Dynamic Analysis of Stochastic Transcription Cycles

Cycling of gene expression in individual cells is controlled by dynamic chromatin remodeling.


Introduction
Gene expression in living cells is dynamic and unstable, and fluctuations in transcription may be subject to stochastic regulation of processes including transcription factor and polymerase recruitment, and chromatin remodeling [1][2][3][4][5]. Cell-to-cell variation in the amount of protein a gene encodes is generally thought to arise from the typically small number of molecules (e.g. gene copies), which are involved in gene expression. The factors leading to this variation have been defined by studies in prokaryotes and lower eukaryotes as either extrinsic (deriving from variations in global, cellular factors, such as varying amounts of transcriptional activators) or intrinsic (i.e. inherently random molecular events, such as the transcription of mRNA or translation of proteins) [4,6,7]. Previous studies addressing the characterization of intrinsic and extrinsic noise have mainly focused on bacteria and yeast models, often using pairs of reporter genes to assess heterogeneity in protein levels as an indirect readout of expression level at a fixed time-point [4,6]. One study has reported a similar fixed time-point analysis in single human cells using dual fluorescent protein read-out [7]. Short-term transcriptional pulses (bursts) have been observed in both prokaryotes [2,3,8] and eukaryotes [5,6,9,10]. Chromatin remodeling has been suggested as one possible intrinsic source of variation that may lead to the intense stochastic transcriptional bursts that have been shown to occur in eukaryotic gene expression [5,6,10].
In mammalian cells, the variation in transcription between cells has been most quantitatively studied by using fluorescent in situ hybridization analysis [10][11][12]. However, these studies do not provide long-term time-course analysis in single cells. One approach to provide real-time semi-quantitative analysis of transcription is the imaging of reporter gene expression-for example, using firefly luciferase [13][14][15]. Such studies support the view that gene expression is very dynamic over long time periods and occurs in transcriptional bursts of varying duration that are not coordinated between different cells. To date, the key aim of understanding realtime dynamics by directly quantifying transcription rates of multiple genes over time in single cells has not been achieved.
One gene that displays dynamic transcription and marked heterogeneity between cells is prolactin (PRL) [14,[16][17][18]. Prolactin is a hormone secreted by pituitary lactotrophic cells that is important for reproductive function, lactation, and control of fertility. Pituitary tumors secreting prolactin are common in man, and the hormonal regulation of prolactin secretion and gene expression has therefore been extensively studied [19][20][21][22]. In the present study, we used single cell reporter gene imaging to explore the pulsatile and cyclical nature of the transcription of PRL. Using measurements of mRNA and protein stability, we were able to quantify transcription rates from separately integrated reporter genes within the same cells and compare the kinetics of transcription over time. Analysis of the response to acute signals and the manipulation of histone acetylation suggested that dynamic chromatin changes control cycle timing.

Cycles in Prolactin Transcription in Single Pituitary Cells
Human PRL (hPRL) promoter-directed transcription was heterogeneous and dynamic in rat pituitary GH3 cells using luciferase reporter genes. Transcriptional pulses were observed in GH3 cell lines stably expressing a 5 kb hPRL-Luciferase (hPRL-Luc) reporter gene [14] or a larger 160 kb hPRL genomic locus reporter, a hPRL-Luc Bacterial Artificial Chromosome (BAC, [16]; Figure 1A, B, and C; Figure S1). Similar patterns were observed in primary cultures of pituitary cells (taken from transgenic rats [16]), where the hPRL-Luc BAC was integrated either into an autosomal ( Figure 1D and E) or an X-chromosome locus ( Figure 1F). In all four model systems distinct transcriptional cycles were discerned (e.g. Figure 1G) showing that these responses were not affected by promoter length or integration site.

