Re-using biological devices: a model-aided analysis of interconnected transcriptional cascades designed from the bottom-up

Background The study of simplified, ad-hoc constructed model systems can help to elucidate if quantitatively characterized biological parts can be effectively re-used in composite circuits to yield predictable functions. Synthetic systems designed from the bottom-up can enable the building of complex interconnected devices via rational approach, supported by mathematical modelling. However, such process is affected by different, usually non-modelled, unpredictability sources, like cell burden. Methods Here, we analyzed a set of synthetic transcriptional cascades in Escherichia coli. We aimed to test the predictive power of a simple Hill function activation/repression model (no-burden model, NBM) and of a recently proposed model, including Hill functions and the modulation of proteins expression by cell load (burden model, BM). To test the bottom-up approach, the circuit collection was divided into training and test sets, used to learn individual component functions and test the predicted output of interconnected circuits, respectively. Results Among the constructed configurations, two test set circuits showed unexpected logic behaviour. Both NBM and BM were able to predict the quantitative output of interconnected devices with expected behaviour, but only the BM was also able to predict the output of one circuit with unexpected behaviour. Moreover, considering training and test set data together, the BM captures circuits output with higher accuracy than the NBM, which is unable to capture the experimental output exhibited by some of the circuits even qualitatively. Finally, resource usage parameters, estimated via BM, guided the successful construction of new corrected variants of the two circuits showing unexpected behaviour. Conclusions Superior descriptive and predictive capabilities were achieved considering resource limitation modelling, but further efforts are needed to improve the accuracy of models for biological engineering. Electronic supplementary material The online version of this article (10.1186/s13036-017-0090-3) contains supplementary material, which is available to authorized users.


Supplementary Figures
. RFP output data for the cascade circuits tested in this work (training and test set) as a function of HSL concentration. Circles represent the average measured values, while error bars represent the 95% confidence intervals of the mean. Magenta and blue colours correspond to the RFP output of circuits without (r suffix) and with (rg suffix) Monitor cassette, respectively. Figure S2. Growth rate data for the cascade circuits tested in this work (training and test set) as a function of HSL concentration. Circles represent the average measured values, while error bars represent the 95% confidence intervals of the mean. Magenta and blue colours correspond to the growth rate of circuits without (r suffix) and with (rg suffix) Monitor cassette, respectively.       in the x-axes were computed as the nominal (i.e., without Monte Carlo approach) values predicted by the model. The data points showed for TetR or LacI = 0 were obtained by measuring the output of constructs similar to X 2 Tr(g) and X 3 Lr(g) but without their input block, and were used in the fitting procedure. This genetic context enables to measure the activity of P LtetO1 and P LlacO1 in absence of their cognate repressor, which cannot be removed in the X 2 Tr(g) and X 3 Lr(g) circuits due to the basic activity of promoters in the X 2 and X 3 input blocks. Figure S10. Univariate sensitivity analysis of the NBM by applying a variation on the δ parameter of the Hill functions. Panels show fitting (X 1 r, X 2 r, X 3 r, X rep r, X 2 Tr and X 3 Lr circuits) and predictions (remaining circuits) of the measured HSL-dependent output in all the training and test set circuits without Monitor cassette.
Circles represent the average measured value and error bars represent the 95% confidence intervals of the mean. Solid line represents the median predicted output of the model calculated via Monte Carlo simulations for each HSL concentration tested. Dashed dark red lines are the 95% confidence bands of the output distribution. Dashed light red lines are the 95% confidence bands of the output distribution calculated after univariate sensitivity analysis. Figure S11. Univariate sensitivity analysis of the NBM by applying a variation on the α parameter of the Hill functions. Panels show fitting (X 1 r, X 2 r, X 3 r, X rep r, X 2 Tr and X 3 Lr circuits) and predictions (remaining circuits) of the measured HSL-dependent output in all the training and test set circuits without Monitor cassette.
Circles represent the average measured value and error bars represent the 95% confidence intervals of the mean. Solid line represents the median predicted output of the model calculated via Monte Carlo simulations for each HSL concentration tested. Dashed dark red lines are the 95% confidence bands of the output distribution. Dashed light red lines are the 95% confidence bands of the output distribution calculated after univariate sensitivity analysis. Figure S12. Univariate sensitivity analysis of the NBM by applying a variation on the K parameter of the Hill functions. Panels show fitting (X 1 r, X 2 r, X 3 r, X rep r, X 2 Tr and X 3 Lr circuits) and predictions (remaining circuits) of the measured HSL-dependent output in all the training and test set circuits without Monitor cassette.
