Cell-Size-Dependent Transcription of FLC and Its Antisense Long Non-coding RNA COOLAIR Explain Cell-to-Cell Expression Variation

Summary

Single-cell quantification of transcription kinetics and variability promotes a mechanistic understanding of gene regulation. Here, using single-molecule RNA fluorescence in situ hybridization and mathematical modeling, we dissect cellular RNA dynamics for Arabidopsis FLOWERING LOCUS C (FLC). FLC expression quantitatively determines flowering time and is regulated by antisense (COOLAIR) transcription. In cells without observable COOLAIR expression, we quantify FLC transcription initiation, elongation, intron processing, and lariat degradation, as well as mRNA release from the locus and degradation. In these heterogeneously sized cells, FLC mRNA number increases linearly with cell size, resulting in a large cell-to-cell variability in transcript level. This variation is accounted for by cell-size-dependent, Poissonian FLC mRNA production, but not by large transcriptional bursts. In COOLAIR-expressing cells, however, antisense transcription increases with cell size and contributes to FLC transcription decreasing with cell size. Our analysis therefore reveals an unexpected role for antisense transcription in modulating the scaling of transcription with cell size.

Graphical Abstract

Highlights

• •The kinetics and variability of FLC expression are quantified in single cells
• •Without antisense transcription, FLC mRNA production scales with cell size
• •FLC transcription shows minimal stochasticity and no large bursts
• •In cells transcribing the antisense RNA COOLAIR, size scaling of FLC is altered

Ietswaart et al. quantify the kinetics of Arabidopsis FLOWERING LOCUS C (FLC) expression on the single-cell level. They reveal that while FLC expression is variable from cell to cell, this is not due to noise. Instead, variability arises from a linear scaling between FLC mRNA number and cell size. The size scaling of FLC expression can be modulated by transcription of its antisense long non-coding RNA, COOLAIR.

Introduction

A thorough understanding of gene regulation requires an accurate quantification of the kinetic parameters influencing the transcription cycle. The rates of transcript production and mRNA degradation directly determine mRNA concentrations (Bentley, 2014, Dolken et al., 2008, Padovan-Merhar et al., 2015, Sidaway-Lee et al., 2014, Wu et al., 2016). However, transcription elongation, intron splicing, and mRNA release from the locus can also feed through to modulate mRNA levels (Bentley, 2014, de la Mata et al., 2003, Hazelbaker et al., 2013, Stuparevic et al., 2013), for example where kinetic coupling occurs (Bentley, 2014, de la Mata et al., 2003, Hazelbaker et al., 2013). Such kinetic couplings between RNA polymerase II (Pol II) elongation, splicing, or termination can quantitatively control the formation of alternative mRNA isoforms (Bentley, 2014).

An element that can affect precise control of gene expression is stochasticity (Chubb and Liverpool, 2010, Corrigan et al., 2016, Dar et al., 2012, Elowitz et al., 2002, Huh and Paulsson, 2011, Lenstra et al., 2015, Raj et al., 2006, Raj et al., 2010, Raj and van Oudenaarden, 2008, Shahrezaei and Swain, 2008, Sherman et al., 2015, Skinner et al., 2016, Thattai, 2016, Zenklusen et al., 2008, Zopf et al., 2013). Any comprehensive quantification of RNA dynamics must therefore also take into account its degree of variability. Fundamentally, transcription and RNA degradation are both stochastic processes. How transcriptional output could be influenced by intrinsic stochasticity has been intensively studied (Chubb and Liverpool, 2010, Corrigan et al., 2016, Dar et al., 2012, Elowitz et al., 2002, Huh and Paulsson, 2011, Lenstra et al., 2015, Raj et al., 2006, Raj et al., 2010, Raj and van Oudenaarden, 2008, Shahrezaei and Swain, 2008, Skinner et al., 2016, Thattai, 2016, Zenklusen et al., 2008). Nevertheless, it still remains unclear as to what extent variation previously often attributed to intrinsic stochasticity is actually caused by extrinsic variation due to cell cycle, cell size, or other fundamentally deterministic features (Battich et al., 2015, Kempe et al., 2015, Padovan-Merhar et al., 2015, Sherman et al., 2015, Zopf et al., 2013).

Measuring the kinetics and variability of transcription and RNA processing in vivo is a challenging task in multicellular organisms. Previous approaches have focused on parts of the RNA life cycle (e.g., production/degradation), or have provided only relative, not absolute kinetic measurements (Battich et al., 2015, Corrigan et al., 2016, Dolken et al., 2008, Elowitz et al., 2002, Huh and Paulsson, 2011, Padovan-Merhar et al., 2015, Raj et al., 2006, Sidaway-Lee et al., 2014, Skinner et al., 2016, Thattai, 2016, Wu et al., 2016). In this study, we combine single-cell assays with mathematical modeling to comprehensively quantitate in vivo the transcription and RNA dynamics of FLOWERING LOCUS C (FLC) (Michaels and Amasino, 1999, Sheldon et al., 1999), a key quantitative developmental regulator in Arabidopsis thaliana (Figure 1). FLC encodes a MADS-box transcription factor that functions as a repressor of the transition to flowering. In warm conditions, FLC is regulated by two antagonistic pathways: it is upregulated through the transcriptional activator FRIGIDA (FRI) (Crevillén and Dean, 2011), and repressed by the so-called Autonomous pathway (Ietswaart et al., 2012). The latter is mediated in part by a group of antisense long non-coding transcripts, termed COOLAIR (Figure 1), whose transcription start site is located immediately downstream of the FLC poly(A) site (Swiezewski et al., 2009). COOLAIR expression is tissue specific and in warm conditions COOLAIR is observed in root prevasculature cells (Figure 1) (Rosa et al., 2016). The quantitative level of FLC established by these antagonistic Autonomous and FRI pathways determines whether the plant goes through winter before flowering. If such overwintering does occur, cellular FLC expression is epigenetically silenced by the prolonged cold of winter, through the process of vernalization (Figure 1) (Berry and Dean, 2015). Such silencing is a stochastic all-or-nothing effect at individual FLC loci, but where the fraction of silenced loci increases quantitatively with an increasing duration of cold exposure (Angel et al., 2011, Song et al., 2012). However, how quantitative regulation and stochasticity interplay to determine FLC expression in warm conditions has remained unclear.

Figure 1.

Overview of Transcriptional Regulation at FLC

Schematic indicating the regulation of transcription at FLC, which encodes a MADS-box transcription factor that represses the Arabidopsis transition to flowering (Michaels and Amasino, 1999, Sheldon et al., 1999). The FLC locus is also transcribed from its 3′ end in the antisense direction, resulting in a group of long non-coding transcript isoforms collectively termed COOLAIR (Swiezewski et al., 2009). In warm conditions, as investigated in this study, unspliced COOLAIR is expressed in root prevasculature cells (inner layer tissue) but was not detected in outer layer cells (mostly from the epidermis and cortex) (Rosa et al., 2016). FLC levels are quantitatively controlled through the antagonistic FRI and Autonomous pathways (Crevillén and Dean, 2011, Ietswaart et al., 2012), which respectively activate and repress FLC transcription. A short period of winter cold temperatures leads to a transient induction of COOLAIR transcription and concomitant FLC transcriptional repression (Rosa et al., 2016, Swiezewski et al., 2009). Prolonged winter cold induces epigenetically stable repression of the FLC locus through the process of vernalization (Angel et al., 2011, Berry and Dean, 2015, Song et al., 2012).

In this work, we determine the kinetics of FLC mRNA production and degradation, Pol II elongation, intron processing, lariat degradation, and mRNA release in cells without observable COOLAIR expression. We also quantitate the degree of stochasticity in the dynamics of FLC RNA. We observe large cell-to-cell variability in FLC mRNA numbers but find that it is not due to intrinsic stochasticity. Instead, it is well explained by a linear scaling of transcript number with cell size. We show that this size scaling results from a total cellular mRNA production that increases linearly with cell size. Our findings are consistent with the entire FLC RNA dynamics being minimally stochastic. Finally, in COOLAIR-expressing cells it is antisense transcription that scales with cell size, which contributes to FLC transcription now decreasing with cell size. Our work therefore reveals an unexpected role for antisense transcription in modulating the cell size dependence of sense transcription.

Results

Cell-to-Cell Variability of FLC mRNA Is Larger than Predicted from Poisson Production and Degradation Processes

We utilized single-molecule fluorescence in situ hybridization (smFISH) (Duncan et al., 2016, Raj et al., 2008, Rosa et al., 2016) in the A. thaliana Columbia ecotype with an active FRI allele (ColFRI) to measure single-cell RNA levels in warm conditions. The samples were prepared using a root squash method that typically yields single cell layers that originate from the outer cell layers of the root (mostly from the epidermis and cortex) (Figure 1), with cells that do not express observable COOLAIR (Rosa et al., 2016). DAPI stain was then used to label nuclei and two distinct smFISH probe sets employed to visualize FLC RNA: one covering sense FLC exons (FLC mRNA) and the second covering sense intron 1 (Figure 2A). Intron 1 FLC signal was only detected in the nucleus (Figure 2A). Using consecutive smFISH and DNA FISH, we found that intron 1 FLC co-localized exclusively with FLC loci (Figure S1A), indicating that sense intron 1 splicing and lariat degradation occurs at the locus. This finding therefore enabled us to use the FLC intron 1 signal to label transcriptionally active FLC loci. Intron 1 FLC foci were found with counts ranging from 0 up to 4 per cell, with most cells exhibiting at least one FLC intron 1 focus (Figure 2B). In Arabidopsis sister-chromatid cohesion is variable and incomplete (Schubert et al., 2006), meaning that the presence of a maximum of four intronic foci per cell is consistent with these root cells being diploid (Hayashi et al., 2013, Yin et al., 2014). Below, we quantify the underlying transcription and RNA degradation kinetics responsible for these observations.

Figure 2.

Cellular Variation of FLC mRNA Production and Degradation in Outer Layer Root Cells

(A) Schematic of FLC gene with exons (boxes) and introns (dashed lines) indicated, and different probe sets for labeling FLC mRNA (green) and FLC full-length intron 1 (red). Fluorescence localization (z-stack projection) of FLC mRNA, full-length intron 1, and an overlay containing mRNA, intron 1 FLC, and DAPI stain (blue) in representative ColFRI outer layer root cells. Scale bar, 5 μm.

(B) Cellular FLC intron 1 foci counts (gray, n = 106 cells from four biological replicates, i.e., roots from different plants).

(C) Histogram of cellular mRNA foci counts (blue, n = 209 cells from eight biological replicates) and a Poisson distribution fit (red), which would be expected from a simple birth/death process of FLC mRNA production/degradation with constant probabilities per unit time (see schematic above).

(D) Cellular FLC intron 1 foci counts after treatment with ActD or DMSO (mock) for 4 hr and 6 hr. With ActD, after 4 hr and 6 hr the vast majority of intron 1 signal has disappeared. Mock-treated FLC mRNA distributions are shown in Figure S1B.

(E) Left panel: histogram of cellular FLC mRNA foci counts after 4 hr of ActD treatment (blue) and Poisson decay process prediction (red). Right panel: cumulative distribution functions (CDFs) of the FLC mRNA foci counts and Poisson decay process prediction. Schematic above histogram shows FLC mRNA degradation only, as appropriate for ActD treatment.

(F) As in (E) but after 6 hr of ActD treatment. Cells in (D), (E), and (F) are pooled from three biological replicates for each treatment and time point.

(G) Scatterplot of cellular FLC mRNA foci counts (same data as in C; blue) as a function of cell volume, together with least-squares fit (red). Schematic above shows FLC mRNA production increasing with cell volume and volume-independent degradation.

(H) Variance plotted against mean of cellular FLC mRNA foci counts, both for given binned cell volume (ColFRI, Volume-binned). Also shown is the behavior predicted by model with Poisson probability distribution with parameter βV(Poisson), as well as a Poisson model that takes into account volume measurement error (Poisson + Volume error). All error bars indicate standard errors on the respective quantities.

Exonic signal was abundant and mostly cytoplasmic, indicating that FLC mRNA can be easily detected with the appropriate probe set (Figure 2A). The cellular distribution of FLC mRNA counts was unimodal with a mean of 58 ± 2 molecules (Figure 2C). Here and elsewhere, unless stated otherwise, we report the mean (±SEM). We estimate our mRNA counting error to be at most 4% by comparing our algorithm (Duncan et al., 2016, Olsson and Hartley, 2016) with FISH-quant, a separate counting method (Mueller et al., 2013). By comparing these cellular levels with a Poisson distribution (Figure 2C), we found that the experimental mRNA distribution from single cells is much broader than for the Poisson case (Kolmogorov-Smirnov [KS] test, p = 10⁻²⁵): the distribution variance is ∼14-fold larger than the mean. Assuming that cellular mRNA production and degradation occur as Poisson processes, i.e., independently of each other and with constant probabilities p and d per unit time, respectively (Chubb and Liverpool, 2010, Gardiner, 2009, Shahrezaei and Swain, 2008), we would expect a Poisson distribution for such a birth-death process (Chubb and Liverpool, 2010, Gardiner, 2009, Shahrezaei and Swain, 2008, Thattai, 2016), with mean mRNA copy number p/d. We therefore conclude that the cellular FLC mRNA variation cannot be explained by a birth-death process with constant production and degradation probabilities per unit time.