Uncorrelated Transcription Cycles from Two Identical Promoters in a Single Cell
Pulses in gene expression in individual cells could arise from the transcription process itself or from signaling events reflecting the cellular environment. To discriminate between these possibilities, a dual-transgene cell line was constructed expressing separate luciferase and d2EGFP (destabilized enhanced Green Fluorescent Protein) reporter genes under the control of identical 5 kb hPRL promoters, integrated as independent gene copies (GH3-DP1 cell line; Figure 2A; one or at most two copies; Figure S2, Figure S3). The luciferase and d2EGFP reporter genes were selected due to their reported short protein half-lives. The use of these very different reporter genes (which have different chemistries for formation of the signal) was considered an advantage because we could measure them entirely independently.
Signal was detected from both reporter genes, but the intensity of the expression of the reporter genes within single cells failed to correlate when measured at a single time-point ( Figure 2A, Figure  S4). To measure the profiles of expression from each reporter gene, fluorescence and luminescence intensities were captured from the same field of single cells over several hours ( Figure S5). Due to the different mRNA and protein half-lives of these two reporter genes ( Figure S2, Figure S10, Table S1, Text S1 Section 3) direct comparison between the timing of expression could not be made. Therefore, in order to make quantitative comparisons between the timing of expression of these two different reporter genes within the same single cell, a mathematical model was developed ( Figure 2B, [23]) which used statistical analysis to reconstruct estimates of the time-dependent transcription rate from the reporter imaging data (Figure S11, Figure S14, Text S1 Section 3).
Autocorrelation analysis was performed on the reconstructed transcription rates from the hPRL-Luc and the hPRL-d2EGFP reporter genes in the dual-reporter GH3-DP1 cell line. This showed that transcription cycles were occurring at each gene with a dominant period of 11.363.3 h ( Figure 3A and Figure S9). This value was measured from the dual reporter experiments and possibly provided an underestimate due to the limited timeframe of the experiments. Cycles of hPRL transcription were also observed from both luciferase and d2EGFP reporter genes in individual clonal pituitary cells from dual BAC-reporter transgenic rats grown in primary culture (see Materials and Methods, [16]), with a slightly longer period (15.264.8 h; Figures 3B, S1, and S8).
The ability to obtain quantitative data for the time-dependent transcription rates from the two reporter genes enabled us to ask whether the transcription cycles observed at individual loci were temporally coordinated or were out-of-phase within a single cell ( Figure 4A, Figure S6). We analyzed the rank correlation coefficient C(T) between the transcription time-series for the two reporter genes over a time window of length T for increasing values of T (see Text S1 Section 3.3). In unstimulated conditions there was no significant correlation (p,.05) in the timing of

Author Summary
Timing of biological processes such as gene transcription is crucial to ensure that cells and tissues respond appropriately to their environment. Until recently it was assumed that most cells in a tissue responded in a similar way, and that changes in cellular activity were relatively stable. However, studies of messenger RNA and protein levels in single cells have shown the presence of considerable heterogeneity. This suggested that transcription in single cells may be highly dynamic over time. Using a combined experimental and theoretical approach, with time-lapse imaging of reporter gene expression over 25 h periods, we measured the rate of prolactin gene transcription in single pituitary cells and detected clear cycles of transcriptional activity. Mathematical analysis, using a binary model that assumed transcription was on or off, showed that these cycles were characterized by a minimum refractory period that involved chromatin remodeling. The timing of transcription from two different reporter constructs driven by identical promoters in the same cell was out-of-phase, suggesting that the pulses of gene expression are due to processes intrinsic to expression of a particular gene and not to environmental effects. We further show that the pulses of transcription are independent chromatin cycles at each gene locus. Therefore, heterogeneous patterns of gene expression may facilitate flexible transcriptional responses in cells within intact tissue, while maintaining a well-regulated average level of gene expression in the resting state.
transcription cycles between the dual reporters in the same single cell ( Figure 4A and B). In order to show that this was not an artifact of the genomic integration site we investigated independently derived cell lines: no significant correlation between the two promoters was detected in two different clones of the stably transfected cell lines or in dual-reporter transgenic primary cells ( Figure 4B, Figure S12). These data demonstrate that cycles of hPRL-promoter activity did not depend on promoter length or on transgene integration site. Most importantly, the lack of correla-tion between the timing of hPRL transcription from promoters within the same cell in time-lapse imaging experiments showed that the expression cycles from distinct loci in a single cell were not synchronized or temporally coordinated. The fact that the cycles at individual loci in unstimulated single cells were uncorrelated (and that this phenomenon occurred in both cell lines and postmitotic primary pituitary cells) suggested that the pulses in PRL gene expression were independent of cell cycle stage. This is in agreement with our previous study that suggested that variation in hPRL-luciferase reporter expression was independent of cell cycle in the GH3 cells (which have a cell cycle timing of approximately 40 h) [18]. Overall, these data therefore suggest that the transcriptional pulses were not a reflection of the cellular status, environment, or autocrine cell signaling but rather were due to an intrinsic property of the transcription process itself.

