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Modular Sample Probability
How to quantify the difference between two different tissues
In general, the difference between two different tissues is determined by observing the tissues through a microscope. There is still no way to quantify the degree of difference between the two tissues, so a method of describing observation results is used. Such a method is merely a description of a phenomenon, and there is no possibility of being extended to a general principle, nor can it be applied to various fields.
Since gene expression data can indicate the biological location of the tissue in a gene space, if we calculate the difference in the locations between two sample groups of different tissues, we can quantify the difference between the two tissues.
The difference between the two tissues can be confirmed by calculating the density matrix for each sample group of two different tissue types and calculating the relative entropy and angular divergence between the two density matrices.
It can be applied between normal and tumor tissues to measure the direction and degree of deviation of cancer from normal.
Genomic modules
Cells perform the tasks assigned by the living body. It is generally rare that the tasks are directly related to the functions of individual genes. Instead, a task is executed by multiple genes that construct a system in most cases. These tasks are related to exhibiting life phenomena of higher order. We, therefore, define the group of genes that make up such a system as a genomic module, the functional unit of the genome.
– Since a genomic module performs a specific cell function, it has low entropy.
– Since individual modules perform different functions, the directions of their first eigenvectors are different.
Utilizing these two characteristics of the genomic modules makes it possible to separate them from the gene expression data.
How to quantify the difference of an individual tissue from normal
Given the density matrix of a genomic module separated from a group of normal tissue samples, the degree to which a new tissue sample deviates from normal can be calculated as a probability with the gene expression data of the sample, called Modular Sample Probability (MSP).
The MSP approaches 1 when the new tissue sample is close to normal, and the group of tissue samples that generated the density matrix is closer to normal. Conversely, the MSP approaches 0 when the new tissue sample deviates from normal.
