Theoretical aspects of pattern formation and neuronal development

Hans Meinhardt

Alfred Gierer

Primary pattern formation, organizing regions and regeneration

Autocatalysis and lateral inhibition are the conditions for de-novo pattern formation; relation to Turing's mechanism

Generation of periodic structures

If the range of the inhibition is smaller than the field size....

A simple BASIC program for simulation of pattern formation

Generate simulations on your own computer

Fading of competence, suppression of supernumerary organizers and the generation tissue polarity

Switching off the capability to generate patterns is important to avoid supernumerary organizers

Generation of complex patterns by the linkage of several pattern forming reactions: the freshwater polyp Hydra as example

Formation of organizing regions at opposite ends of a field and formation of structures next to an organizer

Hy-beta-catenin and WNT have properties as expected from the theory

Pattern formation in aggregates suggest that Hy-beta-catenin and TCF is involved in the primary pattern formation

From simple radial- to bilateral symmetric body plans

Models are worked out on several pages that allow the generation of a near-Cartesian coordinate system. Midline formation is a special problem and different phyla found different solutions

Activation of genes under the influence of morphogenetic signaling

Gene activation require positive feedback loops for stable activation and mutual competition

to allow that only one of the alternative loops is active. Gene activation is thus formally similar to pattern formation

Pattern formation within a segment: dynamic regulation of a neighborhood of structures
A controlled neighborhood emerges if cell states not only exclude each other locally but cross-activate each other on longer ranges

Hierarchical pattern formation for the segmentation of Drosophila

A simultaneous formation of segment needs a scaffold.

Somite formation: sequential conversion of a periodic pattern in time into a periodic pattern in space
Each full cycle of an oscillation adds one pair of half-somites; the oscillation leads to a counting on the (HOX-) gene level

Initiation of legs and wings: borders between differently determined cells obtain organizing properties
A cooperation of differently determined cells leads to new signaling centers at the common border for the next finer subdivision

Pigmentation patterns on shells of mollusks - a natural picture book to study dynamic systems
Sea shells archive time records of highly dynamic patterning processes that can be deciphered.
Quenching of newly formed patterns soon after their generation allows a permanent formation of new pattern elements.

Orientation of chemotactic cells and growth cones
Cells can to detect minute external asymmetries to orient their movement. A permanent ability for reorientation requires a quenching of earlier responses

Veins and tracheae: formation of filament-like branching networks
Moving signals for filament elongation leave behind long extended filamentous structures that may branch

Development of neural networks: Graded cues and growth cone navigation
Navigating growth cones can find their specific target positions if gradients exert an attracting and a repulsive influence; the retinal-tectal and the olfactory system as examples

Phyllotaxis
Where and When: the spacing of leaves can be best explained by two antagonistic effects on the leaf -forming signal, one determines the next position around the shoot, the other determines the time when the next leaf signal can form

Pattern formation in bacteria: Finding the center in E.coli is based on a highly dynamic process
A pole to pole oscillation of an inhibitory signal allows the initiation of division only in the centre;
again, destabilization of a just generated pattern is the crucial step.

Tissue evagination and the generation of biological form
How morphogen signals can elect bending moments changes in cell shapes and evagination within cells sheets. Local bending has consequences also at remote positions

Systems' theoretical approaches to holistic biological features

Original paper: A theory of Biological pattern formation, Kybernetik 12,30-30 (1972) in PDF format

"Models of Biological Pattern Formation" (Academic Press, 1982), a PDF-remake

The book describes several basic principles (as given on this web-site). It was written before the molecular-genetic approach became feasible. Almost all turned out to be correct, showing that modelling is a powerful tool to deduce an underlying mechanisms.

List of publications (partially available as PDF-files)

Feedback to: hans.meinhardt@tuebingen.mpg.de