Evidence of a Refractory Phase between Transcription Cycles
In order to further understand and quantify the dynamics of transcriptional switching between ''on-'' and ''off-''phases, we developed a stochastic binary switch model of transcriptional timing and used statistical algorithms to assess the distribution of times of transcriptional switching between the on and off states ( Figure 5A, Text S1 Section 3). Transcription of the mRNA and translation and activation of the corresponding protein were modeled using a stochastic differential equation with binary on-off transcription and were fitted to time-series imaging data using a Markov Chain Monte Carlo (MCMC) algorithm ( Figure 5A). This produced relatively tight distributions on the levels and the timing of transcription in the on and off periods (Text S1 Section 3.4, example in Figures S15-S17). This model was used to estimate the average and distribution of the times of luciferase transcriptional switching in the GH3-DP1 stable cell line and gave a dominant overall cycle period of 11.063.3 h ( Figure 5B), which was in close agreement with the independent autocorrelation analysis described above (11.3 h; Figure 3B). Furthermore, we estimated that there was an average on-phase duration of 4.061 h (which was slightly longer than the timing previously described for transcriptional bursts in mammalian cells [24]). The average off-phase duration was 6.562 h per transcription cycle. No relationship was detected between the duration of the transcription on-phase and the preceding or subsequent off-phase ( Figure 5C and D).
There was strong evidence for a refractory period of approximately 3 h, in which cells cannot respond to a stimulus with a further transcriptional pulse. For each cell studied, the mean length of the off periods never fell below 3 h ( Figure 5C and D). Thus, two distinct types of mathematical analyses indicated a similar duration for transcriptional cycles, and the stochastic binary switch model further suggested that the transcriptional on-and off-phases were independent, with each having defined average and minimum durations that may account for the kinetics of these cycles.

The Role of Signaling and Chromatin in the Transcriptional Cycles
The regulation of the transcriptional cycles from the hPRL promoter was then investigated by exposing GH3-DP1 cells to (1) combined forskolin and BayK-8644 (FBK) to activate both cAMP and Ca 2+ signaling ( Figure S7, [25]), (2) Trichostatin A (TSA, a histone deacetylase inhibitor), or (3) both treatments combined (TSA+FBK) ( Table S2). All three experimental treatments resulted in an initial synchronization between the transcription profiles of the  two independent hPRL promoter-reporter transgenes: correlation between the profiles of the dual reporters was initially very high (close to 1), both between the two transgenes within individual cells ( Figure 6) and between different cells ( Figure S13). This period of high correlation lasted longer following TSA treatment ( Figure 6C), when compared to the very transient synchronizing effect of FBK ( Figure 6B), and was most prolonged with combined TSA+FBK exposure ( Figure 6D and Figure S13). Chromatin immunoprecipitation assays showed an increase in acetylated histone H3 DNA binding at the hPRL promoter following all treatments, with the highest level induced by TSA ( Figure 7).
Analysis of gene expression kinetics from the hPRL-Luc reporter gene in GH3-DP1 cells showed that the transcriptional cycles persisted following FBK treatment. However, they were only seen in less than 20% of cells treated with TSA ( Figure 8A and B). Analysis with the binary switch model showed that when the cells were treated with FBK, the median time to activation was longer and more variable than with TSA or TSA+FBK ( Figure 8C). This supports the hypothesis of a refractory period of transcription inactivation in which chromatin remodeling may play an important role. Treatment with TSA increased the duration of the on-phase and the initial rate of transcription ( Figure 8D and E). Combined TSA+FBK treatment increased the transcription rate during the on-phase following activation ( Figure 8E), resulting in a pronounced increase in maximum reporter gene expression ( Figure 8A). The response of cells to treatments that included TSA was more rapid and coordinated, suggesting that histone acetylation has a key role in the coordination of the temporal kinetics of transcription. Transcription of the hPRL gene might therefore require a long period of chromatin remodeling that is the source of the observed refractory phase.

