Protein fluctuations can be observed by counting molecules in single cells over time (Figure 1D). Alternatively, noise can be estimated by tagging the two alleles of a gene with distinct fluorescent proteins and measuring fluorescence correlation in individual cells (Figure 1E; Elowitz et al., 2002; Raser and O'Shea, 2004). Protein number from each allele is stochastically fluctuating over time, and their fluctuations are independent of one another. When one fixes a population of cells and measures protein output from each allele per cell, the limited correlation between allele output for the population closely approximates the stochastic variability if one were to measure noise temporally (Swain et al., 2002). We created sens alleles tagged with superfolder GFP (sfGFP) or mCherry (Figure 1F). This was done by modifying a 19.2 kb fragment of the Drosophila genome containing sens by singly inserting either sfGFP or mCherry into the amino terminus of the sens ORF (Figure 1F). These transgenes were independently landed into the 22A3 locus on the second chromosome, a standard landing site for transgenes (Venken et al., 2006; Venken et al., 2009). Endogenous sens activity was inhibited with amorphic loss-of-function mutations (Jafar-Nejad et al., 2003; Nolo et al., 2000). The transgenes completely rescued all detectable sens mutant phenotypes and exhibited normal expression (Figure 1—figure supplement 1). We then mated singly-tagged sfGFP-sens with mCherry-sens animals to generate trans-heterozygous progeny in an endogenous sens null background. Wing imaginal discs of these offspring were fixed and imaged by confocal microscopy (Figure 1—figure supplement 2A). Cells were computationally segmented in order to measure intensity of sfGFP and mCherry fluorescence within each cell (Figure 1—figure supplement 2).

Relative fluorescence units (RFU) were converted into absolute numbers of Sens protein molecules via Fluorescence Correlation Spectroscopy (FCS), which measured the absolute concentrations of sfGFP-Sens and mCherry-Sens protein in live wing discs (Figure 1G). For both sfGFP and mCherry FCS measurements, the highest Sens levels were no greater than 250 nM (Figure 1G), corresponding to approximately 25 RFU obtained from imaging (Figure 1—figure supplement 3A). This gives an approximate conversion factor of 1 RFU equivalent to 10 nM. To validate this estimate, we classified Sens-positive cells and mapped them onto the raw images (Figure 1—figure supplement 3C). An accurate estimate of a conversion factor would recreate the expected expression pattern of Sens, where S-fated cells are periodically dispersed along both sides of the DV boundary surrounded by first and second order neighbors (Figure 1—figure supplement 3B). We reproducibly observed this pattern for a conversion factor of 10 but not when it was varied three-fold lower or higher (Figure 1—figure supplement 3C). Since the average wing disc cell nuclear volume is 23 × 10⁻¹⁵ L (Papadopoulos et al., 2019), 1 RFU is estimated to correspond to ~138 Sens molecules.

Applying the conversion factor, we observed that wing disc cells displayed a broad range of Sens protein molecule numbers (Figure 2A). This observation is consistent with earlier studies using anti-Sens immunofluorescence (Jafar-Nejad et al., 2006). Although both sfGFP and mCherry tagged alleles contributed equally to total Sens protein output on average (Figure 1G), there were significant intracellular differences between sfGFP-Sens and mCherry-Sens molecule numbers (Figure 2A). This was due to two independent sources of noise: (1) stochastic gene expression, (2) stochastic processes in the measurement of protein number. The latter source of noise arises from differential rates of protein folding and turnover, probabilistic photon emission and detection, as well as image analysis errors. To estimate measurement noise, we constructed a third transgene containing both sfGFP and mCherry fused in tandem to the sens ORF (Figure 2B). sfGFP-mCherry-sens was inserted at locus 22A3, and fluorescence was measured in disc cells from such animals. Since sfGFP and mCherry molecule numbers should be perfectly correlated when expressed as a tandem-tagged protein in vivo, we attributed any decrease in fluorescence correlation to measurement noise (Figure 2B). Negligible Fluorescence Resonance Energy Transfer (FRET) was observed between mCherry and sfGFP proteins in tandem-tagged sfGFP-mCherry-sens cells, indicating that stochastic noise was not under-estimated due to FRET interactions (Figure 2—figure supplement 1).

Intrinsic noise of protein expression η² has been defined as the extent to which protein output from two alleles of a gene fail to correlate in the same cell (Elowitz et al., 2002). The value of η² indicates the mean relative difference between the two reporter proteins in the same cell; for instance, a value of 0.10 would indicate the two reporter proteins differ by about 10% of the average expression. Since we had quantified the absolute number of protein molecules, we expressed noise as the Fano factor, which is defined asFanofactor=η2.μwhere µ is the mean protein number. This factor indicates the average difference in number of molecules between the two reporter proteins at any given time.

