Living cells constantly sense and respond to environmental changes. Transcription, the process by which DNA is transcribed into RNA, serves as a critical bridge between external signals and gene expression, ultimately shaping cellular behavior. To unravel the transcription dynamics and the relationship between input signals and gene expression out-put, various transcription models have been developed. This review explores these common models, their computational frameworks, and the resulting distributions for mRNA number and transcriptional event duration, which offer valuable insights into input-output relationships and underlying response mechanisms. We further analyze how different promoter types, chromatin environments, and network motifs influence these relationships. Finally, we probe how information theory can be applied to systems with near-maximum channel capacity to reveal the dynamic range of transcription factor concentrations, input-output dynamics, and the link between these factors and gene expression distribution. Through these multifaceted analyses, we identify key regulators of dynamic input-output relationships and gain deeper insights into how genes respond to transcription factor signals. Quantitative studies of input-output relationships hold promises for identifying key regulatory factors, predicting changes in gene expression patterns, and designing interventions to manipulate cellular functions and behavior.
