Related papers: Pattern Formation in a Coupled Membrane-Bulk React…
We consider a bulk-membrane-coupled partial differential equation in which a single diffusion equation posed within the unit ball is coupled to a two-component reaction diffusion equation posed on the bounding unit sphere through a linear…
Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in development, and symmetry-breaking in cell polarisation. We develop…
It has been argued that there is biological and modeling evidence that a non-linear diffusion coefficient of the type D(b) = D_0 b^{k} underlies the formation of a number of growth patterns of bacterial colonies. We study a…
In this work, we present a computational analysis of the planar wave propagation behavior of a one-dimensional periodic multi-stable cellular material. Wave propagation in these materials is interesting because they combine the ability of…
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…
Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of…
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…
The motion of a eukaryotic cell presents a variety of interesting and challenging problems from both a modeling and a computational perspective. The processes span many spatial scales (from molecular to tissue) as well as disparate time…
Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…
Various molecules exclusively accumulate at the front or back of migrating eukaryotic cells in response to a shallow gradient of extracellular signals. Directional sensing and signal amplification highlight the essential properties in 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…
Protein pattern formation is essential for the spatial organization of many intracellular processes like cell division, flagellum positioning, and chemotaxis. A prominent example of intracellular patterns are the oscillatory pole-to-pole…
Lateral diffusion of molecules on surfaces plays a very important role in various biological processes, including lipid transport across the cell membrane, synaptic transmission and other phenomena such as exo- and endocytosis, signal…
Nonlinear reaction-diffusion systems admit a wide variety of spatiotemporal patterns or structures. In this lecture, we point out that there is certain advantage in studying discrete arrays, namely cellular neural/nonlinear networks (CNNs),…
We introduce a three-dimensional stochastic reaction-diffusion model to describe MinD/MinE dynamical structures in Escherichia coli. This model spontaneously generates pole-to-pole oscillations of the membrane-associated MinD proteins, MinE…
Intracellular protein patterns govern essential cellular functions by dynamically redistributing proteins between membrane-bound and cytosolic states, conserving their total numbers. This review presents a theoretical framework for…
This paper studies a bulk-surface reaction-diffusion system for cell polarization in two-dimensional domains. The model describes the formation of localized patterns through the wave-pinning mechanism, while explicitly incorporating the…
Pattern formation is ubiquitous in nature from morphogenesis and cloud formation to galaxy filamentation. More often than not, patterns arise in a medium driven far from equilibrium due to the interplay of dynamical instability and…
Coupling diffusion process of signaling molecules with nonlinear interactions of intracellular processes and cellular growth/transformation leads to a system of reaction-diffusion equations coupled with ordinary differential equations…
We study nonlinear stability of spatially homogeneous oscillations in reaction-diffusion systems. Assuming absence of unstable linear modes and linear diffusive behavior for the neutral phase, we prove that spatially localized perturbations…