The nuclear organization of eukaryotic cells can play important roles in the regulation of genome function (Pederson, 2002). In particular, the formation of sub-compartments is hypothesized to help increase the local concentration of essential enzymes and render nuclear processes more efficient (Mao et al., 2011). Enzymatic clusters have been reported in many genetic processes in the cell (Carmo-Fonseca, 2002; Cremer et al., 2006; Schneider and Grosschedl, 2007), including replication (Kennedy et al., 2000), DNA repair (Misteli and Soutoglou, 2009), transcription (Cook, 2010; Verschure et al., 1999) and RNA processing (Kumaran et al., 2008). These clusters can form de novo and their stability can be dynamically regulated in vivo making it difficult to capture them and to study their function with mechanistic detail (Sutherland and Bickmore, 2009; Fraser and Bickmore, 2007; Buckley and Lis, 2014).

In mammalian cells, the spatial organization of transcription has been revealed primarily with chemically fixed (non-living) cell techniques. These techniques include fluorescence in situ hybridization (Femino et al., 1998; Mitchell and Fraser, 2008; Fraser and Bickmore, 2007), immunostaining (Iborra et al., 1996), and chromosome conformation capture and immunoprecipitation-based approaches like 3C (Tolhuis et al., 2002; Osborne et al., 2004), HiC (Lieberman-Aiden et al., 2009), ChIA-PET (Li et al., 2012). Clusters of RNA Polymerase II (Pol II) were initially observed in fixed cells (Jackson et al., 1993; Papantonis and Cook, 2013) via anti-body staining against the active forms of the polymerase, and seen to co-localize with sites of nascent RNA synthesis in the fixed cells. From these fixed cells studies emerged theories interpreting the Pol II clusters as static pre-assemblies termed “transcription factories.” However, attempts to directly visualize Pol II clusters in living cells had been initially unsuccessful (Sugaya et al., 2000; Kimura et al., 2002), raising a debate over their existence in vivo (Carter et al., 2008; Sutherland and Bickmore, 2009).

In earlier studies, limitations of conventional live-cell imaging methods may have contributed to the failure to detect non-homogeneous spatiotemporal organization of Pol II in living cells. Specifically, conventional imaging methods do not readily resolve substructures at length scales below the optical diffraction limit. Another difficulty arises if clusters exhibit fast kinetics. For instance clusters that form transiently may not be easily detectable. Capturing and understanding the spatiotemporal organization of Pol II in living cells can unveil hitherto hidden mechanisms for the regulation of gene expression in vivo.

Recent investigations of Pol II (Cisse et al., 2013) or an associated factor (Ghamari et al., 2013) in living cells, and new quantification in fixed cells (Zhao et al., 2014) revealed evidence for a highly dynamic Pol II cluster turnover process. The Pol II cluster dynamics (on the order of seconds) were significantly faster than the period required to complete the transcription of a typical mammalian gene (on the order of minutes) (Cisse et al., 2013). The lack of a correlative quantitative live-cell method, capable of capturing at high spatiotemporal resolution both the protein cluster and the transcriptional output, prevents further functional studies of Pol II clustering. For instance it is unclear whether transient protein clusters occur on actively transcribed genes, and whether the clustering event has a functional consequence on the gene expression process.

Here we develop a quantitative live cell, single molecule and super-resolution assay to capture protein clustering on an endogenous, actively transcribed gene. In live mammalian cells, the assay successfully co-localizes the polymerase clustering, in one color, with nascent RNA transcripts synthesized at the gene loci in a separate color. Our data reveal a previously uncharacterized, direct correlation between Pol II cluster lifetime and the number of nascent mRNA molecules subsequently synthesized. We find that this correlation between Pol II cluster lifetime and nascent mRNA output is predictive in nature, and may be utilized by an experimenter to stall or induce a burst of transcription, at will using a drug treatment. We discuss technical limitations as well as potential avenues for further studies on this largely uncharacterized mechanism for gene expression regulation.

