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Special Semester on Quantitative Biology analyzed by Mathematical Methods
Linz, October 1, 2007 - January 27, 2008
Models of biological pattern formation: from elementary steps to the organization of embryonic axes

Workshop on Pattern Formation and Functional Morphology, Wed, 09 Jan, 2008

Speaker: Hans Meinhardt

Abstract

With the modern molecular-genetic techniques it is possible to monitor simultaneously the mutual interference of hundreds of genes. However, it is notoriously difficult to deduce from such a plethora of data the logic behind the network. Long before the molecular-genetic approach became feasible, we attempted an opposite approach by taking a particular step in development and asking of what would be the minimum molecular machinery that could account for the observed pattern and pattern regulation. It turned out that well-understandable interactions involving relatively few components are able to describe elementary steps in surprising details. By computer simulations it will be shown that the regulatory properties of the models correspond closely to the experimental observations. The models found strong support by more recent observations on the molecular-genetic level. The following processes play a key role:

(i) Local signalling centres and organizing regions can be generated by the coupling of a local self-enhancing reaction with a reaction that accomplishes a long-ranging inhibition. Polar, periodic and strip-like patterns can be generated in this way.
(ii) To avoid multiple organizing regions it is essential that the competence to form an organizing region fades away with increasing distances from an existing organizer.
(iii) Organizing regions for secondary structures such as tentacles or leaves can be initiated a long-range activation and short range exclusion emitted by a primary organizer. The primary organizer generates the precondition for the secondary organizer but also enforces to keep distance.
(iv) Stable gene activation can be achieved by a positive feedback of a gene product on its own gene. If several such autoregulatory genes mutually exclude each other, the cell has to make an unequivocal decision for a particular pathway. Gene activation can be regarded as a pattern formation among alternative genes. Under the influence of a gradient sharply confined regions can emerge in which a particular gene is active.
(v) Segment and somite formation is proposed to be based on the mutual long-range activation of (at least two) feedback loops that locally exclude each other. A controlled neighbourhood of structures emerges in this way.
(vi) An oscillation is involved to make the segments or somites different from each other. Each full cycle leads to a new segment or somite with an anteroposterior subdivision. Due to a sequential activation of (HOX)-genes specifying more posterior structures, the segment or somites become systematically different from each other. Segments are counted on the gene level.
(vii) Borders between different gene activities and especially the intersection of two such borders become the new signalling centres to initiate secondary embryonic fields such as required for leg and wing formation. These new fields emerge within the body in pairs, at the correct positions, orientation and left-right handedness.
(viii) Many systems depend on a quenching of a pattern shortly after its generation. The separation of the hairs of avian feathers, the orientation of a chemotactic cell or growth cone, the centre-finding mechanism in E.coli bacteria to initiate cell division are examples.
(ix) Filamentous structures appear as a trace behind signalling centres that are forced to move.

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