A benefit of calculating the Fano factor is to determine if the protein noise can be modeled as a Poisson-like process. Previous studies using dissociated cells have shown that protein noise, expressed as the Fano factor, remains constant as protein output varies (Bar-Even et al., 2006; Elowitz et al., 2002). This is due to stochastic birth and death of mRNA and protein molecules (Paulsson, 2005; Thattai and van Oudenaarden, 2001). We estimated the empirical Fano factor as a function of Sens protein output in cells expressing either singly-tagged Sens or tandem-tagged Sens (Figure 2C and Figure 2—figure supplement 2). To estimate the Fano factor due to stochasticity of Sens expression, we subtracted out the technical contribution as measured in tandem-tagged cells. The Fano factor for Sens expression displayed a complex relationship to protein output, with a minor peak in cells containing fewer than 200 molecules, and then dropping to a level that slowly rose with higher Sens output (Figure 2C).

To understand the origins of this profile, we created a simplified model of gene expression (Figure 3A). Each reaction in the model was treated as a probabilistic event, reflecting the stochastic nature of gene expression (Figure 3—figure supplement 1A–C; Paulsson, 2005; Thattai and van Oudenaarden, 2001). Using rate parameters that we measured for sens expression in the wing (Figure 3—figure supplement 2 and Figure 3—source data 1), we ran thousands of simulations mimicking protein output from two independent alleles in each virtual cell (Figure 3—figure supplement 1B,C).

We first considered a model in which the promoter was always active (Figure 3A). The simulated Fano factor was constant irrespective of protein number, consistent with the noise being caused by random birth-death events. This somewhat resembled the Sens profile of Fano factor experimentally observed in cells containing more than 200 molecules of Sens (Figure 2C). However, there was a weak rise in the observed Fano factor, and so we hypothesize that one of the post-transcriptional rate constants weakly varies as a function of protein output (Figure 3—figure supplement 1D).

The model predicts that mRNA and protein birth-death processes contribute a uniform level of noise, expressed as the Fano factor, across the entire spectrum of Sens output. Note that the experimentally measured Fano factor is the cumulative sum of Fano noise from each allele. Therefore, expression stochasticity from one allele contributes to half the cumulative sum. This value of the Fano factor is predicted to be equivalent to the average number of protein molecules translated from one mRNA molecule in its lifetime, also called the translation burst size (Paulsson, 2005; Schmiedel et al., 2015; Thattai and van Oudenaarden, 2001). To test this model prediction, we experimentally altered the translation burst size for Sens. We did so by eliminating the post-transcriptional repression of sens by the microRNA miR-9a (Cassidy et al., 2013; Li et al., 2006). Since microRNAs inhibit translation output and/or mRNA lifetime, loss of microRNA-mediated repression should increase the translation burst size of a target gene proportional to the magnitude of de-repression of the target.

We eliminated miR-9a regulation of sens by mutation of the two binding sites for miR-9a in the sens mRNA 3’UTR. This abolishes the impact of miR-9a on sens gene expression (Cassidy et al., 2013). We then estimated the fold-increase in Sens protein number when miR-9a regulation is lost. We did so by comparing Sens output from sens alleles with intact or mutated miR-9a sites (Figure 4A). Loss of miR-9a repression increased Sens protein number an average of 1.8-fold in all cells (Figure 4B,C). Similar fold-repression values were observed irrespective of the fluorescent tag used to estimate the ratio of mutant-to-wildtype Sens molecules (Figure 4—figure supplement 1). If Sens noise arises from birth-death processes, we predicted that the Fano factor would uniformly increase by ~1.8 fold for the mutant sens gene, reflecting its greater translation burst size. We measured the Fano factor for cells where both sens alleles contained mutated miR-9a sites (Figure 4D). Loss of miR-9a regulation increased the Fano factor uniformly across the entire range of Sens protein output. The increase in overall Fano factor was approximately two-fold. This result is consistent with stochastic birth-death processes uniformly contributing to Sens protein noise.

Strikingly, when miR-9 repression was lost, the small peak in Fano factor was strongly enhanced in cells with 300 molecules/cell or less (Figure 4D). The existence of this peak was not predicted by stochastic birth-death processes alone. Therefore, we considered a more complex model of gene expression (Figure 3B). The promoter was allowed to switch between active and inactive states such that it transcribed mRNA molecules in bursts (Figure 3C). When we systematically varied the promoter activation parameter k_on, the in-silico Fano factor profile exhibited a peak when protein output was low (Figure 3E). This trend was seen when the other parameters were fixed at different values, with the amplitude and position of the peak changing but always biased to lower protein output. In contrast, varying the initiation parameter S_m or inactivation parameter k_off did not yield a Fano peak when protein output was low (Figure 3D,F). These trends were also seen when the other parameters were fixed at different values. Thus, the model predicted qualitatively different noise profiles in protein data. The noise profile most similar to the experimentally observed profile was the one in which k_on varies between cells to generate a range of protein output. We surmise from these results that transcription of sens at the DV boundary of the wing disc might be regulated by modulating promoter burst frequency via k_on. Indeed, analysis of mRNA expression in the wing disc by single-molecule fluorescence in situ hybridization (smFISH) indicates that burst frequency is modulated for the sens gene (Bakker et al., 2020). Burst frequency modulation has also been observed for other developmental genes (Bakker et al., 2020; Bartman et al., 2019; Fukaya et al., 2016; Zoller et al., 2018).

