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. 2015 Apr 16;11(4):e1004159.
doi: 10.1371/journal.pcbi.1004159. eCollection 2015 Apr.

The presence of nuclear cactus in the early Drosophila embryo may extend the dynamic range of the dorsal gradient

Michael D O'Connell  1 , Gregory T Reeves  1
Affiliations

The presence of nuclear cactus in the early Drosophila embryo may extend the dynamic range of the dorsal gradient

Michael D O'Connell et al. PLoS Comput Biol. .

Abstract

In a developing embryo, the spatial distribution of a signaling molecule, or a morphogen gradient, has been hypothesized to carry positional information to pattern tissues. Recent measurements of morphogen distribution have allowed us to subject this hypothesis to rigorous physical testing. In the early Drosophila embryo, measurements of the morphogen Dorsal, which is a transcription factor responsible for initiating the earliest zygotic patterns along the dorsal-ventral axis, have revealed a gradient that is too narrow to pattern the entire axis. In this study, we use a mathematical model of Dorsal dynamics, fit to experimental data, to determine the ability of the Dorsal gradient to regulate gene expression across the entire dorsal-ventral axis. We found that two assumptions are required for the model to match experimental data in both Dorsal distribution and gene expression patterns. First, we assume that Cactus, an inhibitor that binds to Dorsal and prevents it from entering the nuclei, must itself be present in the nuclei. And second, we assume that fluorescence measurements of Dorsal reflect both free Dorsal and Cactus-bound Dorsal. Our model explains the dynamic behavior of the Dorsal gradient at lateral and dorsal positions of the embryo, the ability of Dorsal to regulate gene expression across the entire dorsal-ventral axis, and the robustness of gene expression to stochastic effects. Our results have a general implication for interpreting fluorescence-based measurements of signaling molecules.

