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Gene regulation by a protein translation factor at the single-cell level [1]

['Roswitha Dolcemascolo', 'Institute For Integrative Systems Biology', 'Csic University Of Valencia', 'Paterna', 'Lucas Goiriz', 'Roser Montagud-Martínez', 'Guillermo Rodrigo']

Date: 2022-07

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.

In the cell, proteins can bind to DNA to regulate transcription as well as to RNA to regulate translation. However, cells have mainly evolved to exploit transcription factors as specific gene regulators, while translation factors have remained as global modulators of expression. Consequently, transcription regulation has attracted much attention over the last years to unveil design principles of genetic organization and to engineer synthetic circuits for cell reprogramming. In this work, the phage MS2 coat protein was exploited to regulate the expression of a green fluorescent protein at the level of translation. This synthetic system was instrumental to gain fundamental knowledge on stochasticity and regulation at an overlooked level within the genetic information flow.

In this work, we exploited the bacteriophage MS2 coat protein (MS2CP) as a translation factor [ 15 ] to engineer a basic synthetic regulatory circuit from which to study stochastic gene expression when it is regulated translationally. In the natural context, in addition to be a structural protein to form the virion, MS2CP blocks the translation of the viral replicase upon binding to an RNA hairpin in the corresponding 5’ UTR that contains the ribosome binding site (RBS) and the start codon [ 16 ]. Over the years, MS2CP has been used for many applications due to its strong binding affinity to RNA, such as the subcellular tracking of mRNAs with time and space [ 17 ], the study of protein-RNA interactions in vivo [ 18 ], the development of CRISPR scaffold RNAs for programmable transcription regulation (CRISPR stands for clustered regularly interspaced short palindromic repeats) [ 19 ], and the construction of nanoscale architectures that can serve, for example, to improve enzymatic reactions [ 20 ]. With our engineered circuit, we examined gene expression in single cells by using a double reporter system to monitor both the regulator (MS2CP) and the regulated gene, and we also developed a mathematical model to provide a predictive quantitative foundation of the system.

The importance of studying how stochastic gene expression is generated and regulated at different levels in the genetic information flow lies in the fact that living cells implement highly intricate circuitries for multiple signal integration that allow displaying a variety of phenotypes. Certainly, this signal integration becomes easier and more scalable if different layers are exploited (e.g., transcriptional, translational, and post-translational), and this is precisely what has evolved in nature. Only by understanding the particularities of each regulatory mode, we can rationalize the impact of gene expression on the cell behavior. As highlighted before, more studies on stochastic gene expression regulated at a layer other than transcription are mandatory, especially because there are important phenotypes in nature that arise as a consequence of changing expression translationally.

Motivated by the prevalence of transcriptional regulations in the cell [ 6 ], previous work focused on studying the emergence and propagation of noise in genes regulated transcriptionally [ 3 , 7 ]. For example, we now appreciate that some promoters can generate bursts of expression as a consequence of a stochastic switching in their activity [ 8 ], that the sign of the regulation determines the best way to extract information from the environment [ 9 ], and that the stochastic fluctuations can inform about the underlying regulation when time is considered [ 10 ]. In addition, recent studies also focused on post-transcriptional regulations implemented by small non-coding RNAs (in particular, by microRNAs in eukaryotic cells) [ 11 , 12 ]. These studies concluded that microRNAs, by controlling the messenger RNA (mRNA) abundance, can suppress part of the noise generated at the level of transcription, hence resulting in ideal genetic elements to engineer robust circuits. Nevertheless, studies on cell-to-cell variability when protein expression is regulated at the level of translation are scarce, especially when the regulation is exerted by a translation factor. We just know that structured 5’ untranslated regions (UTRs) can generate noise in protein expression [ 13 ], which can even be tuned by trans-acting small RNAs [ 14 ].

The ability to map a given genotype to its corresponding phenotype is perhaps the biggest pursuit in molecular biology [ 1 ], especially in the post-genomic era, as it can provide fundamental insight and predictive power on natural evolution, with clear applications in biomedicine and ecology. However, it is well established that the very same genotype can lead to phenotypic heterogeneity in a non-changing environment [ 2 ]. This is the consequence of the inherent stochasticity of the different biochemical reactions that are needed for gene expression [ 3 ]. While stochastic events are often seen as undesirable, as they are when the optimal gene expression levels are lost [ 4 ], we now realize that a noisy gene expression can also be advantageous for the cell population to face environmental changes or induce time-dependent behaviors [ 5 ]. In this regard, substantial progress has been made over the last years to quantitatively understand and model this non-genetic variability (noise). However, there are still numerous questions regarding the mechanisms that produce and regulate noise in gene expression.

