Related papers: The reaction-diffusion approach to morphogenesis
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…
The pattern of radiation energy deposition in substances at the microscopic level of lattice, molecule size, or the cell's nucleus is not uniform. The energy of radiation is transferred to the substance medium in the form of discrete,…
Most biochemical reactions in living cells rely on diffusive search for target molecules or regions in a heterogeneous overcrowded cytoplasmic medium. Rapid re-arrangements of the medium constantly change the effective diffusivity felt…
Morphogenesis, the process by which an adult organism emerges from a single cell, has fascinated humans for a long time. Modelling this process can provide novel insights into development and the principles that orchestrate the…
During the development of an organism, cells must coordinate and organize to generate the correct shape, structure, and spatial patterns of tissues and organs, a process known as morphogenesis. The morphogenesis of embryonic tissues is…
The cellular environment, characterized by its intricate composition and spatial organization, hosts a variety of organelles, ranging from membrane-bound ones to membraneless structures that are formed through liquid-liquid phase…
We consider a phenotype-structured reaction-diffusion model of avascular glioma growth. The model describes the interaction dynamics between tumour cells and oxygen, and takes into account anisotropic cell movement and oxygen diffusion…
Many organs of higher organisms are heavily branched structures and arise by an at first sight similar process of branching morphogenesis. Yet the regulatory components and local interactions that have been identified differ greatly in…
We reveal that the mechanical pulsation of locally synchronised particles is a generic route to propagate deformation waves. We consider a model of dense repulsive particles whose activity drives periodic change in size of each individual.…
Text-book concepts of diffusion- versus kinetic-control are well-defined for reaction-kinetics involving macroscopic concentrations of diffusive reactants that are adequately described by rate-constants -- the inverse of the…
Phase separation is the thermodynamic process that explains how droplets form in multicomponent fluids. These droplets can provide controlled compartments to localize chemical reactions, and reactions can also affect the droplets' dynamics.…
Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…
The transition from a microscopic model for the movement of many particles to a macroscopic continuum model for a density flow is studied. The microscopic model for the free flow is completely deterministic, described by an interaction…
In this article, I put forward the idea that the neoplastic process (NP) has deep evolutionary roots and make specific predictions about the connection between cancer and the formation of the first embryo, which allowed for the evolutionary…
A common developmental process, called branching morphogenesis, generates the epithelial trees in a variety of organs, including the lungs, kidneys, and glands. How branching morphogenesis can create epithelial architectures of very…
We propose a novel measure valued process which models the behaviour of chemical reaction networks in spatially heterogeneous systems. It models reaction dynamics between different molecular species and continuous movement of molecules in…
We develop a theory of reversible diffusion-controlled reactions with generalized binding/unbinding kinetics. In this framework, a diffusing particle can bind to the reactive substrate after a random number of arrivals onto it, with a given…
Organogenesis is a tightly regulated process that has been studied experimentally for decades. Computational models can help to integrate available knowledge and to better understand the underlying regulatory logic. We are currently…
We review the milestones in the century-long development of the theory of diffusion-controlled reactions. Starting from the seminal work by von Smoluchowski who recognized the importance of diffusion in chemical reactions, we discuss…
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…