Comparison and Calibration of Different Reporters for Quantitative Analysis of Gene Expression

DNA constructs and strains

Please refer to the Supporting Material for a detailed description of the construction of all plasmids and strains. All sequences, plasmids, and strains are available upon request.

Growth conditions and gene expression measurements

Growth conditions are detailed in the Supporting Material. Induction and single cell microscopy was performed on the YFP samples as described in the Supporting Material. Our protocol for measuring LacZ activity is basically a slightly modified version of the one described in Miller (18) and Becker et al. (42). Details are given in the Supporting Material.

Absolute calibration of the reporters

Absolute measurements of gene expression are often reported in arbitrary units, especially for fluorescence measurements where the signal depends on the particular details of the microscope used. Such a quantification of fluorescence makes it hard, if not impossible, to compare results between setups and establish unified standards. On the other hand, having a simple way to turn these arbitrary units into an absolute number of molecules would be helpful in both the context of taking the census of cellular proteins (1,7,43) and of characterizing the limits of each reporter.

In the following sections we obtain an absolute calibration for both the enzymatic and fluorescent reporters characterized throughout this work. In turn, this calibration will allow us to set absolute bounds on the interchangeability of these reporters as well as their effectiveness as reporters of the level of gene expression.

Calibration of the absolute number of EYFP molecules

Several previous experiments have performed absolute calibrations of fluorescence levels by looking at a bulk solution of purified fluorophore in buffer (6,7,44,45) or in cell extract (46). These approaches require a known volume of illumination which can be achieved, for example, by performing either confocal microscopy (44,45) or two-photon microscopy (6).

These methods should be considered in light of at least two caveats:

First, they rely on the extinction coefficient of the fluorophore to determine its concentration. However, the solution will be comprised of active and bleached fluorophores. Therefore the effective extinction coefficient of the solution will be an unknown combination of the extinction coefficients for the active and bleached fluorophores.

Second, they are performed outside the cell. Even in the case of cell extract, the local environment the protein sees might be different than that of the unperturbed cellular interior.

Counting fluorescent proteins inside the cell is, however, not straightforward. Because of the fast diffusion time of free fluorescent proteins in the cytoplasm (47) the signal of individual fluorescent molecules gets blurred over the cell on the timescale of tens of milliseconds. As a result the fluorescence per unit area of a single fluorophore in the cytoplasm becomes comparable to the cell autofluorescence and, hence, not detectable under common continuous illumination conditions. A way to circumvent this is by immobilizing the fluorophore. For example, membrane proteins fused to fluorescent reporters present a much slower diffusion on the membrane than that of proteins in the cytoplasm. Single fluorophores can be then imaged in this way (7,48,49).

Our main approach for calibrating the fluorescence of a single EYFP molecule consists in immobilizing EYFP molecules in vivo by fusing them to a transcription factor which is in turn strongly bound to the genomic DNA of E. coli. Though this method has the advantage of being in vivo, one caveat is that in this case we are not imaging free cytoplasmic EYFP like in the gene expression measurements in this work. The fact that EYFP is fused to another protein that is in turn bound to the DNA could result in a difference of fluorescence.

Puncta of EYFP fused to Tet repressor could be observed inside the cells despite the poor signal/noise ratio of ∼1.5. In some cases these puncta could be observed to disappear in a single step, as shown in the traces in Fig. 3, A and B. We associate this with the photobleaching step of a single EYFP molecule. More often, though, the puncta would correspond to multiple EYFP molecules. These fluorescence traces manifest multiple discrete levels as shown in Fig. 3, C and D. By integrating the fluorescence of the steps over a small area we can obtain the distributions of steps shown in Fig. 3 E. Please refer to the Supporting Material for a detailed discussion of the data analysis process.

We compared the fluorescence per EYFP molecule to the total fluorescence coming from a particular strain, HG105::galK 〈〉 25O2+11-YFP, under the same conditions. This strain expresses cytoplasmic EYFP. As a result we estimate the number of EYFP molecules in this strain to be 2600 ± 600. The reasoning behind choosing a strain where we directly measure the number of EYFP molecules is that all further gene expression measurements with EYFP as a reporter will be measured with respect to this “reference” strain. In this way we can easily estimate the number of EYFP molecules in any other strain we measure. Finally, we also quantified the fluorescence of single purified EYFP molecules and obtained a consistent result within 15%. Please refer to the Supporting Material for details of this in vitro, single-molecule fluorescence quantification.

