Gene regulation by a protein translation factor at the single-cell level

Gene expression is inherently stochastic and pervasively regulated. While substantial work combining theory and experiments has been carried out to study how noise propagates through transcriptional regulations, the stochastic behavior of genes regulated at the level of translation is poorly understood. Here, we engineered a synthetic genetic system in which a target gene is down-regulated by a protein translation factor, which in turn is regulated transcriptionally. By monitoring both the expression of the regulator and the regulated gene at the single-cell level, we quantified the stochasticity of the system. We found that with a protein translation factor a tight repression can be achieved in single cells, noise propagation from gene to gene is buffered, and the regulated gene is sensitive in a nonlinear way to global perturbations in translation. A suitable mathematical model was instrumental to predict the transfer functions of the system. We also showed that a Gamma distribution parameterized with mesoscopic parameters, such as the mean expression and coefficient of variation, provides a deep analytical explanation about the system, displaying enough versatility to capture the cell-to-cell variability in genes regulated both transcriptionally and translationally. Overall, these results contribute to enlarge our understanding on stochastic gene expression, at the same time they provide design principles for synthetic biology.

normal practice in the field. Then, we performed some calculations in the mean-field limit, as done e.g. in Pedraza & van Oudenaarden, Science, 2005, 307:1965-1969 or Rodrigo, Phys. Rev. E, 2019, 100:032415, to derive analytical expressions for the noise (variation in gene expression from cell to cell). See the new supplementary Appendix S1. The model is instrumental to capture the trend of the data and then it supports the underlying regulatory mechanism. The metric for noise propagation is precisely the term that we named "regulation noise". Total noise in gene expression is the sum of extrinsic noise, intrinsic noise, and regulation noise (which is the noise propagated from gene to gene).
5. The noise is treated very loosely. The description suggests that it relates to stochastic concentration variations but no attempt is made to differentiate that from deterministic effects that contribute to the variation. The propagated noise level might be treated as such but it is quite arbitrary to assume so.
Authors' response: In this work, we performed single-cell fluorescence measurements in several induction conditions by flow cytometry. These measurements provide the distribution of expression for a cell population. The variation from cell to cell is essentially due to molecular noise (non-genetic variability), as the population is clonal in lab conditions. From these data, one can calculate the mean and the standard deviation for each condition. Then, noise can be defined as the coefficient of variation (ratio between standard deviation and mean). This is what we did and, as far as we can tell, this a normal practice in the field to investigate noise in gene expression. Thus, we do not understand the question posed by the reviewer.
6. The trends that are presented on the figures are only roughly matched by simulations and sometimes deviate so strongly that it is difficult to see the similarity. The uncertainty of measurements is not presented.
Authors' response: Overall, we see a good agreement between the model and the data. Of course, a larger discrepancy can appear in some cases, but this just reflects the complexity of the biological system, which cannot be fully explained with simple mathematical equations. We suggest the reviewer to examine much of the previous work in the field to realize about this. Moreover, in our plots, we represent on the one hand the mean, and on the other hand the noise. The noise would be the magnitude of the error bar in a classical plot. The mean and the noise (variability, uncertainty, or whatever name) are calculated from ~10^4 single cell measurements.
7. The most interesting aspect is that Gamma distributions match the trends of fluorescence histograms quite nicely. Although, the reasons of this behavior are not quite clear from the text.

Reviewer #2
In this paper Dolcemascolo et al. study noise propagation in a synthetic genetic network where protein expression is regulated at the level of translation. The authors used the MS2-MCP system to inhibit the translation of a super folding GFP (sfGFP) variant and monitored the expression of both the regulator (MCP fused to enhanced blue fluorescent protein 2 or eBFP2) and the target (sfGFP) in E. coli. MCP was expressed under the control of a lac inducible promoter so that the expression level of MCP and hence the translational repression of sfGFP could be controlled by IPTG treatment. The authors empirically determined the steady state distributions of eBFP2 and sfGFP at different IPTG concentrations as well as under tetracycline treatment that modified the growth rate and various kinetic properties of the cells. The empirical data were analyzed by computing noise defined as the CV^2, where the CV is the coefficient of variation.
The empirical contributions of this paper are strong: a new synthetic gene circuit has been established and produces excellent quantitative data at single-cell resolution.
The computational/theoretical contributions however are rather weak. Although the authors call it "stochastic modeling", equations 6 (in Materials and Methods) do not fit the commonly accepted meaning of the term in the field of stochastic gene regulation and can best be described as deterministic curve fitting. A few observations regarding Equations 6: Authors' response: One thing is deterministic modeling and another is analytical treatment, which is important to not confuse. Our work models and analyzes our own-generated experimental data from a stochastic perspective, considering both transcription and translation regulation, as explained in the Methods section. We (the corresponding author) have vast experience in mathematical modeling in biology and we cannot accept the comments raised by the reviewer. Our stochastic modeling is state-of-the-art and very appropriate to analyze the experimental data. Proof of this is the overall nice agreement between theory and experiments that we achieve.