scholarly journals Pattern formation in reaction–diffusion system on membrane with mechanochemical feedback

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Naoki Tamemoto ◽  
Hiroshi Noguchi
Keyword(s):  
Pattern Formation ◽  
Plasma Membranes ◽  
Reaction Diffusion ◽  
Living Cells ◽  
Nonequilibrium Dynamics ◽  
Membrane Deformation ◽  
Brusselator Model ◽  
Diffusion Dynamics ◽  
Curved Membranes ◽  
Membrane Shape

Abstract Shapes of biological membranes are dynamically regulated in living cells. Although membrane shape deformation by proteins at thermal equilibrium has been extensively studied, nonequilibrium dynamics have been much less explored. Recently, chemical reaction propagation has been experimentally observed in plasma membranes. Thus, it is important to understand how the reaction–diffusion dynamics are modified on deformable curved membranes. Here, we investigated nonequilibrium pattern formation on vesicles induced by mechanochemical feedback between membrane deformation and chemical reactions, using dynamically triangulated membrane simulations combined with the Brusselator model. We found that membrane deformation changes stable patterns relative to those that occur on a non-deformable curved surface, as determined by linear stability analysis. We further found that budding and multi-spindle shapes are induced by Turing patterns, and we also observed the transition from oscillation patterns to stable spot patterns. Our results demonstrate the importance of mechanochemical feedback in pattern formation on deforming membranes.

scholarly journals Synchrony and pattern formation of coupled genetic oscillators on a chip of artificial cells

2017 ◽  
Vol 114 (44) ◽  
pp. 11609-11614 ◽  
Author(s):  
Alexandra M. Tayar ◽  
Eyal Karzbrun ◽  
Vincent Noireaux ◽  
Roy H. Bar-Ziv
Keyword(s):  
Pattern Formation ◽  
Large Scale ◽  
Reaction Diffusion ◽  
Biochemical Networks ◽  
Artificial Cells ◽  
Diffusion Dynamics ◽  
Oscillatory Reactions ◽  
Potential Applications ◽  
On Chip ◽  
Genetic Oscillators

Understanding how biochemical networks lead to large-scale nonequilibrium self-organization and pattern formation in life is a major challenge, with important implications for the design of programmable synthetic systems. Here, we assembled cell-free genetic oscillators in a spatially distributed system of on-chip DNA compartments as artificial cells, and measured reaction–diffusion dynamics at the single-cell level up to the multicell scale. Using a cell-free gene network we programmed molecular interactions that control the frequency of oscillations, population variability, and dynamical stability. We observed frequency entrainment, synchronized oscillatory reactions and pattern formation in space, as manifestation of collective behavior. The transition to synchrony occurs as the local coupling between compartments strengthens. Spatiotemporal oscillations are induced either by a concentration gradient of a diffusible signal, or by spontaneous symmetry breaking close to a transition from oscillatory to nonoscillatory dynamics. This work offers design principles for programmable biochemical reactions with potential applications to autonomous sensing, distributed computing, and biomedical diagnostics.

scholarly journals Spatio-temporal Brusselator Model and Biological Pattern Formation

2021 ◽  
pp. 88-99
Author(s):  
Zakir Hossine ◽  
Oishi Khanam ◽  
Md. Mashih Ibn Yasin Adan ◽  
Md. Kamrujjaman
Keyword(s):  
Pattern Formation ◽  
Diffusion Model ◽  
Initial Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Two Dimensions ◽  
Brusselator Model ◽  
Reaction Diffusion Model ◽  
Biological Pattern Formation ◽  
Spatio Temporal

This paper explores a two-species non-homogeneous reaction-diffusion model for the study of pattern formation with the Brusselator model. We scrutinize the pattern formation with initial conditions and Neumann boundary conditions in a spatially heterogeneous environment. In the whole investigation, we assume the case for random diffusion strategy. The dynamics of model behaviors show that the nature of pattern formation with varying parameters and initial conditions thoroughly. The model also studies in the absence of diffusion terms. The theoretical and numerical observations explain pattern formation using the reaction-diffusion model in both one and two dimensions.

Stabilization of Dominant Structures in an Ionic Reaction-Diffusion System

1998 ◽  
Vol 63 (6) ◽  
pp. 761-769 ◽  
Author(s):  
Roland Krämer ◽  
Arno F. Münster
Keyword(s):  
Reaction Diffusion ◽  
Dominant Mode ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Perturbation ◽  
Dimensional System ◽  
One Dimensional ◽  
Brusselator Model ◽  
The One ◽  
Dominant Structure

We describe a method of stabilizing the dominant structure in a chaotic reaction-diffusion system, where the underlying nonlinear dynamics needs not to be known. The dominant mode is identified by the Karhunen-Loeve decomposition, also known as orthogonal decomposition. Using a ionic version of the Brusselator model in a spatially one-dimensional system, our control strategy is based on perturbations derived from the amplitude function of the dominant spatial mode. The perturbation is used in two different ways: A global perturbation is realized by forcing an electric current through the one-dimensional system, whereas the local perturbation is performed by modulating concentrations of the autocatalyst at the boundaries. Only the global method enhances the contribution of the dominant mode to the total fluctuation energy. On the other hand, the local method leads to simple bulk oscillation of the entire system.

scholarly journals The human EDAR 370V/A polymorphism affects tooth root morphology potentially through the modification of a reaction–diffusion system

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Keiichi Kataoka ◽  
Hironori Fujita ◽  
Mutsumi Isa ◽  
Shimpei Gotoh ◽  
Akira Arasaki ◽  
...  
Keyword(s):  
Molecular Mechanisms ◽  
Computational Study ◽  
Reaction Diffusion ◽  
Human Migration ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Tooth Root ◽  
Computed Tomography Images ◽  
Diffusion Dynamics ◽  
Root Morphogenesis

AbstractMorphological variations in human teeth have long been recognized and, in particular, the spatial and temporal distribution of two patterns of dental features in Asia, i.e., Sinodonty and Sundadonty, have contributed to our understanding of the human migration history. However, the molecular mechanisms underlying such dental variations have not yet been completely elucidated. Recent studies have clarified that a nonsynonymous variant in the ectodysplasin A receptor gene (EDAR370V/A; rs3827760) contributes to crown traits related to Sinodonty. In this study, we examined the association between theEDARpolymorphism and tooth root traits by using computed tomography images and identified that the effects of theEDARvariant on the number and shape of roots differed depending on the tooth type. In addition, to better understand tooth root morphogenesis, a computational analysis for patterns of tooth roots was performed, assuming a reaction–diffusion system. The computational study suggested that the complicated effects of theEDARpolymorphism could be explained when it is considered that EDAR modifies the syntheses of multiple related molecules working in the reaction–diffusion dynamics. In this study, we shed light on the molecular mechanisms of tooth root morphogenesis, which are less understood in comparison to those of tooth crown morphogenesis.

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