Cycles of Prolactin Transcription Are Enhanced by a Non-Random Refractory Period in the Off-Phase
The rate at which mRNA is transcribed can be affected by different molecular mechanisms, including binding and dissociation of transcription factors, spatial reorganization, and/or chromatin remodeling. Previous studies [5,10,26] have considered The mean residence times for the active and inactive states are t active = 1/k 2 and t inactive = 1/k + and switch on-and off-times are drawn from an exponential distribution with means t active and t inactive . For the on-times our results fit this hypothesis and the estimated distribution of on-times is exponential ( Figure 9A). Such a system would be memoryless in that the time already spent waiting in that state would not affect how much longer one would have to wait until the switch (Text S1 Section 3.5). The distribution of off-times in our data strongly contradicted this and was not distributed exponentially. This is shown in Figure 9B in which the exponential distribution (black line) is a poor fit of the data. We found that the system had a definite memory, where the length of time already spent in the inactive state affected the length of time remaining in that state ( Figure 9C). Thus the dynamics of these transcription cycles are not compatible with the mathematical models previously derived from analysis of single cell RNA counting [10].
An MCMC algorithm was applied which gave a distribution of estimates for the off-phase durations for single cells. When these estimates were amalgamated into a population distribution, the most likely off duration was at 3 h ( Figure 9B), which is consistent with the individual estimates in Figure 5. Thus, the most likely explanation of the memory effect was the existence of a refractory period of approximately 3 h ( Figure 5C and D). If this refractory period is enforced, by removing any chance of an off duration of less than 3 h, then the excess off durations were distributed approximately exponentially ( Figure 9E). This refractory period means that the system still has a memory ( Figure 9F). Removing the refractory period ( Figure 9H) meant that the system became memoryless ( Figure 9I).
One effect of this memory or refractory period is to cause more cyclicity than would be seen in a telegraph process. In a system with a 3 h refractory period where the excess off-time is exponentially distributed ( Figure 9E), a higher proportion of the off-times would be just over 3 h and the system would appear more cyclic. To quantify the regularity of the transcription cycles, we simulated 1,000 cells with on and off durations drawn from the corresponding distributions. We then performed autocorrelation analysis on this simulated data set and the variance in the timing of the first peak was taken to be our measure of cyclicity. The variance in first peak timing was higher when there was no refractory period ( Figure 9D and J) than when a refractory period was enforced ( Figure 9G). This analysis revealed that the presence of a defined refractory phase increases the regularity of the transcription cycles.