Results from the mathematical model suggest that Sens protein noise comes from two distinct sources: (1) transcriptional bursting kinetics, and (2) mRNA and protein birth-death processes. The latter source generates a constant amplitude of protein fluctuations (Fano factor) across the entire spectrum of Sens output. When cells have a low transcription burst frequency, they experience larger fluctuations in mRNA numbers, which transmits to larger protein fluctuations, and generates the Fano factor peak. As promoter activation events become more frequent, they approximate a constitutively active promoter such that RNA-protein birth-death processes dominate the noise, and the Fano factor drops to a constant level.

When we implemented this more complex model to simulate the loss of miR-9a regulation, the result was similar to the experimental increase in Fano factor (Figure 4D,E). This result was observed whether the translation rate (S_p) or mRNA decay rate (D_m) parameter was altered 1.8-fold to simulate loss of miR-9a repression.

The model predicts that transcription bursting is a significant contributor to Sens protein noise when cells contain fewer than 300 molecules (Figure 3E). To test this prediction, we landed the sens transgene in a different location of the genome. We reasoned that a different genomic neighborhood might change transcriptional bursting dynamics due to altered chromatin accessibility. We chose 57F5 to land sens, since both 22A3 and 57F5 are widely used landing sites for Drosophila transgenes (Figure 5A; Venken et al., 2006; Venken et al., 2009). There was no difference in the percentage of imaged cells positive for Sens between 22A3 (34.3 ± 3.7% positive) and 57F5 wing discs (34.7 ± 3.4% positive). The sens transgene inserted at 57F5 was also comparable to the 22A3 site in its ability to rescue the mutant endogenous sens, as well as express Sens protein in a similar pattern at the wing disc DV boundary (Figure 5B–D). Median Sens output was modestly higher (30–35%) when expressed from 57F5 (Figure 5—figure supplement 1A,B). However, the distribution of Sens output was not significantly different between 57F5 and 22A3 when normalized to the median value (Figure 5—figure supplement 1D). This result indicates that sens expression from 57F5 was uniformly higher across the entire spectrum of cells expressing the protein.

We generated animals where the alleles at 57F5 were singly tagged with sfGFP and mCherry (Figure 5C,D), and we quantitated the Fano factor after correction for measurement noise at 57F5. We then compared the Fano factor profile from the gene located at 57F5 versus 22A3 (Figure 5E). Strikingly, the Fano factor peak from the 57F5 gene was greatly increased in amplitude and width, and was maximal in cells with higher levels of Sens protein, compared to the peak from the 22A3 gene. However, the peak from 57F5 did relax to a constant Fano factor in cells with higher Sens output. This level was indistinguishable from the constant Fano level in 22A3 cells with comparable Sens output (Figure 5E). Thus, the 57F5 alleles do not appear to alter birth-death processes for sens mRNA and protein but do appear to affect some other process related to stochasticity.

We looked for local properties of the genome at 22A3 and 57F5 that might be responsible for the different noise properties of sens inserted at those sites. Metazoan chromosomes are physically segregated into self-associating domains of chromatin called TADs (Topologically Associated Domains) (Dixon et al., 2016; Szabo et al., 2018). Domains vary in length, gene density and chromatin accessibility (Dowen et al., 2014). TADs are separated from each other by insulator sequences (Ali et al., 2016; Stadler et al., 2017; Van Bortle et al., 2014). Using published Hi-C and ChIP-seq data for the Drosophila genome (Stadler et al., 2017), we determined that the sens insertion site at 22A3 is in the middle of a large TAD, ~50 kb from its 5’ and 3’ insulators (Figure 6—figure supplement 1A). In contrast, the sens insertion site at 57F5 is in a small TAD, ~1 kb from its 3’ insulator (Figure 6—figure supplement 1B).

