Dual influence of transcriptional and translational kinetics on gene expression noise

Gene expression noise, the inherent randomness in protein levels, plays a crucial role in cellular heterogeneity and diverse responses to environmental conditions. While transcriptional bursts and their impact on noise have been extensively studied over the past two decades, recent experiments suggest that mRNA folding-unfolding kinetics can also create bursts in gene translation. This means mRNA can switch between active and inactive states, while gene translation occurs only when mRNA is in the active state. However, the combined influence of transcriptional and translational bursts on gene expression noise remains largely unexplored. To address this, we present a gene expression model that integrates both transcriptional and translational bursting phenomena to provide a detailed understanding of the factors governing protein noise. Using the generating function technique, we solve the model and derive analytical expressions for mean protein levels and noise in protein copy numbers. Our findings show that translational bursting significantly contributes to overall noise and the noise from transcriptional bursts further amplifies the relative contribution of translational noise. We also find that translation efficiency, defined as the rate of protein synthesis from a single mRNA transcript, increases the overall noise of gene expression at fixed protein levels. This dependence of gene expression noise on translation efficiency suggests that both translation and transcription kinetics are required to be tuned simultaneously to achieve specific protein levels and gene expression noise. Thus, this study improves our understanding of the factors regulating gene expression noise, providing insights into how transcriptional and translational bursting shape this noise.