FLC mRNA Degradation Is Well Described by a Poisson Process with a Constant Half-Life

To determine whether FLC mRNA degradation might be responsible for the observed broad cell-to-cell variation in mRNA levels, we considered what would happen to the FLC mRNA distribution after inhibition of transcription. Initially the mRNA distribution would be as observed in Figure 2C, but as time progresses mRNA levels will decrease. A simple hypothesis is that mRNA degradation occurs with a constant degradation rate d (units: s⁻¹). The degradation rate d can then be estimated by fitting an exponential function R(t) = R(0) exp (−d t) to the experimentally measured mean mRNA levels (Dolken et al., 2008, Gardiner, 2009, Sidaway-Lee et al., 2014). The corresponding Poisson stochastic process is characterized by a constant degradation probability per unit time d (Gardiner, 2009). If mRNA degradation is well described by this Poisson model, which exhibits inherently minimal stochasticity, the cellular mRNA distribution after transcription inhibition should be completely determined by the mRNA distribution before inhibition and the degradation probability per unit time d. To probe this hypothesis, we first derived the probability distribution for the number of mRNA molecules, r, as a function of time P(r,t), given the observed initial distribution P(r,0) before transcriptional inhibition (STAR Methods). This derivation resulted in:

$$\text{P}\left(r,t\right)=\sum _{b=r}^M\left(\begin{array}{c}b\\ r\end{array}\right){\left(\exp \left(-dt\right)\right)}^r{\left(1-\exp \left(-dt\right)\right)}^{b-r}\text{P}\left(b,0\right)$$ (Equation 1)

where M indicates the maximum amount of cellular mRNA observed in the initial distribution.

To experimentally test whether FLC mRNA degradation is well described by this model with minimal associated stochasticity, we treated plant seedlings with the transcription elongation inhibitor actinomycin D (ActD) (Dolken et al., 2008). We then subsequently performed smFISH in a time series. We observed that intron 1 FLC foci were almost completely absent as compared with a DMSO-treated sample (mock) after 4 hr and 6 hr of ActD addition, indicating that transcription was indeed inhibited (Figure 2D). We used the experimentally measured mean mRNA count levels $\langle R_{\exp }\left(t\right)\rangle$ after 4 and 6 hr of treatment to estimate the mean degradation rate d: $\frac{\langle R_{\exp }\left(4hr\right)\rangle }{\langle R_{\exp }\left(6hr\right)\rangle }=\exp \left[d\left(6hr-4hr\right)\right]$. This resulted in d = 3.3 ± 0.1 × 10⁻⁵ s⁻¹, equivalent to a half-life of approximately t_1/2 ≈ 6 hr.

Using the estimated degradation rate, we then compared the stochastic model prediction from Equation 1 with the experimentally observed mRNA count distributions after 4 hr and 6 hr (Figures 2E and 2F). Here, we used the pooled mock treated FLC mRNA count distributions (Figure S1B) as the initial distribution in the model to minimize the influence of cell size variation (see below) between experiments. Furthermore, we assumed that mRNA degradation started after a time lag τ of 1 hr after ActD treatment (through replacing t by t − τ in Equation 1 for t = 4 or 6 hr). Such a time lag is reasonable considering the ActD penetration time into the plant tissue. The cumulative distribution functions of the model and experiments were then indeed similar at both the 4- and 6-hr time points, as shown in Figures 2E and 2F (KS test, p = 0.66 and 0.21 for 4 and 6 hr, respectively). Furthermore, starting from the experimental 4-hr distribution as an initial condition, we could correctly predict the entire 6-hr distribution using the same degradation rate but with no time lag in Equation 1 (KS test, p = 0.48) (Figure S1C). Note that, since our time window of 2 hr is relatively short compared with the cell cycle time (17 hr) for these Arabidopsis meristematic root cells (Hayashi et al., 2013, Yin et al., 2014), a reduction in mRNA levels due to dilution during cell division (Huh and Paulsson, 2011) is unlikely to affect these results. We conclude that FLC mRNA degradation is well described by a Poisson process with a constant half-life of ∼6 hr in all outer layer cells. The observed broad distribution (Figure 2C) is therefore not caused by variation in FLC mRNA degradation.

Cellular FLC mRNA Levels Scale Linearly with Cell Size, Generated by a Similar Scaling of the Total mRNA Production Rate

Visual inspection suggested that cellular FLC mRNA levels could increase with cell size as observed for certain genes in mammalian cells (Kempe et al., 2015, Padovan-Merhar et al., 2015). We therefore asked whether the broad distribution of FLC mRNA counts could be influenced by cell-to-cell variability in cell size. We quantified cellular volume using two separate methods (STAR Methods), which gave consistent measures to within ≈20% (Figure S1D). We then compared cell volume with the corresponding cellular mRNA counts (Figure 2G). We found a strong linear correlation between FLC mRNA (R) and cell volume (V) using linear regression: R = α + βV (R²-statistic = 0.8, F-statistic: p = 3 × 10⁻⁷⁴), with a slope β = 31 ± 1 pL⁻¹ (Figure 2G). The intercept α was not significantly different from zero (p = 0.4). Given that FLC degradation is well described by a Poisson process with a cell size-independent degradation probability per unit time, we conclude that the total cellular FLC mRNA production rate would need to increase linearly with volume, p(V) = βVd, in order to explain the observed linear scaling between mRNA and cell volume.

The FLC mRNA Distribution Is Consistent with Minimally Stochastic Poisson Dynamics

To disentangle how much of the cell-to-cell variation in FLC mRNA is governed by cell size under warm conditions, we can consider the cellular mRNA levels as a random variable such that its mean value as a function of cell volume V is given by the observed linear relationship: R(V) = βV (Padovan-Merhar et al., 2015). Here, β is the slope of the fit in Figure 2G. If the major determinant of the variation would be cell volume with minimal residual variation, then the resulting distribution for a given volume would be Poisson, characterized by a mean and variance being both equal to βV (Figure 2H, Poisson). To test this hypothesis, we binned the experimental FLC mRNA levels according to volume (bin width: 0.5 pL) and computed the mean and variance for the experimental binned data (Figure 2H, experiments). Indeed, in cells with larger sizes, the mean and variance of FLC mRNA levels increased. However, the variances were systematically higher than the Poisson limit (Figure 2H). The above analysis assumes cell volumes are known precisely. In practice, our measurement error of ≈20% for estimating cell volumes (Figure S1D) generates additional uncertainty in the relation between cellular volume and mRNA levels. This uncertainty feeds through into a lower limit on our observable variance (for a given cell volume) that is higher than the Poisson limit (see derivation in STAR Methods). When we also took into account our error in volume estimation, we found that our experimental data are in fact well described by an underlying Poisson distribution (Figure 2H, Poisson + Volume error). To further establish that our residual variation is consistent with a Poisson distribution, we calculated the volume-corrected noise measure $N_R=\frac{Var\left(R_{\exp }\right)}{{\langle R_{\exp }\rangle }^2}-\frac{Cov\left(R_{\exp },V_{\exp }\right)}{\langle R_{\exp }\rangle \langle V_{\exp }\rangle }$ (STAR Methods and Padovan-Merhar et al., 2015), where V_exp are the experimentally measured cell volumes. This expression for N_R can be evaluated directly from our data, resulting in N_R = 0.04 ± 0.01, which is indeed close to the Poisson limit $\frac{1}{\langle R_{\exp }\rangle }=0.02$. For comparison, N_R has been found to reach values above 1 for certain mammalian high-noise genes (Padovan-Merhar et al., 2015). Altogether, our analysis shows that cell size is the major source of cell-to-cell variation in FLC mRNA levels. Moreover, after controlling for volume measurement errors, the observed residual variation is consistent with minimal, Poisson variation.

To further test that our mRNA distribution can be explained by cell size variation and Poisson residual variation, we performed stochastic simulations using a Gillespie algorithm (Slepoy et al., 2008) of cellular mRNA production and degradation (Figure S1E and STAR Methods). Degradation was simulated with a constant degradation probability per unit time as described above. The total cellular mRNA production probability per unit time was given by p(V) = βVd. To approximate the deterministic cell-to-cell variation in mRNA production, we used our experimentally observed cell size distribution as an input (Figure S1F). As expected, with this procedure we could explain the cellular mRNA distribution (Figure S1G, KS test: p = 0.35), as well as its variance (Levene’s test: p = 0.53).

The FLC mRNA Distribution Is Inconsistent with Large Transcriptional Bursts

To discern whether alternative mechanisms could also explain the mRNA distribution, we altered the above cell-size-dependent Poisson model to include an OFF state in which the production rate was zero, but which could switch back and forth to an ON state characterized by an mRNA production probability per unit time p_on (Figure S1E and STAR Methods). This ON/OFF model can exhibit “bursty” transcription kinetics, whereby multiple transcripts are being produced in bursts as opposed to uncorrelated single transcription events generated by a Poisson process. The transition probability per unit time from OFF to ON is termed the burst frequency (k_on), whilst the mean number of transcripts produced per ON-OFF cycle is termed the burst size $bs=\frac{p_{on}}{k_{off}}$ (Padovan-Merhar et al., 2015). Here, k_off indicates the transition probability per unit time from the ON to the OFF state. Transcription occurs in bursts when k_off ≫ k_on with a burst size bs ≫ 1 (Dar et al., 2012, Shahrezaei and Swain, 2008). We fixed k_off = 0.1 s⁻¹, which effectively ensured that the first condition was met in our simulations, then systematically increased the burst size from 1 upward. The average production rate as determined above is approximately the product of burst size and burst frequency: $p\left(V\right)=\beta Vd=\frac{p_{on}}{k_{off}}\frac{1}{1+\frac{k_{on}}{k_{off}}}{k}_{on}\cong bs{k}_{on}$. We then chose to allow either burst frequency or burst size scale with volume, the latter as proposed for mammalian genes (Padovan-Merhar et al., 2015). In this way the remaining a priori unknown parameters k_on and p_on were also specified (STAR Methods). We found that the ON/OFF model was only consistent with our cellular FLC mRNA distribution if the burst size was maximally three transcripts for both the cases where burst size or burst frequency scale with volume (Figure S1G, Levine's [variance] test: p = 0.10 and 0.05, respectively; see STAR Methods for additional statistical test results). For a volume-dependent burst size, this number reflects the burst size for a cell of average volume (V = 1.8 pL). Increasing the burst size further led to too broad an FLC mRNA distribution (Levine's test: p < 0.05), due to the considerable fraction of cells in either the transcriptionally inactive or “bursty” states. Burst sizes compatible with our data (at most three transcripts) do not reflect a very “bursty” transcriptional mode, and are rather similar to Poisson transcription which can be interpreted in terms of our ON/OFF model as having a burst size per locus of 1. Altogether we conclude that, for a given volume, FLC transcriptional dynamics are inconsistent with large transcriptional bursts.

Estimation of FLC Transcription Initiation Rates

Since we have quantified cellular mRNA levels, we can utilize these data to infer the mean absolute transcript production rate per locus F in root outer layer cells. This quantification of F is important for a full quantitative understanding of FLC transcription, and will also be necessary to subsequently quantify further RNA dynamics, such as intron processing. The average cellular mRNA levels are the ratio of production and degradation: $\langle R\rangle =\frac{p}{d}=\frac{N_{loci}F}{d}$, where N_loci is the number of FLC gene copies. Although the mean degradation rate is constant during the cell cycle, the number of loci and potentially also the production rate per locus will vary. However, averaging mRNA levels over all observed cells is equivalent to averaging over the cell cycle because in this tissue, cells cycle constantly and asynchronously. We can thus consider an average copy number N_loci = 2.5 and mean mRNA production rate per locus F arising from time averaging over the Arabidopsis root meristematic cell cycle time scales (STAR Methods). Above we both experimentally measured 〈R〉 and determined the mean FLC mRNA degradation rate d = 3.3 ± 0.1 × 10⁻⁵ s⁻¹. From the above formula for 〈R〉, we can therefore extract the mean production rate per locus of F = 7.5 ± 0.4 × 10⁻⁴ s⁻¹, approximately once per 20 min. This estimate should be interpreted as an average over the cell cycle and relevant to a cell of average volume 1.8 pL. Altering the relevant cell cycle time scales by up to an hour resulted in N_loci ranging from 2.4 to 2.8 (STAR Methods). It is also possible that the production rate per locus could dynamically change during the cell cycle to buffer against changes in gene copy number, as found for mammalian genes (Padovan-Merhar et al., 2015). This case leads to N_loci = 2.7 (STAR Methods). In all of these cases, the effective value for N_loci is only changed slightly from its original value of 2.5. Hence, a mean production rate per locus of approximately once per 20 min is retained.

