Evaluating the Drosophila Bicoid morphogen gradient system through dissecting the noise in transcriptional bursts

Abstract

Motivation: We describe a statistical model to dissect the noise in transcriptional bursts in a developmental system.

Results: We assume that, at any given moment of time, each copy of a native gene inside a cell can exist in either a bursting (active) or non-bursting (inactive) state. The experimentally measured total noise in the transcriptional states of a gene in a population of cells can be mathematically dissected into two contributing components: internal and external. While internal noise quantifies the stochastic nature of transcriptional bursts, external noise is caused by cell-to-cell differences including fluctuations in activator concentration. We use our developed methods to analyze the Drosophila Bicoid (Bcd) morphogen gradient system. For its target gene hunchback (hb), the noise properties can be recapitulated by a simplified gene regulatory model in which Bcd acts as the only input, suggesting that the external noise in hb transcription is primarily derived from fluctuations in the Bcd activator input. However, such a simplified gene regulatory model is insufficient to predict the noise properties of another Bcd target gene, orthodenticle (otd), suggesting that otd transcription is sensitive to additional external fluctuations beyond those in Bcd. Our results show that analysis of the relationship between input and output noise can reveal important insights into how a morphogen gradient system works. Our study also advances the knowledge about transcription at a fundamental level.

Contact: jun.ma@cchmc.org

Supplementary information: Supplementary data are available at Bioinformatics online.

Fig. 1.

Parameters affecting noise propagation. Activator input noise is converted to external noise (η_ext) in target gene transcription based on Equation (10) in a simplified gene regulatory model. Here, η_ext is shown as a function of ρ_i, the mean number of active copies. The effects of parameters that affect noise propagation are also shown. Such parameters include the activator noise strength (v), the activator threshold concentration (K) and the Hill coefficient (h). Figure 1A shows that η_ext increases as the normalized noise strength (v/K) increases. Figure 1B shows that, at a given v/K, the effect of h on η_ext is sensitive to ρ.

Fig. 2.

hb and otd have distinct noise properties in relation to the Bcd input noise. The experimentally measured η_tot (blue circles) in hb (A) and otd (C) intron dot numbers is dissected into η_ext (green diamonds) and η_int (red squares) according to Equations (5) and (6), and the results are plotted against ρ. Solid lines are theoretical predictions based on Equation (10) in the simplified gene regulatory model. The adjusted R₂-values of fitting the experimental data with the model for η_ext, η_int and η_tot of hb are, respectively: 0.85, 0.99 and 1.00; the adjusted R₂-values for η_ext, η_int and η_tot of otd are, respectively: −0.48, 0.97 and 0.98. The negative R₂ suggests that, constrained by the measured parameter values, the model cannot predict η_ext of otd. Arrowheads show the boundary positions of ρ=ρ_max/2. Here, K–values are measured as the mean Bcd concentrations at the marked boundary positions and h–values are extracted by fitting Equation (7) with the experimentally measured B–ρ profiles (He et al., 2011). Since fluctuations in Bcd concentration are dominated by Poisson-like molecular noise (He et al., 2010a), we perform a simple fitting of the experimentally measured Bcd noise to Poissonian distribution for extracting v-values. Figure 2B and D are scatter plots of dissected η_ext (same as in Figures 2A and C but showing data only from the activation boundary regions for better data spread) against converted η_ext (see text for details). Here, Figures 2B and C are for hb and otd, respectively. A linear regression line is also shown (with the equation in the inset box) for each panel.