Results

Regulation of translation with an RNA-binding protein in single cells We engineered a synthetic genetic system in E. coli in which the RNA-binding protein MS2CP acts as a protein translation factor (Fig 1A). MS2CP was expressed from a synthetic PL-based promoter repressed by LacI (named as PLlac) [21] in a medium copy number plasmid (about 80 copies/cell). This allowed controlling the expression of the regulator (at the transcriptional level) with isopropyl β-D-1-thiogalactopyranoside (IPTG). In addition, we fused the enhanced blue fluorescent protein 2 (eBFP2) [22] to the N terminus of MS2CP (leading to eBFP2-MS2CP) in order to monitor its expression. As a regulated element, here we used the superfolder green fluorescent protein (sfGFP) [23], which was expressed from a constitutive promoter in a low copy number plasmid (about 15 copies/cell). The wild-type RNA motif recognized by MS2CP (with a dissociation constant of about 3 nM) [24] was placed in frame just after the start codon of sfGFP. In this way, MS2CP can block the progression of the ribosome on the regulated gene in the initial phase [15]. This mode of action differs from the natural one, in which MS2CP prevents translation initiation rather than elongation [16]. The resulting circuit behaves like an inverter considering IPTG as input and sfGFP as output, MS2CP being an internal regulator that operates at the level of translation. PPT PowerPoint slide

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TIFF original image Download: Fig 1. Regulation with a protein translation factor. a) Schematics of the gene regulatory system implemented in a bacterial cell. IPTG is the external molecule that controls the expression of the protein translation factor (eBFP2-MS2CP). sfGFP is the final output of the system. b) Histograms of single-cell fluorescence for eBFP2 (fused to the regulatory protein) for different induction conditions with IPTG. On top, sequence details of the cis-regulatory region (DNA level) for transcriptional regulation (PLlac promoter). c) Histograms of single-cell fluorescence for sfGFP (the regulated protein) for different induction conditions with IPTG. On top, sequence details of the cis-regulatory region (RNA level) for post-transcriptional regulation (MS2CP RNA motif). d) Mean and noise of expression for eBFP2 as a function of IPTG. e) Mean and noise of expression for sfGFP as a function of IPTG. f) Noise for eBFP2 as a function of mean expression. g) Noise for sfGFP as a function of mean expression. h) Transfer function of the post-transcriptional regulation in terms of mean expression. i) Transfer function of the post-transcriptional regulation in terms of noise. In plots d-i), points correspond to calculations from the experimental data, while solid lines to predictions with the mathematical model. https://doi.org/10.1371/journal.pcbi.1010087.g001 We performed single-cell measurements of blue and green fluorescence by flow cytometry for a concentration gradient of IPTG (9 conditions) in order to quantitatively study the stochastic regulatory dynamics of this engineered system (Fig 1B and 1C). We found a substantial down-regulation of sfGFP (about 50-fold in expression) as a consequence of the action of MS2CP on the cognate mRNA. From these data, we calculated the mean and the noise of expression for both eBFP2-MS2CP and sfGFP (the noise as the square of the coefficient of variation) [3], which were represented as a function of IPTG (Fig 1D and 1E). The mean gives the average position of the population, and the noise is a measure of the cell-to-cell variability. These measurements were repeated for different populations, finding consistency in the results (S1 Fig). We then constructed a mathematical model relying on a series of algebraic equations from basics on the biochemistry of gene expression and molecular noise propagation [7]. To derive these mathematical expressions for the mean and the noise, we constructed a system of stochastic differential equations for mRNA and protein expression following the Langevin formalism. The rates of concentration changes were subject to stochastic fluctuations of intrinsic and extrinsic nature. This system was analytically solved in steady state with the mean-field approximation for the fluctuations. With a suitable parameterization, our model was able to recapitulate with reasonable agreement the values of mean expression and noise for both eBFP2-MS2CP and sfGFP, highlighting the functional form of the different dose-response curves. In particular, the mean expressions follow Hill-Langmuir equations and the noises non-monotonous curves presenting a maximum at an intermediate IPTG concentration. Indeed, the peak-like noise curve is a consequence of a sigmoidal dynamics at the population level. We also observed that the noise levels in sfGFP are lower than in eBFP2 for all IPTG concentrations. We also performed numerical simulations of the stochastic differential equations (S2 Fig), finding good agreement with the analytical results, as well as sensitivity analyses to reveal the effect of perturbations in the adjusted parameters (S3 Fig), highlighting how the curves of mean expression and noise shift in one direction and even change in form. In addition, we represented the noise versus the mean to show the stochastic expression scaling laws of the system (Fig 1F and 1G). The model was also explicative about the nonlinear transfer functions in terms of mean expression regulation (Fig 1H) and noise propagation (i.e., how the noise of eBFP2-MS2CP impacts on the noise of sfGFP; Fig 1I). Together, these results indicated that the protein translation factor is a suitable element to control expression and that the cell-to-cell variability emerged at this level can be predicted with certain accuracy.

