最近的一篇论文表明，在基因表达空间中，正常组织跨越的流形和相应肿瘤跨越的流形是不相交的。该声明基于基因表达数据的二维投影。在本文中，我们表明，对于定义云样本中心的多维向量：1.距离给定正常组织最近的肿瘤是在该组织中发育的肿瘤，2.两个正常组织定义准正交方向， 3. 肿瘤可能在其相应的正常组织上有投影，但它与所有其他正常组织是准正交的，并且 4. 癌症流形是通过沿全局定义的正交方向平移正常组织流形来粗略获得的癌症进展轴。这些几何特性增加了正常组织和肿瘤的新特征，并且可能具有生物学意义。事实上，高维单纯形顶点的正常组织可以指示给定组织功能的基因型优化，以及避免胚胎发育错误的方法。另一方面，癌症进展轴可以定义相关的泛癌基因，似乎与肿瘤的返祖理论一致。© 2024。Jan van der Hoeven 教授教授 stichting voor theoretische biologie。

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.© 2024. Prof. Dr. Jan van der Hoeven stichting voor theoretische biologie.