Morphogenesis by Coupled Regulatory Networks
Thimo Rohlf and Stefan Bornholdt
Based on a recently proposed non-equilibrium mechanism for spatial pattern formation
we study how morphogenesis can be controlled by locally
coupled discrete dynamical networks, similar to gene regulation networks of cells in a
developing multicellular organism.
As an example we study the developmental problem of domain formation and proportion
regulation in the presence of noise and cell flow.
In the figure below, the hierarchical structure of the network solving this pattern
formation task is shown: inputs from genes in the neighbor cells i-1 and i+1 are
processed by a layer of nine 'hidden' genes. The integrated signals are propagated
to the two genes G1 and G2, which in equilibrium exhibit the spatial target pattern
(compare the corresponding cellular automata model).
The applet demonstrates the dynamics for a system of 70 coupled networks (cells), the first cell
at the left side, the last at the right.
Each row shows the state of one network gene in each cell, color coding is
the same as in the network scheme shown above; if the respective gene is not active in the cell at time
$t$, the cell is shown
in black color. The two bottom rows show the states of the two target (pattern) genes G1 and G2.
You can use the 'run' and 'stop' button to control the dynamics, in the text field 'error rate' you
may enter any value between 0.0 and 1.0 to study the effect of stochastic update errors (error rate
is normalized per gene and per cell).