  In many situations, the gene expression signature is a unique marker of the
biological state. We study the modification of the gene expression distribution
function when the biological state of a system experiences a change. This
change may be the result of a selective pressure, as in the Long Term Evolution
Experiment with E. Coli populations, or the progression to Alzheimer disease in
aged brains, or the progression from a normal tissue to the cancer state. The
first two cases seem to belong to a class of transitions, where the initial and
final states are relatively close to each other, and the distribution function
for the differential expressions is short ranged, with a tail of only a few
dozens of strongly varying genes. In the latter case, cancer, the initial and
final states are far apart and separated by a low-fitness barrier. The
distribution function shows a very heavy tail, with thousands of silenced and
over-expressed genes. We characterize the biological states by means of their
principal component representations, and the expression distribution functions
by their maximal and minimal differential expression values and the exponents
of the Pareto laws describing the tails.
