Accurate measurements of dynamics and reproducibility in small genetic networks

Abstract

Quantification of gene expression has become a central tool for understanding genetic networks. In many systems, the only viable way to measure protein levels is by immunofluorescence, which is notorious for its limited accuracy. Using the early Drosophila embryo as an example, we show that careful identification and control of experimental error allows for highly accurate gene expression measurements. We generated antibodies in different host species, allowing for simultaneous staining of four Drosophila gap genes in individual embryos. Careful error analysis of hundreds of expression profiles reveals that less than ∼20% of the observed embryo-to-embryo fluctuations stem from experimental error. These measurements make it possible to extract not only very accurate mean gene expression profiles but also their naturally occurring fluctuations of biological origin and corresponding cross-correlations. We use this analysis to extract gap gene profile dynamics with ∼1 min accuracy. The combination of these new measurements and analysis techniques reveals a twofold increase in profile reproducibility owing to a collective network dynamics that relays positional accuracy from the maternal gradients to the pair-rule genes.

Figure 1

Simultaneous immunostaining of the four main gap genes. (A) Spectral imaging settings for simultaneous measurements of four fluorescent dyes. Absorption (dashed lines) and emission (solid lines) spectra of the dyes used for four simultaneous immunostainings; laser excitation wavelengths (black arrows) and bandwidths of the emission filters for each detection channel (light color patches) are indicated. (B) Optical sections through the midsagittal plane of a single Drosophila embryo with co-immunofuorescence staining against the four gap genes Kni (green), Kr (yellow), Gt (orange), and Hb (red); scalebar 100 μm. (C) Raw intensity profiles (dorsal side) of 23 selected embryos (light colors); embryo depicted above is highlighted in darker color (anterior pole at x/L=0; posterior pole at x/L=1). (D) Quantification of spectral crosstalk and fluorophore bleed-through. For each channel, the average intensity profile I of 10 embryos immunofluorescently labeled with three antibodies lacking the specific antibody corresponding to that optical channel is shown in gray. Black dashed line shows a cross-talk estimate using a reconstruction algorithm (see Materials and methods). Average profiles from B are shown in color.

Figure 2

Staging of gene expression profiles in fixed embryos with minute precision. (A) Depth of FC (δ_FC) during blastoderm cellularization measured along the dorsal side of a live-imaged wild-type embryo during n.c. 14. Dashed line corresponds to our estimate of mitosis 13. Inset shows a bright field microscopy image of a fraction (40–50%EL) of the dorsal side of the embryo at a time point indicated by red dot; scale bar 10 μm. δ_FC, defined as the distance between the FC and the edge of the embryo, was measured as indicated by red bar. (B) Invagination of the membrane for eight embryos (gray lines) with binned means and s.d.’s in black. The mean of the onsets of n.c. 14 is indicated as a red dashed line and their s.d. is represented by the error bar of the red square. The profile in A is shown in blue here. Scale on the right shows the adjusted length measured in fixed embryos (on average 5% EL shrinkage w.r.t. living embryos). Inset shows the measurement error of the embryo age estimation as a function of time. (C) Raw dorsal Gt intensity profiles of 80 embryos imaged in their midsagittal plane (DV orientation) with T=0–60 min (gray) and a subset of 23 embryos with T=37–49 min (light orange). The mean intensity profile of the 23 embryos is shown in black and its minimum and maximum in the 10–90% EL region are shown as dashed lines (defining the minimum (0) and maximum (1) gene expression levels g, respectively). (D) Intensity measured at position x/L=0.72 (vertical gray dotted line in C) as a function of δ_FC, each point representing a different embryo. The 23 points of the 10–20 μm batch are plotted in light orange. The black line represents a nearest neighbor averaging with a Gaussian filter (σ=5 μm). Inset shows detrended light orange data points with weighted average subtracted, i.e., time-corrected. (E) Variance of Gt gene expression levels σ_g² computed for the same 23 embryos shown in panel C before (light orange) and after (dark orange) time correction, respectively. Error bars obtained by bootstrapping; σ_I² is the variance of the raw intensities (across orange profiles in C). (F) Estimation of residual variance in age determination (gray) due to measurement uncertainty after profile time correction (gray line); for comparison, in dark orange the variance σ_g² of the time-corrected normalized profiles. For a similar analysis of the other gap genes see Supplementary Figure 2.

Figure 3

Quantification of imaging noise and antibody nonspecificities. (A) Schematic representation of a simultaneous staining process by two distinct primary anti-Hb antibodies and their respective secondary antibodies conjugated with differently colored dyes. The systematic error σ_I in nuclear intensity measured in each optical channel comes from imaging noise (mainly owing to photon counting and laser intensity fluctuations) as well as the random binding processes for primary and secondary antibodies. (B) Scatter plot of the nuclear intensities from two channels with different anti-Hb antibodies and Alexa-conjugated dyes (anti-rat(488) and anti-guinea pig(546)). As the two channels are detected separately and have different primary and secondary antibodies, the scatter of gray dots results from the combined errors owing to imaging and staining (primary and secondary). Two dashed lines define the minimum (red dot) and the maximum gene expression levels, I_min and I_max, respectively. Inset shows dependence of measurement noise σ_I (s.d. of the distance of the points to the diagonal divided by ) as a function of the mean intensity I, computed over 40 equally spaced bins along the whole intensity range (only data points with five or more nuclei are shown). S.d. of zero expression level region shown as a red dot. (C) Rescaled measurement noise contribution from imaging and staining (computed from the data shown in inset of panel B) as a function of the gene expression level g. Red dot shows the background noise, and two dashed lines represent the 1 and 4% measurement noise levels, respectively. Error bars computed by bootstrapping.

