Evaluating Dynamic Effects of Copy Number Alterations on Gene Expression Using a Single Transcription Model

DNA copy number alterations (CNAs) are known to be related to genetic diseases, including cancer. The unlimited transcription (UT) model, in which transcription occurs permissively with a simple activation probability, has been proposed to investigate long-term effects of CNAs on gene expression values. Queueing theory was applied, and the copy-number-gene-expression relationship has been shown to be generally nonlinear in the UT model. However, the dynamic effects of CNAs on transcription and the underlying disorders related to diseases remain greatly unknown. Since most genes in a single cell are permissively transcribed in short periods of time interspersed by long periods of limited transcription, an alternative model for transcription in the restrictive state is needed for unraveling the effects of CNAs on gene expression levels with time. To address these issues, herein a single transcription (ST) model is proposed, in which bound TFs are assumed to be unloaded immediately after stimulating a transcription. Using the Laplace-Stieltjes transform and numerical analysis, the relationship between DNA copy number and gene expression level is evaluated. Dynamic modeling reveals that CNAs would potentially alter, or even reverse, the burst-like gene expression modifications while shifting from the ST model to the UT model. Moreover, functional disorders in transcriptional oscillation due to CNAs are shown via simulation. This paper demonstrates how mathematical theories could be helpful to interpret statistical findings from real data and achieve a better understanding of cancer biology.