We captured transient Pol II clusters at the loci of actively transcribed β-actin gene in live MEFs. Our data suggest a transcription regulation mechanism whereby the number of nascent mRNA synthesized is directly correlated with the lifetime of Pol II clusters. The clusters normally occur on the active gene locus during transcription initiation, with a basal average lifetime of ~8 s for β-actin, giving rise to a basal mRNA loading level of ~4 nascent transcripts per allele. Upon stimulation, only the lifetime (and not the size nor the frequency) of Pol II clusters is increased. The longer lifetime during initiation gives rise to a proportional increase in the number of Pol II molecules loaded onto the gene.

A theoretical model recapitulates our observed correlation between Pol II cluster lifetime and mRNA output. The model suggests that during a clustering event, multiple Pol II molecules are loaded on the gene at a rate of one productive Pol II every 2.5 s. With an estimated elongation rate of ~3 kb/min, this loading rate translates into a Pol II packing density of one Pol II complex every ~130 bp, a value close to the maximum density set by the holoenzyme footprint (Perry et al., 2010; Kwak and Lis, 2013; Fazal et al., 2015).

How Pol II clustering is induced, and what controls the dynamics of clustering is currently unknown. We speculate that factors involved in the Pol II pre-initiation complex assembly as well as post-translational modifications that control Pol II promoter escape may also help initiate and control Pol II clustering. However, experimental characterizations are needed to unveil the molecular mechanisms behind Pol II clustering. Nevertheless, our drug treatment results suggest that such detailed mechanistic understanding of how to effect and control Pol II clustering in vivo will provide new ways by which an experimenter may predictably control gene expression, at will.

Our observations support the notion that spatiotemporal clustering of enzymatic factors, through the transient increase of local densities in vivo, are able to effect maximum enzymatic efficiency in a locus-specific manner and when needed. Indeed, beyond components of the Pol II machinery, we speculate that clustering might constitute a general mechanism to build high concentration of factors at discrete genomic loci. For instance, it was recently observed that the nuclear distribution of the pluripotency regulator, Sox2, is highly heterogeneous forming dozens of spatial clusters in the nucleus of embryonic stem cells (Liu et al., 2014), and in another study spatial clusters of CDK9 were observed (Ghamari et al., 2013). Our findings on Pol II and mRNA output suggest such a local enrichment of transcription factors can result in a more efficient transcription process in vivo. Because DNA super-coiling has been suggested to play a role in gene bursting in bacteria (Chong et al., 2014), it is an intriguing possibility that topological constraint on the DNA may also play a role in cluster-dependent transcriptional regulation.

The combination of our quantitative single cell imaging approach with genome-wide analyses can help uncover the hidden mechanisms behind clustering dependent gene expression regulation. For instance, it was recently reported that docked Pol II molecules accumulate upstream of transcription start sites during starvation in C. elegans, primarily near rapidly responding growth and developmental genes (Maxwell et al., 2014) such as the β-actin gene we currently investigated in MEFs. Promoter proximal pausing has also been observed in a wide range of genes (Kim et al., 2005; Muse et al., 2007; Zeitlinger et al., 2007). Our results hint at possible mechanistic relationships between Pol II cluster disassembly and the release of paused polymerase. Although most of beta-actin regulation is thought to be regulated by promoter-proximal sequences (Danilition et al., 1991), another important question is whether distal enhancer elements could regulate the initiation and/or lifetime of Pol II clustering by looping to contact the promoter of their target genes. Future studies bridging quantitative single cell imaging of Pol II recruitment with genome-wide mapping of Pol II occupancy and long-distance regulatory interactions will provide important insights in the relationships between chromatin architecture, docking, pausing/release, and Pol II clustering.

