Mathematical representation of “gene signatures”

Mathematical representation of “gene signatures”

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According to Wikipedia's definition, "a gene signature is a group of genes in a cell whose combined expression pattern is uniquely characteristic of a biological phenotype or medical condition."

While the above definition is very useful to understand the concept, I am looking for a "more practical" definition or, rather, a mathematical representation (e.g., a vector) of gene signatures. Hence my question.

There are mathematical definitions of "gene signature". Please have a look at the supplemental material of Subramanian et al. PNAS 2005, one of the first papers on "gene signatures", and a method and tool which is still commonly used in basic research.

Note that Subramanian et al. have multiple definitions and that copying them here would exceed the scope of this page.

There is no mathematical definition of genetic signature. Please first have a look at Is there a formal definition of signature of natural selection?. As explain the term genetic signature is used in a very broad sense.

There are a number of processes for which one might be looking for a signature of this process. Such signature can take the form of various statistics. For example, a historically important statistics is Tajima's D defined as

$$D = frac{Pi - S/a}{SE}$$

, where $Pi$ is the average number of pairwise differences between two randomly sampled haplotypes, $S$ is the number of segregating sites, $a=sum_i^{k-1}1/i$, where $k$ is the number of sampled haplotypes. $SE$ is the standard error for the numerator which takes a complicated formulation (have a look at Tajima 1989 for more information).

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