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A conserved coupling of transcriptional ON and OFF periods underlies bursting dynamics

Nature Structural & Molecular Biology (2025)Cite this article

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Abstract

Transcription commonly occurs in bursts, with alternating productive (ON) and quiescent (OFF) periods determining mRNA production rates. However, how bursting dynamics regulate transcription is not well understood. Here, we conduct real-time measurements of endogenous transcriptional bursting with single-mRNA sensitivity. Using the diverse transcriptional activities present in early Drosophila embryos, we find stringent relationships between bursting parameters. Specifically, ON and OFF durations are tightly coupled, and each level of gene activity is associated with a characteristic combination of these periods. Lowly transcribing alleles primarily adjust OFF periods (burst frequency), while highly transcribing alleles tune ON periods (burst size). These relationships persist across developmental stages, body-axis positions, cis-regulatory or trans-regulatory perturbations and bursting dynamics observed in other species. Our findings suggest a mechanistic constraint that governs bursting dynamics, challenging the view that regulatory processes independently control distinct parameters.

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Fig. 1: Live single-cell transcription rate measurements of endogenous gap genes.
Fig. 2: Direct estimation of bursting parameters reveals predominant control by the ON probability.
Fig. 3: Characteristic ON and OFF periods underlie each allele-ON probability.
Fig. 4: Transcription parameters collapse for all gap genes.
Fig. 5: Bursting parameters sample a restricted space and follow tight relationships.
Fig. 6: Effect of cis and trans perturbations on ON and OFF times.
Fig. 7: Generality of bursting relationships.
Fig. 8: Decoding bursting regimes from gene expression.

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Data availability

Original movies are available upon request. Full processed datasets are provided as source data and are available on Zenodo (https://doi.org/10.5281/zenodo.15396340)68.

Code availability

Full code is available on GitLab (https://gitlab.pasteur.fr/tglab/liveburstrulepaper).

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Acknowledgements

We thank members of the Gregor laboratory for their discussions and comments on the manuscript. We also thank E. Bertrand, M. Lagha, T. Lenstra, M. Levine, O. Radulescu, T. Sokolowski, G. Tkačik, E. Wieschaus and J. Yuly for comments and discussion at various stages. We thank D. Larson and T. Lenstra for sharing data. This work was supported in part by the US National Science Foundation, through the Center for the Physics of Biological Function (PHY-1734030 to T.G.), and by National Institutes of Health Grants R01GM097275, U01DA047730 and U01DK127429 (to T.G.). M.L. received a Human Frontier Science Program fellowship (LT000852/2016-L), EMBO long-term postdoctoral fellowship (ALTF 1401-2015) and Rothschild postdoctoral fellowship.

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Author notes

  1. These authors contributed equally: Po-Ta Chen, Michal Levo, Benjamin Zoller.

Authors and Affiliations

  1. Joseph Henry Laboratories of Physics & Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA

    Po-Ta Chen, Michal Levo, Benjamin Zoller & Thomas Gregor

  2. Department of Biochemistry and Molecular Biophysics, Columbia University, New York, NY, USA

    Michal Levo

  3. Department of Stem Cell and Developmental Biology, CNRS UMR3738 Paris Cité, Institut Pasteur, Paris, France

    Benjamin Zoller & Thomas Gregor

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  1. Po-Ta Chen
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Contributions

M.L., B.Z. and T.G. conceptualized the project. P.C. designed and constructed the microscope and performed data acquisition of all live-imaging experiments. M.L. engineered genetic constructs and produced fly lines. B.Z. processed raw data and performed image and data analysis. M.L., B.Z. and T.G. wrote the original manuscript and reviewed, edited and proofed the final text. M.L. and T.G. secured the funding.

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Correspondence to Thomas Gregor.

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Extended data

Extended Data Fig. 1 Signal calibration, measurement error and embryo-to-embryo variability.