Insulators physically associate with one another, leading to altered chromatin configurations (Yang and Corces, 2011). When insulators associate in cis, they form loops along a chromosome. DNA loops alter enhancer interactions with cis promoters or prevent the spread of heterochromatin into looped regions (Fujioka et al., 2016; Yang and Corces, 2011). In contrast, when insulators associate in trans, they facilitate enhancer regulation of promoters on other chromosomes by bringing them into close proximity (Fujioka et al., 2016; Lim et al., 2018; Piwko et al., 2019). Such trans regulatory phenomena, called transvection, appear to be a mode of gene regulation in several species including humans (Hark et al., 2000; Liu et al., 2008; Masui et al., 2011; Rassoulzadegan et al., 2002). In Drosophila, homologous chromosomes are extensively paired in somatic cells throughout most life stages (Metz, 1916), leading to physical co-localization of paired alleles in nuclei. This sometimes leads to trans regulation of one allele by its paired allele due to dynamic inter-TAD contacts in trans (Szabo et al., 2018). Since the sens gene was positioned either close to or distant from a TAD insulator in 57F5 or 22A3 respectively, we wondered if insertion altered the cis or trans regulation of sens.

To test this hypothesis, we examined protein output from the mCherry-sens allele alone. When this allele was placed at 22A3 in trans to a sfGFP-sens allele at 22A3, a unimodal distribution of mCherry-Sens protein was observed (Figure 6A). A strikingly different distribution was observed when mCherry-sens was placed at 57F5 in trans to a sfGFP-sens allele at 57F5 (Figure 6A). A sizable fraction of cells expressed higher levels of mCherry-Sens, creating a broader, bimodal distribution. We then placed a 57F5 mCherry-sens allele in trans to a 22A3 sfGFP-sens allele (Figure 6A). If enhanced expression of mCherry-sens at 57F5 was dependent on trans regulation between paired alleles, then unpaired 57F5/22A3 cells would behave like 22A3/22A3 cells. Conversely, if enhanced mCherry-sens expression was due to cis regulation at 57F5, then the mCherry-Sens output from 57F5/22A3 cells would behave like 57F5/57F5 cells. Strikingly, the observed distribution of mCherry-Sens from 57F5/22A3 cells was identical to that of 22A3/22A3 cells (Figure 6A). A similar result was observed when sfGFP-Sens output was monitored (data not shown). Single-molecule FISH analysis of sens nascent RNA confirmed that alleles positioned at the same locus (either 22A3 or 57F5) were physically co-localized in nuclei, whereas alleles positioned at heterologous loci were not co-localized (Bakker et al., 2020). Thus, even though sens alleles are physically paired at either 22A3 or 57F5, they regulate one another in trans when located at 57F5 but not at 22A3.

We then asked whether cis or trans regulation of sens at 57F5 is responsible for the enhanced noise in Sens protein output observed in 57F5/57F5 cells (Figure 5E). We generated animals with the mCherry-sens allele at 57F5 and the sfGFP-sens allele at 22A3, and quantitated the Fano factor after correction for measurement noise (Figure 6B). If cis regulation of sens at 57F5 was responsible for the enhanced noise, then the Fano factor from 57F5/22A3 cells would still be high (Figure 6—figure supplement 2A). However, the observed Fano factor from 57F5/22A3 cells resembled that from 22A3/22A3 and not 57F5/57F5 cells (Figure 6B). This result strongly suggests that the enhanced noise is due to trans regulation of sens at 57F5.

We turned to our modeling framework to elucidate how trans regulation might enhance noise in protein output. Paired alleles sometimes inhibit each other's transcription output (Lim et al., 2018). Such inhibition would lead to greater differences in allelic output of protein, which might explain the enhanced Fano factor. We tested this by simulating trans-inhibitory alleles. When one allele’s transcriptional state was ‘on’, the rate of activation (k_on) of the other allele was decreased. While this resulted in an increased amplitude in the Fano peak, it did not affect peak width and it did not shift the peak position to greater Sens output (Figure 6—figure supplement 2B). Both of these latter features were observed experimentally (Figure 6B). We then considered a simpler scenario in which trans regulation increased transcription, as suggested by the modest increase in protein output from paired 57F5 alleles (Figure 6A, Figure 5—figure supplement 1A,B). When the transcriptional parameters in the model were varied, we found that a small increase in transcription burst size could capture the effect of changing sens gene location from 22A3 to 57F5 on the Fano factor (Figure 6C). This suggests that changing burst size by trans regulation might account for the dramatic effects on Sens protein noise.

Stripes of cells 4–5 cell diameters wide are induced to express Sens by Wg at the DV boundary (Alexandre et al., 2014; Eivers et al., 2009; Phillips and Whittle, 1993). Within each stripe, cells near the center undergo lateral inhibition, and consequently, some of these upregulate Sens to become S cells (Alexandre et al., 2014; Troost et al., 2015). This pattern was experimentally observed whether sens was transcribed from the 22A3 or 57F5 locus (Figures 5D and 7A).