Noise analysis in transcription and translation regulation To further analyze the stochastic behavior, we looked inside the noise. That is, we inspected how a particular noise level is achieved. For that, we first decomposed the total noise of both eBFP2-MS2CP and sfGFP into three fundamental components: extrinsic noise, intrinsic noise, and regulation noise. Extrinsic noise comes from replication and variability in the cellular machinery, intrinsic noise is a consequence of a low number of molecules, and regulation noise accounts for the noise that is propagated from the regulator to the regulated gene [3,7,25]. In previous work, the regulation noise has been considered as a part of the extrinsic noise. Here, we separate this component to study more in detail the stochastic gene expression when it is regulated. Assuming independence between the different stochastic sources, we were able to end with compact mathematical expressions for the noise in which the different components were identified, although at the cost of introducing some inaccuracies since the extrinsic noise may correlate responses. Along the IPTG gradient and according to our mathematical model, the extrinsic noise of the system is constant, the intrinsic noise decreases in the case of eBFP2-MS2CP and increases in the case of sfGFP (as this noise scales inversely with the expression level), and the regulation noise follows a peak-like curve (Fig 2A–2H). Even though for both eBFP2-MS2CP and sfGFP the functional form of the regulation noise is similar, peaking at 50–75 μM IPTG, the maximal noise level is much lower (about four times) in the case of sfGFP. This suggested that with a translational control the noise of the regulator is buffered, i.e., the fluctuations of MS2CP expression are manifested on sfGFP expression in lower extent than the fluctuations of LacI expression on MS2CP expression. This is because in a scenario of translational control the regulated gene is constantly transcribed at high levels, where fluctuations in the number of mRNAs per cell are small in comparison with the mean quantity that is produced. Thus, the transcriptional noise is not significant. In addition, the regulation enters at the level of translation, which prevents the typical amplification process of the noise of the regulator that occurs with a transcriptional control [26]. Indeed, in such a scenario, the transcription rate can be quite low when the promoter is repressed, thereby leading to substantial fluctuations in mRNA amount in comparison with the mean production. Furthermore, in the post-transcriptional case, the fluctuations in mRNA abundance can partly be absorbed by the effect of the translation factor, controlling the number of mRNAs available for translation. This has already been discussed in the case of regulatory RNAs [27], but it also applies to the case of a protein translation factor. Consequently, we can argue that the noise in the regulated gene is reduced when the regulation occurs at the level of translation. PPT PowerPoint slide

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TIFF original image Download: Fig 2. Detailed analysis of stochastic gene expression. a) Model-based calculation of the total noise in eBFP2 expression as a function of IPTG. On top, schematics of the amplification effect by the transcriptional regulation. b-d) Decomposition of the total eBFP2 noise into extrinsic, intrinsic, and regulation noise components. e) Model-based calculation of the total noise in sfGFP expression as a function of IPTG. On top, schematics of the buffering effect by the post-transcriptional regulation. f-h) Decomposition of the total sfGFP noise into extrinsic, intrinsic, and regulation noise components. Insets in c,g) show the scaling of the intrinsic noise with the mean expression. i) Predicted eBFP2 fluorescence distributions for different induction conditions with IPTG (Gamma distributions). j) Gamma shape and scale parameters for eBFP2. k) Predicted sfGFP fluorescence distributions for different induction conditions with IPTG (Gamma distributions). l) Gamma shape and scale parameters for sfGFP. In plots j,l), points correspond to calculations from the experimental values of mean and noise, while solid lines to predictions with the mathematical model. https://doi.org/10.1371/journal.pcbi.1010087.g002 In addition, we aimed at predicting the shape of the whole distribution of protein expression and not only the particular noise value. To this end, we considered a Gamma distribution, which has been shown to describe quite well the stochasticity of genetic systems [28] and which emerges from ab initio calculations [29]. The distribution of protein expression is instrumental to appreciate the degree of heterogeneity in the production with time and from cell to cell (assuming ergodicity). Here, by defining the Gamma shape parameter as the inverse of the noise (equal to the mean square divided by the variance) and the Gamma scale parameter as the product between the mean and the noise (i.e., an effective Fano factor), we were able to predict the distributions for both eBFP2-MS2CP and sfGFP (Fig 2I–2L). This was done with the values of mean expression and noise given by the mathematical model. As a result of a transcriptional control, the Gamma scale parameter for eBFP2-MS2CP depends on the translation rate; but in the case of sfGFP, as this element is controlled at the level of translation, the Gamma scale parameter is nearly independent of that rate. Importantly, these theoretical distributions were very close to those fitted directly against the experimental data (S4 Fig), although some discrepancies were observed between the data and the model at intermediate IPTG concentrations. Overall, this highlighted the generality of the Gamma distribution to describe genetic systems regulated at both transcriptional and translational levels.

