Shi, X.

The central dogma indicates the basic direction of gene expression pathway. For activated gene expression, the relationship between the various links that are from the binding of transcription factor (TF) DNA to synthesis of proteins is still unclear. There is a consensus that at steady state the protein levels are largely determined by mRNA level. How to find this steady state? What factors determine it? Taking TF p53 as an example, on the basis of the previously discovered Hill type equation that can characterize the average steady state of mRNA expression under p53 pulsing, and demonstrating the regulatory ability of duration and frequency beyond saturation. I proved that the average steady state of target protein expression driven by p53 pulsing can also be governed by this equation. Therefore, at steady state the average mRNA and protein expression under TF pulsing are exactly the same. This consensus has been successfully demonstrated. For gene BAX of p53 target, the observed fold changes of mRNA and protein are 1.72, 1.28, while the predictions for both mRNA and protein from the obtained equation are 1.35. The regulatory principle of gene expression revealed by this equation is that TF dynamics and binding affinity control the expression levels; and the half-life of mRNA and protein regulate the expression stability. By introducing two quantitative indicators, we can understand the degree of accumulation and stability of protein expression. Furthermore, this generalized equation broadens the application of classical biochemical theory.