Related papers: Nonlinear degradation enhanced transport of morpho…
We discuss the formation of graded morphogen profiles in a cell layer by nonlinear transport phenomena, important for patterning developing organisms. We focus on a process termed transcytosis, where morphogen transport results from binding…
It is a well known fact that subdiffusion equations in terms of fractional derivatives can be obtained from Continuous Time Random Walk (CTRW) models with long-tailed waiting time distributions. Over the last years various authors have…
The fundamental processes of biological development are governed by multiple signaling molecules that create non-uniform concentration profiles known as morphogen gradients. It is widely believed that the establishment of morphogen…
We show how the nonlinear interaction effects `volume filling' and `adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with…
We present a general theoretical framework to discuss mechanisms of morphogen transport and gradient formation in a cell layer. Trafficking events on the cellular scale lead to transport on larger scales. We discuss in particular the case…
Morphogen profiles allow cells to determine their position within a developing organism, but the mechanisms behind the formation of these profiles are still not well agreed upon. Here we derive fundamental limits to the precision of…
The fundamental biological processes of development of tissues and organs in multicellular organisms is governed by various signaling molecules, which are called morphogens. It is known that spatial and temporal variations in concentration…
We develop a microscopic theory for reaction-difusion (R-D) processes based on a generalization of Einstein's master equation with a reactive term and we show how the mean field formulation leads to a generalized R-D equation with…
Morphogens are secreted signaling molecules that mediate tissue patterning and growth of embryonic tissues. They are secreted in a localized region and spread through the tissue to form a graded concentration profile. We present a…
We propose a reaction-transport model for CTRW with non-linear reactions and non-exponential waiting time distributions. We derive non-linear evolution equation for mesoscopic density of particles. We apply this equation to the problem of…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
Instabilities driven by strong gradients appear in a wide variety of physical systems, including plasmas, neutral fluids, and self-gravitating systems. This work develops an analytic formulation to describe the transport structure and…
The quasi-coherent effects in two-dimensional incompressible turbulence are analyzed starting from the test particle trajectories. They can acquire coherent aspects when the stochastic potential has slow time variation and the motion is not…
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…
We study the asymptotic behaviour of a system of nonlinear reaction--diffusion--advection equations in a domain consisting of two bulk regions connected via microscopic channels distributed within a thin membrane. Both the width of the…
Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such…
In this article we address the problem of the nonlinear interaction of subdiffusive particles. We introduce the random walk model in which statistical characteristics of a random walker such as escape rate and jump distribution depend on…
Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…
We consider a continuum aggregation model with nonlinear local repulsion given by a degenerate power-law diffusion with general exponent. The steady states and their properties in one dimension are studied both analytically and numerically,…
Motivated by a mathematical model for the transport of morphogenes in biological systems, we study existence and uniqueness of entropy solutions for a mixed initial-boundary value problem associated with a nonlinear flux--limited diffusion…