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.

A recent paper shows that in gene expression space the manifold spanned by normal tissues and the manifold spanned by the corresponding tumors are disjoint. The statement is based on a two-dimensional projection of gene expression data. In the present paper, we show that, for the multi-dimensional vectors defining the centers of cloud samples: 1. The closest tumor to a given normal tissue is the tumor developed in that tissue, 2. Two normal tissues define quasi-orthogonal directions, 3. A tumor may have a projection onto its corresponding normal tissue, but it is quasi-orthogonal to all other normal tissues, and 4. The cancer manifold is roughly obtained by translating the normal tissue manifold along an orthogonal direction defined by a global cancer progression axis. These geometrical properties add a new characterization of normal tissues and tumors and may have biological significance. Indeed, normal tissues at the vertices of a high-dimensional simplex could indicate genotype optimization for given tissue functions, and a way of avoiding errors in embryonary development. On the other hand, the cancer progression axis could define relevant pan-cancer genes and seems to be consistent with the atavistic theory of tumors.

Dimensional reduction analysis of available data for white matter of the brain allows to locate the normal (homeostatic), Glioblastoma and Alzheimer's disease attractors in gene expression space and to identify paths related to transitions like carcinogenesis or Alzheimer's disease onset. A predefined path for aging is also apparent, which is consistent with the hypothesis of programmatic aging. In addition, reasonable assumptions about the relative strengths of attractors allow to draw a schematic landscape of fitness: a Wright's diagram. These simple diagrams reproduce known relations between aging, Glioblastoma and Alzheimer's disease, and rise interesting questions like the possible connection between programmatic aging and Glioblastoma in this tissue. We anticipate that similar multiple diagrams in other tissues could be useful in the understanding of the biology of apparently unrelated diseases or disorders, and in the discovery of unexpected clues for their treatment.

The innate immune system is the first line of defense against pathogens. Its composition includes barriers, mucus, and other substances as well as phagocytic and other cells. The purpose of the present paper is to compare tissues with regard to their immune response to infections and to cancer. Simple ideas and the qualitative theory of differential equations are used along with general principles such as the minimization of the pathogen load and economy of resources. In the simplest linear model, the annihilation rate of pathogens in any tissue should be greater than the pathogen’s average replication rate. When nonlinearities are added, a stability condition emerges, which relates the strength of regular threats, barrier height, and annihilation rate. The stability condition allows for a comparison of immunity in different tissues. On the other hand, in cancer immunity, the linear model leads to an expression for the lifetime risk, which accounts for both the effects of carcinogens (endogenous or external) and the immune response. The way the tissue responds to an infection shows a correlation with the way it responds to cancer. The results of this paper are formulated in the form of precise statements in such a way that they could be checked by present-day quantitative immunology.