scholarly journals Beyond Turing: Far-from-equilibrium patterns and mechano-chemical feedback

2021 ◽  
Author(s):  
Frits Veerman ◽  
Moritz Mercker ◽  
Anna Marciniak-Czochra
Keyword(s):  
Evolution Equations ◽  
Active Role ◽  
Homogeneous Steady State ◽  
Future Challenges ◽  
Far From Equilibrium ◽  
Spatially Homogeneous ◽  
Abstract Framework ◽  
Inhibitor Interaction ◽  
Activator Inhibitor ◽  
Two Alternatives

AbstractTuring patterns are commonly understood as specific instabilities of a spatially homogeneous steady state, resulting from activator-inhibitor interaction destabilised by diffusion. We argue that this view is restrictive and its agreement with biological observations is problematic. We present two alternative to the ‘classical’ Turing analysis of patterns. First, we employ the abstract framework of evolution equations to enable the study of far-from-equilibrium patterns. Second, we introduce a mechano-chemical model, with the surface on which the pattern forms being dynamic and playing an active role in the pattern formation, effectively replacing the inhibitor. We highlight the advantages of these two alternatives vis-à-vis the ‘classical’ Turing analysis, and give an overview of recent results and future challenges for both approaches.

scholarly journals Beyond Turing: far-from-equilibrium patterns and mechano-chemical feedback

2021 ◽  
Vol 379 (2213) ◽  
Author(s):  
Frits Veerman ◽  
Moritz Mercker ◽  
Anna Marciniak-Czochra
Keyword(s):  
Evolution Equations ◽  
Active Role ◽  
Theme Issue ◽  
Homogeneous Steady State ◽  
Future Challenges ◽  
Far From Equilibrium ◽  
Abstract Framework ◽  
Inhibitor Interaction ◽  
Activator Inhibitor ◽  
Two Alternatives

Turing patterns are commonly understood as specific instabilities of a spatially homogeneous steady state, resulting from activator–inhibitor interaction destabilized by diffusion. We argue that this view is restrictive and its agreement with biological observations is problematic. We present two alternatives to the classical Turing analysis of patterns. First, we employ the abstract framework of evolution equations to enable the study of far-from-equilibrium patterns. Second, we introduce a mechano-chemical model, with the surface on which the pattern forms being dynamic and playing an active role in the pattern formation, effectively replacing the inhibitor. We highlight the advantages of these two alternatives vis-à-vis the classical Turing analysis, and give an overview of recent results and future challenges for both approaches. This article is part of the theme issue ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’.

Bifurcation Analysis of a Diffusive Activator–Inhibitor Model in Vascular Mesenchymal Cells

2015 ◽  
Vol 25 (10) ◽  
pp. 1530026 ◽  
Author(s):  
Rui Yang ◽  
Yongli Song
Keyword(s):  
Steady State ◽  
Center Manifold ◽  
Normal Forms ◽  
Mesenchymal Cells ◽  
Positive Equilibrium ◽  
Normal Form Theory ◽  
Form Theory ◽  
Spatially Homogeneous ◽  
The Stability ◽  
Activator Inhibitor

In this paper, a diffusive activator–inhibitor model in vascular mesenchymal cells is considered. On one hand, we investigate the stability of the equilibria of the system without diffusion. On the other hand, for the unique positive equilibrium of the system with diffusion the conditions ensuring stability, existence of Hopf and steady state bifurcations are given. By applying the center manifold and normal form theory, the normal forms corresponding to Hopf bifurcation and steady state bifurcation are derived explicitly. Numerical simulations are employed to illustrate where the spatially homogeneous and nonhomogeneous periodic solutions and the steady states can emerge. The numerical results verify the obtained theoretical conclusions.