(a) The four trunk gap genes — giant (gt), hunchback (hb), Kruppel (Kr), and knirps (kni) — were imaged using MS2/PP7 stem-loop labeling. Stem-loop cassettes (black arrow) were inserted in either intronic or 3′UTR regions. These genes feature distinct cis-regulatory architectures, differing in numbers of promoters, enhancers (colored boxes), and regulatory sequence composition (for example, TF binding motifs, core promoter elements). (b) Relative calibration unit (left) and relative error (right) for each gap gene construct related to Fig. 1c. Calibration of live transcriptional signals to absolute units was achieved by matching spatial activity profiles (averaged over nuclei in 2.5% AP bins during a 5-min window in NC13) with smFISH-based measurements (Zoller et al., 2018). (Left) A global calibration unit was obtained from a joint fit across all genes (horizontal black line, ±1 s.e. as dashed lines). Individual fits per construct (colored circles) are shown as a percentage of the global value. (Right) Relative calibration errors remain below 5%, with error bars representing 68% confidence intervals. (c) Higher-order cumulants (mean, variance, 3rd and 4th) of transcriptional activity from live imaging closely match those from smFISH (Zoller et al., 2018). Live data were binned spatially (2.5% AP) and temporally (5 min window in NC13), converted from cytoplasmic mRNA units (C.U.) to Pol II counts for a 3.3 kb gene. Cumulants were normalized using g0, the intercept of a Poisson background (dashed line) and a polynomial fit (solid for live, dotted for smFISH). g0 represents the mean number of Pol II on a 3.3 kb gap gene at peak activity; it is estimated at 13.6 (live) and 15.2 (smFISH), a 12% difference. The higher cumulants versus mean relationships from live imaging and smFISH closely match (black solid versus dotted line), confirming the quantitative accuracy and proper calibration of our live assay. These independent methods, one involving fixation (smFISH), the other gene editing (MS2/PP7), validate each other and indicate that our synthetic modifications do not measurably affect endogenous transcriptional output. (d) Background intensity is temporally stable, showing no bleaching under two-photon imaging. Background levels (C.U.) were measured in nuclei from weakly expressing regions (x/L∈[0.48,0.60]) across 10 hb-MS2 embryos. The mean background (black line, ±1 s.d., σb = 0.53) is stable, with only transient deviations during mitosis due to nuclear envelope dynamics (breaking and reformation) affecting MCP-GFP concentration. Outside mitosis, it closely matches the overall median (red dashed line), confirming the absence of bleaching under two-photon imaging. (e) Imaging noise was assessed via two independent methods. (Left) An interlaced MS2/PP7 cassette in Kr (first intron) labeled by MCP-GFP and PCP-mCherry was used to compare red/green channel intensities. Deviations orthogonal to the diagonal (slope one) quantify the imaging spread σimg, modeled as \({\sigma }_{{\rm{b}}}^{2}+\alpha I\), where \({\sigma }_{{\rm{b}}}^{2}\) is background noise and αI represents Poisson shot noise based on mean intensity I. Dashed lines show the resulting fit for \({\sigma }_{{\rm{img}}}^{2}\), corresponding to ±1 s.d. around the diagonal. (Right) In a second approach, transcriptional time series were analyzed to separate uncorrelated imaging noise from biological fluctuations that are correlated due to the elongation of tagged nascent transcripts. Mean μ(t), variance σ2 (t), and lagged covariance Cov(t, t + Δt) were computed across nuclei (1.5–2.5 AP bins) and for all measured genes. Imaging variance \({\sigma }_{{\rm{img}}}^{2}\) estimated as σ2 (t)-Cov(t, t + Δt) is plotted as a function of μ(t) for all time points. We estimated average \({\sigma }_{{\rm{img}}}^{2}\) by fitting the data with \({\sigma }_{{\rm{b}}}^{2}+\alpha \mu\) (solid line). Overall, the fractional imaging variability \({\sigma }_{{\rm{img}}}^{2}/{\sigma }^{2}\) is ~5%. (f) Both methods in (e) produce consistent estimates of imaging noise. The signal-to-noise ratio (SNR = μ/σimg) approaches unity for low expression (μ ≈ 1), indicating near single-molecule sensitivity. (g) Fractional embryo-to-embryo variability \({\sigma }_{{\rm{emb}}}^{2}/{\sigma }^{2}\), calculated as the ratio of inter-embryo variance (that is, variance of the mean activity across embryos) to total variance, is ~10%, across all gap genes and time points. Since total variance \({\sigma }^{2}={\sigma }_{{\rm{emb}}}^{2}+{\sigma }_{{\rm{img}}}^{2}+{\sigma }_{{\rm{nuc}}}^{2}\), and imaging (\({\sigma }_{{\rm{img}}}^{2}\)) and embryo variability (\({\sigma }_{{\rm{emb}}}^{2}\)) are minor components, the majority of transcriptional variability arises from nucleus-to-nucleus fluctuations (\({\sigma }_{{\rm{nuc}}}^{2}\)). Together, (e–g) support using total variance σ² as a robust proxy for biologically relevant noise from transcriptional bursting.

Extended Data Fig. 2 Dual color measurements to validate single-cell deconvolution and measure elongation rate.