Circles represent the average measured value and error bars represent the 95% confidence intervals of the mean. Solid line represents the median predicted output of the model calculated via Monte Carlo simulations for each HSL concentration tested. Dashed dark red lines are the 95% confidence bands of the output distribution. Dashed light red lines are the 95% confidence bands of the output distribution calculated after univariate sensitivity analysis. Figure S13. Univariate sensitivity analysis of the NBM by applying a variation on the η parameter of the Hill functions. Panels show fitting (X 1 r, X 2 r, X 3 r, X rep r, X 2 Tr and X 3 Lr circuits) and predictions (remaining circuits) of the measured HSL-dependent output in all the training and test set circuits without Monitor cassette.
Circles represent the average measured value and error bars represent the 95% confidence intervals of the mean. Solid line represents the median predicted output of the model calculated via Monte Carlo simulations for each HSL concentration tested. Dashed dark red lines are the 95% confidence bands of the output distribution. Dashed light red lines are the 95% confidence bands of the output distribution calculated after univariate sensitivity analysis. Figure S14. Evolutionary stability of the X 1 TLr and X rep TLr circuits. A) Phenotypic stability of strains with X 1 TLr and X rep TLr. Strains were tested at three different HSL concentrations (test#1), reported in the x-axis, and then re-inoculated and tested in a growth medium without HSL (X 1 TLr) or with 10000 nM of HSL (X rep TLr) (test#2). In this experiment, we evaluated if the strains could restore the RFP output observed at zero (X 1 TLr) or full induction (X rep TLr), corresponding to conditions in which the expression of TetR is repressed, after an experiment carried out at different HSL concentrations. Data points represent the mean of three biological replicates and error bars represent the 95% confidence intervals of the mean. B) Genetic stability of the two strains. Electrophoresis results (ethidium bromide staining) are shown for all the tested strains and HSL concentrations after the experiment above. A description of the GeneRuler 1Kb DNA ladder (Thermo Scientific) is also provided (adapted from the user guide of product #SM0312, Thermo Scientific).
The mutation found in the second replicate of X 1 TLr (previously tested with 10000 nM of HSL) is reported.
Protocol for Panel A. Cultures were tested in microplate reader as described in the Methods section, with HSL concentrations of 0, 10 and 10000 nM (X 1 TLr) or 0, 1 and 10000 nM (X rep TLr). At the end of the test (18h growth in microplate reader), all the X 1 TLr cultures were centrifuged, the supernatant was removed and the pellet was resuspended with 200 µl of fresh selective medium without HSL. This washing step was performed to remove HSL from the induced X 1 TLr cultures. Five hundred µl of M9 were inoculated with 5 µl of the X 1 TLr (washed) or X rep TLr cultures in 2-ml tubes. HSL (final concentration of 10000 nM) was added to the X rep TLr cultures. All the cultures were incubated overnight at 37°C, 220 rpm, and then they were tested again in the microplate reader in absence of HSL (X 1 TLr) or with 10000 nM of HSL (X rep TLr).
Results: all the strains showed stable behaviour, since the RFP output in test#2 is comparable to the RFP output in test#1 for HSL=0 (X 1 TLr) or 10000 nM (X rep TLr), suggesting that HSL-dependent RFP changes in test#1 were not due to stability mutants.
Protocol for Panel B. In parallel with the inoculation of the 500-µl cultures, 2 µl of the X 1 TLr (washed) or X rep TLr cultures were used to inoculate 10 ml of selective medium in 50-ml tubes. Cultures were grown overnight at 37°C, 220 rpm. Plasmid DNA was purified, digested with EcoRI-PstI and ran on 1% agarose gel.
