Pattern formation in early insect embryogenesis - data calling for modification of a recent model

1978 ◽  
Vol 29 (1) ◽  
pp. 1-15
Author(s):  
K. Kalthoff
Keyword(s):  
Mathematical Model ◽  
Pattern Formation ◽  
Lateral Inhibition ◽  
Personal Communication ◽  
Recent Model ◽  
Insect Embryogenesis ◽  
Biological Pattern Formation ◽  
Segment Pattern ◽  
Unusual Type ◽  
Early Insect Embryogenesis

A mathematical model of biological pattern formation based upon lateral inhibition has recently been applied by Meinhardt to insect embryogenesis. This model has stimulated a re-evaluation of previous results, and new experiments designed to test the validity of the model. Split u.v. dose experiments with eggs of the chironomid midge Smittia show that the effective targets for the production of the aberrant ‘double abdomen’ are not subject to the rapid turnover which is required by the model in its currently published version. Certain types of segment pattern, and differences in the length of segments as predicted by the model could not be observed. Other data conflict with the rather unusual type of photoreversal and the particular view of determination associated with the model. The model can be reconciled with part of the conflicting data if the effective targets for double abdomen induction are regarded as morphogen-producing structures, rather than the morphogen itself which specifies the segment pattern (Meinhardt, personal communication). This version of the model, however, is still at variance with some of the data discussed here. A complementary explanation is proposed taking into account relevant aspects of homoeotic transformations.

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.

Modelling of activator-inhibitor dynamics via nonlocal integral operators

2017 ◽  
Vol 1 ◽  
pp. 57 ◽  
Author(s):  
Roumen Anguelov ◽  
Stephanus Marnus Stoltz
Keyword(s):  
Pattern Formation ◽  
Green Algae ◽  
Formation Mechanism ◽  
Lateral Inhibition ◽  
Integral Operators ◽  
Nonlocal Operators ◽  
Blue Green Algae ◽  
Biological Pattern Formation ◽  
Activator Inhibitor

This paper proposes application of nonlocal operators to represent the biological pattern formation mechanism of self-activation and lateral inhibition. The blue-green algae Anabaena is discussed as a model example. The patterns are determined by the kernels of the integrals representing the nonlocal operators. The emergence of patters when varying the size of the support of the kernels is numerically investigated.

Mechanical Patterning in Animal Morphogenesis

2021 ◽  
Vol 37 (1) ◽  
Author(s):  
Yonit Maroudas-Sacks ◽  
Kinneret Keren
Keyword(s):  
Pattern Formation ◽  
Large Scale ◽  
Coarse Grained ◽  
Annual Review ◽  
Publication Date ◽  
Biochemical Processes ◽  
Substantial Progress ◽  
Biological Pattern Formation ◽  
Effective Theories ◽  
Biochemical Signals

Morphogenesis is one of the most remarkable examples of biological pattern formation. Despite substantial progress in the field, we still do not understand the organizational principles responsible for the robust convergence of the morphogenesis process across scales to form viable organisms under variable conditions. Achieving large-scale coordination requires feedback between mechanical and biochemical processes, spanning all levels of organization and relating the emerging patterns with the mechanisms driving their formation. In this review, we highlight the role of mechanics in the patterning process, emphasizing the active and synergistic manner in which mechanical processes participate in developmental patterning rather than merely following a program set by biochemical signals. We discuss the value of applying a coarse-grained approach toward understanding this complex interplay, which considers the large-scale dynamics and feedback as well as complementing the reductionist approach focused on molecular detail. A central challenge in this approach is identifying relevant coarse-grained variables and developing effective theories that can serve as a basis for an integrated framework for understanding this remarkable pattern-formation process. Expected final online publication date for the Annual Review of Cell and Developmental Biology, Volume 37 is October 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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