(a) Validation of the kernel assumptions underlying the deconvolution of initiation events from single-allele transcription time series, using dual-color confocal imaging of hb and Kr. For hb (Kr), fly lines were generated with MS2 (PP7) stem-loop cassettes in the first intron and PP7 (MS2) cassettes in the 3′UTR. Both lines were visualized using MCP-GFP (green) and PCP-mCherry (red). As the two fluorescent signals are correlated via the elongation process, the paired time series impose stricter constraints on the underlying initiation events, making them an effective test of the deconvolution method. Deconvolution is performed jointly on each channel (that is, a single train of polymerases must explain both signals) using two kernels tailored to the stem-loop positions and satisfying the key assumptions: (i) constant, deterministic elongation rate; (ii) no Pol II pausing or dropping in the gene body; (iii) absence of co-transcriptional splicing; and (iv) fast termination. Additionally, the dual-color configuration allows estimation of the average elongation rate based on the time delay between the two signals and the known genomic distance between insertion sites. (b) Dual-color signal reconstruction from deconvolved single-allele time series (black lines: raw data). The transcription rate (gray line with ±1 s.d. envelope) is inferred from a single allele’s measured green and red traces. The denoised reconstructed signals (green and red, with ±1 s.d.) are obtained by re-convolving the inferred transcription rate with the appropriate kernel per channel. The close agreement between reconstructed and raw signals supports the validity of the kernel assumptions (see c). (c) Distribution of residuals between measured and reconstructed dual-color signals. Normalized residuals were computed as the difference between raw and reconstructed signals (panel b), divided by the standard deviation of imaging noise. This was done per allele for hb (N = 2666, blue) and Kr (N = 2594, pink). The spread of mean and standard deviation values of these residuals (black ellipse, 95% confidence) closely matches the expected distribution for a perfect model (dotted ellipse, 95% confidence), indicating good reconstruction fidelity. (d–e) Estimated elongation rate Kelo from dual-color measurements. (d) Mean elongation rate as a function of AP position, averaged over nuclei from 10 embryos, for both hb (blue) and Kr (pink) in NC13 (squares) and NC14 (circles). Error bars indicate the standard deviation across embryo means. (e) Per-embryo elongation rates (symbols and color scheme as in d), with error bars showing standard deviation across AP positions. Elongation rate is consistent across genes and nuclear cycles, with a global estimate of Kelo = 1.8 ± 0.1 kb/min (black line ±1 s.d., dashed).

Extended Data Fig. 3 Single-allele transcription rate distributions reveal common bursting characteristics.

(a) Snapshots of the mean transcription rate R for each gap gene as a function of AP position during late NC13 and early, mid, and late NC14 (specified by time t after mitosis). Colored profiles represent the average deconvolved single-allele transcription rate per AP bin (width: 2.5% in NC13, 1.5% in NC14), averaged over all nuclei and time points (10 s resolution). Black dashed lines show the mean activity (as in Fig. 1c), normalized by the effective elongation time (see Extended Data Fig. 4a, Methods). The strong agreement between measured and deconvolved profiles supports the validity of our approach. Error bars represent ±1 s.d. across embryo means. In total, we analyzed Ng = 7 effective genes (accounting for gt sex-specificity and spatial regions), over Nt = 362 time points and Nx = 9–18 AP positions, yielding 33′214 spatiotemporal bins, each averaging ~200 nuclei (single allele per nucleus). Remarkably, all gap genes reach a similar peak average transcription rate: Rmax = 14.8 ± 0.9 mRNA/min. (b) Fraction of spatiotemporal bins (indexed by position x and time t) whose transcription rate distribution P(r|x,t) is consistent with the conditional distribution P(r|R), computed by pooling nuclei from multiple bins with similar mean rate R (see panel c). We calculated 95% confidence intervals for the cumulative distribution of P(r|R), and assessed for each bin whether its individual cumulative distribution lay within this envelope. This analysis was repeated across four developmental windows: NC13 (6.5 ≤ t min after mitosis), early NC14 (7.5 ≤ t <20.5 min), mid NC14 (20.5 ≤ t < 34.5 min), and late NC14 (34.5 ≤ t < 48 min), as well as across the full NC14 period (7.5 ≤ t < 48 min). Within each time window, bins with the same R exhibit highly similar distributions (median agreement >80%, dashed line), justifying the pooling. However, pooling across the full NC14 window introduces temporal variability, suggesting that P(r|R) may evolve with time. (c) Conditional distributions P(r|R) of single-allele transcription rates at low ([2.1,3.2]), mid [7.5,8.5]), and high [12.8,13.9]) mean transcription rate R (gray bands in a, d), computed over 1-min intervals in NC13 (dotted lines) and early NC14 (solid lines). Despite gene identity, distributions at a given R collapse, suggesting a shared transcriptional regime. All distributions deviate from the Poisson expectation (dashed black line), especially at low and mid R, where they exhibit bimodality: a peak near zero (non- or weakly-transcribing alleles) and an overrepresentation of high-expression alleles. These features are characteristic of transcriptional bursting. (d) Second (variance), third, and fourth cumulants of single-allele transcription rates plotted against the mean rate R, for NC13 (squares) and early NC14 (7.5 ≤ t < 20.5 min; circles). Cumulants are estimated in 1-min intervals. All deviate from the Poisson expectation (σ2 = κ3 = κ4 = R; dashed line), except at the lowest and highest R. The mean–variance relationship forms a concave parabola, consistent with a two-state bursting model where modulation of PON underlies changes in R23. This supports a universal bursting mechanism where gap genes transition from fully OFF (PON = 0) to fully ON (PON = 1). Vertical gray bands mark low, mid, and high R as in panel (a).

