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

O'Connell MD, Reeves GT - PLoS Comput. Biol. (2015)

Bottom Line: We found that two assumptions are required for the model to match experimental data in both Dorsal distribution and gene expression patterns.And second, we assume that fluorescence measurements of Dorsal reflect both free Dorsal and Cactus-bound Dorsal.Our results have a general implication for interpreting fluorescence-based measurements of signaling molecules.

View Article: PubMed Central - PubMed

Affiliation: North Carolina State University Department of Chemical and Biomolecular Engineering, Raleigh, North Carolina, United States of America.

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.

No MeSH data available.


Related in: MedlinePlus

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 , 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 ni, 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.
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pcbi.1004159.g001: 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 , 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 ni, 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.

Mentions: We begin our model formulation from a previously published model [15], and make some adjustments for consistency with recently-acquired data [10]. Here we sketch the essentials for understanding the model. (For full details, see S1 Text.) To simulate the dynamics of dl and Cact during NC10-NC14, a cross section of the embryo was modeled as a linear array of rectangular prism-shaped compartments that each contain a single nucleus (Fig. 1a,b). Each compartment and each nucleus are well mixed, with slow exchange between neighboring compartments [11, 17]. Because the embryo is approximately symmetric about the DV axis, only one half of the axis is simulated and no-exchange boundary conditions are assumed at both the ventral and dorsal midlines. The number of compartments, as well as their dimensions, depends on the number of nuclei, which increases (to the nearest integer) by a factor of at the start of each interphase (Fig. 1b). The length and width of each compartment is calculated as the length of the simulated region, L, divided by the number of nuclei in interphase i, ni; the height, H, remains constant.


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

O'Connell MD, Reeves GT - PLoS Comput. Biol. (2015)

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 , 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 ni, 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.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4400154&req=5

pcbi.1004159.g001: 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 , 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 ni, 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.
Mentions: We begin our model formulation from a previously published model [15], and make some adjustments for consistency with recently-acquired data [10]. Here we sketch the essentials for understanding the model. (For full details, see S1 Text.) To simulate the dynamics of dl and Cact during NC10-NC14, a cross section of the embryo was modeled as a linear array of rectangular prism-shaped compartments that each contain a single nucleus (Fig. 1a,b). Each compartment and each nucleus are well mixed, with slow exchange between neighboring compartments [11, 17]. Because the embryo is approximately symmetric about the DV axis, only one half of the axis is simulated and no-exchange boundary conditions are assumed at both the ventral and dorsal midlines. The number of compartments, as well as their dimensions, depends on the number of nuclei, which increases (to the nearest integer) by a factor of at the start of each interphase (Fig. 1b). The length and width of each compartment is calculated as the length of the simulated region, L, divided by the number of nuclei in interphase i, ni; the height, H, remains constant.

Bottom Line: We found that two assumptions are required for the model to match experimental data in both Dorsal distribution and gene expression patterns.And second, we assume that fluorescence measurements of Dorsal reflect both free Dorsal and Cactus-bound Dorsal.Our results have a general implication for interpreting fluorescence-based measurements of signaling molecules.

View Article: PubMed Central - PubMed

Affiliation: North Carolina State University Department of Chemical and Biomolecular Engineering, Raleigh, North Carolina, United States of America.

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.

No MeSH data available.


Related in: MedlinePlus