scholarly journals A stepwise model of reaction-diffusion and positional information governs self-organized human peri-gastrulation-like patterning

Development ◽  
2017 ◽  
Vol 144 (23) ◽  
pp. 4298-4312 ◽  
Author(s):  
Mukul Tewary ◽  
Joel Ostblom ◽  
Laura Prochazka ◽  
Teresa Zulueta-Coarasa ◽  
Nika Shakiba ◽  
...  
Keyword(s):  
Reaction Diffusion ◽  
Positional Information ◽  
Self Organized

scholarly journals High-throughput micro-patterning platform reveals Nodal-dependent dissection of peri-gastrulation-associated versus pre-neurulation associated fate patterning

2018 ◽  
Author(s):  
Mukul Tewary ◽  
Dominika Dziedzicka ◽  
Joel Ostblom ◽  
Laura Prochazka ◽  
Nika Shakiba ◽  
...  
Keyword(s):  
Reaction Diffusion ◽  
Positional Information ◽  
Significant Heterogeneity ◽  
Gene Profile ◽  
Self Organized ◽  
Micro Patterning ◽  
Post Implantation ◽  
Geometrically Confined

AbstractIn vitro models of post-implantation human development are valuable to the fields of regenerative medicine and developmental biology. Here, we report characterization of a robust in vitro platform that enabled high-content screening of multiple human pluripotent stem cell (hPSC) lines for their ability to undergo peri-gastrulation-like fate patterning upon BMP4 treatment of geometrically-confined colonies and observed significant heterogeneity in their differentiation propensities along a gastrulation associable and neuralization associable axis. This cell line associated heterogeneity was found to be attributable to endogenous nodal expression, with upregulation of Nodal correlated with expression of a gastrulation-associated gene profile, and Nodal downregulation correlated with a neurulation-associated gene profile expression. We harness this knowledge to establish a platform of pre-neurulation-like fate patterning in geometrically confined hPSC colonies that arises due to a stepwise activation of reaction-diffusion and positional-information. Our work identifies a Nodal signalling dependent switch in peri-gastrulation versus pre-neurulation-associated fate patterning in hPSC cells, provides a technology to robustly assay hPSC differentiation outcomes, and suggests conserved mechanisms of self-organized fate specification in differentiating epiblast and ectodermal tissues.

scholarly journals Travelling colourful patterns in self-organized cellulose-based liquid crystalline structures

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Pedro E. S. Silva ◽  
Ricardo Chagas ◽  
Susete N. Fernandes ◽  
Pawel Pieranski ◽  
Robin L. B. Selinger ◽  
...  
Keyword(s):  
Simple Model ◽  
Temporal Variation ◽  
Liquid Crystalline ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Self Organization ◽  
Spatial And Temporal Variation ◽  
Living Matter ◽  
Equilibrium Conditions ◽  
Self Organized

AbstractCellulose-based systems are useful for many applications. However, the issue of self-organization under non-equilibrium conditions, which is ubiquitous in living matter, has scarcely been addressed in cellulose-based materials. Here, we show that quasi-2D preparations of a lyotropic cellulose-based cholesteric mesophase display travelling colourful patterns, which are generated by a chemical reaction-diffusion mechanism being simultaneous with the evaporation of solvents at the boundaries. These patterns involve spatial and temporal variation in the amplitude and sign of the helix´s pitch. We propose a simple model, based on a reaction-diffusion mechanism, which simulates the observed spatiotemporal colour behaviour.

scholarly journals The periodic coloration in birds forms through a prepattern of somite origin

Science ◽  
2018 ◽  
Vol 361 (6408) ◽  
pp. eaar4777 ◽  
Author(s):  
Nicolas Haupaix ◽  
Camille Curantz ◽  
Richard Bailleul ◽  
Samantha Beck ◽  
Annie Robic ◽  
...  
Keyword(s):  
Expression Profile ◽  
Natural Variation ◽  
Reaction Diffusion ◽  
Positional Information ◽  
Pigment Production ◽  
Periodic Patterns ◽  
Local Dynamics ◽  
Step Process ◽  
Early Developmental ◽  
Dose Dependent

