Related papers: Synthesis and materialization of a reaction-diffus…
In the French flag problem, initially uncolored cells on a grid must differentiate to become blue, white or red. The goal is for the cells to color the grid as a French flag, i.e., a three-colored triband, in a distributed manner. To solve…
We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned…
A crucial step in the early development of multicellular organisms involves the establishment of spatial patterns of gene expression which later direct proliferating cells to take on different cell fates. These patterns enable the cells to…
Multicellular organisms exhibit a high degree of structural organization with specific cell types always occurring in characteristic locations. The conventional framework for describing the emergence of such consistent spatial patterns is…
Morphogenesis is central to biology but remains largely unexplored in chemistry. Reaction-diffusion (RD) mechanisms are, however, essential to understand how shape emerges in the living world. While numerical methods confirm the incredible…
We discovered a class of self-similar solutions in nonlinear models describing the formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differention in developing tissues. These models…
The formation of protein patterns inside cells is generically described by reaction-diffusion models. The study of such systems goes back to Turing, who showed how patterns can emerge from a homogenous steady state when two reactive…
This paper proposes a control theoretic framework to model and analyze the self-organized pattern formation of molecular concentrations in biomolecular communication networks, emerging applications in synthetic biology. In biomolecular…
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…
Urban morphogenesis is the process of formation of its elements and the specialization of its suburbs. Street networks are the structural part of the system. Understand their formation reveals crucial information about urban transformation…
Several different enzymes display an apparent diffusion coefficient that increases with the concentration of their substrate. Moreover, their motion becomes directed in substrate gradients. Currently, there are several competing models for…
Complex spatial patterns in biological systems often arise through self-organization without a central coordination, guided by local interactions and chemical signaling. In this study, we explore how motility-dependent chemical deposition…
MicroRNAs are extensively known for post-transcriptional gene regulation and pattern formation in the embryonic developmental stage. We explore the origin of these spatio-temporal patterns mathematically, considering three different motifs…
Spatial and temporal pattern formation in reaction-diffusion systems is typically studied with two or more equations, as scalar reaction-diffusion equations confined to convex domains do not admit stable inhomogeneous states in time or…
Inspired by biology's most sophisticated computer, the brain, neural networks constitute a profound reformulation of computational principles. Remarkably, analogous high-dimensional, highly-interconnected computational architectures also…
In this paper we consider mathematical modeling of the dynamics of self-organized patterning of spatially confined human embryonic stem cells (hESCs) treated with BMP4 (gastruloids) described in recent experimental works. In the first part…
DNA-coated colloids can crystallize into a multitude of lattices, ranging from face-centered cubic to diamond and thereby contribute to our understanding of crystallization and open avenues to producing structures with useful photonic…
The reaction-diffusion models have been extensively applied to explain the mechanism of pattern formations in early embryogenesis based on geometrically confined microtissues consisting of human pluripotent stem cells. Recently, mechanical…
This paper introduces a continuous model for Multi-cellular Developmental Design. The cells are fixed on a 2D grid and exchange "chemicals" with their neighbors during the growth process. The quantity of chemicals that a cell produces, as…
Reaction-diffusion systems have been proposed as a model for pattern formation and morphogenesis. The Fickian diffusion typically employed in these constructions model the Brownian motion of particles. The biological and chemical elements…