Theoretical aspects of stripe formation in relation to Drosophila segmentation

Development ◽  
1988 ◽  
Vol 104 (1) ◽  
pp. 105-113
Author(s):  
T.C. Lacalli ◽  
D.A. Wilkinson ◽  
L.G. Harrison
Keyword(s):  
Hierarchical Control ◽  
Reaction Diffusion ◽  
Positional Information ◽  
Kinetic Mechanism ◽  
Periodic Pattern ◽  
Linear Pattern ◽  
Pattern Forming ◽  
Gradient Models ◽  
Blastoderm Stage ◽  
Pair Rule

Many aspects of Drosophila segmentation can be discussed in one-dimensional terms as a linear pattern of repeated elements or cell states. But the initial metameric pattern seen in the expression of pair-rule genes is fully two-dimensional, i.e. a pattern of stripes. Several lines of evidence suggest a kinetic mechanism acting globally during the syncytial blastoderm stage may be responsible for generating this pattern. The requirement that the mechanism should produce stripes, not spots or some other periodic pattern, imposes preconditions on this act, namely (1) sharp anterior and posterior boundaries that delimit the pattern-forming region, and (2) an axial asymmetrizing influence in the form of an anteroposterior gradient. Models for Drosophila segmentation generally rely on the gradient to provide positional information in the form of concentration thresholds that cue downstream elements of a hierarchical control system. This imposes restrictions on how such models cope with experimental disturbances to the gradient. A shallower gradient, for example, means fewer pattern elements. This need not be the case if the gradient acts through a kinetic mechanism like reaction-diffusion that involves the whole system. It is then the overall direction of the gradient that is important rather than specific concentration values.(ABSTRACT TRUNCATED AT 250 WORDS)

Interactions between the pair-rule genes runt, hairy, even-skipped and fushi tarazu and the establishment of periodic pattern in the Drosophila embryo

Development ◽  
1988 ◽  
Vol 104 (Supplement) ◽  
pp. 51-60 ◽  
Author(s):  
Philip Ingham ◽  
Peter Gergen
Keyword(s):  
Double Mutant ◽  
Early Embryo ◽  
Drosophila Embryo ◽  
Periodic Pattern ◽  
Fushi Tarazu ◽  
Blastoderm Stage ◽  
Pair Rule

The pair-rule genes of Drosophila play a fundamental role in the generation of periodicity in the early embryo. We have analysed the transcript distributions of runt, hairy, even-skipped and fushi tarazu in single and double mutant ernbryos. The results indicate a complex set of interactions between the genes during the blastoderm stage of embryogenesis.

The generation of periodic pattern during early Drosophila embryogenesis

Development ◽  
1988 ◽  
Vol 104 (Supplement) ◽  
pp. 35-50 ◽  
Author(s):  
Ken Howard
Keyword(s):  
De Novo ◽  
Relevant Literature ◽  
Positional Information ◽  
Periodic Pattern ◽  
Gene Interactions ◽  
Segment Polarity Genes ◽  
Segment Polarity ◽  
Pair Rule Gene ◽  
Unique Domain ◽  
Pair Rule

The first indication of the formation of segment primordia in Drosophila is expression of the segment-polarity genes in particular parts of each primordium. These patterns are controlled by another class of genes, the pair-rule genes, which show characteristic two-segment periodic expression. Each pair-rule gene has a unique domain of activity and in one view different combinations of pair-rule gene products directly control the expression of the segment-polarity genes. There is a hierarchy within the pair-rule class revealed by pair-rule gene interactions. It is unlikely that these interactions generate the periodicity de novo. Instead, pair-rule genes respond to positional information generated by a system involving zygotic gap and maternal coordinate genes. In this paper, I will concentrate on the problem of the mechanism that generates these pair-rule patterns, the first periodic ones seen during segmentation. I will review and discuss some of the relevant literature, illustrating certain points with data from my recent work.

