Genes, Morphogenesis, Evolution: Life and ALife Aspects

The gene curcuit method - model of the network of segmentation genes operating in the blastoderm of Drosophila

The model of early neurogenesis in Drosophila

In this model cells are represented as overlapping cylinders in a 2-dimensional hexagonal lattice; the extent of overlap determines the strength of interaction between neighboring cells. Cells in the model express a small number of genes corresponding to genes that are involved in neuroblast and SOP differentiation. The authors [4] use networks of two genes to fit expression patterns corresponding in broad terms to proneural genes on one hand and to epithelial genes, on the other.
Genes interact as nodes in recurrent neural nets with connection weights depending on the kind of the interaction. Two kinds of interaction are possible: an intracellular and a lateral signalling one. A gene a sums inputs from genes in the same cell or in neighboring cells at the time t according to the following equation

where
U is the matrix of gene interactions;
va(t) - gene product concentrations within the cell;
Û -- the matrix of genes interactions with neighboring cells;

- product concentrations in neighboring cell i;
N -- the set of neighboring cells;

- a factor depending on the overlap of the cell with neighboring cell i, as measured for instance by the common chord of the bases of the two adjacent cylinders.
Concentration va(t) of the product of gene a then changes according to

where ya(t) is the linear sum of Eq.(1), g a sigmoid function, Ra the rate of production of gene a's product, ha the threshold of activation of gene a and ma the rate of decay of gene a product.
The model also includes detachment of cells from the epithelium, delamination, perpendicular to the plane of the epithelium -- neuroblasts are known to determinate as they differentiate. Cell delamination is directly controlled by genes within a cell and only indirectly by neighboring cells; there are two parameters that determine how strongly each gene promotes or suppressed delamination, as well as another two that determine delamination rate and a threshold for delamination to be activated. Delamination changes the area of apposition of neighboring cells, i.e. changes the factors

in Eq.(1) above and therefore modulates the strength of interaction between neighboring cells.

References

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