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A spatio-temporal model of Notch signalling in the zebrafish segmentation clock: conditions for synchronised oscillatory dynamics.

Terry AJ, Sturrock M, Dale JK, Maroto M, Chaplain MA - PLoS ONE (2011)

Bottom Line: Consistent with experimental data and a previous spatially non-explicit mathematical model, we have found that signalling can increase the average level of Her1 protein.Biological pattern formation would be impossible without a certain robustness to variety in cell shape and size; our results possess such robustness.Our spatially-explicit modelling approach, together with new imaging technologies that can measure intracellular protein diffusion rates, is likely to yield significant new insight into somitogenesis and other biological processes.

View Article: PubMed Central - PubMed

Affiliation: Division of Mathematics, University of Dundee, Dundee, United Kingdom. aterry@maths.dundee.ac.uk

ABSTRACT
In the vertebrate embryo, tissue blocks called somites are laid down in head-to-tail succession, a process known as somitogenesis. Research into somitogenesis has been both experimental and mathematical. For zebrafish, there is experimental evidence for oscillatory gene expression in cells in the presomitic mesoderm (PSM) as well as evidence that Notch signalling synchronises the oscillations in neighbouring PSM cells. A biological mechanism has previously been proposed to explain these phenomena. Here we have converted this mechanism into a mathematical model of partial differential equations in which the nuclear and cytoplasmic diffusion of protein and mRNA molecules is explicitly considered. By performing simulations, we have found ranges of values for the model parameters (such as diffusion and degradation rates) that yield oscillatory dynamics within PSM cells and that enable Notch signalling to synchronise the oscillations in two touching cells. Our model contains a Hill coefficient that measures the co-operativity between two proteins (Her1, Her7) and three genes (her1, her7, deltaC) which they inhibit. This coefficient appears to be bounded below by the requirement for oscillations in individual cells and bounded above by the requirement for synchronisation. Consistent with experimental data and a previous spatially non-explicit mathematical model, we have found that signalling can increase the average level of Her1 protein. Biological pattern formation would be impossible without a certain robustness to variety in cell shape and size; our results possess such robustness. Our spatially-explicit modelling approach, together with new imaging technologies that can measure intracellular protein diffusion rates, is likely to yield significant new insight into somitogenesis and other biological processes.

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Cell circuitry schematic for Notch signalling between two neighbouring zebrafish PSM cells.Inside each cell, the core oscillator mechanism described in figure 2 holds with the exception that Notch signalling positively regulates the expression of the her1 and her7 genes. The signalling mechanism is as follows. In the nucleus, notch mRNA is transcribed, which then diffuses into the cytoplasm and produces Notch proteins by translation. These Notch molecules diffuse to the cell membrane where they function as receptors. DeltaC proteins from one cell bind to Notch receptors in the neighbouring cell. Each Notch-DeltaC complex is cleaved in two separate locations, causing an intracellular fragment of Notch (called Notch intracellular domain or NICD) to break off and translocate to the nucleus where it upregulates her1 and her7 gene expression. Zebrafish PSM cells vary in shape. For simplicity we chose square cells for this schematic.
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pone-0016980-g006: Cell circuitry schematic for Notch signalling between two neighbouring zebrafish PSM cells.Inside each cell, the core oscillator mechanism described in figure 2 holds with the exception that Notch signalling positively regulates the expression of the her1 and her7 genes. The signalling mechanism is as follows. In the nucleus, notch mRNA is transcribed, which then diffuses into the cytoplasm and produces Notch proteins by translation. These Notch molecules diffuse to the cell membrane where they function as receptors. DeltaC proteins from one cell bind to Notch receptors in the neighbouring cell. Each Notch-DeltaC complex is cleaved in two separate locations, causing an intracellular fragment of Notch (called Notch intracellular domain or NICD) to break off and translocate to the nucleus where it upregulates her1 and her7 gene expression. Zebrafish PSM cells vary in shape. For simplicity we chose square cells for this schematic.

Mentions: In section 2.2 we discussed a model for the core oscillator mechanism in an individual zebrafish PSM cell. In this section we extend the core oscillator model to construct a model for two neighbouring PSM cells which communicate by Notch signalling. Although the role of Notch signalling in zebrafish somitogenesis is not completely understood, a mechanism that fits experimental observations has been proposed by Lewis to explain it [1], [6]. We outlined this mechanism in section 2.1. Figure 6 shows a cell circuitry schematic consistent with the proposed mechanism. We shall use figure 6 to construct our model for two neighbouring PSM cells. Note that we shall attach the subscript to dependent variables in cell () to show that these variables are appropriate to that cell.


