Hot Spots in Chromosomal Breakage: From Description TC Etiology

The genome has evolved from a primitive state (Demongeot and Besson, 1996) to the present human genome organized along the 23 pairs of chromosomes. This evolution has been governed by the mutation process and also by the physiological (crossing-over mechanism) and pathological (translocations, inversions, insertions, deletions, fusions,…) re-organization of the genomic material within or between the chromosomes, which condition genomic variability. This re-organization starts at singular points on the short or long chromosomal arms, called crossing-over, translocation, insertion, …, breakpoints. First we will show that these points, also called weak (chromosomal break) points or hot spots of the genome are correlated, independently of their origin (physiological crossing-over, pathological constitutional or acquired chromosomal abnormal breakage). One of the mechanisms involved in the weakness of certain parts of the chromosomes is the presence of ubiquitous genes (expressed during the whole cell cycle) at methylated parts of the chromosome causing local decoiling and opening of the DNA double strand, hence causing a local fragility of the genome. In order to give arguments in favour of this hypothesis, we will construct partially random interaction matrices for the relationsamong the ubiquitous genes and we will calculate the attractor configurations of expression of these genes. Then we will be able to calculate the probability of expression and compare the location of the highly expressed parts to the weak genomic points. Finally, we will give some properties of the interaction matrices in terms of the number of possible attractors (generalizing some results of (1995); (1998); (1998); (1998) to the discrete case).