Above we found a linear scaling of the total mRNA production rate with cell volume (Figure 2): p(V) = βVd. Since the total production rate is the sum of the production rates at the individual loci, we also have p(V) = F(V)N_loci(V), where we now explicitly include volume dependence in both the number of loci N_loci(V) and the production rates per locus F(V). Rearranging, we conclude that $F\left(V\right)=\frac{\beta Vd}{N_{loci}\left(V\right)}$. Unfortunately, however, the relationship N_loci(V) between gene copy number and cell volume remains unclear. Nevertheless, by using 2 and 4 as respective lower and upper bounds on the gene copy number N_loci(V), we can estimate bounds on the average production rates per locus for a given volume. For small cells (V = 0.5 pL), these bounds are once per 135 min and 65 min. In large cells (V = 4 pL), the average production rate is increased to lie between once per 16 min and 8 min.

In our analysis above, we have extracted mRNA production rates per locus. Such a production rate can be interpreted as a transcription initiation rate provided there is no premature Pol II termination or co-transcriptional degradation of the transcripts. Previous work has failed to find evidence for such processes at FLC in high transcriptional states such as those investigated here (Wu et al., 2016). We therefore interpret our mRNA production rates per locus as transcription initiation rates, with a mean value of approximately once per 20 min per locus.

Finally, we also revisited the ON/OFF model from the previous section to investigate whether bursty transcription dynamics at each locus could be consistent with our cellular mRNA distribution. Here, we used the above mRNA production rate per locus F(V), using the lower (upper) bound values of N_loci = 2 (4) (STAR Methods). The cellular mRNA levels are the sum over N_loci independent simulation outcomes. We then repeated our earlier analysis to find again that a burst size per locus of at most three transcripts remained consistent with our observed mRNA distribution for both N_loci = 2 and 4 (STAR Methods). These results reconfirm that FLC transcriptional dynamics are inconsistent with large transcriptional bursts.

Simultaneous Quantification of Pol II Elongation, Intron 1 Processing, and Lariat Degradation

To further quantitate any relation between cell size and the transcriptional and RNA processing dynamics at FLC, we next investigated FLC intron 1 levels more extensively using smFISH. Generally intronic RNA levels depend on Pol II initiation (F, unit: s⁻¹), Pol II elongation (v, unit: bp/s), and intron processing (σ, unit: s⁻¹) (Figure 3A). The timescale σ⁻¹ equates to the time interval between completion of intron 1 transcription and the start of lariat degradation, and thus includes the acts of splicing and lariat debranching. Intronic RNA levels are additionally dependent on lariat degradation. Since it is unclear how lariat degradation occurs (Hesselberth, 2013), we allow for both 5′ to 3′ and 3′ to 5′ degradation, with rates k₅₃ and k₃₅, respectively (unit: bp/s). Potential other RNA degradation mechanisms, e.g., endoribonuclease cleavage, could be captured through large values of either or both of the degradation rates described above. However, as shown below, we find little evidence for such scenarios at FLC.

Figure 3.

Quantification of Pol II Elongation, FLC Intron 1 Processing, Lariat Degradation, and mRNA Release from the Locus

(A) Schematic of different processes contributing to FLC intron 1 life cycle: transcription initiation rate (F), Pol II elongation (v), and intron processing rate (σ). Time scale σ⁻¹ indicates the time interval between completion of intron 1 transcription and start of lariat degradation, which can occur from 5′ to 3′ end (rate: k₅₃) and/or 3′ to 5′ end (rate: k₃₅). Also shown is mRNA release from the locus (rate: k_x) and subsequent degradation (rate: d).

(B) Fluorescence localization (z-stack projection) of four different FLC intron 1 probe sets, as indicated on schematic: full-length (full, red), 5′ end (red), middle (mid, red), and 3′ end (green). All images are overlays of respective intron 1 signal and DAPI stain (blue) in representative outer layer root cells. Scale bar, 5 μm.

(C) Average foci counts per cell for the four probe sets described in (B) from outer layer cells together with analytical model fits (mean and SEM using all allowed parameter values, see text and STAR Methods). Number of cells analyzed, respectively, for full, mid, 5′, and 3′: 200, 382, 326, and 326 pooled from three, four, four, and four biological replicates, respectively. Error bars denote SEM.

(D) Marginal distributions for intron processing (σ), elongation (v), 5′ to 3′ lariat degradation (k₅₃), and 3′ to 5′ lariat degradation (k₃₅) rates that generate good fits to the data shown in (C) according to a χ² test (degrees of freedom k = 4, acceptance probability p ≥ 0.1) with the “missing” length fraction 1/3. Box plots indicate minimum, 25% quantile, median, 75% quantile, and maximal values.

(E) Volume dependence of average cellular foci counts per cell in outer layer cells for FLC intron 1: full-length (full) and 5′ end. Number of cells analyzed as in (C). Also shown are analytical model fits (black, gray) with parameter values that generated good fits to population averages in (C): v = 3 bp/s, σ = 1.5 × 10⁻³ s⁻¹, k₅₃ = 2 bp/s, and k₃₅ = 2 bp/s. Error lines denote SEM as function of volume.

(F) As in (E) but for middle (mid) and 3′ end FLC intron 1 probe sets.

(G) Locus-associated exonic FLC RNA (R_loc) distributions given presence of full-length FLC intron 1 signal from outer layer cells. Three different quantification methods were used on the same experimental dataset (n = 114 cells pooled from four biological replicates): integration of 2D Gaussian fit to the spatial intensity profile (Int), superposition of point spread functions (PSF), and superposition of amplitudes of PSF at the locus (Amp) (STAR Methods; Mueller et al., 2013).

(H) Volume dependence of average locus-associated exonic FLC RNA levels. Data and three different quantification methods as described in (G). Error lines denote SEM as a function of volume.

To quantify these processes we developed a new methodology, measuring various different intronic RNA levels and using these measurements to determine the above kinetic parameters. Specifically, we designed four different smFISH probe sets (Figure 3B) covering, respectively: the full intron 1 as described above (Figure 2A), the 5′ half, the middle of the intron (symmetrically positioned with a length of half the intron), and the 3′ half. We denote their respective mean RNA levels at an FLC locus as I_f, I_5′, I_m and I_3′. For all of the probe sets, the mean RNA levels are then described by I_j = FT_j. F is the average FLC transcription initiation rate per locus as estimated above and T_j is the mean lifetime of the intronic RNA, which is specific for each probe set location (subscript j = {f,5′,m,3′}). Importantly, for each probe set, the respective lifetime T_j depends on the kinetic parameters (STAR Methods). This timescale is additionally dependent on how many probes need to be bound for a signal to be experimentally detected. We and others have found that having only two-thirds of the probe set bound could already be sufficient to generate a detectable signal (Duncan et al., 2016, Raj et al., 2008, Rosa et al., 2016). Consequently, intronic RNA with a “missing length fraction” of up to one-third of the probe set length is assumed to still generate a detectable smFISH signal (STAR Methods).

To quantify the four unknown kinetic rates (v, σ, k₃₅, and k₅₃), we determined for each of the four probe sets the mean number of foci per cell, indicated respectively as 〈S_f〉, 〈S_5′〉, 〈S_m〉, and 〈S_3′〉 (Figures 3B and 3C). We found that 〈S_f〉 and 〈S_3′〉 were similar and likewise for 〈S_5′〉 and 〈S_m〉 (Figure 3C). Consistent with 〈S_5′〉 being larger than 〈S_3′〉 (Figure 3C), all 3′ foci co-localized with 5′ foci but not the reverse. A positive signal corresponds to at least one intron RNA molecule, which co-localizes with the FLC locus exclusively (Figure S1A). Therefore, the mean foci number per cell equals the average number of FLC loci per cell multiplied by the expectation to observe a signal at a locus (STAR Methods): $\langle S_j\rangle =N_{loci}\left(1-e^{-F{T}_j}\right)$.

Here, we use Poisson transcription initiation and RNA degradation kinetics, consistent with our findings above. To determine which values for the a priori unknowns (v, σ, k₃₅, and k₅₃) generated a good fit to the average foci per cell for each probe set, we systematically varied these four parameters, calculated the respective model values for the average foci per cell, and assessed with a χ² test (degrees of freedom k = 4, acceptance probability p ≥ 0.1) whether the model values were sufficiently probable compared with the experimental data in Figure 3C. As a result, we obtained distributions of parameter values that generated good model fits (Figure 3D), with all the consistent parameter estimates lying in the range v = 2–20 bp/s, σ = 1.0–2.0 × 10⁻³ s⁻¹, k₅₃ = 1–5 bp/s, and k₃₅ = 1–4 bp/s. To determine the robustness of our parameter estimates to uncertainty in the missing length fraction, we repeated the parameter inference also for a range of missing length fractions (STAR Methods). The resulting variation in our kinetic rate estimates was limited (Figures S2A–S2D), yielding similar estimates to the above methodology. Our elongation rate (0.1–1.2 kb/min) and intron processing timescale estimates (8–17 min) are in line with the ranges described for other species (Bentley, 2014).

We next wondered whether the four above kinetic rates might scale with cell size, similar to the transcription initiation rate. To investigate this question, we first examined how the number of intron foci scaled as a function of cell size by sorting and including cells according to their size (STAR Methods). We found that levels of intronic RNA from all four probe sets 〈S_j(V)〉 increased systematically with increasing cell size (Figures 3E, 3F, and S2E), as would be expected with a transcription initiation rate that also increases with cell size.

To investigate whether we could explain these cell size dependencies with our above determined kinetic rate estimates, we first generalized the model prediction for the foci number for a given volume V: $\langle S_j\left(V\right)\rangle =N_{loci}\left(V\right)\left(1-e^{-F\left(V\right)T_j\left(V\right)}\right)$. We next assumed that only the transcription initiation rate varied with size: $F\left(V\right)=\frac{\beta Vd}{N_{loci}}$, with the size-independent probe specific lifetimes T_j(V) = T_j as determined above. To account for the unknown behavior of N_loci(V), we adopted a similar approach as previously, first using the mean N_loci = 2.5, before investigating N_loci = 2 and N_loci = 4 as lower and upper bounds. Using N_loci = 2.5, we were able to reproduce the observed number of foci over the range of observed volumes (see Figures 3E and 3F with v = 3 bp/s, σ = 1.5 × 10⁻³ s⁻¹, k₅₃ = 2 bp/s, and k₃₅ = 2 bp/s). However, fitting using the lower and upper bounds N_loci = 2 and N_loci = 4, for both small volumes (0.9 pL) and large volumes (2.8 pL), yielded fits with 3-fold or more variation in the parameter values for v, σ, k₅₃, and k₃₅ from those given above. Given this spread, we cannot rigorously conclude whether the co-transcriptional parameters v, σ, k₅₃, and k₃₅ depend on cell size. Nevertheless, by analyzing intronic RNA foci we have been able to extract robust mean values for the FLC elongation, intron processing, and lariat degradation.

Quantification of FLC mRNA Release from the Locus

The release of mRNA from a transcribed locus is an important part of the RNA life cycle (Figure 3A) as it can influence transcript fate (Stuparevic et al., 2013). To quantify FLC mRNA release from the locus, we assessed the exonic FLC RNA distribution, i.e., FLC exonic sequences present at the FLC locus itself (Figure 2A). By utilizing the software package FISH-quant (Mueller et al., 2013), we performed an unbiased quantitative image analysis on the FLC exonic intensities at FLC loci. First, a systematic averaging of FLC exonic smFISH signal (Figure 2A) spatial intensity profiles resulted in the point spread function (PSF) that represents a single FLC RNA molecule (Mueller et al., 2013). Next we exploited the full-length FLC intron 1 probe set to label the FLC locus itself (Figures 2A and S1A). The exonic FLC RNA signals co-localizing with intron 1 were then quantitatively compared with the PSF intensity using three different quantification algorithms (STAR Methods; Mueller et al., 2013) each estimating how many exonic RNAs are at the locus (Figure 3G). All three methods gave similar exonic FLC RNA distributions (Figure 3G), with up to at most six transcripts at the locus in all three methods, which indicates the robustness of this approach. We estimate the average exonic FLC RNA at the locus (conditioned on the presence of intron 1 FLC) to be 〈R_loc〉 = 2.2 ± 0.3.