The live-cell single-molecule and super-resolution approaches developed in this study can be applied broadly to study other molecular processes in vivo. We emphasize that the multicolor single–molecule and super-resolution approach is general in nature: the approach can be applied, in principle, to any pair of interacting factors that can be labeled. We anticipate that our method will be an important tool to uncover the spatiotemporal organization of the genome in the cell nucleus. While there has been important recent progress in the understanding of chromatin architecture thanks to 3C-related ensemble techniques (Dekker et al., 2013; de Wit and de Laat, 2012) in fixed cells, our imaging-based single-cell approach provides a powerful assay to address dynamics, and functional output directly in living cells. With the advent of new genetic engineering techniques, molecular enzymes as well as DNA (Chen et al., 2013) can be specifically labeled with photo-convertible fluorescent tags, to achieve single molecule studies with high spatial and temporal resolution in living cells.

A major limitation currently is the lack of long-lived fluorescence tags that span the orders of magnitude timescale difference between protein clustering activity and genome response. Here, Pol II clusters lasted just a few seconds, but the transcriptional response occurs on the timescale of minutes. The ability to synchronize a population of cells, with serum starvation, was necessary for the dual-color quantitative super-resolution approach to bridge the different timescales and uncover the correlation between cluster lifetime and mRNA output. The development of new fluorescent molecules adapted for living cells will help improve correlative quantitative imaging of single living cells.

The two-dimensional pair correlation function g(r) represents the probability of particle detection at distance r from a given detected point in a two dimensional imaging plane (Sengupta et al., 2011). The implementation was previously described (Cisse et al., 2013).

Briefly, if the distribution of proteins is purely random the pair correlation g(r) is given:

with

where ${\displaystyle \rho }$ represents the average surface density of molecules, ${\displaystyle {\text{g}}^{\text{PSF}}}$ denotes the correlation of uncertainty in the point spread function (PSF). ${\displaystyle \sigma }$ denotes standard deviation of distribution of detections of single protein. All data were first subjected to this distribution as a null hypothesis.

In the case where the null hypothesis is rejected, and protein correlation may be approximated by ${\displaystyle {\text{g}}^{\text{protein}}\left(\text{r}\right)=\text{A}\times \mathrm{e}\mathrm{x}\mathrm{p}(-r/\xi )+1}$. Thus the total correlation will be given by,

where ${\displaystyle \xi }$ denote the correlation length of protein cluster, and ${\displaystyle \text{A}}$ denote the amplitude of protein correlation. ${\displaystyle \ast }$ is the convolution operator.

For pcPALM analysis, the pair-correlations of Dendra2-alone (fixed cell) and Dendra2-Pol II (fixed cell and live cell) were first subjected to Equation 1. Data of Dendra2-alone in fixed cells were well fitted by Equation 1 while Dendra2-Pol II data in both fixed and live cells did not fit well with Equation 1, indicating that Dendra2-alone molecules are distributed randomly in cell nucleus, whereas Dendra2-Pol II are not. The data were then fitted with Equation 2, Dendra2-alone data were mainly fitted by the stochastic component of Equation 2 and the amplitude (${\displaystyle \text{A}}$) of protein correlation and the correlation length (${\displaystyle \xi }$) of it were negligible, whereas the protein correlations for Dendra2-Pol II were apparently influenced to the fitting of Equation 2, more effectively in live cells (Figure 1—figure supplement 1A–C).

The pointillist data were obtained by 2D-Gaussian fitting of the point-spread function for individual particles using the MTT software package and the two-dimensional correlation function was computed using the 2D Fast Fourier Transform (fft2) function in MATLAB as described previously (Sengupta et al., 2011). Fitting of correlation data was performed using Curve Fitting Toolbox (cftool) in MATLAB.

