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.

scholarly journals Molecular mechanisms underlying simplification of venation patterns in holometabolous insects

Development ◽  
2020 ◽  
Vol 147 (23) ◽  
pp. dev196394
Author(s):  
Tirtha Das Banerjee ◽  
Antónia Monteiro
Keyword(s):  
Gene Expression ◽  
Pattern Formation ◽  
Molecular Mechanisms ◽  
Positional Information ◽  
Butterfly Species ◽  
Central Research ◽  
Bicyclus Anynana ◽  
Wing Vein ◽  
Text Book ◽  
Research Theme

ABSTRACTHow mechanisms of pattern formation evolve has remained a central research theme in the field of evolutionary and developmental biology. The mechanism of wing vein differentiation in Drosophila is a classic text-book example of pattern formation using a system of positional information, yet very little is known about how species with a different number of veins pattern their wings, and how insect venation patterns evolved. Here, we examine the expression pattern of genes previously implicated in vein differentiation in Drosophila in two butterfly species with more complex venation Bicyclus anynana and Pieris canidia. We also test the function of some of these genes in B. anynana. We identify both conserved as well as new domains of decapentaplegic, engrailed, invected, spalt, optix, wingless, armadillo, blistered and rhomboid gene expression in butterflies, and propose how the simplified venation in Drosophila might have evolved via loss of decapentaplegic, spalt and optix gene expression domains, via silencing of vein-inducing programs at Spalt-expression boundaries, and via changes in expression of vein maintenance genes.

Models for positional signalling, the threefold subdivision of segments and the pigmentation pattern of molluscs

Development ◽  
1984 ◽  
Vol 83 (Supplement) ◽  
pp. 289-311
Author(s):  
Hans Meinhardt
Keyword(s):  
Pattern Formation ◽  
Long Range ◽  
Positional Information ◽  
Pigmentation Pattern ◽  
Intercalary Regeneration ◽  
Biological Pattern Formation ◽  
Appendage Formation ◽  
Triggering Events ◽  
A Chain ◽  
P Cells

Models of biological pattern formation are discussed. The regulatory features expected from the models are compared to those observed experimentally. It will be shown that: (i) Stable gradients appropriate to supply positional information can be produced by local autocatalysis and long-range inhibition. (ii) Spatially ordered sequences of differentiated cell states can emerge if these cell states mutually activate each other on long range but exclude each other locally. Segmentation results from the repetition of three such cell states, S, A and P (and not of only two, as is usually assumed). With a repetition of three states, each segment has a defined polarity. The confrontation of P cells and S cells lead to the formation of a segment border (…P/SAP/SAP/S…) while the A—P confrontation is a prerequisite for appendage formation. Mutations of Drosophila affecting larval segmentation are discussed in terms of this model. (iii) The two models for the generation of sequences of structures in space (positional information including interpretation versus mutual activation) lead to different predictions with respect to intercalary regeneration. This allows a distinction between the two models on the basis of experiments. (iv) The pigmentation patterns of certain molluscs emerge from a coupled oscillation of cells (that is, a lateral inhibition in time, instead of space). The oblique lines result from a chain of triggering events.

scholarly journals Biological notion of positional information/value in morphogenesis theory

2020 ◽  
Vol 64 (10-11-12) ◽  
pp. 453-463
Author(s):  
Yue Wang ◽  
Jérémie Kropp ◽  
Nadya Morozova
Keyword(s):  
Pattern Formation ◽  
Molecular Mechanisms ◽  
Positional Information ◽  
Theoretical Models ◽  
Cell Development ◽  
Information Value ◽  
Morphogen Gradients ◽  
Cell Position ◽  
Positional Value

The notions of positional information and positional value describe the role of cell position in cell development and pattern formation. Despite their frequent usage in literature, their definitions are blurry, and are interpreted differently by different researchers. Through reflection on previous definitions and usage, and analysis of related experiments, we propose three clear and verifiable criteria for positional information/value. Then we reviewed literature on molecular mechanisms of cell development and pattern formation, to search for a possible molecular basis of positional information/value, including those used in theoretical models. We conclude that although morphogen gradients and cell-to-cell contacts are involved in the pattern formation process, complete molecular explanations of positional information/value are still far from reality.