To quantify the mean exonic FLC RNA release rate from the locus, we first assume that the mean total release is equal to k_x〈R_loc〉, where k_x is the release rate. Equating this to the mean initiation rate F, we find that k_x = 3.4 × 10⁻⁴ s⁻¹. However, this analysis overlooks any possible correlations between the presence of exonic and intronic signal. Since our measurements of exonic RNA are conditioned on the presence of intronic RNA signal, such correlations might alter our estimate for k_x. To quantitatively investigate this possibility, we performed stochastic simulations of the transcriptional dynamics at an individual FLC locus using a spatiotemporal Gillespie algorithm (Figures 3A and S3A; STAR Methods). This methodology simulated the spatiotemporal transcriptional dynamics at FLC, including FLC mRNA release from the locus as a single-step Poisson process with an a priori unknown probability per unit time k_x. This analysis generated results that could then be compared with the experimental exonic FLC RNA distributions. We used the kinetic parameters determined previously (v = 3 bp/s, σ = 1.5 × 10⁻³ s⁻¹, k₅₃ = 2 bp/s, k₃₅ = 2 bp/s) to simulate an FLC locus in a cell of average size 〈V〉 = 1.8 pL, where the mean transcription initiation probability per unit time was given by $F=\frac{\beta \langle V\rangle d}{N_{loci}}$, with β = 31 pL⁻¹, d = 3.3 × 10⁻⁵ s⁻¹,and N_loci = 2.5, assuming also a missing length fraction of 1/3 for all smFISH species. As expected, with this procedure we could reproduce the mean levels of the FLC mRNA as well as the four different intron 1 probe sets. We next output the simulated distributions of exonic RNA at the locus given that at least one intron was present at the locus and fitted k_x, the mean release probability per unit time, through the mean value of the experimental exonic RNA distribution 〈R_loc〉. This resulted in k_x = 5 × 10⁻⁴ s⁻¹, approximately once per half an hour, similar to our earlier estimate.

We next checked that our Gillespie algorithm simulations could account for our earlier data on intron foci number as a function of cell size. Using a size-dependent transcription initiation probability per unit time per locus of $F\left(V\right)=\frac{\beta Vd}{N_{loci}}$, we could again reproduce these data satisfactorily (Figure S3B), confirming our earlier analytic approach.

Finally, we measured experimentally the amount of exonic RNA at the locus as a function of cell size (Figures 3H and S3C). Notably, this quantity varied only weakly with cell size, quite unlike the intronic foci signal (Figures 3E and 3F). This result suggests that the RNA release rate from the locus should scale linearly with cell size in order to compensate for a similarly increasing transcription initiation rate, thereby generating an approximately constant exonic signal. Overall, we have succeeded in quantitating the size scaling of total mRNA production and the size-independent mRNA degradation rate, as well as the mean rates for transcription elongation, intron processing, lariat degradation, and mRNA release from the locus (Table 1).

Table 1.

Overview of Kinetic Rates and Quantities Estimated in This Study

Symbol	Definition	Estimate
R	cellular FLC mRNA counts (in outer layer cells)	average: 58 ± 2; min–max: 7–145
V	cell volume (in outer layer cells)	average: 1.8 pL; min–max: 0.5–4 pL
β	slope of linear relationship between cellular FLC mRNA count and cell volume	31 ± 1 pL−1
d	mRNA degradation rate	3.3 ± 0.1 × 10−5 s−1
p	cellular mRNA production rate	average: 1.8 × 10−3 s−1; min–max: 0.5–4 × 10−3 s−1
Nloci	cell cycle averaged number of FLC loci per cell	2.5; range: 2.4–2.8
F	cell cycle averaged FLC transcription initiation rate	7.5 ± 0.4 × 10−4 s−1
v	Pol II elongation rate	2–20 bp/s
σ	intron processing rate	1.0–2.0 × 10−3 s−1
k53	intron lariat 5′ to 3′ degradation rate	1–5 bp/s
k35	intron lariat 3′ to 5′ degradation rate	1–4 bp/s
Rloc	FLC mRNA levels at locus	average: 2.2 ± 0.3; min–max: 0–6
kx	mRNA release rate from locus	3.4–5 × 10−4 s−1
bs	burst size in ON/OFF model	1–3
koff	transition rate from ON to OFF state in ON/OFF model	0.1 s−1

Antisense Transcription Contributes to a Decrease of Intronic FLC Levels with Cell Size in Prevasculature Cells

FLC expression is quantitatively repressed by the Autonomous pathway, in a mechanism involving antisense (COOLAIR) transcription. The COOLAIR transcription start site is located immediately downstream of the sense FLC poly(A) site (Swiezewski et al., 2009) (Figure 4A). In the root outer layer (epidermis and cortex) cells studied above (Figure 1), from where our estimates for FLC transcriptional kinetics are extracted, we detected no antisense COOLAIR expression (Figure 4B). To investigate the role of antisense transcription on sense regulation, we therefore shifted our focus onto the inner prevasculature cells (Figure 1), which show higher levels of COOLAIR transcription (Figure 4B) (Rosa et al., 2016).

Figure 4.

Antisense Transcription Contributes to a Reduction of FLC Intron 1 Expression with Cell Size in Prevasculature Tissue

(A) Fluorescence localization of full-length sense intron 1 (red, top right) and antisense (COOLAIR) 5′ end distal intron (green, bottom right) and wider-field merge (left), all with DAPI stain (blue), in representative ColFRI prevasculature root cells, with the same cells in different images identified by ^∗ or ^∗∗, respectively. Scale bar, 5 μm. Also shown (top) is schematic of FLC gene with sense transcript as in Figure 2A, and antisense proximal and distal isoforms together with corresponding sense and antisense probe sets.

(B) Average cellular foci number of full-length FLC intron 1 and COOLAIR 5′ end distal intron in outer layer (black) and prevasculature cells (white), from one and three biological replicates, respectively. Error bars denote SEM. ^∗p < 0.05, ^∗∗∗∗p < 10⁻⁴.

(C) Area dependence of average cellular foci count per cell of full-length FLC intron 1 and COOLAIR 5′ end distal intron in ColFRI root outer layer cells (outer) and full-length FLC intron 1 in prevasculature (prevasc) root cells. Data as in (B) and Figure 2B. Error lines denote SEM as a function of area.

(D) As in (C), here for FLC and COOLAIR expression in prevasculature cells.

(E) Area dependence of average cellular foci counts per cell of full-length FLC intron 1 from terminator exchange (TEX) or wild-type FLC transgenes (CTL), in outer layer (outer) or prevasculature (prevasc) root cells, all from four biological replicates per condition. Error lines denote SEM as a function of area.

(F) As in (E), here for FLC and COOLAIR 5′ end distal intron expression in prevasculature cells.

(G) Schematic of FLC regulation by cell-size-dependent COOLAIR transcription in prevasculature cells.

Due to the dense packing of prevasculature cells (Figure 4A), accurate cellular volume and FLC mRNA estimates could not be obtained. This difficulty precluded quantification of transcriptional kinetics in these cells. However, cell area as well as sense and antisense intronic smFISH foci (Figure 4A) could still be determined manually, the small number of intron signals being much easier to definitely assign to cells, as compared with the much larger number of FLC mRNA foci. With this approach, it was therefore still possible to investigate the cell size dependencies of sense and antisense transcription using the intronic signals.

Average cellular FLC intron 1 foci counts were lower in prevasculature tissue than in the root outer layer (Figure 4B), partly because prevasculature cells are smaller (Figure 4C). As expected, in outer layer cells, FLC intron 1 foci counts increased with cell size, consistent with transcription initiation increasing with cell size in these cells. However, in prevasculature cells the intron 1 foci counts generally reduced with cell size (Figure 4C). Moreover, using probes at the 5′ end of the distal COOLAIR intron (Figure 4A), COOLAIR foci counts increased with cell size in the prevasculature cells (Figure 4D). We found previously that COOLAIR and FLC expression are mutually exclusive at single FLC loci (Figure S4 and Rosa et al., 2016). Consistently, we find here that mean sense/antisense levels as a function of cell size in prevasculature tissue are strongly anticorrelated (Figure 4D, Pearson correlation coefficient r = −0.9, p = 10⁻⁷³). To investigate whether COOLAIR transcription caused the reduction in sense intronic RNA levels with cell size, we measured sense intronic RNA foci counts in plants with reduced antisense expression using a previously described FLC Terminator EXchange (FLC-TEX) transgene (Csorba et al., 2014, Rosa et al., 2016). This transgene exchanges the FLC terminator/COOLAIR promoter with the strong RBCS terminator from Arabidopsis RBCS3B, acting to reduce antisense expression. As expected, in outer layer cells without observable antisense expression in ColFRI (Figures 4B and 4C), FLC intron 1 foci in FLC-TEX still increased with cell size (Figure 4E). Moreover, compared with an FLC control (FLC-CTL) transgene (Csorba et al., 2014, Rosa et al., 2016), antisense expression was now almost absent in prevasculature tissue in FLC-TEX (Figure 4F). In these cells, FLC intron 1 RNA foci counts were now increased (Figure 4F), most notably in larger cells where antisense expression was highest in ColFRI (Figure 4D) and FLC-CTL (Figure 4F). This result strongly favors a causal role for COOLAIR in repressing sense transcription. However, sense intron 1 RNA foci counts in FLC-TEX prevasculature cells did not revert to increasing with cell size, as in the outer cells, but were instead roughly constant with cell size (Figure 4F). We conclude that in prevasculature cells COOLAIR expression increases with cell size and that COOLAIR contributes to repression of sense FLC transcription (Figure 4G). As a result, sense FLC expression in prevasculature cells reduces with increasing cell size.

Discussion

In this work, we have dissected with high resolution the cell-size-dependent RNA kinetics and variability of FLC, an important developmental regulator in a multicellular eukaryote. Our analysis has indicated that in outer layer cells without observable COOLAIR expression, total cellular mRNA production increases linearly with cell size, while the mRNA degradation rate is cell size independent. In these cells, we also quantified the mean rates for transcription elongation, intron processing, and lariat degradation, as well as mRNA release from the locus (Table 1) using a new methodology measuring intronic RNA levels. The net result of these dependencies is a cytoplasmic FLC mRNA number that scales linearly with cell size (Figure 2G). We also found low levels of stochasticity at FLC, with little evidence for bursty transcription.

The low levels of stochasticity at FLC do not support the conventional picture of bursty gene regulation. Instead, the apparent broad width of the cellular FLC mRNA distribution is almost entirely explained by a linear scaling of total mRNA production with cell size. This striking conclusion suggests that previous work on stochastic gene expression may need to be revisited, more carefully controlling for sources of deterministic variation between cells, as recently argued for mammalian cells (Battich et al., 2015, Kempe et al., 2015, Padovan-Merhar et al., 2015). Potentially, the large cell size diversity (∼8-fold) predisposes this feature as being particularly important in plants. When controlling for cell size, the residual FLC mRNA variation is then consistent with Poissonian transcription initiation dynamics. Limited bursty transcription kinetics are also consistent with our data but where the burst size is at most only three transcripts. These conclusions are supported by the low levels of transcript accumulation observed at FLC loci and are also compatible with a burst size of about five transcripts found for a number of endogenous mammalian genes (Levesque and Raj, 2013). Importantly, transcriptional bursts, often modeled as purely stochastic events, could arise not only due to intrinsic noise in biochemical reactions, but also through deterministic sources of cell-to-cell or time-dependent variation (Sherman et al., 2015, Zopf et al., 2013). Altogether, our findings significantly advance our understanding of gene regulation in plants, where issues such as transcriptional scaling with cell size and stochastic or bursty gene expression have not previously been investigated.

A further key outcome of our analysis is quantification of transcription initiation and elongation rates for FLC. We found that in an outer layer cell of average size, the typical time between initiation events (∼20 min) is similar to the time to elongate (5–50 min) through the gene. Previous work has indicated that the FLC locus adopts a 5′ to 3′ end looped configuration (Crevillen et al., 2013). We propose as a possible scenario that in outer layer cells, which lack observable antisense expression, a single Pol II could transcribe the sense strand almost continuously and reinitiate soon after termination. This mechanism could also explain the apparent absence of large transcriptional bursts at FLC. Furthermore, intron processing and degradation of FLC intron 1 (∼3.5 kb in length) takes a considerable time (15–45 min) and appears to occur on a similar timescale as Pol II elongation through the gene. Our estimates are also consistent with recent findings in budding yeast that splicing (exon/exon ligation) occurs mostly up to 50 bp downstream of the intron acceptor site (Carrillo Oesterreich et al., 2016). With our Pol II elongation rates, this would be within a minute and thus much shorter than our intron-processing timescale (8–17 min), which reflects the timescale from intron birth until the start of lariat degradation. Overall, our transcription and RNA-processing kinetic estimates indicate that these processes occur in parallel and with relatively similar timescales.

We have found that in prevasculature tissue, cell-size-dependent COOLAIR transcription represses sense expression. This contributes to an overall decrease of sense FLC transcription with cell size in these cells in contrast to the positive scaling observed in outer layer cells. Interestingly, it is antisense transcription that positively correlates with size in prevasculature tissue, indicating that its expression could be prioritized over sense transcription in these cells. The mechanistic basis for such prioritization remains unclear, but is an intriguing question for future investigation both at FLC and genome-wide. Our previous whole plant studies showed that co-transcriptional proximal COOLAIR processing contributes to FLC repression (Marquardt et al., 2014, Wang et al., 2014), likely through a repressed chromatin state at the locus (Liu et al., 2010, Wu et al., 2016). Distally polyadenylated COOLAIR also influences transcription of the sense FLC strand (Li et al., 2015). How nascent COOLAIR transcription in prevasculature cells connects with these mechanisms remains to be addressed. Nevertheless, given the widespread prevalence of antisense expression in different organisms (Lenstra et al., 2015, Mayer et al., 2015, Pelechano and Steinmetz, 2013), antisense transcription could be a general mechanism to modulate size scaling of transcription.