Data in Figure 1—figure supplement 1F,G were independently recorded under identical imaging condition on a custom-built 3-camera RAMM frame microscope (ASI, Eugene, OR) using an Olympus 1.4 NA PLAPON 60x OSC objective (Olympus, Tokyo, Japan), and a custom tube lens (LAO-300.0, Melles Griot, Albuquerque, NM), resulting in 100x overall magnification (Grimm et al., 2015; Piatkevich et al., 2014). A 2 mm thick quad-band excitation dichroic (ZT405/488/561/640rpc, Chroma, Cambridge, MA), a 2 mm thick emission dichroic (T560lpxr, Chroma), and a band-pass emission filter (FF01-609/54-25, Semrock, Rochester, NY) filtered the emitted light. Stroboscopic 405 nm excitation of the Stradus 405–100 laser (Vortran, Sacramento, CA) was achieved using a NI-DAQ-USB-6363 acquisition board (National Instruments, Austin, TX), which also controlled the 555 nm laser (CrystaLaser, Reno, NV). Z-stacks through the entire nucleus were generated by stepping through a sample using four 0.6 μm steps using a Piezo scanning stage (P-454.3C7, Physik Instrumente, Auburn, MA). Fluorescence images were recorded with a back-illuminated EMCCD camera (Andor Technology, Ixon Ultra DU-897U, 17 MHz EM amplifier, 300 x gain, center quadrant) at 20 frames/s. Dendra2 was photo-converted by 0.5 ms long excitation pulses of 405 nm (10 W/cm²) every 2000 ms. During all imaging experiments, cells were maintained at 37°C in a humidified 5% CO2 3% O2 and 92% N2 environment supplied by a live-cell incubator (Tokai Hit, Shizuoka-ken, Japan).

We detected individual molecules and measured their 2D position using a maximum intensity projection of the stacks generated at each time point, using a MATLAB software previously described (Lionnet et al., 2011a). We manually generated mask images encompassing the cell nucleus in each movie using ImageJ. The nucleus was subdivided in a square grid (the sides of each square within the grid were set to 500 nm), and the molecule detections were assigned to the corresponding unit cell of the grid based on their position. Grid cells with more than 10 detections over the duration of the movie were automatically sorted. Time traces of cumulated detections per cell were then randomly selected from the set of cells with more than 10 detections and plotted. All analysis steps were performed using MATLAB code.

The localization precision of individual fluorescent molecules was investigated for our live-cell super-resolution microscope using the approach described by Thompson, Larson and Webb (Thompson et al., 2002) and adapted for multi-color PALM (Betzig et al., 2006). In this approach the precision of localization is given by,

where ${\displaystyle s}$ is standard deviation of the PSF, ${\displaystyle a}$ is the size of pixel, ${\displaystyle N}$ is total number of photons of a signal and ${\displaystyle b}$ is number of the back ground photons (Thompson et al., 2002; Betzig et al., 2006; Shroff et al., 2007).

To measure the detection accuracies for Dendra2 and JF646 in this study, we determined the total number of photons of fluorophore and the background noise from the intensity profile of detections, considering the EM-gain, electron amplification level and quantum efficiency of Andor Ultra iXon 897 EMCCD for each wavelength. The standard deviations were obtained by 2D-fitting of the PSF, and the pixel size was 160 nm for imaging with 100X magnification objective lens on the CCD panel of original pixel size of 16µm. The results for dual-color super-resolution are depicted in Figure 2—figure supplement 1D–I.

MEF cells were fixed using paraformaldehyde at 12 min after serum stimulation. These samples were then imaged to exhaustion. Putative beta-actin transcription loci were chosen by selecting the brightest foci in a summed-intensity projection of the cells. Regions of interest (ROIs) were selected by identifying the grouping of polymerase localizations that was closest to the beta-actin locus.

To obtain estimates for the number of molecules within a region of interest, the fluorescence emission of the photo-convertible fluorescent protein Dendra2 was modeled as a four state system (Figure 3—figure supplement 1A). Upon 405-nm irradiation, Dendra2 is switched from the pre-converted, green fluorescent state to the converted, red fluorescent state.

From the red fluorescent state, the molecule can transition to a transient, reversible dark state with rate k_dark = 9.61/s or an irreversibly bleached state with rate k_bleach= 3.0/s. Recovery from the dark state with rate k_rec = 2.33/s leads to blinking of the fluorophore. The average number of blinking cycles is given by the expression, k_dark/k_bleach = 3.2. All rate constants were determined from fixed cell controls under conditions identical to the actual experiments (Figure 3—figure supplement 1B–D and see Appendix 5: Estimation Photo-physical Parameters of Dendra2).