A boundary model for pattern formation in vertebrate limbs

Development ◽  
1983 ◽  
Vol 76 (1) ◽  
pp. 115-137
Author(s):  
Hans Meinhardt
Keyword(s):  
Pattern Formation ◽  
Positional Information ◽  
Cell Types ◽  
Cooperative Interaction ◽  
Main Body ◽  
Polar Coordinate ◽  
Coordinate Model ◽  
Supernumerary Limbs ◽  
Boundary Model

We postulate that positional information for secondary embryonic fields is generated by a cooperative interaction between two pairs of differently determined cell types. Positional information is thus generated at the boundaries between cells of different determination. The latter are assumed to result from the primary pattern formation in the embryo. The application of this model to vertebrate limbs accounts for the pairwise determination of limbs at a particular location, with a particular handedness and alignment to the main body axes of the embryo. It accounts further for the gross difference in the regeneration of double anterior and double posterior amphibian limbs as well as for the formation of supernumerary limbs after certain graft experiments including supernumeraries in which the dorsoventral polarity changes or which consist of two anterior or two posterior halves. Our model provides a feasible molecular basis for the polar coordinate model and successfully handles recently found violations, for instance formation of supernumerary limbs after ipsilateral grafting with 90° rotation. The most frequent types of developmental malformations become explicable. The models allow specific predictions which are fully supported by recent experiments (see the accompanying paper of M. Maden).

Preface

Development ◽  
1991 ◽  
Vol 113 (Supplement_1) ◽  
pp. NP-NP
Keyword(s):  
Pattern Formation ◽  
Developmental Plasticity ◽  
Molecular Mechanisms ◽  
Full Range ◽  
British Society ◽  
Molecular Models ◽  
Division Plane ◽  
Wide Range ◽  
Biological Pattern Formation ◽  
Selector Genes

The organisers of the 9th John Innes Symposium, who were beginning to plan their programme around the theme of plant development, and in particular, on pattern formation, were delighted when the British Society for Developmental Biology suggested a joint meeting with them. This enabled the full range of biological pattern formation to be addressed, with talks including work on both plant and animal systems. Unusually for a meeting of this kind, there was a slight bias in favour of the number of plant speakers, but this helped to focus our attention on two themes that ran through the meeting. The first was the emergence of a number of underlying molecular mechanisms and strategies in development, perhaps better publicised in animal systems, that are also held in common with plants, for example, cell polarity, homeotic selector genes. In contrast to this was the clear message that there are also developmental strategies that are rather specific to plants, for example, the great importance of division plane alignment, the establishment of meristems, and enormous developmental plasticity. The meeting was an ideal opportunity to hear about the rapid progress that is being made through the application of molecular genetics, and to make connections from either side of the green-red divide between the emerging molecular models that underlie pattern formation in a very wide range of organisms.

scholarly journals ECM-mediated positional cues are able to induce pattern, but not new positional information, during axolotl limb regeneration

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0248051
Author(s):  
Warren A. Vieira ◽  
Shira Goren ◽  
Catherine D. McCusker
Keyword(s):  
Pattern Formation ◽  
Connective Tissue ◽  
Limb Regeneration ◽  
Positional Information ◽  
Cell Types ◽  
Induce Pattern ◽  
Tissue Cells ◽  
Pattern Information

The Mexican Axolotl is able to regenerate missing limb structures in any position along the limb axis throughout its life and serves as an excellent model to understand the basic mechanisms of endogenous regeneration. How the new pattern of the regenerating axolotl limb is established has not been completely resolved. An accumulating body of evidence indicates that pattern formation occurs in a hierarchical fashion, which consists of two different types of positional communications. The first type (Type 1) of communication occurs between connective tissue cells, which retain memory of their original pattern information and use this memory to generate the pattern of the regenerate. The second type (Type 2) of communication occurs from connective tissue cells to other cell types in the regenerate, which don’t retain positional memory themselves and arrange themselves according to these positional cues. Previous studies suggest that molecules within the extracellular matrix (ECM) participate in pattern formation in developing and regenerating limbs. However, it is unclear whether these molecules play a role in Type 1 or Type 2 positional communications. Utilizing the Accessory Limb Model, a regenerative assay, and transcriptomic analyses in regenerates that have been reprogrammed by treatment with Retinoic Acid, our data indicates that the ECM likely facilities Type-2 positional communications during limb regeneration.