The periodic stripes and spots that often adorn animals’ coats have been largely viewed as self-organizing patterns, forming through dynamics such as Turing’s reaction-diffusion within the developing skin. Whether preexisting positional information also contributes to the periodicity and orientation of these patterns has, however, remained unclear. We used natural variation in colored stripes of juvenile galliform birds to show that stripes form in a two-step process. Autonomous signaling from the somite sets stripe position by forming a composite prepattern marked by the expression profile of agouti. Subsequently, agouti regulates stripe width through dose-dependent control of local pigment production. These results reveal that early developmental landmarks can shape periodic patterns upstream of late local dynamics, and thus constrain their evolution.

scholarly journals Analysing diffusion and flow-driven instability using semidefinite programming

2019 ◽  
Vol 16 (150) ◽  
pp. 20180586 ◽  
Author(s):  
Yutaka Hori ◽  
Hiroki Miyazako
Keyword(s):  
Mathematical Optimization ◽  
Reaction Diffusion ◽  
Reaction Model ◽  
Optimization Program ◽  
Chemical Systems ◽  
Self Organized ◽  
Analysis Process ◽  
Spatial Modes ◽  
Spatially Distributed ◽  
The Stability

Diffusion and flow-driven instability, or transport-driven instability, is one of the central mechanisms to generate inhomogeneous gradient of concentrations in spatially distributed chemical systems. However, verifying the transport-driven instability of reaction–diffusion–advection systems requires checking the Jacobian eigenvalues of infinitely many Fourier modes, which is computationally intractable. To overcome this limitation, this paper proposes mathematical optimization algorithms that determine the stability/instability of reaction–diffusion–advection systems by finite steps of algebraic calculations. Specifically, the stability/instability analysis of Fourier modes is formulated as a sum-of-squares optimization program, which is a class of convex optimization whose solvers are widely available as software packages. The optimization program is further extended for facile computation of the destabilizing spatial modes. This extension allows for predicting and designing the shape of the concentration gradient without simulating the governing equations. The streamlined analysis process of self-organized pattern formation is demonstrated with a simple illustrative reaction model with diffusion and advection.

scholarly journals Self-organized criticality and pattern emergence through the lens of tropical geometry

2018 ◽  
Vol 115 (35) ◽  
pp. E8135-E8142 ◽  
Author(s):  
N. Kalinin ◽  
A. Guzmán-Sáenz ◽  
Y. Prieto ◽  
M. Shkolnikov ◽  
V. Kalinina ◽  
...  
Keyword(s):  
Mirror Symmetry ◽  
Tropical Geometry ◽  
Scaling Limit ◽  
Reaction Diffusion ◽  
Auction Theory ◽  
Discrete Models ◽  
Self Organized ◽  
Reaction Diffusion Model ◽  
Pure Mathematics ◽  
Self Organized Criticality

Tropical geometry, an established field in pure mathematics, is a place where string theory, mirror symmetry, computational algebra, auction theory, and so forth meet and influence one another. In this paper, we report on our discovery of a tropical model with self-organized criticality (SOC) behavior. Our model is continuous, in contrast to all known models of SOC, and is a certain scaling limit of the sandpile model, the first and archetypical model of SOC. We describe how our model is related to pattern formation and proportional growth phenomena and discuss the dichotomy between continuous and discrete models in several contexts. Our aim in this context is to present an idealized tropical toy model (cf. Turing reaction-diffusion model), requiring further investigation.

scholarly journals Control of traveling localized spots

2021 ◽  
Author(s):  
Steffen Martens ◽  
Christopher Ryll ◽  
Jakob Löber ◽  
Fredi Tröltzsch ◽  
Harald Engel
Keyword(s):  
Reaction Diffusion ◽  
Open Loop ◽  
Open Loop Control ◽  
Loop Control ◽  
Reaction Diffusion Systems ◽  
Self Organized ◽  
Nonlinear Reaction ◽  
Diffusion Systems ◽  
Goldstone Modes ◽  
Analytical Expressions

Traveling localized spots represent an important class of self-organized two- dimensional patterns in reaction-diffusion systems. We study open-loop control intended to guide a stable spot along a desired trajectory with desired velocity. Simultaneously, the spot's concentration profile does not change under control. For a given protocol of motion, we first express the control signal analytically in terms of the Goldstone modes and the propagation velocity of the uncontrolled spot. Thus, detailed information about the underlying nonlinear reaction kinetics is unnecessary. Then, we confirm the optimality of this solution by demonstrating numerically its equivalence to the solution of a regularized, optimal control problem. To solve the latter, the analytical expressions for the control are excellent initial guesses speeding-up substantially the otherwise time-consuming calculations.

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