Extended Data Fig. 4 Mean transcription rate explains dynamic pattern establishment.

(a) A simple model to estimate protein accumulation from measured mean transcription rates. The mean transcription rate (left column), across space and time, is computed by normalizing the measured activity by the elongation time and applying a minor correction for the loop-insertion delay (<1 min). Horizontal white dashed lines mark the mitotic transition from NC13 to NC14. Protein accumulation (middle column) is modeled as the convolution of the transcription rate with a kernel that captures protein decay, diffusion, and a combined time delay due to mRNA export, translation, and nuclear import. This model involves three free parameters: protein lifetime, diffusion constant, and time delay (see panel b), which were optimized to minimize the mean squared error relative to gap gene protein patterns measured via antibody staining of carefully staged embryos (right column; Dubuis et al., 2013). Minor residual differences between model and experiment can be attributed to staging inaccuracies or, in the case of hb, to unmodeled maternal mRNA contributions (see c). (b) Estimated model parameters for protein accumulation, as described in (a). Parameters were either fitted individually for each gene (colored bars) or globally across all genes (dashed lines, used for middle column in a). The inferred values are broadly consistent with previous estimates⁶⁷. (c) Quantitative comparison between modeled and measured protein patterns shown in (a). Absolute errors were computed across the patterns in space and time. The generally low errors confirm a strong match between model and experiment. For hb, larger discrepancies are observed in the anterior, likely due to maternal mRNA contributions not captured by the model. (d) Overall root mean square errors (RMSE) between the measured protein pattern (from antibody staining), the modeled protein pattern (with either individual or global parameters), and the transcription rate data. Protein models (individual: colored, global: light gray) yield low RMSE values (mean 0.09), while using the transcription rate directly leads to higher error (mean 0.23), mainly due to the time lag between transcription and protein accumulation. For reference, the RMSE between live and fixed (smFISH) mean profiles (see Fig. 1c) is shown as a dashed line at 0.08. (e) Structural comparison of modeled and measured protein patterns, assessing pattern shape and features (for example, peaks, boundaries). We computed the local spatiotemporal correlation (akin to a structural similarity index without luminance or contrast terms) using a 4-AP-bin (6% egg length) and 5-min window (black rectangle). Local correlations are generally high (near 1), indicating strong structural agreement. Discrepancies mainly occur during the first 20 minutes, when few stained embryos were available for accurate staging (see Dubuis et al., 2013). As in panel c, hb displays residual differences at later stages due to unmodeled maternal input. (f) Mean correlation across space and time between measured transcription rate (dark gray), modeled protein concentration (individual: color; global: light gray), and measured protein pattern. Correlation values were averaged over the full spatiotemporal pattern using the local measure from (e). The modeled protein patterns show high agreement with experimental data (mean correlation ≈ 0.9), while transcription rates alone correlate less well (≈0.6), consistent with expected temporal lag between transcription and protein levels.

Extended Data Fig. 5 Single-allele transcription rate fluctuations reveal key bursting characteristics.