We used two processes to determine the number of molecules within a cluster. First, the number of molecules in each ROI was estimated using an Aggregated Markov Model approach, as described in Rollins et al. (Rollins et al., 2015). For each region, the likelihood of a given trajectory was calculated for varying guesses of the number of molecules, and the number which maximized the likelihood of the trajectory was called the estimate for the number of observed molecules. As can be seen in Figure 3D, the ROIs can be roughly partitioned into two groups on the basis of the cumulative number of localizations. These two groups are tentatively identified as ‘Clustered’ and ‘Un-clustered’. We were able to obtain estimates for the number of molecules inside of the ‘Un-clustered’ ROIs. This number ranged between 1 and 20, consistent with the expected number of elongating polymerases. ‘Clustered’ regions, however, contain a much greater number of molecules. In these cases, the running time for the software was too long for accurate estimates to be obtained for the number of molecules in a cluster. We were, however, able to find a lower bound of approximately 60 molecules.

To obtain estimates for the number of molecules within the ‘Clustered’ regions, we made use of a second approach using single molecule simulations. To simulate fluorescence emission from a cluster of a number of molecules N_sim, the time-course from photo-conversion to irreversible bleaching was calculated for each of the molecule. Subsequently, the continuous time simulation was binned according to the kinetic cycle time of 60 ms. When any of the molecules resided in the red fluorescent on state for more than half of the frame interval, a detection was counted in the respective frame. Note that multiple molecules in the on state at the same time can only lead to a single detection. The cumulant of all detections in a cluster was calculated for comparison with experimental data. Wait times for photo-activation were drawn randomly from a bimodal exponential distribution with rate constants determined by fitting the experimentally observed cumulant with the function,

The number of blinks was drawn from a geometric distribution with an average of 3.2. The dwell times in the visible and transient dark states were drawn from an exponential distribution with times constants of 79.8 ms and 431 ms respectively (Figure 3—figure supplement 1B–D).

To estimate the number of molecules in a cluster, the experimentally observed cumulant was compared to results for 100 simulated clusters each for values of N_sim = 1–200. The mean squared deviation between experimental and simulated cumulant was calculated and averaged over all 100 simulations. The value of N_sim yielding the minimum average deviation is stated as the most likely number of molecules in the respective cluster (Figure 3—figure supplement 1E).

We note that this approach is less precise than Aggregated Markov Model approach. However, it yields similar results for cumulants from the ‘Un-clustered’ regions, but in a fraction of the time. This allowed us to obtain the estimates for clusters that were too large for the aggregated markov model approach.

In order to determine that photo-physical parameters of the Dendra2 molecule, we performed experiments where we transiently transfected U2OS cells with free Dendra2, and then fixed the cells with paraformaldehyde. Free Dendra2 was chosen for the experiment to ensure that the fluorophores would not cluster on small length scales, and the cells were fixed to eliminate any biological dynamics. Single molecules were identified from the pointillist reconstruction by exhaustively choosing regions of interest containing more than one localization approximately within a pixel (160 nm). Localizations within a region of interest were then group into independent events. Groups of localizations larger than 2 that occurred within a fixed region of space and were well separated in time from other localizations were identified as single molecules.

Within a single Dendra2, we could count the number of blinking events as the number of continuous stretches of bright frames to generate the blink number distribution. The average lifetime in the bright state and in the blink state were determined by examining the dwell time distribution of stretches of continuous localizations and stretches of a continuous lack of localizations respectively. From the average number of blinks, and the average lifetimes in the bright and blink states, we could calculate three of the four rate constants in our model, k_dark, k_bleach, and k_rec (Figure 3—figure supplement 1A). In total, we identified 2627 proteins. All data is an aggregate of 13 cells imaged over the course of three separate days (Figure 3—figure supplement 1B–D).

