  A chain of connected genes with activation-repression links is analysed. It
is shown that for various promoter activity functions (parametrised by Hill
coefficient) the equations describing the concentrations of transcription
factors, are differential-difference KdV-type with perturbations. In the case
of large Hill coefficient the proteomic signal along the gene network is given
by a superposition of perturbed dark solitons of defocusing
differential-difference mKdV equation. Biological implications are discussed.
