Pre-steady-state decoding of the Bicoid morphogen gradient

Abstract

Morphogen gradients are established by the localized production and subsequent diffusion of signaling molecules. It is generally assumed that cell fates are induced only after morphogen profiles have reached their steady state. Yet, patterning processes during early development occur rapidly, and tissue patterning may precede the convergence of the gradient to its steady state. Here we consider the implications of pre-steady-state decoding of the Bicoid morphogen gradient for patterning of the anterior-posterior axis of the Drosophila embryo. Quantitative analysis of the shift in the expression domains of several Bicoid targets (gap genes) upon alteration of bcd dosage, as well as a temporal analysis of a reporter for Bicoid activity, suggest that a transient decoding mechanism is employed in this setting. We show that decoding the pre-steady-state morphogen profile can reduce patterning errors caused by fluctuations in the rate of morphogen production. This can explain the surprisingly small shifts in gap and pair-rule gene expression domains observed in response to alterations in bcd dosage.

Figure 1. In Silico Simulation of the Gap Gene Network

(A) A scheme of the gap gene interactions used: Bcd activates the expression of the gap genes in a concentration-dependent manner. Most gap genes mutually suppress each other (see Figure 9 in [45,46]). These interactions were modeled by a set of reaction diffusion equations, as specified in Protocol S1. (B) Spatial distributions of the different network proteins (color-coded as in [A]), at a time when the Bcd gradient has fully evolved and is close to exponential are shown for different bcd dosages. The gap genes are expressed in adjacent stripes, consistent with their in vivo expression domains. (C) The position of the Hb expression boundary in wild-type embryos (with 2 copies of bcd) and in embryos bearing altered bcd dosage (one and four copies, as shown). The results in our simulation (black circles) are compared to the experimental measurements (blue bars). Also shown is the prediction based on a steady-state gradient (red bars). (D) The temporal change in the position of the Hb expression boundary (diamonds) and in the Bcd concentration at this position (circles) are shown. We considered the wild-type situation (2 × bcd) and show the behavior following the initialization of gap gene expression. (E) We performed the simulations for different values of the Bcd diffusion constant D. Shown here is the shift of the Hb expression boundary in embryos with one bcd allele (1 × bcd) with respect to the wild-type as a function of D. (F) Same as in (E) but for different values of the gap gene diffusion constant. (G) Shifts of gap gene expression domains (center, left and right boundary, if applicable) in embryos with one functional bcd allele (1 × bcd) as a function of the wild-type (2 × bcd) position. (H) Same as in (G) but simulating embryos with four copies of bcd (4 × bcd).

Figure 2. Properties of the Pre-Steady-State Morphogen Distribution

(A) The morphogen distribution M(x, t) is plotted as a function of position x for different times t (legend). The plots were obtained by solving the reaction diffusion Equation 1 in one dimension (see Protocol S1). The position x is in units of the decay length scale , while the time t is in units of the decay time τ. (B) Same as in (A), except that each profile was rescaled such that it has unit concentration at x = 0 and decays to 1/e at x = 1. Note the logarithmic scale. At early times, the profile tail decays super-exponentially, while at later times the morphogen distribution is well approximated by an exponential. (C) Alteration of the steady-state morphogen concentration upon 2-fold reduction in morphogen production rate. The original profile corresponds to the solid line and the altered profile to the dotted line. Note that the indicated positional shifts Δx = |x − x′| at different morphogen thresholds do not depend on the position x. (D) Same as in (C) but for the pre-steady-state profile. (E) The shift Δx is shown as a function of x for different times t (see legend in [A]). For pre-steady-state profiles, Δx decreases as a function of x. (F) The shift Δx as a function of time t is shown for different positions x, as indicated. While at late times the shift is almost independent of the position, at early times the shift decreases with increasing distance from the source. (G) The exact solution for the pre-steady-state profile was fitted to the phenomenological approximation M_p(x, t) = M ₀(t) exp[−(x/λ(t))^{p (t)}]. The best-fitted exponent p is shown as a function of time (in units of the decay time τ). (H) To estimate the deviation of the time-dependent solution from an exponential, we compared the residual error obtained for the best-fit p approximation (R_p) to the residual error obtained when fitting to exponential with p =1 (R _lin). The ratio of these residual errors is shown as a function of time. (I) The best-fitted exponent p for quantitative Bcd profiles corresponding to wild-type embryos between cycles 10 and 14. Data were downloaded from the FlyEx database [56]. For embryos in cycles 10–12, the average p is significantly larger than 1, indicating superexponential decay, while Bcd profiles at cycles 13 and 14 are consistent with p = 1. Note, however, the large fluctuations.

Figure 3. Quantitative Effects of Altered Maternal bcd Gene Dosage on Zygotic Target Gene Expression

(A) Dorsal view of a representative cycle-14 wild-type Drosophila embryo stained for the Eve (green) and Kr (red) proteins. The contours of the embryo were determined from the transmitted light image (blue). (B) (C) Quantitative analysis of stripe positions was performed by semiautomated software as follows: the positions of the embryo poles and of the first and last Eve stripes were defined manually. Based on these definitions, a rectangular area (yellow dashed in [A]) corresponding in height to 10% EL was extracted automatically. Intensity profiles (solid lines in [C]) were obtained by averaging the fluorescence signal along the dorsal–ventral axis in this area and subsequent smoothing. Stripe positions (green dotted lines in [C]) and boundaries (red dotted lines in [C]) were defined based on local maxima of these profiles and their first derivative, respectively. (D) Expression domains of Eve (green) and the gap genes Gt, Hb, or Kr (red; as indicated) in embryos derived from females bearing one, two, or four copies of bcd. In each panel, the top part displays a representative confocal image, while quantitative results obtained from multiple embryos are shown at the bottom part. The widths of the stripes correspond to the standard errors (bright) and deviations (shaded). n denotes the number of embryos used in each analysis. (E) Observed shifts of target gene expression domains (center, left, and right boundaries, if applicable) in embryos with one functional bcd allele (1 × bcd) as a function of the wild-type (2 × bcd) position. Gray lines indicate theoretical predictions for different Bcd decay times (compare with Figure 1G and 1H). (F) Same as in (G) but for embryos with four copies of bcd (4 × bcd).

Figure 4. Analysis of Bcd-Dependent lacZ Reporter Expression over Cleavage Cycles 11, 12, and 13

The posterior boundary of the lacZ expression domain is shown as a function of the normalized nuclear density for each embryo (colored dots). Embryos fall into three classes of nuclear density corresponding to their cleavage cycle (11, red; 12, green; and 13, blue). Average nuclear density and domain boundary for each cycle are indicated by big circles, and whiskers denote standard deviations. (B) The distribution of the expression boundary is shown for the three cycles (bin size is 2% EL). Note the progression in time of the boundary.