Fig 1. Coupling gene transcription with cell cycle.

Actively dividing eukaryote cells go through G₁, S, G₂ and M phases in one cell cycle. In our model, we divide one cycle into two stages: ${\mathbb{S}}_1$ (from last division to gene duplication) and ${\mathbb{S}}_2$ (from gene duplication to next division). Cells orderly rotate between ${\mathbb{S}}_1$ and ${\mathbb{S}}_2$ stages with constant rates κ₁ and κ₂. The promoter transits randomly between active and inactive states, and the transcription kinetics changes with the cell cycle stages. During ${\mathbb{S}}_1$ stage, the kinetics is parameterized by activation rate λ₁, inactivation rate γ₁, synthesis rate ν₁, and mRNA degradation rate δ₁. After DNA replication, the gene is duplicated into two identical copies that are transcribed independently with constant rates λ₂, γ₂, ν₂ and δ₂ in the same cell during ${\mathbb{S}}_2$ stage.