Discussion
Physiologically important hormones such as PRL may be subject to both acute short-term regulation and long-term seasonal control. This could be achieved at the individual cell level by graded gene expression with feedback control of PRL expression. Such a model would suggest that each cell would express similar levels of PRL. Alternatively individual cells could dynamically switch between on-and off-phases producing a stable population average level of prolactin expression across the whole tissue. Studies of PRL promoter activity in intact pituitary tissue showed the whole tissue response was synchronized, although adjacent cells were not coordinated [27].
We have previously shown that expression from the PRL promoter is heterogeneous over time in individual cells from cell lines [14] and more recently in intact pituitary tissue [27]. The latter study suggested that isolated cells show greater heterogeneity than cells in tissue but that tissue-level cellular heterogeneity is still important. In a different study we recently described data that suggested that cellular heterogeneity may be genetically encoded by the timing of negative feedback loops in the NF-kB signaling system and that this may lead to out-of-phase oscillations in NF-kB signaling between cells [28]. This study raised the hypothesis that cellular heterogeneity may in fact be advantageous, leading to more robust tissue-level responses. (Studies in other systems are in support of the idea that cellular variability is advantageous; e.g. [29].) The present study quantifies the level of heterogeneity in the dynamics of PRL gene expression in single cells. This heterogeneity may ensure stability in gene expression at the tissue level, while ensuring the readiness of the tissue as a whole to respond rapidly to signals.
These data suggest that the overall level of hPRL transcription in pituitary tissue may be determined by three variables: (1) the frequency of transcriptional bursts, (2) the duration of the on-phase, and (3) the rate of transcription during the on-phase. Our studies suggest that within a population of cells there is a continuous transition from an activated ''on'' state to a basal ''off'' or ''low'' state, with an overall cycle of around 11 h. This cycle is longer than previously described transcriptional cycles/pulses [10][11][12], with a different structure due to the presence of a defined refractory period of transcriptional inactivation. Because of the much longer timescales involved, the source of the stochasticity would not be expected to derive directly from that due to random molecular processes involving small molecule numbers. However, within this cycle, the average transcriptional on-phase is ,4 h, which is closer to previously defined transcriptional bursts and cycles [24]. The majority of the overall cycle time described here is therefore dominated by the off-phase. This could be due to a repressive chromatin state or alternatively could be regulated by chromosome topology with the timing dependent on the movement of the genes into and out of transcription factories [30][31][32].
Although the transcription cycle maintains relatively defined dynamics, the timing of transcription cycles from two independent promoters within a cell were heterogeneous, indicative of a system where intrinsic noise generated by local chromatin dynamics dominates extrinsic noise. Strong correlation between promoters could only be achieved following disruption of chromatin, suggesting that the cycles of hPRL transcription might involve epigenetic cycles of histone acetylation and deacetylation ( Figure 10). Thus, an independent chromatin-regulated cycle of gene activity may occur at each locus. Cycles in the binding of transcription factors and polymerase at certain genes in the nucleus have been  observed following oestrogen stimulation [24,33,34]. In that system, a refractory period also seems to occur [24,34], as well as cycles of epigenetic chromatin modification [33].
The current study illustrates the importance of new integrated experimental and mathematical approaches for dynamic single cell analyses. Providing high-frequency time-lapse imaging data of the same cells over long time periods enabled the identification of dynamic transcription processes, phenomena which are invisible to the single cell RNA counting snapshots used for previous analyses of transcriptional bursting [35,36]. Biologically meaningful model parameters can be directly measured from the imaging data without requiring prior assumptions about the nature of the timings inherent in the system. As such, models fitted to these data accurately represent the underlying processes that lead to the timecourse data.
The data described in this study and by others [37] suggest that transcription cycles might emerge de novo from the intrinsic kinetics of the processes of transcription initiation, elongation, and termination. In our study we find that a transcriptional refractory period can have a dominant effect that leads to increased regularity in the timing of transcriptional cycles. This is in marked contrast with other cellular oscillatory systems such as NF-kB [38,39], p53 [40], Erk2 [41], and the circadian clock [42] where negative feedback loops are believed to lead to the oscillatory dynamics with varying frequencies [43]. In particular in the NF-kB system, where a transcriptional delay (refractory period) of 45 min in IkBe activation following TNFa stimulation leads to cell-to-cell heterogeneity through the precise timing of this feedback loop [38]. This transcriptional delay is precisely timed to maximize the effect of IkBe transcriptional noise on ensuring out-of-phase oscillations [28].
A key question is whether the signals that activate hPRL in vivo are themselves graded or pulsatile. hPRL is itself under the control of NF-kB [44], which responds dynamically to pulsatile cytokine stimulation [38]. Recently, glucocorticoid receptor, which also regulates hPRL expression [44], has also been shown to cycle in response to pulsatile stimulation [45]. Although the secreted hormone PRL is stored in secretory granules and displays both pulsatile and circadian patterns, is it not yet clear how transcription relates to secretory events in individual cells.
This system may be a new paradigm for understanding gene expression dynamics in vivo and may be important for understanding natural cell-to-cell variation in protein levels [46,47]. We have previously shown that gene promoter activity in lactotroph cells within pituitary tissue is non-uniform, with varying expression levels from adjacent cells [27]. However, these stochastic patterns together provide tissue-wide long-term coordinated behavior. If we include the new information gained in this present article we can start to build up a picture of a mosaic tissue structure, where, at any one time, a subset of cells are expressing PRL, a subset are in an inactive and refractory state, and a further subset are in an activatable state, ready to respond to a stimulus. A transient hormonal stimulus to the tissue would recruit this last subset of cells immediately, whereas sustained stimulus would progressively recruit additional cells exiting the refractory phase, resulting in a more sustained increase in PRL expression. If these stochastic and cyclical patterns of gene expression occur normally in intact tissue, such a mechanism would facilitate highly flexible transcriptional responses, allowing tissues to mount either acute or chronic responses to environmental cues, while maintaining a controlled average level of gene expression in the resting state. Figure 9. Non-random timing of off-phases increases the cyclicity of transcriptional cycles. Histograms showing the distribution of (A) on-times, (B) off-times, (E) off-times greater than 3 h with the refractory period, and (H) off-times greater than 3 h without the refractory period, estimated from the Markov Chain Monte Carlo algorithm (Text S1 Section 3.4). The superimposed black lines show the fit of an exponential distribution with the same mean value as the data. (C, F, and I) The off-phases in the system are not memoryless. The probability of having to wait for t hours in the off state given that the off-time has already lasted for s hours is plotted for a range of values of t for the distributions in (B, E, and H), respectively. The dashed lines represent the exponential probabilities, and the solid lines are the sample probability estimates. The uppermost lines are calculated when t = 0, the lines beneath that are calculated for t = 0.5, and so on in increments of 0.5. In a memoryless system such as that described by the telegraph process this is independent of s (hence s is constant for a given value of t), but for our system this probability decreases significantly with s during the refractory period (F). The decrease of this probability for higher values of s is due to the finite length of our time-series. (D, G, and J) Autocorrelation functions for a number of mRNA time-series simulated using on and off durations selected at random from the distributions above (B, E, and H, respectively). The variance of the time of the first peak (which estimates period) is given in each plot. In (E) the refractory period is indicated by RF. doi:10.1371/journal.pbio.1000607.g009

