Inference of promoter activity from luminescence measurements. (A) Quantitative mathematical model used to infer the underlying promoter activity from luminescence time-series. Here, the promoter activity is reflected in a time-dependent transcription rate, α(t). luxABCDE mRNA is degraded at rate log(2)/τm , translated at rate β into Lux proteins, which are in turn degraded at rate log(2)/τp. For simplicity, the model assumes a single Lux protein species, which is rate-limiting for luciferase activity and considered to be directly proportional to luminescence output. (B) As a test case for our method, the luciferase activity of pBS3Clux-P
(TMB1858) induced with 30 μg/ml bacitracin (symbols) was fitted by our quantitative mathematical model (solid lines). Since the luxABCDE mRNA half-life is unknown in B. subtilis, we fitted the data using a physiological spectrum of half-lives (τm = 3, 5 and 10 min) and found that the model can reproduce the highly dynamic luciferase activity (arrow) only for mRNA half-lives of 5 min and shorter. (C) Underlying apparent promoter activity in arbitrary units (au) for the fits in (B). For all details see main text.