Mathematical modelling in genetic networks: relationships between the genetic expression and both chromosomic breakage and positive circuits

The human genome has evolved from a primitive genome to its present state dispatched along the 23 pairs of chromosomes. This evolution has been ruled by the mutation process and also by the physiological and pathological reorganization of the genomic material inside or between the chromosomes, which condition the genomic variability. This reorganization starts at singular points on the short or long chromosomic arms, called crossover, translocation, insertion or break-points. In this paper, we show that these points, also called "weak points" or "hot spots" of the genome, are correlated independently of their origin. In addition, we give some properties of the interaction matrices in terms of attractors (generalizing some earlier results to the discrete case).