The fourth rate constant, k_on can be measured by fitting the cumulative number of detections in the entire nucleus to an exponential plus a constant background detection rate,

where ${\displaystyle \text{C}\left(\text{t}\right)}$ is the cumulant, ${\displaystyle \text{A}}$ is the estimated number of localization generated by the fluorophore and ${\displaystyle \text{B}}$ is the constant background detection rate, ${\displaystyle 1/\tau }$ is the empirical activation rate. Because the empirical activation rate (~1/150 s^-1; data not shown) is two orders of magnitude slower than the three previously determined rate constants, we expect that k_on dominates the empirical activation rate. Indeed, simulations using our estimated transition rates reveal that the fit time constant of the cumulant is equivalent to the activation time constant, k_on, of the simulation within 2.6% (Data not shown). We therefore identify the empirical rate constant as k_on, and can easily estimate it in live cells for each individual cell, and fixed cell experiments are unnecessary for its determination.

Our measured parameters are in fair agreement with the results of S-.H. Lee et al. (Lee et al., 2012) considering the differences in laser illumination intensities and the different chemical environment of fixed cell nuclei versus in vitro.

After serum stimulation, cells typically displayed a unique transcription burst lasting 15–30 min. We tested whether a model where short Pol II clustering events (seconds), which duration is modulated over time scales of minutes, could explain the nascent transcription temporal profiles we measured in our experiments. The main model assumption was that productive beta-actin transcription initiation could only occur during clustering events. Clustering events occured stochastically as a zeroth order reaction with rate ${\displaystyle f_{\text{cluster}}}$ (${\displaystyle f_{\text{cluster}}}$ remains constant over time to match our experimental observations, Figure 5—figure supplement 1B). We assumed that mRNA initiation events could occur at random during each clustering event, with a constant probability per unit time, ${\displaystyle f_{\text{mRNA init}}}$. The duration of each cluster was assumed to be exponentially distributed with a time-dependent average duration ${\displaystyle ⟨\tau \left(t\right)⟩}$. From the moment the mRNA initiated, the elongation process was modeled as a deterministic process, with a constant elongation rate, ${\displaystyle k_{\text{elong}}}$ followed by a termination step with fixed duration, ${\displaystyle t_{\text{term}}}$ (Larson et al., 2011; Lionnet et al., 2011b). The fluorescence profile of the nascent mRNA as a function of time after initiation, ${\displaystyle MS2\left(t\right)}$ was modeled the following way: zero before Pol II reaches the MBS cassette; a linear ramp through the cassette as more loops are transcribed; a plateau for the remainder of elongation until termination (defined as the mRNA leaving the transcription site). Based on the model assumptions, one can compute the average nascent chain fluorescence as a function of time ${\displaystyle ⟨N\left(t\right)⟩}$ as follows: the average nascent chain fluorescence at the gene locus is the result of the convolution of the fluorescence timetrace of one nascent mRNA ${\displaystyle MS2\left(t\right)}$ by the frequency of productive initiation events ${\displaystyle ⟨P_{prodinititiation}\left(t\right)⟩}$:

where

with the following notations (all lengths in nucleotides):

${\displaystyle L_{\text{upstream}}}$ = 3425 nt (length separating the transcription start site from the start of the MBS cassette)

${\displaystyle L_{\text{array}}}$ = 1256 nt (length of the MBS cassette)

${\displaystyle L_{\text{downstream}}}$ = 309 nt (length separating the end of the MBS cassette from the polyadenylation site)

The frequency of productive initiation events ${\displaystyle ⟨P_{prodinititiation}\left(t\right)⟩}$ is the product of the probability to find a cluster at the gene ${\displaystyle f_{\text{cluster}}⟨\tau \left(t\right)⟩}$ (following from zeroth order kinetics) by the initiation frequency from a cluster (${\displaystyle f_{\text{mRNA init}}}$):

In Equation 4, the time profile ${\displaystyle \tau \left(t\right)}$ is measured (Figure 5A); the only unknown variable in ${\displaystyle MS2\left(t\right)}$ is the elongation rate ${\displaystyle k_{\text{elong}}}$ (we set a the termination time to 1 min in order to account for 3`end processing; this ~1 min delay is consistently observed across a wide variety of biological systems (Larson et al., 2011; Boireau et al., 2007; Zenklusen et al., 2008; Brody et al., 2011)); also unknown are ${\displaystyle f_{\text{mRNA init}}}$ and ${\displaystyle f_{\text{cluster}}}$ (although we measure an effective value for ${\displaystyle f_{\text{cluster}}}$, the sparse nature of the tcPALM observation technique means that we most likely miss some clusters, i.e. underestimate ${\displaystyle f_{\text{cluster}}}$).

