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

A bird's eye view to the homeostatic, Alzheimer and Glioblastoma attractors

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 Geometry of Normal Tissue and Cancer Gene Expression Manifolds

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.

On the gene expression landscape of cancer

Kauffman picture of normal and tumor states as attractors in an abstract state space is used in order to interpret gene expression data for 15 cancer localizations obtained from The Cancer Genome Atlas. A principal component analysis of this data unveils the following qualitative aspects about tumors: 1) The state of a tissue in gene expression space can be described by a few variables. In particular, there is a single variable describing the progression from a normal tissue to a tumor. 2) Each cancer localization is characterized by a gene expression profile, in which genes have specific weights in the definition of the cancer state. There are no less than 2500 differentially-expressed genes, which lead to power-like tails in the expression distribution functions. 3) Tumors in different localizations share hundreds or even thousands of differentially expressed genes. There are 6 genes common to the 15 studied tumor localizations. 4) The tumor region is a kind of attractor. Tumors in advanced stages converge to this region independently of patient age or genetic characteristics. 5) There is a landscape of cancer in gene expression space with an approximate border separating normal tissues from tumors.