Bulk measurement of mRNA and protein levels. (a) Millions of cells are grown in a flask, samples are taken at different times, and the cellular contents extracted from the cells. The amount of specific mRNA or protein in the sample can then be read by various means, e.g., biochemically amplifying the mRNA to a detectable amount, and assaying the enzymatic activity of the protein. (b) mRNA and protein kinetics during gene induction. E. coli cells were grown in glycerol media, and expression of the lacZ gene was induced by adding Isopropyl -D-1-thiogalactopyranoside (IPTG). mRNA data is from (Wang et al., 2019), protein data by Seunghyeon Kim and Sangjin Kim (unpublished; see (Kim et al., 2019) for method). The experimental data is captured by Eqs. 5–6. Model fitting by Tianyou Yao and Yuncong Geng.