Mathematical Modeling of Alternative Polyadenylation in the Human Gene, CSTF3

A large number of human genes have been found to contain more than one polyadenylation site (poly(A) site). These lead to multiple messenger ribonucleic acid (mRNA) transcripts, although some of them do not yield protein products. Like alternative initiation and alternative splicing, alternative polyadenylation (APA) contributes to the complexity of the overall pool of mRNA transcripts in human cells. However, little is known about how the cell utilizes different poly(A) sites in response to different cell conditions and developmental stages. Several protein factors have been identified as being necessary for in vitro cleavage and polyadenylation. If the gene of a polyadenylation factor has multiple poly(A) sites, producing variable protein products with different functions, then their APA can control the polyadenylation activity under different cell conditions. The dynamics of the gene expression levels among APA products so far has been studied by experimental approaches only. Here we propose a novel mathematical model consisting of differential equations with a time delay to study the dynamical behavior of the gene expression levels. Numerical simulations have been provided for some of the theoretical analyses of the equations. Our model suggests an oscillatory pattern of APA of CSTF3, indicating APA is employed to maintain homeostasis of its function, perhaps general polyadenylation activity as well, in the cell.