As ${\displaystyle f_{\text{cluster}}}$ and ${\displaystyle f_{\text{mRNA init}}}$ only appear as a product in our equation, the fitting is underdetermined: given a best fit value for the product ${\displaystyle F}$, there is an infinite number of (${\displaystyle f_{\text{cluster}}{f}_{\text{mRNA init}}}$) pairs that satisfy ${\displaystyle F=f_{\text{cluster}}{f}_{\text{mRNA init}}}$. This means that models with identical ${\displaystyle F}$ values but different pairs of parameters (${\displaystyle f_{\text{cluster}};f_{\text{mRNA init}}}$) cannot be discriminated. The physical interpretation of this indetermination is the following: models with infrequent clusters (low ${\displaystyle f_{\text{cluster}}}$) can generate the experimentally observed average nascent transcription level provided they rapidly fire mRNAs within each cluster (high ${\displaystyle f_{\text{mRNA init}}}$); this would correspond to infrequent clusters producing each a large number of mRNAs. Conversely, the same average nascent transcription profile can be obtained with more frequent clusters, each producing a modest number of productive initiation events (high ${\displaystyle f_{\text{cluster}}}$, low ${\displaystyle f_{\text{mRNA init}}}$).

Models with the same ${\displaystyle F}$ value but different (${\displaystyle f_{\text{cluster}};f_{\text{mRNA init}}}$) pairs might yield identical average nascent transcription profiles but they differ in the variability between nascent transcription trajectories of single alleles. We used the fact that our experiments have single allele resolution to solve the indetermination stemming from fitting only the average transcription level (Equation 4). We measured the variance in the number of nascent chains as a function of time. The theoretical variance of the nascent chain fluorescence as a function of time ${\displaystyle \sigma \left(t\right)}$ can be calculated as previously:

where

Fits were performed as follows:

1) We approximated the experimental time trace ${\displaystyle \tau \left(t\right)}$ as a Gaussian profile offset by a baseline using a non-linear least squares fit. This step provides a simple formula for ${\displaystyle \tau \left(t\right)}$ that accurately reflects the data while simplifying subsequent calculations.

2) We computed the integral in Equation 4 numerically using the global adaptive quadrature approximation (Matlab). We wrote custom Matlab software (code available on GitHub at https://github.com/timotheelionnet/Pol-II-Stochastic-Dynamics) to fit the numerical integral ${\displaystyle ⟨N\left(t\right)⟩}$ to our experimental data for the nascent chains (chi-squared minimization using the Quasi-Newton method). The floating parameters were the elongation rate ${\displaystyle k_{\text{elong}}}$ (implicit in the profile ${\displaystyle MS2\left(t\right)}$) and the product ${\displaystyle F=f_{\text{cluster}}{f}_{\text{mRNA init}}}$.

3) Using the values of ${\displaystyle k_{\text{elong}}}$ and ${\displaystyle F}$ obtained from the fit in 2), we then fitted our measurements for the variability in the number of nascent chains as a function of time to the predicted formula for ${\displaystyle \sigma \left(t\right)}$. Once again, we used a global adaptive quadrature approximation for the integral and fitted the numerical integral ${\displaystyle \sigma \left(t\right)}$ to our experimental data using chi-squared minimization (Quasi-Newton method). The only floating parameter in this fit was ${\displaystyle f_{\text{cluster}}}$.

