Related papers: The biological frontier of pattern formation
Pattern formation from homogeneity is well-studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is nontrivial to separate observed spatial patterning due to inherent spatial heterogeneity from…
Liesegang patterns emerge from precipitation processes and may be used to build bulk structures at submicron lengthscales. Thus they have significant potential for technological applications provided adequate methods of control can be…
Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational…
Interconnected ensembles of biological entities are perhaps some of the most complex systems that modern science has encountered so far. In particular, scientists have concentrated on understanding how the complexity of the interacting…
The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex systems has been successfully described as networks whose…
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…
In his seminal paper on morphogenesis (1952), Alan Turing demonstrated that different spatio-temporal patterns can arise due to instability of the homogeneous state in reaction-diffusion systems, but at least two species are necessary to…
The genetic instructions stored in the genome require an additional layer of information to robustly determine cell fate. This additional regulation is provided by the interplay between chromosome-patterning biochemical ("epigenetic") marks…
A model of the oscillatory component of interaction of inner boundaries is studied; and the features of generation of the composite structure in interim asymptotics are considered. A model of a multiscale net of inner boundaries was used to…
A classification of dynamical systems in terms of their variational properties is reviewed. Within this classification, front propagation is discussed in a non-gradient relaxational potential flow. The model is motivated by transient…
The development of multicellular organisms proceeds through a series of morphogenetic and cell-state transitions, transforming homogeneous zygotes into complex adults by a process of self-organization. Many of these transitions are achieved…
In certain biological contexts, such as the plumage patterns of birds and stripes on certain species of fishes, pattern formation takes place behind a so-called "wave of competency". Currently, the effects of a wave of competency on the…
Genetic sequences are known to possess non-trivial composition together with symmetries in the frequencies of their components. Recently, it has been shown that symmetry and structure are hierarchically intertwined in DNA, suggesting a…
Morphogen profiles play a vital role in biology by specifying position in embryonic development. However, the factors that influence the shape of a morphogen profile remain poorly understood. Since morphogens should provide precise…
Metamaterials are artificial composite structures designed for controlling waves or fields, and exhibit interaction phenomena that are unexpected on the basis of their chemical constituents. These phenomena are encoded in effective material…
Spatial patterns arising spontaneously due to internal processes are ubiquitous in nature, varying from regular patterns of dryland vegetation to complex structures of bacterial colonies. Many of these patterns can be explained in the…
Interactions between neighboring cells are essential for generating or refining patterns in a number of biological systems. We propose a discrete filtering approach to predict how networks of cells modulate spatially varying input signals…
As proposed by Alan Turing in 1952 as a ubiquitous mechanism for nonequilibrium pattern formation, diffusional effects may destabilize uniform distributions of reacting chemical species and lead to both spatially and temporally…
In this review, we discuss modularity and hierarchy in biological systems. We review examples from protein structure, genetics, and biological networks of modular partitioning of the geometry of biological space. We review theories to…
Mathematical modelling is a cornerstone of computational biology. While mechanistic models might describe the interactions of interest of a system, they are often difficult to study. On the other hand, abstract models might capture key…