A spatio-temporal model of Notch signalling in the zebrafish segmentation clock: conditions for synchronised oscillatory dynamics.

Terry AJ, Sturrock M, Dale JK, Maroto M, Chaplain MA - PLoS ONE (2011)

Cell circuitry schematic for Notch signalling between two neighbouring zebrafish PSM cells.Inside each cell, the core oscillator mechanism described in figure 2 holds with the exception that Notch signalling positively regulates the expression of the her1 and her7 genes. The signalling mechanism is as follows. In the nucleus, notch mRNA is transcribed, which then diffuses into the cytoplasm and produces Notch proteins by translation. These Notch molecules diffuse to the cell membrane where they function as receptors. DeltaC proteins from one cell bind to Notch receptors in the neighbouring cell. Each Notch-DeltaC complex is cleaved in two separate locations, causing an intracellular fragment of Notch (called Notch intracellular domain or NICD) to break off and translocate to the nucleus where it upregulates her1 and her7 gene expression. Zebrafish PSM cells vary in shape. For simplicity we chose square cells for this schematic.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3046134&req=5

pone-0016980-g006: Cell circuitry schematic for Notch signalling between two neighbouring zebrafish PSM cells.Inside each cell, the core oscillator mechanism described in figure 2 holds with the exception that Notch signalling positively regulates the expression of the her1 and her7 genes. The signalling mechanism is as follows. In the nucleus, notch mRNA is transcribed, which then diffuses into the cytoplasm and produces Notch proteins by translation. These Notch molecules diffuse to the cell membrane where they function as receptors. DeltaC proteins from one cell bind to Notch receptors in the neighbouring cell. Each Notch-DeltaC complex is cleaved in two separate locations, causing an intracellular fragment of Notch (called Notch intracellular domain or NICD) to break off and translocate to the nucleus where it upregulates her1 and her7 gene expression. Zebrafish PSM cells vary in shape. For simplicity we chose square cells for this schematic.
Mentions: In section 2.2 we discussed a model for the core oscillator mechanism in an individual zebrafish PSM cell. In this section we extend the core oscillator model to construct a model for two neighbouring PSM cells which communicate by Notch signalling. Although the role of Notch signalling in zebrafish somitogenesis is not completely understood, a mechanism that fits experimental observations has been proposed by Lewis to explain it [1], [6]. We outlined this mechanism in section 2.1. Figure 6 shows a cell circuitry schematic consistent with the proposed mechanism. We shall use figure 6 to construct our model for two neighbouring PSM cells. Note that we shall attach the subscript to dependent variables in cell () to show that these variables are appropriate to that cell.

Bottom Line: Consistent with experimental data and a previous spatially non-explicit mathematical model, we have found that signalling can increase the average level of Her1 protein.Biological pattern formation would be impossible without a certain robustness to variety in cell shape and size; our results possess such robustness.Our spatially-explicit modelling approach, together with new imaging technologies that can measure intracellular protein diffusion rates, is likely to yield significant new insight into somitogenesis and other biological processes.

View Article: PubMed Central - PubMed

Affiliation: Division of Mathematics, University of Dundee, Dundee, United Kingdom. aterry@maths.dundee.ac.uk

ABSTRACT
In the vertebrate embryo, tissue blocks called somites are laid down in head-to-tail succession, a process known as somitogenesis. Research into somitogenesis has been both experimental and mathematical. For zebrafish, there is experimental evidence for oscillatory gene expression in cells in the presomitic mesoderm (PSM) as well as evidence that Notch signalling synchronises the oscillations in neighbouring PSM cells. A biological mechanism has previously been proposed to explain these phenomena. Here we have converted this mechanism into a mathematical model of partial differential equations in which the nuclear and cytoplasmic diffusion of protein and mRNA molecules is explicitly considered. By performing simulations, we have found ranges of values for the model parameters (such as diffusion and degradation rates) that yield oscillatory dynamics within PSM cells and that enable Notch signalling to synchronise the oscillations in two touching cells. Our model contains a Hill coefficient that measures the co-operativity between two proteins (Her1, Her7) and three genes (her1, her7, deltaC) which they inhibit. This coefficient appears to be bounded below by the requirement for oscillations in individual cells and bounded above by the requirement for synchronisation. Consistent with experimental data and a previous spatially non-explicit mathematical model, we have found that signalling can increase the average level of Her1 protein. Biological pattern formation would be impossible without a certain robustness to variety in cell shape and size; our results possess such robustness. Our spatially-explicit modelling approach, together with new imaging technologies that can measure intracellular protein diffusion rates, is likely to yield significant new insight into somitogenesis and other biological processes.

Show MeSH