Results: from electrophoresis screening, all the constructs showed the correct bands, corresponding to vector backbone (3.2 Kbp) and insert (4.1 Kbp); however, X 1 TLr cultures grown in test#1 with HSL=10000 and 10 nM also showed bands of unexpected size. From sequencing results, only the X 1 TLr culture grown in test#1 with 10000 nM of HSL showed DNA alterations, in a small portion of the population (according to the chromatogram), while the other sequenced plasmids did not show detectable mutations with the used primers. The observed mutation was a deletion of all the circuit after the luxR gene and before the transcriptional terminator of the RFP gene. Figure S15. Simulation of X 1 TLr and X rep TLr with the NBM for different values of γ tet and γ lac parameters.
Data are reported (circles and error bars represent the 95% confidence intervals of the mean) and the simulated RFP output is shown (solid line). The parameters of the NBM reported in Table 1 were used for the simulations. The γ tet and γ lac parameter values were set at the nominal ones (see Methods section) or they were decreased by 100-fold (marked as "low") to qualitatively evaluate the effect of enzymatic queuing, which might cause slower TetR and LacI degradation, since they share the same LVA tag. Figure S16. Fitting and prediction results for the NBM learned and simulated against RFP data of the circuits with the Monitor cassette. Panels show fitting (X 1 r, X 2 r, X 3 r, X rep r, X 2 Tr and X 3 Lr circuits) and predictions (remaining circuits) of the measured HSL-dependent output in all the training and test set circuits. Circles represent the average measured value and error bars represent the 95% confidence intervals of the mean.    Figure S19. Results of fitting using all the available data (training and test set) using NBM and BM: RFP data.
Fitting of the measured HSL-dependent RFP output in all the circuits with Monitor cassette. Circles represent the average measured value and error bars represent the 95% confidence intervals of the mean.
Solid lines represent the median predicted output of the NBM (magenta) and BM (blue) calculated via Monte Carlo simulations for each HSL concentration tested. Figure S20. Results of fitting using all the available data (training and test set) using BM: GFP data. Fitting of the measured HSL-dependent GFP output in all the circuits with Monitor cassette. Circles represent the average measured value and error bars represent the 95% confidence intervals of the mean. Solid lines represent the median predicted output of the BM calculated via Monte Carlo simulations for each HSL concentration tested. Figure S21. OD 600 , raw GFP and raw RFP values measured in culture, supernatant and pellet of three strains. TOP10 (black; non-fluorescent), X 2 Tr (red; expressing RFP) and X rep Tr (blue; containing RFP, not expressed) were inoculated as described in the Methods section; the 100-fold dilution was carried out in a final volume of 6 ml in 50-ml tubes and the cultures were incubated in the same conditions as before until they reached an OD 600 of about 0.05. Then, they were sampled every 2 hours. At each sampling time, absorbance, GFP and RFP were measured for 200 µl of culture; then, 1 ml was withdrawn, transferred into a 1.5-ml tube and centrifuged (13,000 rpm, 2 min). Absorbance, GFP and RFP were measured in the supernatant (200 µl).
Finally, supernatant was discarded, pellet was resuspended with 1 ml of fresh medium and absorbance, GFP and RFP were measured (200 µl). Green data points and dotted line represent the raw GFP of the medium without cells. All the measurements were carried out with the Infinite F200 reader (Tecan), as described in the Methods section. The reported data show that the raw GFP autofluorescence is due to the supernatant (see raw GFP in culture and supernatant), not to the cell pellet (see raw GFP in the resuspended pellet), although it increases during cell growth. On the other hand, red fluorescence is due to cell RFP expressing cells in the pellet. Figure S22. Raw GFP autofluorescence depends on OD 600 and also cell growth rate. A) OD 600 vs raw GFP characteristic of two strains showing fast (relative to the whole circuit collection) growth (X 2 Tr and X rep r; black and red diamonds, respectively) and two strains showing slow growth (X rep Tr and X rep TLr; magenta and blue squares, respectively) without HSL. They are reported, as single biological replicate, as an example to highlight distinct characteristics, dependently on growth rate. Curves like the ones shown here were fitted (with exponential regression), estimating m and q parameters (see Methods section) to obtain the autofluorescence background of the circuits. B-C) The m and q parameters for all the circuits in all the conditions are plotted against growth rate values. The m parameter (B) shows a significant growth ratedependent trend, as expected from Panel A, while the growth rate-dependent trend of the q parameter (C) is not statistically significant (confidence intervals of the slope include zero).