Materials
All animals were handled in strict accordance with U.K. Home Office License regulations and subject to local ethical committee review.

Production of Stable Cell Lines and Cell Culture
The GH3-DP stable cell lines were generated by incorporating a 5 kb hPRL-d2EGFP reporter gene into the previously described GH3/hPRL-Luc cell line [14]. This was co-transfected with a hygromycin-selectable plasmid to enable antibiotic clonal selec-tion. Generation of stable BAC-transfected rat pituitary GH3 cells containing the 160 kb hPRL-Luc gene was described previously [16]. GH3-DP1 cells, GH3-BAC cells, and collagenase type I dispersed primary pituitary cells were cultured in DMEM containing 10% FCS and maintained at 37uC 5% CO 2 .

Generation of Dual Reporter Transgenic Primary Rat Pituitary Cells
Generation of BAC-transgenic rats expressing luciferase and d2EGFP under the control of identical hPRL 160 kb genomic fragments was described previously [16]. Transgenic line 37 was a luciferase-BAC transgenic rat line which was found to have two single reporter insertion sites. Further breeding of this line was undertaken to create two separate transgenic lines each with single integration sites. Line 37A had a single autosomal integration site, and line 37B an X-chromosomal integration site. (These lines were the source of the pituitary cells used in Figure 1.) Independently, a destabilized EGFP reporter transgenic rat line was constructed, termed line 455, which also had a single insertion site. The copy number of the luciferase-BAC transgene in line 37A was measured as #2 and that of the d2EGFP line 455 was #5. In order to generate the dual reporter rat cell line (previously referred to as PRL-Luc/d2eGFP in [16]), line 37A was crossed with line 455.

Luminescence Imaging
GH3-DP1 cells were seeded in 35 mm glass coverslip-based dishes (IWAKI, Japan) 20 h prior to imaging. Luciferin (1 mM) was added at least 10 h before the start of the experiment, and the cells were transferred to the stage of a Zeiss Axiovert 200 equipped with an XL incubator (maintained at 37uC, 5% CO2, in humid conditions, carefully monitored to ensure equivalent conditions to a standard cell incubator) maintained within a dark room. Luminescence images were obtained using a Fluar 620, 0.75 NA (Zeiss) air objective and captured using a photon-counting charge coupled device camera (Orca II ER, Hamamatsu Photonics, U.K.). Bright field images were taken before and after luminescence imaging to allow localization of cells. Sequential images, integrated over 30 min, were taken using 4 by 4 binning and acquired using Kinetic Imaging software AQM6 (Andor, Belfast, U.K.). In the relevant experiments, 5 mM forskolin and 0.5 mM BayK-8644 (FBK), 30 ng/ml TSA, or both stimuli were added directly to the dish at the indicated times.

Fluorescence Imaging
Cells were prepared and imaged using the conditions and microscope described above. Excitation of d2EGFP was performed using an argon ion laser at 488 nm. Emitted light was captured through a 505-550 nm bandpass filter from a 545 nm dichroic mirror. Data were captured and analyzed using LSM510 software with consecutive autofocus.