(a) Interpreting auto-correlation functions using a two-state model of transcriptional bursting. In this model (top), a single gene copy switches stochastically between OFF and ON states with rates kOFF and kON, respectively. While ON, Pol II loads at a rate K(1) and elongates at rate Kelo. The superscript (1) indicates parameters for a single gene copy. The auto-correlation function (AC) was computed using: a switching correlation time \({T}_{C}^{\;(1)}=1/({k}_{{\rm{OFF}}}+{k}_{{\rm{ON}}})=2\min\), a Pol II elongation time \({\tau }_{{\rm{elo}}}={L}_{g}/{K}_{{\rm{elo}}}=2\) min (where Lg is the gene length) and an initiation rate K(1) = 8 mRNA/min. The steady-state ON-probability \({P}_{{\rm{ON}}}^{(1)}={k}_{{\rm{ON}}}/({k}_{{\rm{ON}}}+{k}_{{\rm{OFF}}})\) ranges from 0 to 1 (blue to red). While promoter switching introduces temporal correlations in the transcriptional activity (‘Activity AC’), these are often masked by elongation-induced correlations, especially when \({T}_{C}^{\;(1)}\le {\tau }_{{\rm{elo}}}\) (left). However, using deconvolved single-allele transcription rates removes elongation effects and reveals pure switching dynamics (‘Transcription AC’, right), allowing direct estimation of \({T}_{C}^{(1)}\) by exponential fitting of the decay. (b) Expected dependence of the magnitude of correlated fluctuations ΣAC, on the ON-probability \({P}_{{\rm{ON}}}^{(1)}\) (left) and initiation rate K(1) (right), for fixed \({T}_{C}^{\;(1)}=2\min\). (Left) At fixed K(1), as \({P}_{{\rm{ON}}}^{(1)}\) increases, the transcription rate \(R=2{K}^{(1)}{P}_{{\rm{ON}}}^{(1)}\) (for 2 sister chromatids) increases, while ΣAC decreases and vanishes at \({P}_{{\rm{ON}}}^{(1)}=1\), consistent with the Poisson (constitutive) regime. This trend agrees with data in panel (d). (Right) At fixed \({P}_{{\rm{ON}}}^{(1)}\), increasing K(1) raises both R and ΣAC, contrary to observations. In both cases, the dotted line represents the exact solution, well approximated by \({\Sigma }_{{AC}}=\Delta t{K}^{\left(1\right)}(1-{P}_{{\rm{ON}}}^{\left(1\right)})/(1+\Delta t{K}^{\left(1\right)}(1-{P}_{{\rm{ON}}}^{\left(1\right)}))\), with Δt = 10 s (data sampling interval). (c) Auto-correlation functions of single-allele transcription rates measured in gap genes, averaged over time and grouped by AP position (color-coded). (d) Magnitude of correlated fluctuations ΣAC as a function of mean transcription rate R, computed from the gap gene data. All genes collapse onto a single curve, indicating a universal trend. As R increases, ΣAC decreases, consistent with a transition toward a Poisson regime. The trend is captured by a model with a constant K(1) = 8.2 mRNA/min and variable \({P}_{{\rm{ON}}}^{(1)}\) (dashed line; see Methods and panel b). (e) Deconvolution reliably recovers correlation times and fluctuation magnitudes. Using the Gillespie algorithm, we simulated transcription traces under the two-state model for various \({P}_{{\rm{ON}}}^{(1)}\) (from 0.03 to 0.9) and \({T}_{C}^{\;(1)}\) (from 0.5 to 10 min), with 200 simulated nuclei per condition (50 min recordings). Following deconvolution, we estimated \({T}_{C}^{\;(1)}\) and ΣAC by fitting an exponential to the transcription AC. Both parameters were recovered accurately with minimal bias. Color encodes \({P}_{{\rm{ON}}}^{(1)}\)); dashed line indicates slope 1. (f) Assessing bias from elongation rate misestimation during deconvolution. Simulations were repeated as in (e), with \({T}_{C}^{\;(1)}=2\) min, and deconvolution performed using incorrect elongation rates: overestimated (orange), underestimated (yellow), or accurate (blue). While estimates remain broadly consistent, underestimating elongation rate introduces greater bias, especially at high \({P}_{{\rm{ON}}}^{(1)}\).

Extended Data Fig. 6 Direct estimation of instantaneous mean transcription parameters for hunchback in NC14.