Many cells in the center of stripes contain 500–1000 Sens molecules (Figure 7A and Figure 7—figure supplements 1A and 2). Thus, cells undergoing lateral inhibition are comparable in Sens protein number to those cells with highest noise from the 57F5 gene. To confirm that these central cells were high-noise for 57F5, we mapped the values of each cell’s Fano factor to their spatial positions within wing discs. For the 57F5 gene, cells with abnormally high noise were located throughout the stripe, including the center from which S cells are chosen (Figure 7B and Figure 7—figure supplement 1B). Thus, it is highly likely that some 57F5 cells undergoing lateral inhibition were experiencing enhanced fluctuations in Sens protein number. In contrast, 22A3 cells with the highest noise were located at the edges of each stripe, distant from the central region from which S cells normally emerge (Figure 7B and Figure 7—figure supplement 1B). Thus, 22A3 cells experiencing the largest fluctuations contain very low Sens protein and are unlikely to adopt S-cell fates. We had observed that only paired alleles at 57F5 caused Sens noise enhancement, and unpaired alleles at 57F5 and 22A3 did not. When we mapped 57F5/22A3 cells with the highest noise, they were largely restricted to the edge of stripes closest to the DV boundary (Figure 7—figure supplement 1B).

We reasoned that if cells undergoing lateral inhibition experienced a large enough fluctuation in Sens number, then an error in cell fate determination might occur. We had measured Sens protein in cells undergoing decisions to make chemosensory bristles. Chemosensory bristles are periodically positioned in a row near the adult wing margin, such that approximately every fifth cell is a bristle (Figure 7C). Mechanosensory bristles form in a continuous row most proximal to the adult wing margin, and they are selected 8–10 hr after the chemosensory cells are selected (Hartenstein and Posakony, 1989). Thus, mechanosensory bristles positioned incorrectly in the chemosensory row might be derived from proneural cells that escaped lateral inhibition during chemosensory specification (Figure 7C).

We quantified ectopic bristles in 57F5 versus 22A3 adults and determined the frequency with which a wing contained one or more ectopic bristles. The frequency was ten-fold higher in 57F5/57F5 adults compared to 22A3/22A3 adults (Figure 7D, Figure 7—source data 1). Indeed, an error was seen in one of three adult wings. Consistent with this, chemosensory bristles were also more frequently specified in 57F5 adult wings compared to 22A3 (Figure 7C and Figure 7—figure supplement 3). The increase in pattern disorder was not due to disruption of genes residing in the 57F5 TAD since none are annotated as neurogenic (Cassidy et al., 2013). Nor was it due to genetic background in the different lines since the 22A3 and 57F5 parental stocks had identical chemosensory and mechanosensory bristle frequencies (Figure 7D, Figure 7—figure supplement 3 and Figure 7—source data 1). Moreover, adults with unpaired alleles (57F5/22A3) had an ectopic bristle frequency of 1.7%, not significantly different from 22A3/22A3 adults (Figure 7D and Figure 7—source data 1). Thus, pairing between alleles at 57F5 caused greater pattern disorder.

The pairing of sens at 57F5 led to a modest increase in the level of Sens output and a dramatic increase in the noise of Sens output. The greater pattern disorder could be due to the enhanced noise or level or both. To distinguish between these possibilities, we analyzed patterning of the adult wing margin when sens was rendered insensitive to miR-9a repression. Loss of miR-9a repression increased Sens protein levels 80–85% in all proneural cells (Figure 4C and Figure 5—figure supplement 1A,C,E) and modestly increased protein noise (Figure 4D). If pattern disorder was caused by enhanced protein levels, we reasoned that loss of miR-9a repression would generate even greater pattern disorder than genome position, since protein levels were only increased ~35% in 57F5/57F5 cells (Figure 5—figure supplement 1A,B,D). However, loss of miR-9a repression did not increase the frequency of patterning errors in adult wings (Figure 7E, Figure 7—figure supplement 3, and Figure 7—source data 1). In a different perspective, the miR-9a mutant sens paired at 22A3 expressed 36% more protein than the wildtype sens paired at 57F5 (Figure 5—figure supplement 1A). However, its phenotypic error frequency was 3.6% in contrast to 29.1% for wildtype sens at 57F5 (Figure 7E). The most parsimonious explanation is that bristle pattern disorder in 57F5/57F5 animals is caused by the greatly enhanced noise in sens gene expression.

For all experiments, Drosophila melanogaster was raised using standard lab conditions and food. Stocks were either obtained from the Bloomington Stock Center, from listed labs, or were derived in our laboratory (RWC). A list of all mutants and transgenics used in this study is in the Key Resources Table. All experiments used female animals unless stated otherwise. The sample sizes were not computed when the study was designed. Sample sizes were determined such that >12,000 cells were measured for each genotype, as detailed in the section Quantitation and Statistics. Since only ~1,000 cells could be segmented per disc sample,>12 discs were analyzed for each genotype.