Examination of global effects on regulated gene expression Subsequently, we decided to study how global perturbations can impact the single-cell response of the system. To this end, we considered the effect of a global signal affecting translation. Here, we used sublethal concentrations of tetracycline (TC), a bacteriostatic antibiotic known to inhibit the formation of active ribosomes (Fig 3A) [30]. Paradoxically, this inhibition leads to an increase in translation rate as a result of an over-production of ribosomes (a global response mechanism in bacteria against this type of antibiotics) [31,32]. That is, the cell is able to sense that a substantial amount of ribosomes is being inhibited upon binding to TC and produces more. In particular, TC binds to the 30S subunit and interferes with the transfer RNAs (tRNAs). In turn, the cell growth rate is compromised due to the action of TC. Importantly, this parameter has been shown to modulate the mean and noise of gene expression [33,34], so we decided to exploit it as a predictor variable. Over a two-dimensional concentration gradient of IPTG and TC (81 conditions), we first generated growth curves (S5 Fig). Basically, only TC showed a significant impact on growth rate (Fig 3B), with a maximal reduction of almost 3-fold, which was well explained by a Michaelis-Menten function (Fig 3C). PPT PowerPoint slide

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TIFF original image Download: Fig 3. Growth-dependent regulation with a protein translation factor. a) Extended schematics of the gene regulatory system in which TC further modulates it through its negative impact on growth rate and positive impact on translation rate (global effects). b) Heatmap of the mean growth rate as a function of IPTG and TC. c) Dose-response curve between growth rate and TC. Points correspond to experimental data, while solid line comes from the mathematical model. d) Projected two-dimensional histograms of single-cell fluorescence for eBFP2 and sfGFP for different induction conditions with IPTG and TC. e) Heatmap of the mean eBFP2 fluorescence as a function of IPTG and TC. f) Heatmap of the mean sfGFP fluorescence as a function of IPTG and TC. g) Heatmap of the mean eBFP2 synthesis rate as a function of IPTG and TC. h) Heatmap of the mean sfGFP synthesis rate as a function of IPTG and TC. i) Heatmap of the eBFP2 noise as a function of IPTG and TC. j) Heatmap of the sfGFP noise as a function of IPTG and TC. https://doi.org/10.1371/journal.pcbi.1010087.g003 In parallel, we performed single-cell measurements of blue and green fluorescence for each condition (Fig 3D). We observed that the mean expression levels of both eBFP2-MS2CP and sfGFP remained almost constant at low TC concentrations, but they increased significantly from 500 ng/mL TC, irrespective of the induction with IPTG (Fig 3E and 3F). Because protein expression comes from the ratio between the protein synthesis rate (accounting for both transcription and translation) and the growth rate (in the case of stable proteins, as it is the case here), this indicated that the protein synthesis rate of both eBFP2-MS2CP and sfGFP scales with the growth rate (Fig 3G and 3H). It was interesting to note here the logical NOR behavior of the sfGFP synthesis rate and the difference between protein expression and synthesis rate. In addition, we calculated the noise levels for each condition (Fig 3I and 3J). We observed that the regulation noise decreases with TC for both eBFP2-MS2CP and sfGFP, as well as that TC leads to a substantial increase in the sfGFP noise when this gene is fully repressed by MS2CP.

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