of real systems are composed by entities in relationships which can be represented by networks. In many of these systems, elements are embedded in the space and location information impacts properties and evolution. Local…
Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described…
Intracellular protein patterns govern essential cellular functions by dynamically redistributing proteins between membrane-bound and cytosolic states, conserving their total numbers. This review presents a theoretical framework for…
Morphogenesis is the biological process that causes the emergence and changes of patterns (tissues and organs) in living organisms. It is a robust, self-organising mechanism, governed by Genetic Regulatory Networks (GRN), that hasn't been…
Flocks of birds and schools of fish are familiar examples of spatial patterns formed by living organisms. In contrast to the patterns on the skins of, say, zebra and giraffe, the patterns of our interest are {\it transient} although…
Many networks describing complex systems are directed: the interactions between elements are not symmetric. Recent work has shown that these networks can display properties such as trophic coherence or non-normality, which in turn affect…
In forced wetting, a rapidly moving surface drags with it a thin layer of trailing fluid as it is plunged into a second fluid bath. Using high-speed interferometry, we find characteristic structure in the thickness of this layer with…
Turing patterns are a central paradigm for describing spatial patterns in nature. The corresponding theory of reaction-diffusion dynamics combines ideal diffusion with nonlinear reactions, resulting in patterns when species diffuse at…
Complexity in biology is often described using a multi-map architecture, where the genotype, representing the encoded information, is mapped to the functional level, known as the phenotype, which is then connected to a latent phenotype we…
Bacteria can form a great variety of spatially heterogeneous cell density patterns, ranging from simple concentric rings to dynamical spiral waves appearing in growing colonies. These pattern formation phenomena are important as they…
Turing's theory of pattern formation is a universal model for self-organization, applicable to many systems in physics, chemistry and biology. Essential properties of a Turing system, such as the conditions for the existence of patterns and…
Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems ranging from biology to galaxies build-up. We propose a new instability mechanism leading to pattern formation in…