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 Formation of Vertebral Precursors: Past Models and Future Predictions

2003 ◽  
Vol 5 (1) ◽  
pp. 23-35 ◽  
Author(s):  
Ruth E. Baker ◽  
Santiago Schnell ◽  
Philip K. Maini
Keyword(s):  
Cell Cycle ◽  
Reaction Diffusion ◽  
Periodic Pattern ◽  
Cycle Model ◽  
Reaction Diffusion Model ◽  
Somite Formation ◽  
Vertebrate Embryos ◽  
Vertebral Development ◽  
Experimental Findings ◽  
Sequential Formation

Disruption of normal vertebral development results from abnormal formation and segmentation of the vertebral precursors, called somites. Somitogenesis, the sequential formation of a periodic pattern along the antero-posterior axis of vertebrate embryos, is one of the most obvious examples of the segmental patterning processes that take place during embryogenesis and also one of the major unresolved events in developmental biology. We review the most popular models of somite formation: Cooke and Zeeman's clock and wavefront model, Meinhardt's reaction-diffusion model and the cell cycle model of Stern and co-workers, and discuss the consistency of each in the light of recent experimental findings concerning FGF-8 signalling in the presomitic mesoderm (PSM). We present an extension of the cell cycle model to take account of this new experimental evidence, which shows the existence of a determination front whose position in the PSM is controlled by FGF-8 signalling, and which controls the ability of cells to become competent to segment. We conclude that it is, at this stage, perhaps erroneous to favour one of these models over the others.

scholarly journals Regime shifts in models of dryland vegetation

2013 ◽  
Vol 371 (2004) ◽  
pp. 20120358 ◽  
Author(s):  
Yuval R. Zelnik ◽  
Shai Kinast ◽  
Hezi Yizhaq ◽  
Golan Bel ◽  
Ehud Meron
Keyword(s):  
Alternative Stable States ◽  
Bare Soil ◽  
Periodic Pattern ◽  
Stable States ◽  
Open Problems ◽  
Self Organized ◽  
Pattern Dynamics ◽  
Vegetation Patchiness ◽  
Pattern Forming ◽  
Abrupt Shifts

Drylands are pattern-forming systems showing self-organized vegetation patchiness, multiplicity of stable states and fronts separating domains of alternative stable states. Pattern dynamics, induced by droughts or disturbances, can result in desertification shifts from patterned vegetation to bare soil. Pattern formation theory suggests various scenarios for such dynamics: an abrupt global shift involving a fast collapse to bare soil, a gradual global shift involving the expansion and coalescence of bare-soil domains and an incipient shift to a hybrid state consisting of stationary bare-soil domains in an otherwise periodic pattern. Using models of dryland vegetation, we address the question of which of these scenarios can be realized. We found that the models can be split into two groups: models that exhibit multiplicity of periodic-pattern and bare-soil states, and models that exhibit, in addition, multiplicity of hybrid states. Furthermore, in all models, we could not identify parameter regimes in which bare-soil domains expand into vegetated domains. The significance of these findings is that, while models belonging to the first group can only exhibit abrupt shifts, models belonging to the second group can also exhibit gradual and incipient shifts. A discussion of open problems concludes the paper.

CHEMICAL PATTERNS IN SIMPLE FLOW SYSTEMS

2003 ◽  
Vol 06 (01) ◽  
pp. 155-162 ◽  
Author(s):  
ANNETTE TAYLOR
Keyword(s):  
Chemical Reaction ◽  
Reaction Diffusion ◽  
Stationary Concentration ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Differential Flow ◽  
Chemical Waves ◽  
Pattern Forming ◽  
Simple Flow ◽  
Concentration Patterns

The addition of flow to chemical reaction-diffusion systems provides robust pattern-forming mechanisms which are expected to occur in a wide variety of natural and artificial systems. Experiments demonstrating some of these mechanisms are presented here, including the differential-flow-induced chemical instability (DIFICI), which gives rise to traveling chemical waves, and flow-distributed oscillations (FDO), which produce stationary concentration patterns.

scholarly journals Multi-spike solutions of a hybrid reaction–transport model

2021 ◽  
Vol 477 (2247) ◽  
pp. 20200829
Author(s):  
P. C. Bressloff
Keyword(s):  
Transport Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Strongly Nonlinear ◽  
Diffusion Systems ◽  
Spike Solution ◽  
Classical Pattern ◽  
Final Steady State ◽  
Reaction Transport ◽  
Pattern Forming