Figure 4

Contribution of azimuthal embryo orientation uncertainty to Gt gene expression profile reproducibility. (A) Schematic representation of the absolute azimuthal angle distribution of the embryos depending on their imaging plane. (B) Mean and s.d. of dorsal time-corrected Gt intensity profiles of embryos whose imaging plane is closer to the midsagittal plane (dark orange, DV orientation, 23 samples, δ_FC=10–20 μm) or closer to the coronal plane (light orange, LR orientation, 23 samples, δ_FC=10–20 μm). (C) Linear estimate of the DV dependence of raw dorsal Gt intensity at the fractional EL x/L=0.2. The systematic error in intensity owing to embryo orientation uncertainty of the dark brown profiles σ_I (shown in black) is estimated by propagating the uncertainty on the azimuthal angle σ_φ (uniform distribution ϕ=0–45°), σ_I=σ_φ·dI/dφ, where dI/dϕ is the slope of the dashed line (see text). (D) Variance of Gt gene expression profiles due to embryo orientation uncertainty (in black), computed as ; total variance of gene expression profiles of the time-corrected dorsal profiles is shown in dark orange for comparison, gray line shows an estimation of the variance induced by the embryo orientation uncertainty by the alternative method of Supplementary Figure 4.

Figure 5

Summary of systematic errors of the gap gene expression profiles. (A) Squared mean dorsal profiles (light gray) and corresponding time-corrected variances (dark color) measured across 23 embryos (δ_FC=10–20 μm) as a function of fractional EL x/L. Estimated summed total variance from major sources of measured systematic errors (staining, imaging, orientation, and time) are shown in blue. (B) S.d. of gene expression levels in time-corrected normalized profiles (color) and s.d. owing to systematic error (blue) as a function of gene expression level g (for 100 equally spaced bins along the AP axis). (C) For each gap gene, we show a scatter plot of the variances owing to the major sources of systematic error versus the total variance measured across embryos: imaging and staining (light gray), age (dark gray), and orientation (black). For each source of systematic error, data points were fitted with a straight line; slopes represent estimated average contributions to the overall variance. For reference, dashed line represents the case .

Figure 6

Dynamics of the main boundaries of the gap gene expression profiles. (A) Positions of anterior (◂) and posterior (▸) boundaries (inflection points) of the gap gene expression profiles for Kni (green), Kr (yellow), Gt (orange), and Hb (red) as a function of time. As a guide-to-the-eye, the peaks of the major stripes are plotted in dashed lines and the interstripe local minimum of Gt is plotted in short-dashed line. (B) Developmental progression of the intensity at the posterior Kr boundary (yellow) and the anterior Kni boundary (green). For each embryo and each gene, intensity at the inflection point is plotted as a function of embryo age in n.c. 14 (dim dots). Darker circles represent the averages and s.d.’s of the intensities of these data points over eight equally populated time bins (10 embryos per bin). Data have been normalized by I_max, the maximum intensity reached over all embryos, positions, and bins during n.c. 14. (C) Developmental progression of the absolute value of the slope at the crossing of the Kr (yellow) and Kni (green) boundaries, as in B. (D) Summary of the time dependences of the intensities at the anterior (solid) and posterior (dashed) boundaries (inflection points) for all gap genes (green and yellow lines correspond to the dark circles in B; for all stripes anterior and posterior intensities are nearly identical and thus overlap). (E) Summary of the time dependences of the slopes at the anterior (plain) and posterior (dashed) boundary of all gap gene borders (green and yellow lines correspond to dark circles in C).

Figure 7

Developmental progression of gap gene expression profile reproducibility. Position dependence of the reproducibility of the markers, computed as the s.d. of their positions across embryos σ_x/L for eight time windows covering 90% of n.c. 14 (T₁=10–25 min, T₂=26–29 min, T₃=30–33 min, T₄=34–36 min, T₅=37–40 min, T₆=41–45 min, T₇=46–50 min, and T₈=51–55 min) are shown as blue circles. The positional error obtained by simultaneously decoding all four gap genes (four-dimensional extension of Supplementary Figure 7) is shown in black for 100 AP positions. For reference, the mean gap gene profiles are shown in the background, color coded as above. Profiles have been scaled such that the maximum level of gene expression of their mean over the eight time windows is G₀. The internuclear distance and half-internuclear distances are shown as dotted and dashed lines, respectively.

Figure 8

Temporal evolution of gap gene expression profile reproducibility. Time dependences of the average reproducibility <σ_x/L> of the markers in Figure 7 (80 dorsal profiles were sorted according to age and then divided into eight bins of 10 profiles). For each time bin, the average and s.d. across the blue markers is shown as a function of time. The time dependence of the positional error is shown as a black line. For comparison, the maximum positional reproducibility of Bcd profiles 15 min into n.c. 14 (average between 10–60% EL) (Gregor et al, 2007a) is shown with a violet square, and the average positional reproducibility of the pair-rule genes rnt, eve, and prd 45 min into n.c. 14 is shown with a magenta square (Dubuis et al, 2011; Dubuis, 2012). For reference, the internuclear distance and the half-internuclear distance are shown in dotted and dashed lines, respectively.