A stabilizing effect of vanishing diffusion in electrohydrodynamics

1997 ◽  
Vol 8 (2) ◽  
pp. 217-227
Author(s):  
EDUARD FEIREISL
Keyword(s):  
Weak Solution ◽  
Steady State ◽  
Electric Field ◽  
Diffusion Coefficients ◽  
Dielectric Liquid ◽  
Recombination Process ◽  
Homogeneous Steady State ◽  
Stabilizing Effect ◽  
Dc Electric Field ◽  
Spatially Homogeneous

We consider a model of the motion of a viscous dielectric liquid subjected to a DC electric field when the bulk conduction results from the presence of a dissociation-recombination process. It is shown that any weak solution approaches a neighbourhood of a spatially homogeneous steady state with radius r≈(d+ +d−)&14frac;, where d+, d− are the diffusion coefficients.

scholarly journals THE SINGULARITY IN GENERIC GRAVITATIONAL COLLAPSE IS SPACELIKE, LOCAL AND OSCILLATORY

1998 ◽  
Vol 13 (19) ◽  
pp. 1565-1573 ◽  
Author(s):  
B. K. BERGER ◽  
D. GARFINKLE ◽  
J. ISENBERG ◽  
V. MONCRIEF ◽  
M. WEAVER
Keyword(s):  
Numerical Simulations ◽  
Gravitational Collapse ◽  
Evolution Equations ◽  
Oscillatory Behavior ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Spatial Point ◽  
Spatially Inhomogeneous ◽  
Homogeneous Universe ◽  
Spatially Homogeneous

A longstanding conjecture by Belinskii, Khalatnikov and Lifshitz that the singularity in generic gravitational collapse is spacelike, local and oscillatory is explored analytically and numerically in spatially inhomogeneous cosmological space–times. With a convenient choice of variables, it can be seen analytically how nonlinear terms in Einstein's equations control the approach to the singularity and cause oscillatory behavior. The analytic picture requires the drastic assumption that each spatial point evolves toward the singularity as an independent spatially homogeneous universe. In every case, detailed numerical simulations of the full Einstein evolution equations support this assumption.

scholarly journals Phase Transitions for Nonlinear Nonlocal Aggregation-Diffusion Equations

2021 ◽  
Vol 382 (1) ◽  
pp. 485-545
Author(s):  
José A. Carrillo ◽  
Rishabh S. Gvalani
Keyword(s):  
Phase Transition ◽  
Porous Medium ◽  
Phase Transitions ◽  
Weak Interactions ◽  
Stationary Solutions ◽  
Diffusion Equations ◽  
Degenerate Diffusion ◽  
Homogeneous Steady State ◽  
Spatially Homogeneous ◽  
Medium Type

AbstractWe are interested in studying the stationary solutions and phase transitions of aggregation equations with degenerate diffusion of porous medium-type, with exponent $$1< m < \infty $$ 1 < m < ∞ . We first prove the existence of possibly infinitely many bifurcations from the spatially homogeneous steady state. We then focus our attention on the associated free energy, proving existence of minimisers and even uniqueness for sufficiently weak interactions. In the absence of uniqueness, we show that the system exhibits phase transitions: we classify values of m and interaction potentials W for which these phase transitions are continuous or discontinuous. Finally, we comment on the limit $$m \rightarrow \infty $$ m → ∞ and the influence that the presence of a phase transition has on this limit.

Role of spectrin in membrane fusion and in shape change of human erythrocyte ghost

1978 ◽  
Vol 36 (2) ◽  
pp. 328-329
Author(s):  
Hideo Hayashi ◽  
Yoshikazu Hirai ◽  
John T. Penniston
Keyword(s):  
Conformational Changes ◽  
Human Erythrocyte ◽  
Shape Change ◽  
Membrane Surface ◽  
Slight Modification ◽  
Active Role ◽  
Main Role ◽  
Bank Blood ◽  
Human Erythrocyte Ghost

Spectrin is a membrane associated protein most of which properties have been tentatively elucidated. A main role of the protein has been assumed to give a supporting structure to inside of the membrane. As reported previously, however, the isolated spectrin molecule underwent self assemble to form such as fibrous, meshwork, dispersed or aggregated arrangements depending upon the buffer suspended and was suggested to play an active role in the membrane conformational changes. In this study, the role of spectrin and actin was examined in terms of the molecular arrangements on the erythrocyte membrane surface with correlation to the functional states of the ghosts.Human erythrocyte ghosts were prepared from either freshly drawn or stocked bank blood by the method of Dodge et al with a slight modification as described before. Anti-spectrin antibody was raised against rabbit by injection of purified spectrin and partially purified.

Sign in / Sign up

Export Citation Format

Share Document