Mathematical modeling of eukaryotic gene expression

Abstract

Using the Gillespie algorithm, the export of the mRNA molecules from their transcription site to the nuclear pore complex is simulated. The effect of various structures in the nu- cleus on the efficiency of export is discussed. The results show that having some of the space filled by chromatin near the mRNA synthesis site shortens the transport time. Next, the complete eukaryotic gene expression including transcription, splicing, mRNA export, translation, and mRNA degradation is modeled using delay stochastic simulation. This allows for the study of stochastic effects during the process and on the protein production rate patterns. Various protein production patterns can be produced by adjusting the poly-A tail length of the mRNA and the promoter efficiency of the gene. After that, the opposing effects of the chromatin density on the seeking time of the transcription factors for the promoter and the exit time of the mRNA product are discussed.