Overall, our precise quantification of the FLC RNA kinetics is a vital step in the functional dissection of FLC regulation. In the future it will be interesting to see how quantitative FLC kinetics are modulated by temperature, ranging from the relatively high temperatures (20°C) analyzed here to winter cold (4°C). In the latter case the vernalization pathway is activated, which represses FLC transcription at a single-cell level via the Polycomb system in a digital and epigenetically stable manner (Angel et al., 2011, Berry and Dean, 2015, Song et al., 2012). How quantitative FLC regulation in the warm interfaces with digital vernalization is a critical matter for future investigation. Such investigations are expected to benefit from the single-cell kinetic quantification methods developed in this study.

STAR★Methods

Key Resources Table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Antibodies
anti-DIG-fluorescein antibody	Roche	Cat#11207741910; RRID: AB_514498
Chemicals, Peptides, and Recombinant Proteins
Digoxigenin-dUTP	Roche	Cat#11745816910
Actinomycin D	SigmaTM	Cat# A4262-2MG
Glucose oxidase	Sigma TM	Cat# G0543
Bovine liver catalase	Sigma TM	Cat# C3155
Experimental Models: Organisms/Strains
Arabidopsis ColFRI: Col-0 ecotype with an introgressed active FRIGIDA allele from the Spanish San Feliu 2 (Sf2) accession.	Caroline Dean laboratory, first described in (Lee et al., 1994).	N/A
Arabidopsis FLC-TEX: transformation of 12-kb FLC genomic DNA fragment composed of the promoter region, gene body, and replacement of the 3′ region by rbcs3B terminator into the flc-2 FRI genotype. flc-2 is a loss-of-function FLC genotype, which has a deletion/rearrangement within the endogenous FLC gene. A representative FLC-TEX line (no. 577) was selected.	Caroline Dean laboratory, first described in (Wang et al., 2014)	N/A
Arabidopsis FLC-CTL: transformation of FLC genomic construct (15 kb of the FLC locus, FLC-15) into flc-2 FRI background.	Caroline Dean laboratory, first described in (Csorba et al., 2014)	N/A
Oligonucleotides
smFISH probes, see Table S1	Biosearch Technologies	N/A
Software and Algorithms
Cellular RNA count and Z-projected cell area script	Duncan et al., 2016, Olsson and Hartley, 2016	https://github.com/ri23/FISHmodel
Cell volume estimation script	This study	https://github.com/ri23/FISHmodel
Cellular mRNA production and degradation simulations	This study	https://github.com/ri23/FISHmodel
FLC transcription and RNA processing simulations	This study	https://github.com/ri23/FISHmodel
FISH-quant	Mueller et al., 2013	https://code.google.com/archive/p/fish-quant/

Contact for Reagent and Resource Sharing

Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Martin Howard (martin.howard@jic.ac.uk).

Experimental Model and Subject Details

Species and Genotype of Experimental Models

Arabidopsis ColFRI, first described in (Lee et al., 1994): Col-0 ecotype with an introgressed active FRIGIDA allele from the Spanish San Feliu 2 (Sf2) accession. Arabidopsis FLC-TEX, first described in (Wang et al., 2014): transformation of 12-kb FLC genomic DNA fragment composed of the promoter region, gene body, and replacement of the 3′ region by rbcs3B terminator into the flc-2/FRI genotype. flc-2/FRI is a loss-of-function FLC genotype, which has a deletion/rearrangement within the endogenous FLC gene in a ColFRI background (Michaels and Amasino, 1999). A representative FLC-TEX line (no. 577) was selected (Csorba et al., 2014, Wang et al., 2014). Arabidopsis FLC-CTL, first described in (Csorba et al., 2014): transformation of FLC genomic construct (15 kb of the FLC locus, FLC-15) into flc-2/FRI background.

Plant Material and Growth Conditions

Seeds were surface sterilized in 5% v/v sodium hypochlorite for 5 min and rinsed three times in sterile distilled water. Seeds were stratified for 3 days at 5°C before germination in a growth cabinet (Sanyo MLR-351H) in vertically oriented Petri dishes containing MS media minus glucose (16 hours light, 100 μmol m⁻² s⁻¹, 22°C ± 1°C) for 1 week.

For Actinomycin D (ActD) experiments, plants were initially germinated in non-supplemented media for 6 days and then transferred to new plates containing ActD. Before pouring into plates, molten media was supplemented with a stock solution of ActD (1mg/ml dissolved in DMSO) to a final concentration of 20ug/ml. ActD was obtained from SigmaTM (catalogue # A4262-2MG).

Method Details

smFISH Procedure on Root Squashes

Seedlings were removed from the media and root tips were cut using a razor blade and placed into glass wells containing 4% paraformaldehyde and fixed for 30 min. Roots were then removed from the fixative and washed twice with nuclease free 1X PBS (Thermo Scientific, Lutterworth, UK). Several roots were then arranged on a Poly-L-Lysine slide (Thermo Scientific, Lutterworth, UK) and covered by a glass coverslip (Slaughter, Uppminster, UK). The meristems were then squashed by tapping the coverslips, before each slide was submerged (together with the coverslips) for a few seconds in liquid nitrogen until frozen. The coverslips were then flipped off the slides using a razor blade and the roots were left to dry at room temperature for 30 min.

Tissue permeabilization was achieved by immersing the samples in 70% ethanol for a minimum of one hour. The ethanol was then left to evaporate at room temperature for 5 min before two washes were carried out with wash buffer (containing 10% formamide and 2x SSC). 100μl of hybridization solution (containing 10% dextran sulfate, 2x SSC and 10% formamide), with each probe set at a final concentration of 250nM, was then added to each slide. Coverslips (Slaughter, Uppminster, UK) were carefully laid over the samples to prevent evaporation of the buffer and the probes were left to hybridize at 37°C overnight in the dark.

The hybridization solution containing unbound probes was pipetted off the following morning. Each sample was then washed twice with wash buffer with the second wash left to incubate for 30 min at 37°C. 100μl of the nuclear stain DAPI (100ng/mL) was then added to each slide and left to incubate at 37°C for 30 minutes. The DAPI was removed and 100μl 2xSSC was added and then removed. 100μl GLOX buffer minus enzymes (0.4% glucose in 10mM Tris, 2X SSC) was added to the samples and left to equilibrate for 2 min. This was removed and replaced with 100μl of GLOX buffer containing the enzymes glucose oxidase and catalase, where 1μl of each enzyme (Glucose oxidase (#G0543 from Sigma) and catalase (#C3155 from Sigma)) was added to a total of 100μl of GLOX minus enzymes. The samples were then covered by 22mm x 22mm No.1 coverslips (Slaughter, Uppminster, UK), sealed with nail varnish and immediately imaged.

Synthesis of the Probes

The probes for FLC mRNA, full-length FLC intron 1 and COOLAIR were as described in (Duncan et al., 2016, Rosa et al., 2016). We used the online program Stellaris Probe Designer version 2.0 from Biosearch Technologies to design probe sequences for the 5′ half, 3′ half and middle of FLC intron 1 (Table S1).

Image Acquisition

For imaging we used a Zeiss Elyra PS1 inverted microscope, with a x100 oil-immersion objective (1.46 NA) and cooled EM-CCD Andor iXon 897 camera (512x512 QE>90%); or a Zeiss CellObserver HS system equipped with a PlanApo 1.4/100x objective, an Axiocam MRm Rev. The following wavelengths were used for fluorescence detection: for probes labeled with Quasar570 an excitation line of 561 nm was used and signal was detected at 570-640 nm; for probes labeled with Quasar670 an excitation line of 642 nm was used and signal was detected at 655-710 nm; for DAPI an excitation line of 405 nm was used and signal was detected at 420-480 nm.

Maximum projections and analysis of 3D pictures were performed using Fiji (an implementation of ImageJ, a public domain program by W. Rasband available from http://rsb.info.nih.gov/ij/).

Combined RNA-DNA FISH

For sequential RNA-DNA FISH, after imaging RNA by smFISH (protocol outlined above), coverslips were removed and washed three times in 4X-SSC/0.2% Tween at 37°C. Slides were then re-fixed with 4% (w/v) paraformaldehyde (PFA) in 1XPBS buffer for 10 min and washed again several times in 1X PBS. Afther that slides were treated with 100 μg/mL RNase for 1 h at 37°C and washed twice in 1X PBS. Samples were then digested in a mixture of 1% driselase, 0.5% cellulase, and 0.025% pectolyase for 10 min at 37°C. Slides were then washed and re-fixed with 4% PFA for 10 min and transferred to a series of ethanol steps increasing to 70%, 85% and 100%.

Probes were labeled with Digoxigenin-dUTP (#11745816910, Roche) by nick translation. Bacterial artificial chromosome (BAC) clone JAtY71K18, which contains an insert of 75 kb, was used as a probe. The hybridization mixture (20 ng/mL labeled DNA, 50% formamide, 10% dextran sulfate, 2X SSC, 1mg/ml salmon sperm (D9156, Sigma)) was denatured at 85°C for 10 min and applied to the slides. Slides containing the hybridization mixture were denatured for 7 min at 75°C (in an omnislide), and hybridized overnight at 37°C. After hybridization, slides were washed at 42°C once in 2X SSC, twice in 20% formamide plus 0.1X SSC and twice in 2X SSC, and finally twice in 2X SSC at room temperature and twice in 4X SSC plus 0.2% Tween-20. Then the slides were blocked in TNB (0.1M TrisHCl, 0.15M NaCl, 3% BSA) for 30 min at 37°C. Digoxigenin–dUTP probes were detected with anti-DIG-fluorescein antibody (#11207741910, Roche) prepared in TNB buffer (1:100). Nuclei were counterstained with 1 mg/mL DAPI, and slides were mounted in Vectashield (Vector Laboratories). In order to find the cells previously imaged for smFISH, we saved the stage positions of the cells imaged and acquired large image tiles in order facilitate the identification of the cells.

Quantification and Statistical Analysis

smFISH RNA Count Quantification

Cellular count quantification of FLC mRNA dots from the z projection of optical sections of outer layer cells consisted of two components - segmentation and mRNA counting, as described in (Duncan et al., 2016). These two components were combined into an overall workflow that resulted in an image where each cell was annotated with the number of probes located inside it. The image analysis workflow operated on image collections where each image represented a unique channel/z-stack pair. To separate the captured microscopy image into individual channel/z-stack pairs, Bioformats was used and the pipeline was implemented in the Python programming language, available at https://github.com/JIC-CSB/FISHcount and https://github.com/ri23/FISHmodel. To determine the counting error we also determined mRNA counts on the same data sets using FISHquant, as described in brief in the last section below and also in (Mueller et al., 2013). Cellular levels of FLC intron 1 and COOLAIR (all probe sets) were determined manually using ImageJ or ZEN (proprietary software from Zeiss).

Estimation of Cellular Volumes and Areas

Volume estimation for outer layer cells was performed using two methods: the projection method and 3D segmentation method (Duncan et al., 2016, Olsson and Hartley, 2016). In the first method, we determined the cell area in pixels from the z-stack projection image that was also utilized to determine the cellular FLC mRNA counts (Duncan et al., 2016). This value was then multiplied by the average number of images along the z direction that contained cells in focus. Lastly we multiplied by the voxel size 0.1×0.1×0.2 μm³ for images generated using the Zeiss Elyra, and 0.075×0.075×0.1 μm³ for images generated by the Zeiss CellObserver. The second method determined the cell area in pixels for each z-plane using the same algorithm as described in (Duncan et al., 2016, Olsson and Hartley, 2016) that was previously used for the z-projection area calculation. Cell volume was then estimated as the sum of cell area pixels over all z-planes multiplied by the above voxel size. The two segmentation methods are implemented in the Python programming language and are available at https://github.com/ri23/FISHmodel.

For prevasculature cells, manual inspection indicated that the above described computational algorithms (Duncan et al., 2016, Olsson and Hartley, 2016) did not generate accurate segmentation results. This was because the prevasculature cells were more tightly packed in the root squash such that the cell outlines were less pronounced. Instead, by using ImageJ (ROI manager plugin), we manually segmented these cells to determine their cell area in pixels in one z-plane that was in focus with the DAPI signal. This value was then multiplied by the pixel area (0.1×0.1 μm² for Zeiss), resulting in the cell area. We confirmed that for outer layer cells, manual and computational cell area segmentation methods generated similar results.