N-terminal 3xFlag-TEV-StrepII-sfGFP-FlAsH tagged sens, originally generated from the CH322-01N16 BAC, was a kind gift from K Venken and H Bellen (Venken et al., 2006; Venken et al., 2009). It has been shown to rescue sens^E1 and sens^E2 mutations (Cassidy et al., 2013; Venken et al., 2006). To generate mCherry tagged sens, the sfGFP coding sequence in 3xFlag-TEV-StrepII-sfGFP-FlAsh was swapped out for mCherry by RpsL-Neo counter-selection (GeneBridges). The sfGFP-mCherry tandem tagged sens transgene was generated similarly by overlap PCR such that sfGFP and mCherry sequences were separated by a 12 amino acid (GGS)₄ linker. The miR-9a binding site mutant alleles of the tagged sens transgenes were created by deletion of the two identified binding sites in the 607 nt sens 3’’ UTR as had been described previously (Cassidy et al., 2013) to generate sens^m1m2 mutant transgenes. Cloning details are available on request. All BACs were integrated at PBacy+-attP-3BVK00037 (22A3) and PBacy+-attP-9AVK00022 (57F5) landing sites by phiC31 recombination (Venken et al., 2006).Transgenic lines were crossed with sens mutant lines to construct stocks in which sens transgenes were present in a sens^E1/sensE^E2 trans-heterozygous mutant background. Both mutant alleles show greatly reduced levels of anti-Sens staining in cells, and the E2 allele is a nonsense mutant that cuts off the protein’s DNA-binding domain.

As an additional control, we checked by various means if indeed sfGFP-Sens and mCherry-Sens proteins behaved similarly in vivo such that the nature of the protein tag did not affect quantitative assays.

First, we measured the molecule counts of sfGFP-Sens and mCherry-Sens in the same cells using Fluorescence Correlation Spectroscopy (FCS). As can be seen in Figure 1G, we obtained similar numbers of Sens molecules irrespective of which fluorescent tag was attached. This indicated that both alleles express equal numbers of proteins in vivo.

Second, using the microRNA repression assay detailed in Figure 4A–C, we sensitively assayed whether the nature of the tag affects protein output quantitatively. If one tag were differentially expressed relative to the other, we would expect the fold-repression values calculated using mCherry tagged sens alleles to be different from sfGFP tagged sens alleles. This was not observed (Figure 4—figure supplement 1).

Third, to ensure that we did not under-estimate stochastic noise due to Fluorescence Resonance Energy Transfer (FRET), we imaged tandem tagged sfGFP-mCherry-Sens samples in both channels after exciting only the donor (sfGFP) molecules. There was negligible FRET from sfGFP to mCherry when using imaging parameters identical to experimental runs (Figure 2—figure supplement 1).

We used the following formula to calculate intrinsic noise (Elowitz et al., 2002). Mathematically, it is the variance remaining after the co-variance term of two variables is subtracted from their total variance. This value is then normalized to the squared mean (η2=σ2/μ2) to obtain the following dimensionless quantity:ηintrinsic2=⟨(x−y)2⟩2⟨x⟩⟨y⟩

Here x and y represent number of sfGFP molecules and mCherry molecules, respectively, in a given cell. Angled brackets denote averages over a population of cells. This term provides a single value of intrinsic noise for the entire cell population. Since Sens expression varies over three orders of magnitude, we partitioned cells into small bins according to their Sens protein number (x + y). Sens RFU was log-transformed and we used a bin width of 0.02 log(RFU) to partition cells (Figure 2—figure supplement 2B, C). We then calculated intrinsic noise and mean Sens protein number for each binned sub-population. These were multiplied together to calculate the Fano factor for each bin.Fanofactor=(σ2μ)=η2.μ

Given that the number of cells in each bin was not constant, and that variance estimates are affected by sample size, we calculated confidence intervals around the calculated Fano factor for each bin by bootstrapping. We resampled bin populations 50,000 times with replacement. The 2.5^th and 97.5^th percentile estimates were used to construct a 95% confidence interval for that bin’s Fano factor (Figure 2—figure supplement 2D).

Intrinsic noise and the Fano factor were calculated as described above for tandem-tagged sfGFP-mCherry-sens wing discs. The Fano factor profile was identical for tandem-tagged sens genes inserted at either 22A3 or 57F5. Therefore, we pooled data generated from both locations before binning into sub-populations. We expect the tandem-tag construct, along with our analysis pipeline, to account for lack of correlation in red-green fluorescence due to non-linearities in imaging and detection, differences between the two tags such as folding time and spectral properties, as well as increased variance due to image analysis or segmentation errors.

