Defining diversity, specialization, and gene specificity in transcriptomes through information theory

The transcriptome is a set of genes transcribed in a given tissue under specific conditions and can be characterized by a list of genes with their corresponding frequencies of transcription. Transcriptome changes can be measured by counting gene tags from mRNA libraries or by measuring light signals in DNA microarrays. In any case, it is difficult to completely comprehend the global changes that occur in the transcriptome, given that thousands of gene expression measurements are involved. We propose an approach to define and estimate the diversity and specialization of transcriptomes and gene specificity. We define transcriptome diversity as the Shannon entropy of its frequency distribution. Gene specificity is defined as the mutual information between the tissues and the corresponding transcript, allowing detection of either housekeeping or highly specific genes and clarifying the meaning of these concepts in the literature. Tissue specialization is measured by average gene specificity. We introduce the formulae using a simple example and show their application in two datasets of gene expression in human tissues. Visualization of the positions of transcriptomes in a system of diversity and specialization coordinates makes it possible to understand at a glance their interrelations, summarizing in a powerful way which transcriptomes are richer in diversity of expressed genes, or which are relatively more specialized. The framework presented enlightens the relation among transcriptomes, allowing a better understanding of their changes through the development of the organism or in response to environmental stimuli.