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Open Access Research article

Distance measurements via the morphogen gradient of Bicoid in Drosophila embryos

Feng He123, Ying Wen3, David Cheung3, Jingyuan Deng35, Long J Lu35, Renjie Jiao1* and Jun Ma34*

Author Affiliations

1 State Key Laboratory of Brain and Cognitive Science Institute of Biophysics Chinese Academy of Sciences 15 Datun Road Beijing 100101, China

2 Graduate School of the Chinese Academy of Sciences Beijing 100049, China

3 Divisions of Biomedical Informatics Cincinnati Children's Research Foundation 3333 Burnet Avenue Cincinnati, OH 45229, USA

4 Developmental Biology Cincinnati Children's Research Foundation 3333 Burnet Avenue Cincinnati, OH 45229, USA

5 Department of Biomedical Engineering University of Cincinnati Cincinnati, OH 45221, USA

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BMC Developmental Biology 2010, 10:80  doi:10.1186/1471-213X-10-80

Published: 2 August 2010

Additional files

Additional file 1:

Theoretical 2-D consideration of geometry and positional information.

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Additional file 2:

Figure S1: Analysis of D-V differences for Bcd and Hb profiles in 1×-bcd embryos. (A and B) Average raw Bcd intensity profiles on the dorsal (blue) and ventral (red) sides of 24 1×-bcd embryos when measured as a function of projected distance x from the anterior (A) or contour distance c (B). In each panel, the inset shows a magnified view of the region surrounding the Hb expression boundary positions (solid arrowheads). Listed below are p values from Student's t-tests at the indicated locations in the insets: 10-5, 10-5, 0.0003, 0.002, and 0.02 for panel A, and 0.004, 0.0004, 0.002, 0.01 and 0.05 for panel B. (C and D) Average normalized Hb intensity profiles on the dorsal (blue) and ventral (red) sides of the same 1×-bcd embryos when measured as a function of projected distance x from the anterior (C) or contour distance c (D). See Additional file 9-Table S1 for measured values. (E-H) Bcd-Hb input/output relationship of 1×-bcd embryos analyzed in a scatter plot (E), average input-output relationship (F), profiles of Hb expression noise in response to Bcd concentration (G) and Bcd intensity noise (H). These analyses, together with those obtained in wt embryos (Fig. 3) and 3×-bcd embryos (Fig. S2), reveal a fundamentally similar Bcd-Hb relationship on both sides of the embryos. See Additional file 9- Table S1 for measured values.

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Additional file 3:

Figure S2: Analysis of D-V differences for Bcd and Hb profiles in 3×-bcd embryos. (A and B) Same as panels A and B of Fig. S1, except the data are from 29 3×-bcd embryos. Listed below are p values from Student's t-tests at the indicated locations in the insets: 0.01, 0.02, 0.01, 0.02, and 0.13 for panel A, and 0.15, 0.39, 0.81, 0.36 and 0.71 for panel B. (C-H) Same as panels C-H of Fig. S1, except the data are from 3×-bcd embryos. See Additional 9- Table S1 for measured values.

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Additional file 4:

Figure S3: Analysis of distance measurements in 1× and 3×-bcd embryos. (A and C) Profiles of distance differences between the dorsal and ventral sides of the 1×-bcd (A) and 3×-bcd (C) embryos when measured as either projected distance from the anterior (blue, left scale) or contour distance (red, right scale). (B and D) Iso-concentration contour lines for Bcd plotted on the average frames for 1×-bcd (B) or 3×-bcd (D) embryos, respectively. The intensity increments between neighboring contour lines (red) are 0.5 (B) and 1.5 (D), respectively. See main text and Fig. 4A legend for further details.

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Additional file 5:

Figure S4: Raw Bcd intensity data. (A and B) Raw Bcd intensity profiles on the dorsal (blue) and ventral (red) sides of 24 1×-bcd embryos when measured as a function of projected distance x from the anterior (A) or contour distance c (B). (C and D) Same as panels A and B, except the data are from 28 wt embryos. (E and F) Same as panels A and B, except the data are from 29 3×-bcd embryos.

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Additional file 6:

Figure S5: Normalized Hb intensity data. (A and B) Normalized Hb intensity profiles on the dorsal (blue) and ventral (red) sides of 24 1×-bcd embryos when measured as a function of projected distance x from the anterior (A) or contour distance c (B). (C and D) Same as panels A and B, except the data are from 28 wt embryos. (E and F) Same as panels A and B, except the data are from 29 3×-bcd embryos.

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Additional file 7:

Figure S6: Simulating an embryo that has an asymmetric geometry. (A) A heat map of local total Bcd concentration on the midsagittal plane of a simulated embryo, which is approximated by two semi-ellipsoids joined on the coronal plane, with a height of 92 μm and 128 μm for the dorsal and ventral sides, respectively, and a length of 560 μm. For consistency, all other parameters here are set the same as those used to generate the results shown in Fig. 5. Color bar represents normalized local total Bcd concentration. (B and C) Heat maps of local total Bcd concentration of the same simulated embryo on transverse planes at xOtd/L (panel B) and xHb/L (panel C). Color bar represents normalized local total Bcd concentration only showing the range for the cortical layer. (D and E) Nuclear Bcd concentration profiles from the cortical layer of the dorsal (blue) and ventral (red) sides of the simulated embryo, measured as a function of either projected distance x from the anterior (panel D) or contour distance c (panel E).

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Additional file 8:

Figure S7: Testing the effects of bcd mRNA location and DNA binding on Bcd gradient properties. In these simulations, the center location of the bcd mRNA sphere was systematically moved either along the A-P axis (panels A-C; Rx denotes distance from anterior pole) or along the D-V axis (panels D-F; Ry denotes distance from the A-P axis). We also systematically changed the ratio of Bbound/Bfree at nuclear cycle 10 (panels G-I). Here, the shape of the simulated embryo is the same as in Fig. 5; for reference, the parameter values used in the simulations shown in Fig. 5 and Fig. S6 are marked with arrowheads. The resulting Bcd gradient profiles on the dorsal and ventral sides were then evaluated for their Bmax values (A, D and G), λ values expressed as either c or x (B, E and H), and the values of ΔxBcd and ΔcBcd at target boundary positions of both Hb and Otd (C, F and I). As shown in individual panels, these simulated results remain consistent with the three experimentally observed properties: 1) Bmax is higher on the dorsal side than on the ventral side (A, D and G), 2) λ measured as either x or c is larger on the ventral side than on the dorsal side (B, E and H; compare dashed lines with solid lines), and 3) ΔxBcd at target boundary locations is larger than their corresponding ΔcBcd (C, F and I; compare blue lines with red lines). As further discussed in the theoretical consideration above, the value of ΔxBcd - ΔcBcd in the middle section of the embryo reflects the geometric properties of the embryo. This value is 11.1 μm at xHb/L in our simulation results shown in this figure and, as expected, is insensitive to bcd mRNA location or the Bbound/Bfree ratio. It is also fully consistent with both experimental (10.7 μm as shown in Fig. 4A) and theoretical values (11.7 μm as shown in Fig. 1C).

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Additional file 9:

Table S1: Experimentally determined parameter values for the Bcd-Hb relationship.

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