(a) Transcription rate R versus the product of initiation rate K and ON-probability PON for hb in NC14 across all time points and AP positions (color-coded as in Figs. 2 and 3). As expected, R = K∙PON by construction. (b) Leaking rate KL as a function of time in NC14 for all AP positions. KL is computed by averaging single-allele transcription rates conditioned on the locus being OFF (in contrast to K, computed conditioned on ON allele). (c) Leaking rate as a percentage of the initiation rate, KL/K, plotted against transcription rate R. Across all conditions, KL remains below 5% of K, indicating well-defined bursting and minimal transcriptional leakage. (d) Fraction of changes in R attributable to PON, plotted as a function of PON. The black line shows \(d\log {P}_{{\rm{ON}}}/d{P}_{{\rm{ON}}}\) normalized by \(d\log K/d{P}_{{\rm{ON}}}+d\log {P}_{{\rm{ON}}}/d{P}_{{\rm{ON}}}\). The dotted line accounts for two independent sister chromatids (see panels e–j). Results indicate that changes in R are predominantly driven by PON. (e–g) Inferred single-gene-copy (SGC) parameters for hb in NC14, under the assumption of two independent sister chromatids (Methods). Color encodes AP position as in panel (a). (e) The SGC transcription rate R(1) and (f) the SGC ON-probability \({P}_{{\rm{ON}}}^{(1)}\) closely follow their effective counterparts R and PON. (g) In contrast, the SGC initiation rate K(1) is spatially uniform but varies over time. It decreases by ~38% during NC14, from 8.0 mRNA/min (early, first dotted line) to 5.0 mRNA/min (late, third dotted line), with most of the change occurring between 16 and 34 min (second dotted line at 6.1 mRNA/min). The resulting mean Pol II spacing, \({K}_{{\rm{elo}}}/{K}^{\left(1\right)}=303\pm 73\) bp, aligns with classical EM estimates (330 ± 180 bp) from Miller spreads⁴¹. (h–j) Temporal variation in K(1) and chromatid independence explain the observed dependence of K on PON. Colors denote three NC14 windows: early (cyan, 2.5–16.7 min), mid (purple, 16.7–34.2 min), and late (magenta, 34.2–50 min). (h) Most variation in K(1) arises from time rather than \({P}_{{\rm{ON}}}^{(1)}\); dotted lines mark the values from panel (g). (i) R(1) scales nearly linearly with \({P}_{{\rm{ON}}}^{(1)}\), with modest deviations explained by temporal changes in K(1). Dotted lines show slopes matching the K(1) values from panels (g) and (h). (j) Under the independent chromatid assumption, the effective rate K depends on both PON and time-varying K(1). As PON increases, the likelihood of simultaneous transcription from both chromatids increases, explaining a ~ 2-fold rise in K. The additional time variation in K(1) accounts for a total ~3.2-fold increase in K. The predicted relationship (black line) agrees well with observed data, supporting the idea that K depends weakly on PON directly. (k) Binarized heatmap from Fig. 2c showing instantaneous mean OFF-times (TOFF, gray) and ON-times (TON, blue), computed as weighted averages across all nuclei (Methods). Weights reflect the inverse of the number of time points within each period. (l) Zoom into the first 10 minutes of NC14 from Fig. 2f reveals a rapid transient in PON for hb. A vertical dashed line at 7.5 min marks the transition from the post-mitotic transient phase to a near steady state, as also shown in panel (c). (m) Evidence for an initial out-of-steady-state regime. Beyond 7.5 min, \({P}_{{\rm{ON}}}\approx {T}_{{\rm{ON}}}/({T}_{{\rm{ON}}}+{T}_{{\rm{OFF}}})\) holds (gray circles lie along the diagonal; see Fig. 3b). Prior to that (~3–7.5 min), strong deviations at all positions (color curves) indicate rapid post-mitotic relaxation toward steady state. (n) Distributions and cumulative distributions of OFF-times, ON-times, and burst sizes across AP positions (color-coded). These are compiled across all alleles and time points at a given position (see heatmaps in k and Fig. 2b). Since they reflect non-stationary dynamics (see Figs. 2d-f and 3a), these distributions are not well-suited for direct interpretation, such as assessing deviations from the exponential OFF- and ON-interval distributions expected under a stationary two-state model.

Extended Data Fig. 7 Further transcription parameters collapse.

(a) Kymograph of ON-probability PON for gt transcription in male embryos, shown as a function of AP position and time. As with other gap genes, the spatiotemporal transcription pattern results from complex regulation of PON. (b) Transcriptional parameters for gt in male embryos during NC13 and NC14, plotted as a function of PON (orange), overlaid with data from all other gap genes (gray) for comparison. (c) Initiation rate K as a function of PON. Data collapse across all gap genes, time points, and positions reveals a shared K–PON relationship. Colored points correspond to individual genes (color code as in panel b and Fig. 4a–e); gray points represent pooled data from all other genes. The corresponding curve for hb is shown in Fig. 2h. (d) Near–steady-state relationship between PON and TON/(TON + TOFF), shown for all gap genes in NC13 (t ≥ 6.5 min) and NC14 (t ≥ 7.5 min). While most data points follow the expected relationship (dashed line), a slight but consistent bias appears at the extremes of the PON range (solid line): TON/(TON + TOFF) slightly exceeds zero at PON = 0 and slightly undershoots one at PON = 1. This bias arises from the finite duration of our recordings (18.4 min in NC13 and 50 min in NC14), which imposes an upper bound on the detectable lengths of ON and OFF intervals, thereby affecting the estimates near the boundaries of PON.

Extended Data Fig. 8 Common bursting relationships across developmental time and for single gene copy.