Calculation of Mean and Standard Error of Parameter Estimates Using Propagation of Errors

Throughout this study we utilized the theory of propagation of errors to estimate the mean and error (SEM) on a quantity (e.g. parameter values) that is generally a function f(X₁,.., X_n) of n experimentally determined quantities X₁…X_n with given means 〈X₁〉…〈X_n〉 and errors (SEM) dX₁…dX_n. Assuming statistical independence and relatively small errors:

Mean of quantity of interest: 〈f(X₁,.., X_n)〉 = f(〈X₁〉,.., 〈X_n〉),

Error on quantity of interest: $df\left(X_1,\mathrm{..},X_n\right)=\sqrt{\sum _{i=1}^n{\left(\frac{\partial f}{\partial X_i}d{X}_i\right)}^2}$.

Poisson Process Describing FLC mRNA Degradation

To model cellular FLC mRNA levels after transcription inhibition, we consider a Poisson process with a constant probability per unit time d for degradation of a single mRNA. The probability that a given mRNA does not degrade during a time t is therefore e^−dt, while the probability that it does is 1−e^−dt. If the system is initialized with b mRNA molecules, then the probability P(r,t) that r ≤ b survive at time t is therefore $\left(\begin{array}{c}b\\ r\end{array}\right){\left(e^{-dt}\right)}^r{\left(1-e^{-dt}\right)}^{b-r}$. Generalising to the case where the system is initialized with any number of mRNA b up to a maximum of M, with probability P(b,0), then the probability P(r,t) is then given by $P\left(r,t\right)=\sum _{b=r}^M\left(\begin{array}{c}b\\ r\end{array}\right){\left(e^{-dt}\right)}^r{\left(1-e^{-dt}\right)}^{b-r}P\left(b,0\right)$, as stated in the main text.

More formally this result can also be derived as follows. The master equation for P(r,t) is given by (Gardiner, 2009): $\frac{\partial }{\partial t}\text{P}\left(r,t\right)=d\left(r+1\right)\text{P}\left(r+1,t\right)-dr\text{P}\left(r,t\right)$. First, we define the generating function $G\left(w,t\right)=\sum _{b=0}^{\infty }{w}^b\text{P}\left(b,t\right)$ (Gardiner, 2009, Shahrezaei and Swain, 2008). We then convert the master equation into a partial differential equation for G(w,t): $\frac{\partial }{\partial t}G\left(w,t\right)=d\left(1-w\right)\frac{\partial }{\partial w}G\left(w,t\right)$. We solve this equation analytically for G(w,t), given the Dirichlet boundary conditions $G\left(w,0\right)=\sum _{b=0}^{\infty }{w}^b\text{P}\left(b,0\right)$, using the method of characteristics (Shahrezaei and Swain, 2008, Zwillinger, 1998). This results in the following expression: $G\left(w,t\right)=\sum _{b=0}^{\infty }{\left(w{e}^{-dt}+1-e^{-dt}\right)}^b\text{P}\left(b,0\right)$. By the definition of the generating function we can make use of its Taylor series expansion to obtain $\text{P}\left(r,t\right)={\frac{1}{r!}\frac{\partial }{\partial w^r}G\left(w,t\right)|}_{w=0}$. We then obtain the desired result: $\text{P}\left(r,t\right)=\sum _{b=r}^M\left(\begin{array}{c}b\\ r\end{array}\right)\left(e^{-dt}\right){\left(1-e^{-dt}\right)}^{b-r}\text{P}\left(b,0\right)$.

Mathematical Characterization of Variation Due to Cell Volume and Intrinsic Noise

To assess the relation between FLC mRNA and volume for the data shown in Figure 2H, we investigated the mean and variances as follows. We took a bin size of ΔV = 0.5 pL and binned the data ranging from V_min = 0.5 pL up to V_max = 3.5 pL accordingly. We then calculated for the data in each bin the mean (with errorbars: SEM) and variance (with error bars: standard error on the variance $S{E}_{Var\left(X\right)}=\frac{Var\left(X\right)}{\sqrt{n-1}}$, with n the number of relevant data points). Furthermore we compared these results with a model where the FLC mRNA scales linearly with cell volume, as described previously (Padovan-Merhar et al., 2015). We also extended this analysis to include the effects of our volume estimation error, as described below.

As described in the main text and supported by our experimental observations (Figure 2G), we consider the cellular mRNA levels as a random variable R(V) such that its expectation conditioned on cell volume V is given by the observed linear relationship: E(R|V) = βV (Padovan-Merhar et al., 2015). If the residual variation would be minimal, the conditional distribution would be Poissonian: P(R|V) = Pois(λ = βV). In this case, the variance as a function of volume is Var(R|V) = βV (Figure 2H, Poisson limit). To assess the mean and variance of this Poisson model in the presence of our experimental volume measurement error of $\varepsilon$ = 0.3pL (≈20% of the average cell volume, Figure S1D), we instead computed $\text{E}\left(R\left(\tilde{V}\right)|\tilde{V}\in \left[V-\varepsilon ,V+\varepsilon \right]\right)$ and $Var\left(R\left(\tilde{V}\right)|\tilde{V}\in \left[V-\varepsilon ,V+\varepsilon \right]\right)$ as follows.

First note that by definition we have

$$\text{E}\left(R\left(\tilde{V}\right)|\tilde{V}\in \left[V-\varepsilon ,V+\varepsilon \right]\right)=\underset{0}{\overset{\infty }{\int }}r\text{P}\left(R\left(\tilde{V}\right)=r|\tilde{V}\in \left[V-\varepsilon ,V+\varepsilon \right]\right)dr\text{.}$$

The conditional probability can be computed by invoking Bayes’ rule:

$$\text{P}\left(R\left(\tilde{V}\right)=r|\tilde{V}\in \left[V-\varepsilon ,V+\varepsilon \right]\right)=\frac{\underset{V-\varepsilon }{\overset{V+\varepsilon }{\int }}\text{P}\left(R\left(V\right)=r|V\right)\text{P}\left(V\right)dV}{\underset{V-\varepsilon }{\overset{V+\varepsilon }{\int }}\text{P}\left(V\right)dV}\text{.}$$

We computed in a custom-written MATLAB script, the (non-normalized) probability density P(V) directly from our experimental data by binning our volume estimates with bin size ΔV=0.02pL. Then by inserting the underlying Poisson distribution $\text{P}\left(R\left(V\right)=r|V\right)=\frac{{\left(\beta V\right)}^r}{r!}{e}^{-\beta V}$ with our experimentally observed volume distribution we can approximate the conditional probability by a sum:

$$\text{P}\left(R\left(\tilde{V}\right)=r|\tilde{V}\in \left[V-\varepsilon ,V+\varepsilon \right]\right)=\frac{\sum _{\tilde{V}=V-\varepsilon }^{V+\varepsilon }\frac{{\left(\beta \tilde{V}\right)}^r}{r!}{e}^{-\beta \tilde{V}}\text{P}\left(\tilde{V}\right)}{\sum _{\tilde{V}=V-\varepsilon }^{V+\varepsilon }\text{P}\left(\tilde{V}\right)}\text{.}$$

With this expression we then approximated the conditional expectation and variance as sums:

$$\text{E}\left(R\left(\tilde{V}\right)|\tilde{V}\in \left[V-\varepsilon ,V+\varepsilon \right]\right)=\sum _{r=0}^{R_{\max }}r\text{P}\left(R\left(\tilde{V}\right)=r|\tilde{V}\in \left[V-\varepsilon ,V+\varepsilon \right]\right)$$

and

$$\begin{array}{c}Var\left(R\left(\tilde{V}\right)|\tilde{V}\in \left[V-\varepsilon ,V+\varepsilon \right]\right)=\\ \text{E}\left[{\left(R\left(\tilde{V}\right)-\text{E}\left(R\left(\tilde{V}\right)|\tilde{V}\in \left[V-\varepsilon ,V+\varepsilon \right]\right)\right)}^2|\tilde{V}\in \left[V-\varepsilon ,V+\varepsilon \right]\right]\\ =\sum _{r=0}^{R_{\max }}{\left[r-\text{E}\left(R\left(\tilde{V}\right)|\tilde{V}\in \left[V-\varepsilon ,V+\varepsilon \right]\right)\right]}^2\text{P}\left(R\left(\tilde{V}\right)=r|\tilde{V}\in \left[V-\varepsilon ,V+\varepsilon \right]\right)\end{array}$$

Here, R_max indicates the maximal FLC mRNA number as observed in our data set.

Lastly, to assess intrinsic variability in mRNA levels in the presence of external variability arising from cell volume, we computed the volume-corrected noise measure, as previously described in Ref. (Padovan-Merhar et al., 2015): $N_R:=\frac{Var\left(R\right)-Var\left(\text{E}\left(R|V\right)\right)}{\text{E}{\left(R\right)}^2}$. In our case of the linear relation E(R|V) = βV the second variance term can be expressed as Var(E(R|V)) = Var(βV) = β²Var(V). Furthermore by taking the expectation over E(R|V), we find that E(R) = βE(V). We use this result to find an expression for the covariance:Cov(R,V) = E(RV)−E(R)E(V) = βE(V²)−βE(V)² = βVar(V). We can now combine these results to obtain Var(E(R|V)) = βCov(R,V). Altogether, this leads to (Padovan-Merhar et al., 2015): $N_R=\frac{Var\left(R\right)}{\text{E}{\left(R\right)}^2}-\frac{Cov\left(R,V\right)}{\text{E}\left(R\right)\text{E}\left(V\right)}$. Error bars were determined by bootstrapping as in (Padovan-Merhar et al., 2015). For the Poisson limit model, we can instead calculate the volume-corrected noise measure directly from its definition. First we note that from the law of total probability (Shahrezaei and Swain, 2008, Sherman et al., 2015), we have Var(R) = E(Var(R|V))+Var(E(R|V)). This expression then leads to the final result: $N_R=\frac{\text{E}\left(Var\left(R|V\right)\right)}{\text{E}{\left(R\right)}^2}=\frac{\text{E}\left(\beta V\right)}{\text{E}{\left(R\right)}^2}=\frac{1}{\text{E}\left(R\right)}$.

Time Averaging of FLC Gene Copy Number throughout the Cell Cycle

We used Arabidopsis cell cycle stage time period estimates determined by (Hayashi et al., 2013, Yin et al., 2014) to approximate the average FLC gene copy number N_loci. The cell cycle for meristematic root cells (as analysed in our smFISH assay) is, on average, 17h (Hayashi et al., 2013, Yin et al., 2014). In these cells FLC gene copy number increases from 2 in G1 to 4 by the end of S phase. During mitosis, transcription seems not to occur so that the copy number is effectively zero (Duncan et al., 2016, Rosa et al., 2016). If N_loci(t) represents the gene copy number throughout the cell cycle for $0\le t\le 17h$, then the copy number changes over time as follows:

$$N_{loci}\left(t\right)=\{\begin{array}{cc}2& if0\le t\le 7h\\ 3& if7h\le t\le 8h\\ 4& if8h\le t\le 14.5h\\ 0& if14.5h\le t\le 17h\end{array}$$

The time average of N_loci(t) throughout the cell cycles is then N_loci = 2.5. As described, the cell cycle averaged production rate per locus F then equals: $F=\frac{\langle R\rangle d}{N_{loci}}$, with 〈R〉 the average cellular FLC mRNA level and d the mRNA degradation rate. We also varied the above dynamics such that the time points where N_loci(t) changed (i.e. at 7h, 8h and 14.5h), could deviate by at most 1 hour from these values. Such alterations resulted in a maximal average loci value of N_loci = 2.8 and a minimum of N_loci = 2.4.

In the scenario where the production rate per locus F(t) dynamically changes to counteract changes in gene copy number N_loci(t) throughout the cell cycle time t, we would have the following situation: C = N_loci(t)F(t), with C a constant that is not dependent on the cell cycle time (except during mitosis where F(t)=0). As explained in the main text, integrating over the cell cycle is equivalent to averaging over the observed cell population: $\langle R\rangle =\frac{1}{d}\frac{1}{17h}\underset{0}{\overset{17h}{\int }}{N}_{loci}\left(t\right)F\left(t\right)dt$. This results in $C=\frac{17}{14.5}\langle R\rangle d$. The time averaged production rate per locus (F) is then obtained again by integrating over the cell cycle: $F=\frac{1}{17h}\underset{0}{\overset{17h}{\int }}F\left(t\right)dt=\frac{\langle R\rangle d}{2.7}$. This shows that this scenario is effectively equivalent to having the cell-cycle averaged copy number N_loci = 2.7.