As a sanity check on these results, we estimate the expected number of EYFP molecules. The average number of EYFP molecules in steady state can be approximated by

where α is the mRNA production rate, b is the number of proteins made per mRNA molecule, and β is the protein decay rate (50). Due to the long lifetime of EYFP, the “decay rate” is actually nothing more than the cell doubling time because each cell division effectively halves the number of proteins. For the experiments considered here, we have a cell division time of ∼1 h. The number of proteins per mRNA has been measured for the lac operon to be ∼20 protein molecules per mRNA molecule (40) and hence we take b = 20 proteins/mRNA. This number is within the range of the various protein/mRNA measurements performed previously (7). Finally, the transcription rate for the fully induced lac operon has been reported to be between 1 min⁻¹ and 20 min⁻¹ (51,52). However, the lacUV5 promoter is ∼30% weaker than the fully induced, wild-type lac promoter (53) resulting in a range of α = 0.7–14 min⁻¹. When combining the decay rate β, the translation rate b and the transcription rate α we obtain an expected number of EYFP molecules of 1200–20,000 per cell, a range comparable to the intracellular number of EYFP molecules we measure.

Calibration of the absolute number of LacZ molecules

A simplified version of the reaction describing the breakdown of ONPG into ONP by β-galactosidase is given by

From this reaction scheme we can derive the rate equation for the production of the yellow compound ONP, which is given in turn by

and a rate equation for the decay in ONPG concentration due to its hydrolysis,

We wish to obtain the concentration of β-galactosidase, [LacZ], in our reaction to calculate the number of LacZ molecules per cell in the culture that was used to perform it.

If we assume that we have an excess concentration of ONPG and that the time of the reaction is short compared to 1/(k[LacZ]), we can neglect its depletion during the reaction. As a result we take [ONPG] as a constant in Eq. 3. The reaction described by Eq. 3 is the one we perform in the β-galactosidase assay to measure the amount of LacZ molecules per cell in Miller Units (MU). In this assay we monitor the production of ONP over time given by the increase in absorbance at 420 nm of the solution. The standard definition of the Miller Units (18) is

where v is the volume of cells used in mL at a cell density given by OD₆₀₀ and t is the reaction time in minutes. These Miller Units were defined such that the fully induced wild-type lac operon has an activity of 1000 MU, and its noninduced level would yield ∼1 MU. We seek to relate these arbitrarily-defined Miller Units defined in Eq. 5 to Eq. 3 to obtain an actual number of LacZ molecules inside the cell.

First, the term OD₄₂₀ – 1.75 × OD₅₅₀ in Eq. 5 is a measure of the amount of ONP, the product of the breakdown of ONPG by β-galactosidase, in the reaction corrected for the cell debris (see Materials and Methods). We relate the absolute concentration of ONP in the reaction to the absorption reading through this term such that γ[ONP] = OD₄₂₀ – 1.75 × OD₅₅₀. From an experimental point of view, the key assumption is that of a linear increase in the amount of ONP over time. Given that at the moment the experiment starts, there is as yet no ONP, we can obtain d[ONP]/dt simply by taking the accumulated ONP at time t and dividing by this elapsed time; that is,

We also invoke a relation between the OD₆₀₀ reading and the density of cells such that OD₆₀₀ × v × δ = N_cells, where N_cells is the number of cells. Finally, we wish to obtain the number of LacZ tetramers present in the reaction N_LacZ from this previous equation. This can be done by rewriting the concentration as [LacZ] = N_LacZ/V, where V is now the reaction volume of the standard Miller LacZ assay. If we insert this in our definition of MU, we get

We determined δ for our strains to be (8.9 ± 0.8) × 10⁸/mL through plating and counting of colonies. The relation between ONP absorption at 420 nm and concentration is ∼0.0045/μM_ONP (54,18). The volume of the reaction in the standard Miller assay is V = 1.2 mL. However, before the ONP reading the sample gets diluted to ∼1.7 mL by the addition of Na₂CO₃. Therefore we define γ = 0.0045/μM_ONP × (1.7 mL/1.4 mL). Finally, we need to obtain the turnover rate of LacZ given by k. Wallenfels and Weil (55) report a turnover rate of $138\times {10}^6{\text{M}}_{\text{ONP}}/\text{min}\times {\text{M}}_{\text{LacZ}}\times {\text{M}}_{\text{ONPG}}$, where we are referring to LacZ tetramers. Similar values have been reported by Kennell and Riezman (52) and Craven et al. (56). Because the initial concentration of ONPG in the reaction is 1.86 mM, we get

Although this is only a rough estimate because of a lack of error bars associated with the reported values for the specific activity of LacZ, this gives us a direct connection between Miller Units and number of LacZ molecules per cell.