In order to construct a statistical model for measurement noise at each level of Sens output, we used a Lowess regression to fit a continuous line through the data (as seen in Figure 2C). The Lowess algorithm fits a locally weighted polynomial onto x-y scatter data and therefore does not rely upon specific assumptions about the data itself. The local window used to calculate a fit was kept constant for all Lowess fits. Using our statistical model, we generated a predicted Fano factor that was due to measurement noise for each bin. This predicted value was subtracted from the Fano factor that was due to both measurement and gene expression noise for each bin. The difference obtained is an estimate of the Fano factor due to noise in sens gene expression.

White pre-pupal wing discs were dissected in PBS and sunken into LabTek 8-well chambered slides containing 400 µl PBS per well (Papadopoulos et al., 2019). Discs were positioned such that the pouch region was facing the bottom of the well to be imaged. FCS measurements were made using an inverted Zeiss LSM780, Confocor 3 instrument with APD detectors. A water immersion 40x objective with numerical aperture of 1.2 (which is optimal for FCS measurements) was used throughout. Fast image scanning was utilized for identification of cell nuclei to be measured by FCS. Prior to each session, we used 10 nM dilute solutions of Alexa488 and CF586 dyes to calculate the average number of particles, the diffusion time and define the structural parameters wxy2 and z0. Using these we calibrated the Observation Volume Element (OVE) whose volume can approximated by a prolate ellipsoid (VOVE=π32wxy2z0). Measurements were performed in Sensory Organ Precursor cells (SOPs or S-fated), as well as first and second order neighbors, residing dorsally or ventrally of the S-fated cell (Figure 1G). Measurements were subjected to analysis and fitting, using a two components model for three-dimensional diffusion and triplet correction as follows:G(τ)=1+1N1-y1+ττD11+wxy2τwz2τD1+y1+ττD21+wxy2τwz2τD21+T1-Te-ττT

FCS measurements were excluded from analysis if they exhibited marked photobleaching or low CPM that is counts per molecule (CPM < 0.5 kHz per molecule per second). Due to the higher CPM of sfGFP, it was expected that Sens-sfGFP measurements are more accurate. We, nevertheless, observed fairly similar molecular numbers for both sfGFP-Sens and mCherry-Sens. Normalized auto correlation curves allowed us to compare the differential mobilities of the tagged Sens protein molecules in the nucleus and their degree of interaction with chromatin. Consistently, for both sfGFP and mCherry tagged transcription factors, we observed similar amplitudes and decay times of the slow FCS component, suggesting that the interaction with chromatin is not substantially different for differently tagged Sens molecules or even at different Sens concentrations.

We compared Sens protein concentrations as measured by FCS to single cell fluorescence data from confocal imaging of the fixed tissue (Figure 1—figure supplement 3). All comparisons were done for the genotype shown below since all FCS measurements were made in trans-heterozygous mCherry-sens[22A3]/sfGFP-sens[22A3] animals in a sens mutant (sens^E1/sens^E2) background.

In order to measure the fold-decrease in Sens protein output due to miR-9a repression of sens mRNA, we compared the ratio of mCherry-Sens to sfGFP-Sens in the following genotypes:

Single cell fluorescence values were obtained after cell segmentation and background subtraction as described earlier. Cells from individual discs were pooled together and red-green fluorescence was linearly correlated using least squares fit (QR factorization) to determine a slope and intercept for each disc. Next the average slope was calculated for each genotype (shown above). Fold reduction in mCherry-Sens protein output due to miR-9a was calculated as the ratio of slope-(1) to slope-(2) with relative errors propagated. Similarly, fold reduction in sfGFP-Sens protein output due to miR-9a was calculated as the ratio of slope-(2) to slope-(3).

Heat maps of aggregate Hi-C data were used to calculate chromosomal contact frequency for embryonic nc14 datasets (Stadler et al., 2017) for landing sites at 22A3 and 57F5. DNase accessibility data (Li et al., 2008) and ChIP-seq of the insulator proteins CP190, BEAF-32, dCTCF, GAF and mod(mdg4) (Nègre et al., 2010) for the corresponding coordinates were analyzed as well.