Determination of Cellular FLC Intron 1 and Exonic Foci Count Scaling with Cell Size

In order to determine how the cellular intron foci counts for the various probe sets scale with cell size (either volume or cell area), as shown in Figures 3E, 3F, and 3H, 4C–4F, S2E, S3B, and S3C, we wrote a custom MATLAB script that first ordered the cells according to their cell size. For volumes, this procedure generated the sequence V₁≤V₂ ….≤V_N, where N is the total number of cells. We then calculated the range of attained sizes $\langle V_k\rangle =\frac{1}{k}\sum _{i=1}^k{V}_i$ for k = 1… N and $\langle V_{N+k}\rangle =\frac{1}{N-k}\sum _{i=1+k}^N{V}_i$ for k=1… N-1, which are thus averages over the relevant cell subpopulations. Note that by construction, the 〈V_j〉 are monotonically increasing with j = 1 … (2N − 1) and range from the minimal size 〈V₁〉 = V₁ to the maximal size 〈V_2N−1〉 = V_N. Then, with the given cell order above, we calculate the corresponding (average) cellular intron foci counts for a given volume 〈V_j〉: $S\left(\langle V_k\rangle \right)=\frac{1}{k}\sum _{i=1}^{k}S\left(V_i\right)$ for k = 1… N, and $S\left(\langle V_{N+k}\rangle \right)=\frac{1}{N-k}\sum _{i=1+k}^{N}S\left(V_i\right)$ for k = 1… N-1. Error bars of these estimates are the standard error on the mean: $S{E}_{S\left(\langle V_k\rangle \right)}=\frac{1}{\sqrt{k}}\sqrt{\frac{1}{k-1}\sum _{i=1}^k{\left(S\left(V_i\right)-S\left(\langle V_k\rangle \right)\right)}^2}$ for k = 1… N, and $S{E}_{S\left(\langle V_{N+k}\rangle \right)}=\frac{1}{\sqrt{N-k}}\sqrt{\frac{1}{N-k-1}\sum _{i=1+k}^N{\left(S\left(V_i\right)-S\left(\langle V_{N+k}\rangle \right)\right)}^2}$ for k = 1… N-1. To ensure precise estimates, we have only included averages calculated from at least 10 experimentally observed cells in all plots shown.

Inference of Pol II Elongation, FLC Intron 1 Processing and Lariat Degradation Rates

For the estimation of the Pol II elongation rate (v), intron processing (σ) and lariat degradation rates, respectively 5′ to 3′ (k₅₃) and 3′ to 5′ (k₅₃), we investigated the levels observed from four different intron 1 smFISH probe sets (Figure 3). One covered the full intron 1, the second covered the 5′ half, the third covered the middle of the intron symmetrically, also with a length of half the intron, and the fourth covered the 3′ half. We denote their respective RNA levels at an FLC locus as I_f, I_5′, I_m and I_3′ (Figure 3B). The gene length covered by the 5′, mid and 3′ probe sets is L_p=1.8 kb (Table S1), i.e. half the intron length, with a covered gene length of 2L_p for the full-length intron probe set (Duncan et al., 2016, Rosa et al., 2016). We, and others have found that having only two thirds of the probe set bound could already be sufficient to generate a detectable focus signal (Duncan et al., 2016, Raj et al., 2008, Rosa et al., 2016). Consequently, intronic RNA with a “missing length fraction” f_Lp of up to one-third of the probe set length could in principle still be detected.

Full-length intron 1 has, by the definition of σ (Figure 3A), a lifetime of $T_f=\frac{1}{\sigma }$. However, detected intron 1 RNA with a missing length 2L_pf_Lp could arise from two sources: partially complete transcripts where Pol II has not yet transcribed this missing length or a previously full-length lariat RNA that is already partly degraded. Therefore, we find the expectation value: $\text{E}\left(I_f\right)=\frac{F}{\sigma }+\frac{2F{L}_p{f}_{Lp}}{v}+\frac{2F{L}_p{f}_{Lp}}{k_{53}+k_{35}}$, where F is the population averaged FLC transcription initiation rate per locus. Effectively, the lifetime in the presence of a missing length is then $T_f=\frac{1}{\sigma }+\frac{2L_p{f}_{Lp}}{v}+\frac{2L_p{f}_{Lp}}{k_{53}+k_{35}}$.

I_5′ is constituted by full-length intron 1, but also Pol II elongating in the 3′ half of the intron. Then by taking into account again the missing length fraction arising from the same two sources: not yet fully transcribed RNA and lariat degradation intermediates, we obtain: $T_{5\text{'}}=\frac{1}{\sigma }+\frac{L_p}{v}+\frac{L_p{f}_{Lp}}{v}+\min \left(\frac{L_p{f}_{Lp}}{k_{53}},\frac{L_p\left(1+f_{Lp}\right)}{k_{53}+k_{35}}\right)$.

I_3′ is constituted by full-length intron 1, but with similar missing length fraction contributions as for I_5′: $T_{3\text{'}}=\frac{1}{\sigma }+\frac{L_p{f}_{Lp}}{v}+\min \left(\frac{L_p{f}_{Lp}}{k_{35}},\frac{L_p\left(1+f_{Lp}\right)}{k_{53}+k_{35}}\right)$.

Lastly, I_m is constituted of full-length intron 1, Pol II elongating in the 3′ quarter of intron 1 and the missing length fractions:

$$T_m=\frac{1}{\sigma }+\frac{0.5L_p}{v}+\frac{L_p{f}_{Lp}}{v}+\min \left(\frac{L_p\left(0.5+f_{Lp}\right)}{k_{53}},\frac{L_p\left(0.5+f_{Lp}\right)}{k_{35}},\frac{L_p\left(1+f_{Lp}\right)}{k_{53}+k_{35}}\right)$$

.

Our observed quantities are the respective average FLC intron 1 foci numbers per cell: $\langle S_f\rangle ,\langle S_{5\text{'}}\rangle ,\langle S_m\rangle \text{and}\langle S_{3\text{'}}\rangle$. We next assume that the variables $I_j$ (subscript $j\in \left\{f,5\text{'},m,3\text{'}\right\}$ ) are Poisson distributed with mean production rate F and degradation rate $T_j^{-1}$. Given our average FLC copy number N_loci, the 〈S_j〉 can then be modelled by: $\text{E}\left(S_j\right)=N_{loci}P\left(I_j>0\right)=N_{loci}\left(1-\text{P}\left(I_j=0\right)\right)=N_{loci}\left(1-\exp \left(-F{T}_j\right)\right)$.

To estimate the four unknown kinetic parameters (v, σ, k₃₅ and k₅₃) from our average cellular foci numbers $\langle S_j\rangle$, we wrote a custom MATLAB script that performed a systematic parameter sweep for all parameter combinations lying in the range: v=0.1-20 bp/s, k₅₃=0.1-20 bp/s and k₃₅=0.1-20 bp/s, and σ=3x10⁻⁴ – 20x10⁻⁴ s⁻¹, while we varied the missing length fraction $f_{Lp}\in \left\{0,\frac{1}{9},\frac{2}{9},\frac{1}{3}\right\}$. We then calculated our chi-square statistic:${\mathit{\chi }}^2={\sum _{j\in \left\{f,5\text{'},m,3\text{'}\right\}}\left(\frac{\langle S_j\rangle -\text{E}\left(S_j\right)}{S{E}_{\langle S_j\rangle }}\right)}^2$. Assuming normally distributed standard errors on our estimates $S{E}_{\langle S_j\rangle }$, χ² then follows a chi-square distribution with four degrees of freedom. For all resulting χ² statistics, we determined their probabilities P(χ²) and accepted the statistic as a good fit when P(χ²) ≥ 0.1. This resulted in a set of consistent parameter sets for which the marginal distribution are shown in Figures S2A–S2D and, for $f_{Lp}=\frac{1}{3}$, in Figure 3D (boxplot: median, Q1, Q3 and min/max). Similar results were also obtained using P(χ²) ≥ 0.05. Note that for f_Lp = 0, the mathematical expressions for I_f and I₃ are equal. As a consequence, k₅₃ and k₃₅ remain undetermined with this missing length fraction (Figures S2C and S2D). We also performed the same procedure for a wide range of parameter values outside the above described regions, but we could not find any further good fits according to the criteria above. Lastly, we repeated the above described parameter fitting procedure to the average intron foci numbers S_j(〈V_k〉) (Figures 3E and 3F) for small (〈V_k〉 = 0.9pL) and large cells (〈V_k〉 = 2.8pL), using the lower and upper bounds N_loci = 2 and N_loci = 4 in the expression $F\left(\langle V_k\rangle \right)=\frac{\beta \langle V_k\rangle d}{N_{loci}}$ for the per locus transcription initiation probability per unit time.

Stochastic Simulations of Cellular FLC mRNA Production and Degradation

To investigate the potential consistency of transcriptional bursting with the observed cellular FLC mRNA levels (Figure 2C), we simulated stochastic cellular FLC mRNA production and degradation in root outer layer cells (see Figure S1E for a graphical representation) by implementing a Gillespie algorithm (Slepoy et al., 2008) in C++ (https://github.com/ri23/FISHmodel).

Cellular FLC mRNA production occurred with probability per unit time (propensity): p_t = βVd. This reaction resulted in a sense FLC mRNA: sFLC. This mature transcript could then be degraded with probability per unit time d. Here, β = 31pL⁻¹ indicates the slope of the linear FLC mRNA scaling with cell volume V (Figure 2G). Furthermore, d = 3.3 × 10⁻⁵s⁻¹ indicates the experimentally determined FLC mRNA degradation rate.

For the ON/OFF transcription model (see Figure S1E for a graphical representation) we include reactions for the Boolean STATE variable to transition from an active (inactive) into an inactive (active) state with probability per unit time p_t = k_off STATE (p_t = k_on(1−STATE)). Production can occur with propensity: $p_t=\{\begin{array}{cc}{p}_{on}& ifSTATE=1\\ 0& ifSTATE=0\end{array}$. The production probability per unit time in the ON state p_on is related to the burst size $bs=\frac{p_{on}}{k_{off}}$, where bs is defined as the mean number of transcripts produced per ON-OFF cycle. In order to be considered bursty transcription, two conditions have to be met (Dar et al., 2012, Shahrezaei and Swain, 2008): k_off≫k_on with a burst size bs ≫ 1. To investigate whether FLC production could be bursty, we set the off rate sufficiently fast, k_off = 0.1 s⁻¹, which effectively ensured that the first condition was met (see below). The total production rate (per locus) has to be equal to the time-averaged transcription rate (per locus), leading to: $F\left(V\right)=\frac{\beta Vd}{N_{loci}}=\frac{p_{on}}{k_{off}}\frac{1}{1+\frac{k_{on}}{k_{off}}}{k}_{on}=bs\frac{1}{1+\frac{k_{on}}{k_{off}}}{k}_{on}$. Here N_loci represents the number of FLC loci in each cell. In the main text we first described a cellular ON/OFF production model: in this case N_loci equals 1. We then also simulated the more realistic cases where ON/OFF transcription occurs from N_loci = 2 or 4 (independent) loci. These considerations lead to two distinct scenarios:

• 1)Burst size scales with volume, as proposed for mammalian genes (Padovan-Merhar et al., 2015), with burst frequency k_on independent of volume:

$$bs\left(V\right)=\langle bs\rangle \frac{V}{\langle V\rangle }\text{and}{k}_{on}=\frac{k_{off}\beta \langle V\rangle d}{k_{off}{N}_{loci}\langle bs\rangle -\beta \langle V\rangle d}\text{.}$$

Here 〈bs〉 is a chosen constant, the burst size in a cell of average volume 〈V〉 = 1.8pL.

• 2)Burst size bs is a chosen constant and burst frequency scales with volume: $k_{on}=\frac{k_{off}\beta Vd}{k_{off}{N}_{loci}bs-\beta Vd}$.

To investigate how large the burst sizes could be, bs (and in scenario 2: 〈bs〉) was then systematically varied from 1 upwards. Through the expressions above for each scenario, setting these burst size parameters then fully determined both the burst frequency k_on and p_on.

As a model input parameter, we provided to each simulation an experimentally observed cell volume V (Figure S1F). To obtain robust model distributions of the simulated mRNA levels, we repeated the procedures described above over 50 simulations for each cellular volume as observed from the full-length FLC intron 1 data set (Figure S1F). We then repeated this procedure for N_loci batches, resulting in 10000 simulations per batch. Simulations started at time t = 0 and ran until (simulated) time t, updated according to the Gillespie algorithm, exceeded a predefined time of 10 days, to allow the system to reach steady state. We then output the cellular volume and simulation FLC mRNA levels (Figure S1G). For the simulations with N_loci = 2 and 4, we summed the 10000 simulations from the first batch with the other batches to generate 10000 simulated cells with associated cellular mRNA levels, in accordance with the observed cellular volume distribution. We then compared the experimentally observed cellular mRNA distribution (n = 209, Figure 2C) with the 10000 simulated cells using a Levene’s test, a Brown-Forsythe test and a Kolmogorov-Smirnov test. The former two test for equal variance by using the mean or median in their test statistics, while the latter tests for equal distributions. When the resulting p values were smaller than 0.05, we considered the chosen burst size incompatible with our experimental results. Maximal consistent burst sizes were, respectively:

Scenario 1, burst size scales with volume:

Levene’s test: 3 (N_loci=1: p=0.10, N_loci=2: p=0.07, N_loci=4: p=0.05);

Brown-Forsythe test: 5 (N_loci=1: p=0.07, N_loci=2: p=0.05) and 6 (N_loci=4: p=0.05);

Kolmogorov-Smirnov test: 8 (N_loci=1: p=0.05) and 7 (N_loci=2: p=0.07, N_loci=4: p=0.06).

