Reconstructing promoter activity from Lux bioluminescent reporters

Abstract

The bacterial Lux system is used as a gene expression reporter. It is fast, sensitive and non-destructive, enabling high frequency measurements. Originally developed for bacterial cells, it has also been adapted for eukaryotic cells, and can be used for whole cell biosensors, or in real time with live animals without the need for euthanasia. However, correct interpretation of bioluminescent data is limited: the bioluminescence is different from gene expression because of nonlinear molecular and enzyme dynamics of the Lux system. We have developed a computational approach that, for the first time, allows users of Lux assays to infer gene transcription levels from the light output. This approach is based upon a new mathematical model for Lux activity, that includes the actions of LuxAB, LuxEC and Fre, with improved mechanisms for all reactions, as well as synthesis and turn-over of Lux proteins. The model is calibrated with new experimental data for the LuxAB and Fre reactions from Photorhabdus luminescens-the source of modern Lux reporters-while literature data has been used for LuxEC. Importantly, the data show clear evidence for previously unreported product inhibition for the LuxAB reaction. Model simulations show that predicted bioluminescent profiles can be very different from changes in gene expression, with transient peaks of light output, very similar to light output seen in some experimental data sets. By incorporating the calibrated model into a Bayesian inference scheme, we can reverse engineer promoter activity from the bioluminescence. We show examples where a decrease in bioluminescence would be better interpreted as a switching off of the promoter, or where an increase in bioluminescence would be better interpreted as a longer period of gene expression. This approach could benefit all users of Lux technology.

Fig 1. New experimental data and model fits.

(a) NADPH time course for three different concentration of FMN for the Fre reaction, and (b) for the LuxAB reaction (means and standard errors from 3 replicates). The concentration values in the above data are obtained from the absorption measurements from the spectrophotometer. The conversion is carried out by relating the concentration (C) to the measured values (A) with the formula A = K*C, where K is the proportionality constant and is estimated using initial measurement(A₀) and starting concentration (C₀ = 200μM). The velocity of the reaction increases as FMN concentration is increased. Normalised (using max. velocity in the assay) LuxAB reactions velocity time series for different FMN concentrations. The velocity of the reaction increases from the lowest concentrations of FMN, is greatest for FMN concentrations of 1μM, and decreases for higher concentrations of FMN. This is best explained by product inhibition of the LuxAB reaction through competition between FMN and the substrate FMNH₂. (c) Model fits for Fre, (d) LuxAB, and (e) LuxEC reactions. The model fits to the data are good, showing that kinetic parameters for the reaction rates can be inferred. Summarized data are displayed: for Fre—NADPH concentrations at t = 10 min; for LuxAB, the maximal veclocity for each FMN concentration; for LuxEC—only the AMP time-course data are shown. The full data and fits for all three reactions are shown in Figures A, B, F and J in S1 Text. Total flavin = 88uM, O₂ = 550uM, NADPH = 560uM, and ATP = 1310.

Fig 2. Histogram of inferred Lux protein turnover rates.

The histogram shows low variability about a mean value of 0.378h⁻¹.

Fig 3. Relationship between promoter activity and light output.

Nonlinear relationship between promoter activity and light output for a synthetic pulse or switch of gene expression at different levels. The bioluminescence displays different qualitative and quantitative behaviours from the underlying gene expression. With the switch data, the bioluminescence has slower onset compared with gene expression, and, for high levels of gene expression, shows a transient pulse not present in the gene expression. With the pulse data, the bioluminescence shows much longer persistence than the underlying gene expression. These data show that bioluminescence alone could be a misleading measure of gene expression.

Fig 4. Reverse engineered promoter activity from light output.

Here, the promoter inference is for a simulated transient pulse experiment, showing effective and accurate recovery of the known gene expression profile. The shaded areas in the graphs represent 50 simulations resampling from the posterior distribution; they are barely visible because the posterior distribution in this case is very tight.

Fig 5. Reverse engineering of promoter activity from experimental data.

(a) Bioluminescent data and (b) reverse engineered gene expression from the safA-ydeO promoter in E. coli. The pattern of gene expression is very different from the light output pattern. In particular, the increased bioluminescence is partly explained by greater duration of gene expression not just level of gene expression; gene expression in the WT and yodel mutant appears to be switched off after induction, which is not apparent in the bioluminescence; and the inferred expression shows pulses which are an artefact of the experimental arrangement, in which plates were moved every 15 minutes between a spectrophotometer and a luminometer, demonstrating that the agitation has an impact upon the cells. The shaded areas in the graphs represent 50 simulations resampling from the posterior distribution.(c) Bioluminescent data and (d) reverse engineered gene expression from data from the uhpT promoter in S. aureus showing that the peak of gene expression occurs earlier than the light output, and that the duration of gene expression is shorter than would appear from the light output.