The values extracted from the fit are the following: ${\displaystyle f_{\text{cluster}}}$= 1.37 min^-1; ${\displaystyle k_{\text{elong}}}$= 3.1 kbp/min; ${\displaystyle f_{\text{mRNA init}}}$= 0.43 s^-1. The value of ${\displaystyle f_{\text{cluster}}}$ is higher than the observed value; this is not surprising as our method tcPALM only allows observing a fraction of all Pol II molecules at each given time, and therefore is subject to missing events (see Figure 5—figure supplement 2).

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Author details

1. Won-Ki Cho

   Department of Physics, Massachusetts Institute of Technology, Cambridge, United States

   Contribution

   W-KC, Acquired and analyzed all data in the main manuscript, Conceived the time dependent mRNA output and cluster lifetime experiments, Conceived the drug experiments, Drafting or revising the article, Contributed unpublished essential data or reagents

   Competing interests

   The author declares that no competing interests exist.

   "This ORCID iD identifies the author of this article:" 0000-0001-9336-0686

2. Namrata Jayanth

   Department of Physics, Massachusetts Institute of Technology, Cambridge, United States

   Contribution

   NJ, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article, Contributed unpublished essential data or reagents

   Competing interests

   The author declares that no competing interests exist.

3. Brian P English

   Janelia Research Campus, Howard Hughes Medical Institute, Ashburn, United States

   Contribution

   BPE, Conceived the project, Conceived and acquired H2B control data, Analysis and interpretation of data, Drafting or revising the article, Contributed unpublished essential data or reagents

   Competing interests

   The author declares that no competing interests exist.

4. Takuma Inoue

   Department of Physics, Massachusetts Institute of Technology, Cambridge, United States

   Contribution

   TI, Co-built the original microscopes used for imaging, Acquisition of data, Contributed unpublished essential data or reagents

   Competing interests

   The author declares that no competing interests exist.

5. J Owen Andrews

   Department of Physics, Massachusetts Institute of Technology, Cambridge, United States

   Contribution

   JOA, Developed the analyses software used, Co-developed the molecular counting analysis, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article, Contributed unpublished essential data or reagents

   Competing interests

   The author declares that no competing interests exist.

6. William Conway

   Department of Physics, Massachusetts Institute of Technology, Cambridge, United States

   Contribution

   WC, Acquisition of data, Analysis and interpretation of data, Contributed unpublished essential data or reagents

   Competing interests

   The author declares that no competing interests exist.

7. Jonathan B Grimm

   Janelia Research Campus, Howard Hughes Medical Institute, Ashburn, United States

   Contribution

   JBG, Developed the JF dyes, Contributed unpublished essential data or reagents

   Competing interests

   The author declares that no competing interests exist.

8. Jan-Hendrik Spille

   Department of Physics, Massachusetts Institute of Technology, Cambridge, United States

   Contribution

   J-HS, Co-developed the molecular counting analyses, Analysis and interpretation of data, Drafting or revising the article

   Competing interests

   The author declares that no competing interests exist.

9. Luke D Lavis

   Janelia Research Campus, Howard Hughes Medical Institute, Ashburn, United States

   Contribution

   LDL, Developed the JF dyes, Contributed unpublished essential data or reagents

   Competing interests

   The author declares that no competing interests exist.

10. Timothée Lionnet

    Janelia Research Campus, Howard Hughes Medical Institute, Ashburn, United States

    Contribution

    TL, Conceived the project, Supervised all aspects of the cell engineering and the theoretical modeling, Analysis and interpretation of data, Drafting or revising the article

    For correspondence

    lionnett@janelia.hhmi.org

    Competing interests

    The author declares that no competing interests exist.

11. Ibrahim I Cisse

    Department of Physics, Massachusetts Institute of Technology, Cambridge, United States

    Contribution

    IIC, Supervised all aspects of the project, Conceived the project, Analysis and interpretation of data, Drafting or revising the article

    For correspondence

    icisse@mit.edu

    Competing interests

    The author declares that no competing interests exist.

    "This ORCID iD identifies the author of this article:" 0000-0002-8764-1809

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