Vertebrate solution: a moving organizer elongates the midline

The vertebrate solution: formation of the midline behind a moving organizing region

The simulation below shows the generation of a stripe-like organizing region (a, red) that is induced by a spot-like organizer (cgreen). The stripe-forming system repels the spot-forming activation by the removal of a substance (e, grey, BMP?) on which the spot-forming system depends. The activity of the spot system becomes displaced in front of the incipient midline, causing its local elongation. 

 

The activator (a) and inhibitor (b) of the stripe system:

 

The activator (c) and inhibitor (d) of the spot system:

 

 

The substance (e) removed by the stripe system: 

 

The (a,b) system generates stripes due to the saturation of the autocatalysis via the term sa. Due to a baseline inhibitor production (term bb) a spontaneous trigger of is not possible but requires the trigger from the spot system (term bac). The spot-system c, d is a similar pattern forming system but due to the absence of saturation (sa = 0), it generates spot-like activation patterns. The maximum becomes regularly displaced and moves along a straight line because autoregulatory formation c depends of a substance e (BMP?)  that is removed by the stripe system. The local destabilization of the spot-like maximum leads to its displacement in front of the tip of the incipient midline, triggering there its elongation, and so on.

Calculated with

Da  = 001; r a  =  0.01; ba  =  0.01; sa =  0.3000;

autoregulatory production rates = 0.01 + 1% fluctuation;

Db =  0.2; rb =  0.015; bb =  0.003;

Dc =  0.002; rc =  0.015; bc =  0.001; Dd =  0.2; r d =  0.01; b d =  0.001;

D e  =  0.03; r e  =  0.005; b e  =  0.005; s e =  0.04



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