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bioRxiv · 10.1101/2021.08.20.457160

The tissue differentiation and cancer manifolds in gene and protein expression spaces

Nieves Cuadrado, J. A.·Gonzalez, A. A.
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Abstract

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.

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Nieves Cuadrado, J. A., Gonzalez, A. A.. 2021-08-23. The tissue differentiation and cancer manifolds in gene and protein expression spaces. https://doi.org/10.1101/2021.08.20.457160

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