(a) Global scatter of effective transcriptional parameters as a function of PON, estimated for all gap genes across three developmental time windows: NC13 (6.5 ≤ t min) plus early NC14 (7.5 ≤ t < 20.5 min), mid NC14 (20.5 ≤ t < 34.5 min), and late NC14 (34.5 ≤ t < 48 min). Due to the high degree of nuclear synchronization in the blastoderm embryo (with respect to the cell cycle), it is possible to assess global temporal changes by comparing these windows. The bursting relationships are further refined when accounting for temporal changes (color scatter), compared to time-pooled data (gray scatter, Fig. 5a). Modest developmental decreases in K and TC (~40%) help explain part of the spread observed in Fig. 5a. The origin of these changes remains unclear but may reflect overall temporal regulation of the gap gene network or maternal-to-zygotic transitions previously associated with mid-NC14. (b) Bursting relationships inferred from NC13 and early NC14 data are consistent with parameters previously derived from fixed smFISH measurements 23. We converted mid-to-late NC13 single gene copy (SGC) parameters from smFISH into effective two-chromatid parameters (colored points), with 68% confidence intervals. The resulting effective correlation time from smFISH, TC = 2.06 ± 0.66 min, is slightly shorter than reported in the original study (\({T}_{{\rm{C}}}=3.0\pm 1.2\,\min\)). This discrepancy arises from two corrections: (1) our updated elongation rate of 1.8 kb/min (versus 1.5 kb/min previously) reduces TC by 17%, and (2) the effective correlation time becomes up to twofold shorter than the SGC correlation time \({T}_{{\rm{C}}}^{(1)}\) at high PON, due to the relationship \({T}_{{\rm{C}}}^{\;(1)}=2\,{T}_{{\rm{C}}}/(1+{(1-{P}_{{\rm{ON}}})}^{1/2})\), (see Methods), accounting for an additional ~17% decrease on average. Overall, the smFISH effective parameters closely verify our relationships derived from live measurements (TC = 2.06 ± 0.66 min fixed versus TC = 1.25 ± 0.37 min live), albeit with small deviations likely stemming from a technical origin (differences in experimental protocol and microscopy, as well as limitations imposed by fixed measurements on parameter estimation). These small deviations, along with simulations (Supplementary Figs. 1 and 2), suggest that the observed data spread is largely attributable to estimation uncertainty rather than biological variability. (c) Same as in (a), but showing SGC parameters inferred from effective measurements under the assumption of independent sister chromatids (see Supplementary Fig. 4 for weakly correlated case with ρ = 0.16). The differences between the independent and weakly correlated assumptions are minor. Notably, in both cases, the relationship between SGC transcription rate \({R}^{(1)}\) and SGC ON-probability \({P}_{{\rm{ON}}}^{(1)}\) is nearly linear, supporting the conclusion that K(1), the SGC initiation rate, is largely independent of \({P}_{{\rm{ON}}}^{(1)}\). Thus, the apparent dependence of effective K on PON arises as an emergent property of two-gene-copy measurements, not from intrinsic single-copy regulation.

Extended Data Fig. 9 Bursting relationships verified by cis- and trans-perturbations.

(a) Cis-regulatory mutant for kni: deletion of the distal kni enhancer. MS2 stem-loops are inserted at the same genomic position in both the mutant and wild-type fly lines. (b) Quantification of transcriptional phenotypes for kni wild-type and cis-mutant. The transcription rate R as a function of position x/L (left) and the kymograph of PON (right) both show a pronounced reduction in expression in the mutant. The dotted arrow indicates the time point in the kymograph corresponding to the rate profiles on the left. Error bars denote ±1 standard deviation across embryo means. (c) Transcriptional parameters for the kni cis-mutant (olive) collapse onto the corresponding wild-type relationships (gray), as observed for the hb cis-mutant (Fig. 6c). Solid black lines show the endogenous bursting relationships from Fig. 5a, b. (d) Trans-regulatory mutant: kni-MS2 measured in a hb null background. In the absence of hb, the regulatory network is altered, which in turn affects the concentrations of input transcription factors sensed by kni. (e) Quantification of kni transcription in wild-type and trans-mutant. Both the transcription rate R and PON kymograph exhibit a clear anterior shift in the mutant. The dotted arrow marks the time point at which rate profiles are extracted. Error bars indicate ±1 standard deviation across embryo means. (f) Comparison of kni expression at the protein level for wild-type and trans-mutant embryos, using staged antibody staining from Haroush et al., 202344. While these measurements (solid lines, left) are not fully quantitative, they display a similar anterior shift in expression. Predicted protein profiles based on measured transcription rates (dashed lines, using the model from Extended Data Fig. 4) reproduce the same shift qualitatively. (g–j) Bursting parameters, initiation rate K (g), correlation time TC (h), burst size B (i), and burst frequency F (j), for hb cis-mutant (cyan), kni cis-mutant (olive), and kni trans-mutant (light green) collapse onto the wild-type trends (gray). Solid black lines represent wild-type bursting relationships (Fig. 5a–c). (k–p) Predicting mutant modulation type based on wild-type-derived bursting relationships (Fig. 5a–c). Mutant bursting behavior, whether modulated through TOFF vs. TON, or F vs. B, is predicted using look-up tables from wild-type data. (k) Predicted modulation type using TOFF and TON. For each mutant–wild-type pair of PON values, the expected fold changes \({T}_{{\rm{OFF}}}^{\;{\rm{mut}}}/{T}_{{\rm{OFF}}}^{\;{\rm{wt}}}\) and \({T}_{{\rm{ON}}}^{\;{\rm{mut}}}/{T}_{{\rm{ON}}}^{\;{\rm{wt}}}\) are computed based on wild-type relationships. The dotted line separates regimes where changes in R are driven primarily by TOFF (gray region: \(|\,\log {T}_{{\rm{OFF}}}^{\;{\rm{mut}}}/{T}_{{\rm{OFF}}}^{\;{\rm{wt}}}| > |\log {T}_{{\rm{ON}}}^{\;{\rm{mut}}}/{T}_{{\rm{ON}}}^{\;{\rm{wt}}}|\)) or TON (blue region: opposite inequality). Solid black lines bound regions where neither change is significant, based on 95% confidence intervals. This framework forms a look-up table for predicting modulation type from PON pairs. (l) Same as (k), but using burst frequency F and burst size B instead of TOFF and TON. (m) Scatter plot of all PON pairs from hb wild-type and cis-mutant at matched spatiotemporal positions. Color indicates the predicted modulation type (gray: TOFF-dominated; blue: TON-dominated), based on the look-up table in (k). (n) Same as (m), but using F and B modulation types from panel (l). (o) Empirical verification of predictions in (k). For each PON pair, we compute fold changes in \({T}_{{\rm{OFF}}}^{\;{\rm{mut}}}/{T}_{{\rm{OFF}}}^{\;{\rm{wt}}}\) and \({T}_{{\rm{ON}}}^{\;{\rm{mut}}}/{T}_{{\rm{ON}}}^{\;{\rm{wt}}}\) from the data (Fig. 6c, d). Nrly all blue points (predicted TON-modulation) lie above the diagonal (slope 1, dashed), while gray points (predicted TOFF-modulation) lie below, yielding >85% prediction accuracy (Fig. 6e). (p) Same as (o), using F and B instead of TOFF and TON. Predictions are highly accurate: >95% of data points fall in the expected quadrants (Fig. 6g), validating the predictive framework.