Simulations of classical pattern-forming reaction–diffusion systems indicate that they often operate in the strongly nonlinear regime, with the final steady state consisting of a spatially repeating pattern of localized spikes. In activator–inhibitor systems such as the two-component Gierer–Meinhardt (GM) model, one can consider the singular limit D a  ≪  D h , where D a and D h are the diffusivities of the activator and inhibitor, respectively. Asymptotic analysis can then be used to analyse the existence and linear stability of multi-spike solutions. In this paper, we analyse multi-spike solutions in a hybrid reaction–transport model, consisting of a slowly diffusing activator and an actively transported inhibitor that switches at a rate α between right-moving and left-moving velocity states. Such a model was recently introduced to account for the formation and homeostatic regulation of synaptic puncta during larval development in Caenorhabditis elegans . We exploit the fact that the hybrid model can be mapped onto the classical GM model in the fast switching limit α  → ∞, which establishes the existence of multi-spike solutions. Linearization about the multi-spike solution yields a non-local eigenvalue problem that is used to investigate stability of the multi-spike solution by combining analytical results for α  → ∞ with a graphical construction for finite α .

scholarly journals The amplitude system for a Simultaneous short-wave Turing and long-wave Hopf instability

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Guido Schneider ◽  
Matthias Winter
Keyword(s):  
Numerical Simulation ◽  
Analytical Approach ◽  
Reaction Diffusion ◽  
Short Wave ◽  
Reaction Diffusion Systems ◽  
Long Wave ◽  
Diffusion Systems ◽  
Schnakenberg Model ◽  
Pattern Forming ◽  
Amplitude System

<p style='text-indent:20px;'>We consider reaction-diffusion systems for which the trivial solution simultaneously becomes unstable via a short-wave Turing and a long-wave Hopf instability. The Brusseletor, Gierer-Meinhardt system and Schnakenberg model are prototype biological pattern forming systems which show this kind of behavior for certain parameter regimes. In this paper we prove the validity of the amplitude system associated to this kind of instability. Our analytical approach is based on the use of mode filters and normal form transformations. The amplitude system allows us an efficient numerical simulation of the original multiple scaling problems close to the instability.</p>

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.

Applications of a Theory of Biological Pattern Formation Based on Lateral Inhibition

1974 ◽  
Vol 15 (2) ◽  
pp. 321-346 ◽  
Author(s):  
H. MEINHARDT ◽  
A. GIERER
Keyword(s):  
Pattern Formation ◽  
Lateral Inhibition ◽  
Molecular Mechanisms ◽  
Positional Information ◽  
Cell Types ◽  
Model Calculations ◽  
Slime Moulds ◽  
Biological Pattern Formation ◽  
Pattern Forming ◽  
Differentiation And Proliferation

Model calculations are presented for various problems of development on the basis of a theory of primary pattern formation which we previously proposed. The theory involves short-range autocatalytic activation and longer-range inhibition (lateral inhibition). When a certain criterion is satisfied, self-regulating patterns are generated. The autocatalytic features of the theory are demonstrated by simulations of the determination of polarity in the Xenopus retina. General conditions for marginal and internal activation, and corresponding effects of symmetry are discussed. Special molecular mechanisms of pattern formation are proposed in which activator is chemically converted into inhibitor, or an activator precursor is depleted by conversion into activator. The (slow) effects of primary patterns on differentiation can be included into the formalism in a straightforward manner. In conjunction with growth, this can lead to asymmetric steady states of cell types, cell differentiation and proliferation as found, for instance, in growing and budding hydra. In 2 dimensions, 2 different types of patterns can be obtained. Under some assumptions, a single pattern-forming system produces a ‘bristle’ type pattern of peaks of activity with rather regular spacings on a surface. Budding of hydra is treated on this basis. If, however, gradients develop under the influence of a weak external or marginal asymmetry, a monotonic gradient can be formed across the entire field, and 2 such gradient-forming systems can specify ‘positional information’ in 2 dimensions. If inhibitor equilibrates slowly, a spatial pattern may oscillate, as observed with regard to the intracellular activation of cellular slime moulds. The applications are intended to demonstrate the ability of the proposed theory to explain properties frequently encountered in developing systems.

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