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 N_g = 7 effective genes (accounting for gt sex-specificity and spatial regions), over N_t = 362 time points and N_x = 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: R_max = 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 P_ON underlies changes in R²³. This supports a universal bursting mechanism where gap genes transition from fully OFF (P_ON = 0) to fully ON (P_ON = 1). Vertical gray bands mark low, mid, and high R as in panel (a).