Estimating the number of available states for normal and tumor tissues in gene expression space

The topology of gene expression space for a set of 12 cancer types is studied by means of an entropy-like magnitude, which measures the volumes of the regions occupied by tumor and normal samples, i.e., the number of available states (genotypes) that can be classified as tumor-like or normal-like, respectively. Computations show that the number of available states is much greater for tumors than for normal tissues, suggesting the irreversibility of the progression to the tumor phase. The entropy is nearly constant for tumors, whereas it exhibits a higher variability in normal tissues, probably due to tissue differentiation. In addition, we show an interesting correlation between the fraction (tumor/normal) of available states and the overlap between the tumor and normal sample clouds, interpreted as a way of reducing the decay rate to the tumor phase in more ordered or structured tissues.