This LacZ calibration that we have just calculated is consistent with previous experimental results on the lac operon. For example, the expression level of the repressed operon is ∼0.6 MU (4). Our calibration suggests that this corresponds to 0.3 LacZ tetramers/cell. Using single molecule techniques, the average number of LacZ tetramers under repressed conditions was estimated to be 1.2 tetramers/cell (40). The internal consistency of these different estimates is encouraging.

Limits of LacZ and YFP as absolute reporters of gene expression

Recall that our aim was to compare enzymatic and fluorescence reporters for the same promoters in a way that spans the large dynamic range found in natural bacterial and viral promoters.

As we have already noted, the level of expression in such bacterial promoters spans over six orders of magnitude as shown in Fig. 1 and Table S4 in the Supporting Material. Our interest was to design an experiment that would permit us to capture a similar dynamical range in a way that would result in a systematic comparison between the enzymatic and fluorescent reporters. To that end, we use an approach based on induction. We use an inducible lacUV5 promoter with a single binding site for Lac repressor (Oid) located directly downstream from its transcriptional start (see Fig. S7). Two versions of this construct regulating the expression of either the lacZ or EYFP genes were created. These constructs were either located on the bacterial chromosome or a low copy plasmid in strains that bear wild-type levels of Lac repressor (lacI+), high levels of Lac repressor (lacI++), or no Lac repressor (lacI−). By growing the different combinations of resulting strains at different concentrations of the inducer IPTG we were able to compare the total EYFP fluorescence and LacZ enzymatic activity per cell. These induction curves are shown in Fig. S8.

In Fig. 4 we present the corresponding expression levels measured using the two reporters over four orders of magnitude. For comparison, these results are juxtaposed with the literature expression levels of some naturally occurring promoters such as those presented in Fig. 1 and Table S4. The blue line corresponds to a fit to a linear model showing that the data is consistent with a linear relation between the two reporters. This observation is consistent with recently published results (7). The slope or conversion factor is (9.6 ± 0.7) × 10⁻⁵ arbitrary fluorescence units/MU. Even if we fit the relation between the two reporters with a more general functional form such as a power law, we find a linear dependence as shown in Fig. S10.

Although β-galactosidase activity is measured in absolute units, the fluorescence intensity depends strongly on details of the experimental apparatus used for the measurement such as the illumination intensity and transmission of the optical elements. The calibrations mentioned above that convert YFP arbitrary fluorescent units and LacZ Miller Units into a number of molecules allows for our expression levels to be converted into an approximate absolute number of molecules of each reporter as shown by the labeling on the alternative axes in Fig. 4. We estimate the EYFP-LacZ relation to be (roughly) ∼0.1 EYFP molecules/LacZ monomer. This value seems to be at odds with the fact that they are being expressed from the same promoter. If the transcription rate is the same for both genes, then that leaves some difference at the translation initiation and translation levels (please refer to the Supporting Material for more information on this issue). However, we lack sufficient information to estimate those differences. Alternatively, an underestimation of the number of EYFP molecules inside the cells could be due to issues related to the fluorescence of the molecule itself such as quenching, misfolding, and the presence of immature fluorophores (57,58).

Fluorescence measurements are fundamentally limited for low levels of gene expression. When the fluorescence signal becomes comparable to the autofluorescence level (<10 molecules/cell) the determination of the level of gene expression has a high associated error. In contrast to free cytoplasmic fluorescent proteins, this limitation is less stringent in the case of fluorescent proteins that are immobilized on the cell membrane (48,57) or DNA by a fusion (this work and (59)). The high error in the determination of low expression levels is reflected in the fluorescence distributions shown in Fig. S12. For the lowest expression levels, the dominant error comes from variations in the autofluorescence. For example, we observe a slight systematic bias toward overestimating the level of autofluorescence. Given the size of the autofluorescence variation, we do not regard the mean value of fluorescence as statistically significant.