Scenario 2, burst frequency scales with volume:

Levene’s test: 3 (N_loci=1: p=0.05, N_loci=2: p=0.06, N_loci=4: p=0.06);

Brown-Forsythe test: 4 (N_loci=1: p=0.06, N_loci=2: p=0.09, N_loci=4: p=0.06);

Kolmogorov-Smirnov test: 5 (N_loci=1: p=0.06, N_loci=2: p=0.07, N_loci=4: p=0.08).

Stochastic Simulations of Spatiotemporal FLC Transcriptional Dynamics

To quantify mRNA release from the FLC locus (Figure 3A), we simulated stochastic FLC transcription and RNA dynamics in root outer layer cells by implementing a spatiotemporal Gillespie algorithm (Slepoy et al., 2008) in C++ (https://github.com/ri23/FISHmodel). The reactions included are described below and illustrated in Figure S3A.

The FLC locus (∼ 6 kb) was divided into L=209 sites of length N_bp= 30 bp (see Figure S3A for a graphical representation). The sites are numbered 0…(L-1). The sense / antisense Transcription Start Sites (TSSs) are represented by site 4 and 208 respectively. Each site can be occupied by at most one Pol II. If a TSS site is unoccupied, a Pol II can bind to that TSS. We refer to this process as transcription initiation. Since outer layer cells exhibit very low antisense expression (Figures 4B and 4C), we set the antisense transcription initiation rate to zero. Once a Pol II has bound to a sense TSS we assume it is competent to elongate in the sense direction. Of course, transcription initiation, subsequent formation of a transcription elongation complex and possibly promoter proximal pausing are themselves complex processes. Nevertheless, within our minimal modelling approach we account for these processes within a single “coarse-grained” transcriptional initiation probability. Incorporating these processes in more detail would not qualitatively alter our conclusions on FLC regulation. If the TSS site is unoccupied, sense initiation can occur with probability per unit time (propensity): $p_t=\frac{\beta Vd}{N_{loci}}$.

Based on previously published Pol ChIP expression in ColFRI (Li et al., 2015) and consistent with previous modelling of FLC regulation (Wu et al., 2016), we assume the magnitude of the elongation rate is independent of position along the FLC gene. Furthermore, within our minimal modelling approach we do not explicitly incorporate Pol II pausing, backtracking or arrest. Including these processes in more detail would not qualitatively alter our conclusions. In case of sense transcription, a Pol II at site i (P_i = 1) can elongate to a neighbouring site i+1, if that neighbouring site is unoccupied, with propensity: $p_t=\frac{v}{N_{bp}}{P}_i$

Here, v = 3 bp/s represents the elongation rate, consistent with the range determined through our parameter inference procedure (Figure 3D).

Consistent with previous findings (Wu et al., 2016), we assume that there is no early termination, only termination of a transcribing Pol II as a consequence of cleavage/polyadenylation of the RNA transcript. We used the annotated RNA 3′ ends to determine where Pol II could drop off the template after elongation. We assume that Pol II ceases to elongate soon after it transcribes its canonical pA sequence (Wu et al., 2016): when a sense Pol II reaches the Transcription End Site (TES), site 204, it can terminate with probability per unit time of k_pA = 0.02s⁻¹, resulting in a free Pol II and a 3′ processed sense transcript that remains at the locus (Figure S3A). The exact value of k_pA has little influence on our results as long it is shorter than the mRNA release rate k_x, as is the case in our choice of parameters (see below).

The creation of sense RNA is modelled as follows (Figure S3A). A sense Pol II at site i (P_i) has produced unspliced RNA corresponding to the sites TSS…i-1. Splicing of sense FLC intron 1 is explicitly modelled: as soon as Pol II elongates past the intron 1 acceptor site I1A=131, Pol II can continue to elongate and, in addition, splicing of intron 1 can occur with a probability per unit time σ = 1.5 × 10⁻³s⁻¹, consistent with the range determined through our parameter inference method (Figure 3D). This reaction results in a Pol II with nascent, spliced RNA attached: $P_i^s$. This Pol II species can elongate with the same dynamics as for Pol II with unspliced nascent RNA (P_i). After splicing, lariat degradation is assumed here to occur immediately (see below). In the main text, the σ⁻¹ timescale was defined slightly differently as the time from when intron 1 is completely transcribed to the moment of splicing, plus the extra waiting time until lariat degradation begins. However, our results (Figure 3) do not depend on this model simplification because our simulation output, i.e. all the RNA species that were measured experimentally (described below in detail), are unaffected by this detail. Therefore, despite this simplification, we can directly compare the simulation output with our experimental observations.

A splicing reaction results in cleaved intronic (lariat) RNA with the 5′ end at site I1D=14 and 3′ end at site I1A-1. We term this RNA species IN_I1D,I1A−1, with the first index indicating the 5′ end and the second index the 3′ end. This RNA and in general IN_i,j can then be degraded from 5′ to 3′ in a first order reaction with rate k₅₃ and propensity $p_t=\frac{k_{53}}{N_{bp}}I{N}_{i,j}$. As a result of this reaction, IN_i+1,j is formed, corresponding to intronic RNA with a 5′ end at site i+1 (and 3′ end at j>i+1). In the case of the last step of intron RNA degradation such that i+1=j, this reaction occurs without a reaction product. Similar to 5′ to 3′ degradation, we also allowed 3′ to 5′ lariat degradation with propensity $p_t=\frac{k_{35}}{N_{bp}}I{N}_{i,j}$ resulting in reaction product, IN_i,j−1. The k₅₃ and k₃₅ estimates were both set to 2 bp/s consistent with our experimental estimates.

We only explicitly modelled splicing reactions of sense intron 1 in the simulations. Incorporating splicing of additional sense introns in the model would not affect our results provided that each splicing reaction is independent of the others. Splicing can also occur after sense Pol II has terminated (Figure S3A). If Pol II has terminated with intron 1 spliced out, s1FLC is created, a cleaved full-length RNA at the locus with intron 1 spliced out. If Pol II has terminated prior to splicing of intron 1, a full-length, unspliced RNA termed unsFLC is produced. unsFLC can be spliced in intron 1 with probability per unit time σ resulting in s1FLC and IN_I1D,I1A−1. The lariat can then be degraded as described above. s1FLC can be released from the locus with probability per unit time: p_t = k_xs1FLC, i.e. we performed simulations with a constant export rate k_x = 5 × 10⁻⁴s⁻¹ in the presence of missing length fraction f_Lp=1/3, see below. Lastly, FLC mRNA release from the locus leads to a mature (spliced) sense FLC mRNA: sFLC. This mature transcript can then be degraded with probability per unit time d.

We output the cell volume, simulation RNA levels corresponding to FLC mRNA, the number of RNAs corresponding to the four intron 1 probe sets (I_f,I_5′ I_m and I_3′) and the number of exonic RNAs (R_loc, only considered in further analyses when I_f > 0), whilst taking into consideration a missing length fraction f_Lp=1/3, as follows:

$$\begin{array}{l}{I}_f=\mathit{unsFLC}+{\sum }_{i=I1D+\frac{2}{3}\left(I1A-I1D\right)}^{L-1}{P}_i+{\sum }_{i=I1D}^{I1D+\frac{1}{3}\left(I1A-I1D\right)-1}{\sum }_{j=i+\frac{2}{3}\left(I1A-I1D\right)}^{I1A-1}I{N}_{i,j};\\ I_m=unsFLC+{\sum }_{i=I1D+\frac{7}{12}\left(I1A-I1D\right)}^{L-1}{P}_i+{\sum }_{i=I1D}^{I1D+\frac{1}{4}\left(I1A-I1D\right)-1}{\sum }_{j=I1D+\frac{7}{12}\left(I1A-I1D\right)}^{I1A-1}I{N}_{i,j}+{\sum }_{i=I1D+\frac{1}{4}\left(I1A-I1D\right)}^{I1D+\frac{5}{12}\left(I1A-I1D\right)-1}{\sum }_{j=i+\frac{1}{3}\left(I1A-I1D\right)}^{I1A-1}I{N}_{i,j};\\ I_{5^{\prime }}=unsFLC+{\sum }_{i=I1D+\frac{1}{3}\left(I1A-I1D\right)}^{L-1}{P}_i+{\sum }_{i=I1D}^{I1D+\frac{1}{6}\left(I1A-I1D\right)-1}\left({\sum }_{j=i+\frac{1}{3}\left(I1A-I1D\right)}^{I1D+\frac{1}{2}\left(I1A-I1D\right)-1}I{N}_{i,j}+{\sum }_{j=I1D+\frac{1}{2}\left(I1A-I1D\right)}^{I1A-1}I{N}_{i,j}\right);\\ I_{3^{\prime }}=unsFLC+{\sum }_{i=I1D+\frac{5}{6}\left(I1A-I1D\right)}^{L-1}{P}_i+{\sum }_{i=I1D}^{I1D+\frac{1}{2}\left(I1A-I1D\right)-1}{\sum }_{j=I1D+\frac{5}{6}\left(I1A-I1D\right)}^{I1A-1}I{N}_{i,j}+{\sum }_{i=I1D+\frac{1}{2}\left(I1A-I1D\right)}^{I1D+\frac{2}{3}\left(I1A-I1D\right)-1}{\sum }_{j=i+\frac{1}{3}\left(I1A-I1D\right)}^{I1A-1}I{N}_{i,j};\\ R_{loc}=unsFLC+\mathit{s1FLC}+{\sum }_{i=sTES-11}^{sTES}\left(P_i+P_i^s\right)\text{.}\end{array}$$

The number of cellular FLC mRNA equals: N_loci × sFLC. The number of intron foci per cell were then for each simulation calculated as S_j = N_lociI_J with j∈{f,5′,m,3′}. Simulated time and number of simulations were as described for the cellular FLC mRNA dynamics simulations. Calculations of population average and averages for various attained volumes were performed in the same manner as described above for the experimental data points.

Quantification of FLC mRNA Release from the Locus

To determine the amount of exonic FLC RNA at the locus given the presence of FLC full-length intron 1, we utilized FISH-quant, a MATLAB software suite (Mueller et al., 2013). We followed the quantification procedures as detailed in the manual available from http://dev.mri.cnrs.fr/documents/95. This method requires abundant mRNA smFISH signal as well as a method to indicate the locations of loci: in our case FLC full-length intron 1 smFISH signal as this co-localizes exclusively with FLC loci (Figure S1A). Cell area outlines (using an overlay of mRNA and DAPI signal) and loci (using the intron 1 focus signal) were segmented manually. FISH-quant then determined computationally for each cell the (predominantly cytoplasmic) mRNA foci locations and background intensity profile. The resulting foci were manually inspected to confirm the accuracy of the algorithm. Cell areas and corresponding mRNA counts were then output to a text file. Cell areas were then converted into cell volumes using the projection method described above. As part of the mature mRNA quantification procedure, an overall average mRNA spatial intensity focus profile (point spread function, PSF) was then calculated from all determined mRNA foci. This background corrected intensity profile represents one mRNA molecule. The next step was to quantitatively compare the mRNA signal at the indicated loci with the PSF. Here, we considered three different algorithms that have been shown to be accurate for intensity quantification in the regime of relatively low RNA copy number with a spatially confined transcription site (Mueller et al., 2013):

• 1.Comparison of integrated intensity of the transcription site and individual mRNA molecules (Int).
• 2.Superimposition of PSFs to reconstruct an image of the transcription site (PSF).
• 3.Comparison of the estimated amplitude of the transcription site and individual mRNA molecules (Amp).

The results which indicated the number of molecules for each transcription site were then output. Lastly, we manually included the appropriate cell area as obtained from the mature mRNA output in the nascent RNA output list in order to relate cell area and exonic RNA number. The resulting three distributions were relatively similar, albeit with means varying from 1.9 up to 2.5 exonic RNA molecules (Figure 3H).

Data and Software Availability

Cell volume and area estimation and RNA foci count code, as well as code for stochastic simulations of (1) FLC mRNA production and degradation and (2) FLC transcription and RNA processing kinetics, all as described above, are available on https://github.com/ri23/FISHmodel. FISH-quant software, used to estimate the number of exonic FLC RNA at the locus, is available on https://code.google.com/archive/p/fish-quant/.

Author Contributions

R.I., S.R., Z.W., C.D., and M.H. conceived the study; S.R. and Z.W. performed the experiments; R.I., S.R., and Z.W. performed data analysis; R.I. and M.H. constructed the mathematical models; R.I. performed the simulations; R.I., C.D., and M.H. wrote the manuscript, with assistance from S.R. and Z.W.

Published: June 14, 2017