The Hill-type equation reveals the regulatory principle of target protein expression led by p53 pulsing

The central dogma indicates the basic direction of gene expression pathways. For activated gene expression, the quantitative relationship between various links from the binding of transcription factors (TFs) to DNA to protein synthesis remains unclear and debated. There is consensus that at a steady state, protein levels are largely determined by the mRNA level. How can we find this steady state? Taking p53 as an example, based on the previously discovered Hill-type equation that characterizes mRNA expression under p53 pulsing, I proved that the same equation can be used to describe the average steady state of target protein expression. Therefore, at steady state, the average fold changes in mRNA and protein expression under TFs pulsing were the same. This consensus has been successfully demonstrated. For the p53 target gene BAX, the observed fold changes in mRNA and protein expression were 1.40 and 1.28, respectively; the fold changes in mRNA and protein expression calculated using the Hill-type equation were both 1.35. Therefore, using this equation, we can not only fine-tune gene expression, but also predict the proteome from the transcriptome. Furthermore, by introducing two quantitative indicators, we can determine the degree of accumulation and stability of protein expression.