Extended Data Fig. 10 A bursting regime with a minimal ON-OFF cycle recapitulated the data.

An ON-OFF transcriptional regime, with a lower limit on these period durations and a minimal mean burst cycle duration \({T}_{{\rm{ON}}}+{T}_{{\rm{OFF}}}=1/F\) shown in red, closely recapitulates the observed bursting relationships in black. The horizontal dotted line corresponds to a lower bound of 1.8 min providing the best-fit to the data. An allele at mid-activity level (PON = 0.5) minimizes \({T}_{{\rm{ON}}}+{T}_{{\rm{OFF}}}\). Various ON-OFF combinations can yield \({P}_{{\rm{ON}}} > 0.5\), but increasing OFF periods prolong encoding PON compared to solely increasing ON durations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–5, Supplementary video legends, Extended methods.

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Supplementary Video 1

Representative videos of four gap gene transcription rate measurements: for hb, Kr, kni and gt (female), respectively. Anterior is on the left. We measured the dorsal side of the embryos. Red channel shows nuclei marked by histone–RFP label; green channel shows the MCP–GFP signal, in particular highlighting one site of nascent transcription in each nucleus when it binds to MS2 stem-loops. Each video was mean-projected in the axial (z) direction. Projected image size is about 210 × 120 μm2. Timestamp is in units of minutes. The video display frame rate is 15 Hz, which is equivalent to 2.5 min of imaging time per display second. Video contrast was adjusted for better visualization.

Supplementary Video 2

Same as above.

Supplementary Video 3

Same as above.

Supplementary Video 4

Same as above.

Supplementary Video 5

Temporal progression of transcriptional activity along developmental time. X axis: normalized embryo length (0–1). Top, the mean activity directly from the MS2 signal; bottom, calculated mean transcription rate (Section 7.2) that is no longer gene-length dependent.

Supplementary Video 6

Temporal progression of relative protein abundance along developmental time. Top, protein accumulation predicted from measured mean transcription rate based on a simple model. Bottom, previously measured protein patterns from carefully staged gap gene antibody staining [4]. Major differences observed for hb are likely related to maternal mRNAs, whose contribution is not observed in our live measurements, reflecting only zygotic gene expression.

Supplementary Video 7

Mean transcription rate for wild-type hb-MS2 (dark blue) and its distal enhancer deletion mutant (light blue).

Supplementary Video 8

Mean transcription rate for wild-type kni-MS2 (green) and its distal enhancer deletion mutant (dark yellow-green).

Supplementary Video 9

Mean transcription rate for wild-type kni-MS2 (green) and its expression in the background of the hb null mutant (light yellow-green).

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Chen, PT., Levo, M., Zoller, B. et al. A conserved coupling of transcriptional ON and OFF periods underlies bursting dynamics. Nat Struct Mol Biol (2025). https://doi.org/10.1038/s41594-025-01615-4

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