We modeled the various steps of gene expression, based on central dogma, as linear first order reactions (Figure 3—figure supplement 1A). To simulate the stochastic nature of reactions, we implemented the model as a Markov process using Gillespie’s Stochastic Simulation Algorithm (SSA) (Gillespie, 1977). A Markov process is a memoryless random process such that the next state is only dependent on the current state and not on past states. Simple Markov processes can be analyzed using a chemical master equation to provide a full probability distribution of states as they evolve through time. The master equation defining our three-variable gene expression Markov process is as follows:∂P(nP,nM,nG,t)/∂t=Sm[P(nP,nM+1,nG,t)−P(nP,nM,nG,t)]+Dm[(nM+1)P(nP,nM+1,nG,t)−nMP(nP,nM,nG,t)]+SpnM[P(nP−1,nM,nG,t)−P(nP,nM,nG,t)]+Dp[(nP+1)P(nP+1,nM,nG,t)−nPP(nP,nM,nG,t)]+kon[(nGtotal−nG+1)P(nP,nM,nG−1,t)−(nGtotal−nG)P(nP,nM,nG,t)]+koff[(nG+1)P(nP,nM,nG+1,t)−(nG)P(nP,nM,nG,t)]

Here nP and nM denote the number of protein and mRNA molecules respectively. nGtotal is the total number of genes of which nG are genes in the ‘ON’ state capable of transcription. Therefore, nG/nGtotal is the fraction of active genes. Time is denoted by t. The rate constants are defined in Figure 3—source data 1.

As the Markov process gets more complex, the master equation can become too complicated to solve. Gillespie’s SSA is a statistically exact method which generates a probability distribution identical to the solution of the corresponding master equation given that a large number of simulations are realized.

Only numbers of cells identified as ‘Sens-positive’ were used for the data analysis. We identified N = 50,788 Sens-positive cells that were singly-tagged wildtype sfGFP-sens and mCherry-sens alleles inserted in locus 22A3. For the miR-9a binding site mutant sens allele pair at locus 22A3 we identified N = 106,738 cells. Tandem tagged sfGFP-mCherry-sens data was gathered for N = 24,970 cells pooled from both loci since cells from individual loci produced identical Fano factor profiles. For the repression assay, we measured genotypes with both alleles wildtype for N = 20,353 cells; mCherry tagged sens wildtype paired with a mutant sfGFP tagged sens for N = 19,088 cells, and sfGFP tagged sens wildtype paired with a mutant mCherry tagged sens for N = 12,947 cells. A second set of repression measurements shown in Figure 4B was done for both alleles mutant (N = 6369 cells) or wild type mCherry-sens paired with mutant sfGFP-sens (N = 7557 cells). Fano factor profiles comparing the effect of genomic locus contain data from N = 19,549 cells (22A3/22A3), N = 27,221 cells (57F5/57F5) and N = 13,776 cells (22A3/57F5).

Due to the nature of the experiments, there is no technical replication. Rather, the numbers listed above refer to each Sens-positive cell as a biological replicate. Since ~1,000 cells could be measured in one wing disc sample, the experiments utilized 12–100 wing disc biological replicates per genotype.

For ectopic mechanosensory bristle measurements, we counted the frequency of adult wings with at least one ectopic sensory organ. The number of adult wings analyzed per genotype ranged from 60 to 88. Each wing is considered a biological replicate. For parent stocks containing the ψC31 docking site only and no sens transgene, the following frequencies were observed: N = 0/60 wings (parent-22A3/22A3 and parent-22A3/57F5) and N = 0/88 wings (parent 5757/57F5). For transgenic stocks with wildtype sens we observed N = 2/62 wings (sens [+ miR-9a] - 22A3/22A3), N = 1/60 wings (sens [+ miR-9a] - 22A3/57F5) and N = 23/79 wings (sens [+ miR-9a] - 5757/57F5). For transgenic stocks with mutant sens we observed N = 3/83 wings (sens [- miR-9a] - 22A3/22A3), N = 4/64 wings (sens [- miR-9a] - 22A3/57F5) and N = 12/65 wings (sens [- miR-9a] - 5757/57F5).

The 95% confidence intervals for all point estimates (mean, Fano factor) of Sens protein data and model simulations were built by bootstrapping with resampling within individual binned cell populations. In all cases, the distribution generated by bootstrapping was checked for normality before obtaining the 2.5^th and 97.5^th percentile values. The error frequencies of adult bristle patterns were statistically tested by calculating the odds ratio of error frequency between pairs of genotypes. A Fischer’s exact test was applied to determine if the odds ratio significantly deviated from one.

For ectopic chemosensory bristle measurements, we measured the average distance between pairs of neighboring bristles. N = 174 bristle neighbors (parent-22A3), N = 177 bristle neighbors (parent-57F5), N = 1004 bristle neighbors (wild type sens at 22A3), N = 1063 bristle neighbors (wild type sens at 57F5), N = 944 bristle neighbors (mutant sens at 22A3) and N = 605 bristle neighbors (mutant sens at 57F5). Each pair of neighboring bristles comprises one biological replicate. 95% confidence intervals were calculated by bootstrapping empirical distributions of bristle pair distances across genotypes, and these were compared statistically using a student’s t-test. All other statistical tests and image quantification procedures are listed in the corresponding methods and figure legends sections.

There was no exclusion of any data or subjects.