Dynamics of pattern formation in lateral-inhibition type neural fields

1977 ◽  
Vol 27 (2) ◽  
pp. 77-87 ◽  
Author(s):  
Shun-ichi Amari
Keyword(s):  
Pattern Formation ◽  
Lateral Inhibition ◽  
Neural Fields

scholarly journals Pattern formation with a compartmental lateral inhibition system

2014 ◽  
Author(s):  
Ana S. Rufino Ferreira ◽  
Justin Hsia ◽  
Murat Arcak ◽  
Michel Maharbiz ◽  
Adam Arkin
Keyword(s):  
Pattern Formation ◽  
Lateral Inhibition

scholarly journals Pattern Formation by Lateral Inhibition with Feedback: a Mathematical Model of Delta-Notch Intercellular Signalling

1996 ◽  
Vol 183 (4) ◽  
pp. 429-446 ◽  
Author(s):  
Joanne R. Collier ◽  
Nicholas A.M. Monk ◽  
Philip K. Maini ◽  
Julian H. Lewis
Keyword(s):  
Mathematical Model ◽  
Pattern Formation ◽  
Lateral Inhibition ◽  
Intercellular Signalling

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.

BMPs mediate lateral inhibition at successive stages in feather tract development

Development ◽  
1998 ◽  
Vol 125 (19) ◽  
pp. 3775-3787 ◽  
Author(s):  
S. Noramly ◽  
B.A. Morgan
Keyword(s):  
Pattern Formation ◽  
Lateral Inhibition ◽  
Retroviral Vectors ◽  
Receptor Expression ◽  
Fgf Receptor ◽  
Inhibitory Signal ◽  
Size And Shape ◽  
Morphological Sign ◽  
Necessary And Sufficient ◽  
Do So

The spacing of feather buds in a tract is thought to arise from the interaction between an inducing signal from the dermis and an inhibitory signal generated in the nascent buds. Local BMP-2 expression in the ectoderm precedes the formation of the ectodermal placodes, which are the first morphological sign of bud differentiation. We have altered the activity of BMP-2 or BMP-4 in the ectoderm of the feather field by expressing them or their inhibitor noggin using retroviral vectors. These experiments demonstrate that BMP-2 is necessary and sufficient to mediate the lateral inhibition that positions buds in a tract. After buds are initiated, BMP-2 and BMP-4 continue to inhibit the adoption of bud fates and help to specify the size and shape of the bud. They may do so in part by their regulation of Fgf receptor expression in both the ectoderm and dermis. Additional insights into pattern formation in the feather bud can be inferred from the effects of altered BMP activity on bud morphogenesis.

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