Alternate Longitudinal Imaging of Fluorescence and Luminescence
Cells were prepared and visualized using confocal microscopy as described above. A single field of cells was selected and five sequential fluorescence images were captured using autofocus. After a 10 min delay, the microscope and surrounding lightemitting devices were turned off or covered and a single luminescence image was captured using a cooled CCD camera (30 min integration). The equipment was then restarted (taking 5 min), and after a 10 min delay (to ensure laser stability), fluorescence images were taken. This hourly cycle was repeated for up to 21 h.

ChIP Assays and RT-PCR
GH3/hPRL-luc (D44) cells (3610 6 ) were plated in 10 cm 2 dishes and left for 40 h. Dishes were treated for 2 h (unstimulated, FBK, TSA, TSA+FBK) and then ChIP assays were performed as described previously [38] based on the protocol by Upstate Biotechnology.
Immunoprecipitation was carried out using 5 mg of either Anti-Acetylated H3 or Anti-IgG antibodies (Upstate Biotechnology). DNA was extracted and amplified by PCR as described previously [38]. The following primer sequences were used: hPRL Promoter1 left GCAATCTTGAGGAAGAAACTTGA, right AGGCAT-TCGTTTCCCTTTTC amplifying 347 bp of DNA. PCR products were resolved using agarose gel electrophoresis and were analyzed by AQM Advance 6.0 software (Kinetic Imaging, U.K.).

Analysis of Imaging Data
Analysis was carried out using Kinetic Imaging AQM6 software (Andor). Regions of interest were drawn around each single cell, and mean intensity data were collected. Data were collected from every single cell within the field. The average instrument dark count (corrected for the number of pixels being used) was subtracted from the luminescence signal. In dual reporter experiments, cells dividing within the experiment were eliminated from the analysis. For single reporter experiments, analysis ceased at the point of cell division. For the GH3 cell line, the cell cycle time is approximately 40 h [14,18].

Inference of Transcription Models
We use the following ordinary differential equations model for the reconstruction of transcription profiles from protein data (see also [23], Text S1 Section 3.2).
where M and P denote concentration of reporter mRNA and protein, respectively. The first equation describes the dynamics of mRNA molecules with transcription function t(t) and degradation rate d M . Protein is synthesized at a rate proportional to the abundance of mRNA and is degraded at rate d P . The various parameters will be different for the d2EGFP and Luc reporters. The transcription profile can be reconstructed via where the unobserved mRNA profile is expressed as a function of the observed solution path of P(t), i.e. aM(t) = dP/dt+d P P(t). Since M is not observed, prior knowledge of the rates d M and d P is necessary for the identification of the transcription profiles. We estimated these from two separate experiments where translation of reporter protein was inhibited by adding cycloheximide and transcription was inhibited by adding Actinomycin D (see Text S1 Sections 1 and 3.2.2). The rates estimated for d M and d P associated with d2EGFP and Luc are treated as known parameters. For inference on the transcription profile, the solution path P(t) is approximated by a flexible continuous function, here a spline representation, fitted to the observed protein data (Text S1 Section 3.2.3). The transcription profile is then reconstructed using the discrete Euler approximation to the differential equations for a small time interval, replacing P(t) by the fitted continuous function. In order to study the correlation in transcription of the dual reporter constructs within a cell, we compute the rank correlation coefficient between the two reconstructed transcription profiles of the two reporters d2EGFP and Luc within a cell (Text S1 Section 3.3). As this may vary over time (in particular for stimulated experiments), all correlations are computed as a function of the length of time since a stimulus (TSA, FBK) was added starting from 1.5 h (to allow for a reasonable minimal length over which any correlation is computed) to 8 h. For unstimulated experiments we computed correlations after 2 h into the experiment to avoid any initial bias. The question of estimating and including protein maturation times is addressed in [48]. In calculating the correlations, the relevant quantity is the difference in maturation times between the two reporters. We have therefore included this process with a constant difference of up to 1 h. We have verified that such delays do not change our correlation results. It is clear from this that if we instead assumed an exponentially distributed delay with a similar difference in means, then this would not affect the correlation results. Figure