This limitation is indicated as a gray-shaded area in Fig. 4. To give a sense of the scale, the expression level of the repressed wild-type lac promoter could not be measured with fluorescence unless a more sophisticated technique to visualize single fluorescent proteins is invoked (48). By way of contrast, no significant analogous background was observed in any of our LacZ measurements, showing that this method is more reliable for quantifying very low levels of gene expression. In fact, linearity of the LacZ activity has been reported down to 0.03 MU (4). Of course, this autofluorescence limit is related to the particular choice made of fluorescent protein, growth media, organism, and strain (36). As such it will be important to perform similar comparisons in these different contexts to generalize the results presented here.

When performing a measurement of gene expression using reporters it is important to demonstrate that the presence of the reporter itself is not affecting the state of the cell. We choose the growth rate as an indicator of the cellular state. For all the expression levels shown in Fig. 4 the doubling rate is ∼1 h regardless of the reporter. However, strain lacI- bearing a plasmid with LacZ as a reporter showed a longer doubling time of (74 ± 1) min, which was not the case for the corresponding EYFP strain. These growth rates are shown in Table S1 and the corresponding growth curves are shown in Fig. S11. We confirm previous observations that expression levels above 20,000 LacZ tetramers/cell start affecting the cell significantly (60). Unlike the low end of expression, where EYFP was limited by the autofluorescence, we find that for the high end of expression LacZ becomes limiting not because of signal issues, but because the cell is affected by the fact that high levels of LacZ are being expressed. Interestingly, even some of the stronger promoters such as rrnB and the T7 A1 promoter have levels below this threshold.

Although our measurements primarily focused on the use of microscopy to quantify EYFP fluorescence, it is by no means the only option. An alternative, for example, is to use a plate reader. Although this method is limited to only reporting the mean level of gene expression of a population of cells (it does not provide single-cell information), it is able to produce data in much higher throughput than microscopy. On the other hand, plate readers will be more limited in terms of the minimum level of fluorescence they can quantify reliably. We perform a comparison between fluorescence measurements on the same strains using microscopy and a plate reader in the Supporting Material leading to Fig. S6. We reach the conclusion that they are completely interchangeable, but that the lower limit of detection is now ∼50 molecules/cell—roughly five-times more than with microscopy.

Limits of LacZ and YFP as reporters of the fold-change in gene expression

The fold-change in gene expression due to regulation by a transcription factor is defined as the level of gene expression in the presence of that molecule divided by the level of gene expression in its absence. In particular, it is the key magnitude predicted by thermodynamic models of transcriptional regulation (11,12). These models can predict fold-changes in gene expression that span over multiple orders of magnitude for both repression (fold-change < 1) and activation (fold-change > 1).

To test these models, it is then necessary to be able to decide which reporter will be the best to assay a particular type of regulatory architecture. For example, in the previous section we found that we can reliably measure EYFP fluorescence down to 10 molecules/cell. If we are dealing with a promoter with a basal expression level of ∼3000 YFP molecules/cell like the lacUV5 promoter integrated on the chromosome used in this work, this means that the lowest fold-change we can measure with YFP is 10/3000 ≈ 10⁻³. On the other hand, the maximum LacZ activity attainable before cell growth starts being compromised is ∼20,000 LacZ tetramers/cell. This means that we can only increase the number of LacZ tetramers beyond the basal level up to this level before the cell senses the presence of these molecules as measured by its growth rate. Because the basal level of our promoter corresponds to 4000 LacZ tetramers/cell, this translates into a maximum measurable fold-change of 20,000/4000 ≈ 10¹ using LacZ as a reporter.

To test part of this assertion about the maximum fold-change in repression, we performed fold-change measurements on constructs bearing the operators O1, O2, or Oid, and the reporters LacZ or EYFP. Fig. 5 shows the fold-change measured using EYFP as a function of the fold-change measured using LacZ for the different single binding site constructs (O1, O2, and Oid) in two different Lac repressor backgrounds: lacI+ and lacI++. We see that the fold-change levels measured with both reporters are in good correspondence. As expected, when the fold-change in gene expression reaches 10⁻³, the EYFP readings start becoming too noisy to determine the fold-change in gene expression reliably, setting a limit on the range of fold-change that can be measured using EYFP as a reporter.