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.

Models for positional signalling with application to the dorsoventral patterning of insects and segregation into different cell types

Development ◽  
1989 ◽  
Vol 107 (Supplement) ◽  
pp. 169-180 ◽  
Author(s):  
Hans Meinhardt
Keyword(s):  
Positional Information ◽  
Cell Types ◽  
Ventral Side ◽  
Homogeneous Distribution ◽  
Dorsoventral Patterning ◽  
High Concentration ◽  
Low Concentrations ◽  
Homogeneous Cell ◽  
Pattern Forming ◽  
Different Cell Types

Models of pattern formation and possible molecular realizations are discussed and compared with recent experimental observations. In application to the dorsoventral patterning of insects, it is shown that a superposition of two pattern-forming reactions is required. The first system generates the overall dorsoventral polarity of the oocyte, the second generates the positional information proper with a stripe-like region of high concentration along the ventral side of the embryo. A single reaction would be insufficient since the two reactions require different parameters. The model accounts for the orientation of the DV axes of the oocytes in the ovary of Musca domestica and Sarcophaga, independent of the DV axis of the mother, for the formation of several ventral furrows in the absence of the primary gurken/torpedo system in Drosophila, as well as for the good size regulation of the dorsoventral axis as observed in some insect species. Segregation of a homogeneous cell population into different cell types requires autocatalytic processes that saturate at relatively low concentrations and nondiffusible substances responsible for the autocatalytic feedback loops. Thus, these loops can be realized directly on the gene level via their gene products, for instance, by the mutual repression of two genes. A balance of the two cell types is achieved by a long-ranging substance interfering with the self-enhancing process. This substance is expected to have a more or less homogeneous distribution. This model accounts for the reestablishment of the correct proportion after an experimental interference and the change of determination after transplantation. Applications to the segregation of prestalk and prespore cells in Dictyostelium and of neuroblast cells from the ventral ectoderm in Drosophila are provided.

Pattern formation in Dictyostelium discoideum

Development ◽  
1977 ◽  
Vol 40 (1) ◽  
pp. 229-243
Author(s):  
D. Forman ◽  
D. R. Garrod
Keyword(s):  
Life Cycle ◽  
Pattern Formation ◽  
Single Cells ◽  
Cell Mass ◽  
Positional Information ◽  
Cell Types ◽  
Immunofluorescent Staining ◽  
Cell Contact ◽  
Slime Mould ◽  
Normal Life

Cells of the cellular slime mould D. discoideum were allowed to form into spherical aggregates, by shaking vegetative cells as a suspension in phosphate buffer. In such conditions, grex polarity is never established and surface sheath is not formed (Loomis, 1975 a). Despite the absence of such characteristics of normal development, differentiation of prespore cells, as tested for by immunofluorescent staining, and the organization of such cells into a patterned structure still occurred within the aggregates. Differentiation of prespore cells was found to occur within the cultures at times equivalent to those in the normal life cycle; such differentiation could be advanced by pulsation of the cultures with cyclic-AMP. When cell contact and aggregate formation was prevented, differentiation never occurred within the single cells. Our results suggest that the prespore cells develop randomly within the aggregate and that a pattern is subsequently formed as a result of sorting out of cell types within the cell mass. Aggregates shaken for extended periods of time showed development into cyst-like structures. The process of pattern formation that occurred within these aggregates which possess neither polarity nor a grex tip, would be unlikely to involve any mechanism of positional information signalling. The relevance of polar organization in the generation of pattern in the normal life cycle may therefore be questionable. We present a model of pattern formation in the slime mould in which sorting out of predetermined cell types is viewed as the major mechanism in bringing about patterned organization of the grex precursor cells.

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.

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