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Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Fig 1
Fig 1. Description of geometry.
(a) The model consists of a linear array of compartments, each containing a single nucleus, representing one-half of the DV axis. All three species can enter and exit the nuclei and diffuse across the compartmental wall. The Toll signal is represented by a Gaussian curve along the ventral half of the embryo. (b) At the beginning of each nuclear cycle, the number of nuclear compartments increases by 2, to the nearest integer. The height of the compartments remains constant, while the length/width is calculated by the length of the compartmental array divided by n i, the number of nuclei in nuclear cycle i. (c) At the end of interphase, the nuclear concentration of each protein is distinct from its cytoplasmic concentration. At the start of mitosis, the nuclear and cytoplasmic protein concentrations from the end of interphase are mixed. At the start of the next interphase, the concentration profile of a nucleus is initially the same as the surrounding cytoplasm.
Fig 2
Fig 2. Model results without nuclear dl/Cact.
(a) Simulations of the model assuming nuclei begin interphase empty and that only free cytoplasmic dl is imported into the nucleus. (b) 3D surface plot of the best-fit parameter set. (c) Snapshots of the end of each nuclear cycle according to this model. (d) Same as in (c), normalized.
Fig 3
Fig 3. Model results with nuclear dl/Cact.
(a) Surface plot of the best-fit parameter set (U nuc + W nuc). (b) Surface plot of nuclear free dl (U nuc, Equation 1). (c) Surface plot of nuclear dl/Cact complex (W nuc, Equation 3). (d) The best-fit simulation result compared to the nuclear dl-Venus data from [10], normalized to dl-Venus maximum. Width refers to σ value when fit to a Gaussian function; dotted line represents average dl gradient width of 0.15 as in [10]. (e) Comparing snapshots at the end of each nuclear cycle. (f) Comparison of NC14 gradient snapshots.
Fig 4
Fig 4. Import/export parameter analysis.
(a,c,e) Scatter plot of logarithms of nuclear export vs import rates for dl (a), dl/Cact (c) and Cact (e). Each point is a weighted mean of the 100 parameter sets from a single evolutionary optimization run, with error bars representing the weighted standard deviation for those parameter sets. Color indicates weighted median RSS error for each set. (b,d,f) Equilibrium constant distributions: logarithms of quotients of all import/export parameter values (ζ i and ξ i, respectively).
Fig 5
Fig 5. Gene expression simulations.
(a, b) Using the free (active) dl gradient, we were able to accurately simulate the gene expression patterns measured with FISH [10]. (c, d) Using the total dl gradient, we obtain poor fits to Type III genes (sog, zen), as was expected. In (b, d) the fuchsia curve indicates the active dl gradient at the end of NC14, plotted on a log scale. Horizontal lines indicate median threshold parameter values, and vertical dotted lines indicate where in the DV axis we expect the final expression borders of each gene, according to where the gradient crosses the threshold. Note that the zen threshold is below the NC14 gradient in the total dl case (c, d), and that zen expression is thus a result of noise. (Note: each run is an average of 10 runs for each parameter set to reduce randomness in the plot due to noise.)
Fig 6
Fig 6. Gene expression parameter sensitivity analysis.
(a-d) A 10% change in dl-sog threshold, θ dl:sog (a,b), or noise parameter, η (c,d), causes a greater difference in the total dl case than the free dl only case. (e-h) In the same way, a 10% change in dl-zen threshold, θ dl:zen (e,f), or noise parameter (g,h) causes a greater difference to the total dl case than the free dl case. For each case, sensitivity was analyzed using the best parameter set for η = 0.2, and each line shown is the average of 10 simulations. The data to which the model was optimized are shown as dotted lines. (Note: each run is an average of 10 runs for each parameter set to reduce randomness in the plot due to noise.)
Fig 7
Fig 7. Effect of Cact background subtraction.
(a) From raw fluorescence measurements (red), lateral and dorsal nuclei should have trouble interpreting their position in the DV axis because of signal noise (dotted curves). If only the active pool of dl is taken into account (blue), noise is not prohibitive to accurate boundary placement, meaning that dl can indeed pattern the whole of the DV axis. (b) If we consider a simple example of background subtraction, the shape of the dl gradient remains the same (solid lines, from red to blue) while the relative error due to noise (dotted lines, in no. of nuclei) at each point in the DV axis significantly decreases (especially beyond 40% DV) as a greater percentage of the basal concentration is subtracted.
Fig 8
Fig 8. Summary.
(a) In the classical model of dl/Cact dynamics, the import of dl is of primary concern. (b) In our extended model, the coexistence of dl, Cact and dl/Cact complex due to nuclear porosity must be taken into account to interpret the results of fluorescence studies. (c) Our modeling results predict the export of dl/Cact complex from dorsal nuclei contributes to a decrease in nuclear fluorescence, and the import of cytoplasmic dl contributes to the increase in nuclear fluorescence in ventral nuclei. (d) In all nuclei, free dl and dl/Cact complex are both fluorescently tagged but only free dl contributes to gene expression.
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References

    1. Roth S, Stein D, Nüsslein-Volhard C. A Gradient of Nuclear Localization of the dorsal Protein Determines Dorsoventral Pattern in the Drosophila Embryo. Cell. 1989;59:1189–1202. - PubMed
    1. Steward R, Zusman SB, Huang LH, Schedl P. The dorsal Protein is Distributed in a Gradient in Early Drosophila Embryos. Cell. 1988;55:487–495. 10.1016/0092-8674(88)90035-9 - DOI - PubMed
    1. Reeves GT, Stathopoulos A. Graded dorsal and differential gene regulation in the Drosophila embryo. CSH Persp Bio. 2009. October;1(4):a000836. - PMC - PubMed
    1. Moussian B, Roth S. Dorsoventral axis formation in the Drosophila embryo: shaping and transducing a morphogen gradient. Curr Bio. 2005. November;15(21):R887–99. 10.1016/j.cub.2005.10.026 - DOI - PubMed
    1. Roth S, Hiromi Y, Godt D, Nüsslein-Volhard C. cactus, a maternal gene required for proper formation of the dorsoventral morphogen gradient in Drosophila embryos. Dev. 1991. June;112(2):371–88. - PubMed

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Grants and funding

During this work, GTR was supported by a CAREER award funded by the United States National Science Foundation (www.nsf.gov), grant number CBET-1254344; and MDO was supported by a Graduate Assistance in Areas of National Need Fellowship in Computational Science from the United States Department of Education (www.ed.gov), grant number P200A120047. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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