Related papers: The reaction-diffusion approach to morphogenesis
We describe the construction of a conserved reaction-diffusion system that exhibits self-organized critical (avalanche-like) behavior under the action of a slow addition of particles. The model provides an illustration of the general…
Explaining the origin of life requires us to explain how self-replication arises. To be specific, how can a self-replicating entity develop spontaneously from a chemical reaction system in which no reaction is self-replicating? Previously…
This paper studies a longitudinal shape transformation model in which shapes are deformed in response to an internal growth potential that evolves according to an advection reaction diffusion process. This model extends prior works that…
Molecular phenotypes are important links between genomic information and organismic functions, fitness, and evolution. Complex phenotypes, which are also called quantitative traits, often depend on multiple genomic loci. Their evolution…
The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The intra-layer diffusion constants act as small parameter in the expansion and the unperturbed state…
We discuss several qualitative properties of the solutions of reaction-diffusion systems and equations of the form $u_t = \epsilon^2 D \Delta u + f(u,x,\epsilon t)$, that are used in modeling pattern formation. We analyze the diffusion…
We consider here the morphogenesis (pattern formation) problem for some genetic network models. First, we show that any given spatio-temporal pattern can be generated by a genetic network involving a sufficiently large number of genes.…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
At finite concentrations of reacting molecules, kinetics of diffusion-controlled reactions is affected by intra-reactant interactions. As a result, multi-particle reaction statistics cannot be deduced from single-particle results. Here we…
Tissues are subjected to large external forces and undergo global deformations during morphogenesis. We use synthetic analogues of tissues to study the impact of cell-cell adhesion on the response of cohesive cellular assemblies under such…
The replication and differentiation of spots in reaction diffusion equations are studied by extending the Gray-Scott model with self-replicating spots to include many degrees of freedom needed to model systems with many chemicals. By…
In most natural sciences there is currently the insight that it is necessary to bridge gaps between different processes which can be observed on different scales. This is especially true in the field of chemical reactions where the…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
We study reaction-diffusion processes with concentration-dependent diffusivity. First, we determine the decay of the concentration in the single-species and two-species diffusion-controlled annihilation processes. We then consider two…
We present a spatially-extended system of chemical reactions exhibiting adaptation to time-dependent influxes of reactants. Here adaptation is defined as improved reproductive success, namely the ability of one of the many locally stable…
Evolutionary success depends on the capacity to adapt: organisms must respond to environmental challenges through both genetic innovation and lifetime learning. The gene-centric paradigm attributes evolutionary causality exclusively to…
Morphogenetic dynamics of tissue sheets require coordinated cell shape changes regulated by global patterning of mechanical forces. Inspired by such biological phenomena, we propose a minimal mechanochemical model based on the notion that…
A mathematical model for emerging contaminants sorption in multispecies biofilms, based on a continuum approach and mass conservation principles is presented. Diffusion of contaminants within the biofilm is described using a…
A mesoscopic multi-particle collision model for fluid dynamics is generalized to incorporate the chemical reactions among species that may diffuse at different rates. This generalization provides a means to simulate reaction-diffusion…
Various resonant and near-resonant patterns form in a light-sensitive Belousov-Zhabotinsky (BZ) reaction in response to a spatially-homogeneous time-periodic perturbation with light. The regions (tongues) in the forcing frequency and…