Delta-Notch Signaling Pathway Model by HFPN

This section provides you with the explanation of modeling of biological phenomena that "Delta-Notch signaling pathway" with Genomic Object Net.

1 Delta-Notch Signaling Pathway

Cell-to-cell interactions mediated by Delta-Notch signaling pathway play essential roles in development of a multicellular organism. The molecular mechanism of the pathway is rooted in interaction of the ligand, Delta, and its receptor, Notch. Both of Delta and Notch proteins are initially expressed as trans-membrane proteins. In canonical Notch signaling pathway, Delta binds to inactive Notch protein of adjacent cells, and triggers activation of Notch. After a few steps of activation, the intracellular domain of Notch is released by twice proteolytic cleavage and becomes active. The active form of Notch causes a change in gene expression pattern, including a down-regulation of Delta gene expression. In addittion to the activation of Notch protein of adjacent cells, Delta has a suppressive effect on Notch signaling within Delta-positive cells. This is a core feature of the Delta-Notch pathway common to various patterning systems of the multicellular animal development (Figure 1). There are two different patterns by Delta-Notch signaling pathway: boundary formation in Drosophila melanogaster large intestine and Lateral inhibition in Drosophila melanogaster neurogenesis.

Figure 1: Core pathway of Delta-Notch signaling pathway
The area marked with solid or dashed line represents a cell. A normal arc represents activation. After activation by adjacent Delta, Notch is cut off twice proteolytically, and becomes Intermediate I, Intermediate II. Then, active Notch moves into the nucleus and activates target gene to inhibit Delta expression. In addition, The inhibitory arc coming from Delta to Notch represents Delta's suppressive effect on Notch (described above).

1.1 Boundary Formation in Drosophila Large Intestine

The large intestine is a major middle portion of the hindgut, and subdivided into the dorsal and ventral domains. A one-cell-wide strand of boundary cells develops between the two domains (Figure 2). Delta-Notch signaling pathway works in boundary formation as follows.: Initially, Delta protein is expressed only in the ventral domain while Notch is expressed in both domains. First, the ventral Delta binds to inactive Notch in the adjacent dorsal cells and triggers activation. Second, Notch becomes active by cutoff of intracellular domain of Notch. Third, active form of Notch migrate into the nuclear and regulate Delta gene expression. Finally, the cells with the active Notch become boundary cells whereas Notch in the ventral domain is not activated because of suppressive effect of Delta of themselves. Furthermore, cells in the dorsal domain has no cell-to-cell interaction because they have no Delta. Eventually, a single row of boundary cells is induced between the dorsal and ventral domains (Figure 3).

Click. Click.
Figure 2: Boundary formation in the hindgut of drosophila melanogaster
Left: Diagram, Right: Picture of the hindgut (Provided by Murakami Lab. of Yamaguchi Univ.)

Figure 3: Molecular mechanism of boundary cell formation in Drosophila large intestine
(1) Initially, only ventral cells express Delta proteins, whereas Notch proteins are expressed equivalently. In this situation, Delta in ventral domains binds to adjacent Notch in dorsal domains and triggers activation.
(2) Activated Notch is cleaved twice proteolytically and migrates into the nuclear. In the nuclear, Notch represses the expression of Delta gene. In result, cells in which Notch proteins are activated produce no Delta proteins.
(3) Consequently, the cells (marked with dashed line, colored in green) become boundary cells. On the other hand, dorsal cells are not able to become boundary cells because Notch proteins are not activated due to lack of Delta proteins.
(4) In addition, Delta has supressive effect on Notch signaling in Deltapositive cells so that ventral cells which express Delta proteins are not able to become boundary cells either.

1.2 Lateral Inhibition in Drosophila Neurogenesis

Lateral inhibition is the process where one developing element prohibits the development of similar elements nearby, where Delta-Notch signaling pathway is generally involved. This process is genetically conserved among various vertebrates, especially the spacing pattern of Drosophila melanogaster neurogenesis is well investigated (Figure 4). Delta, expressed by specified cells, activates Notch in neighboring cells directing them into alternative developmental pathways. Delta and Notch are initially expressed equivalently in the precursor cells of Drosophila melanogaster epidermis. Delta represses the expression of Delta in neighboring cells by activating their Notch. This cell-to-cell interaction creates competitive situation among the precursor cells. When a cell expresses Delta more than others nearby, this difference amplifies by Delta-Notch signaling. Eventually, a cell that preponderates Delta differentiates as a neural cell (Figure 5). Finally, the spacing pattern of neural cells is formed by Delta-Notch signaling pathway.

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Figure 4: Lateral inhibition in drosophila melanogaster neurogenesis
Left: Diagram, Right: Picture of the spacing pattern of nerve cells (Provided by Murakami Lab. of Yamaguchi Univ.)

Figure 5: Molecular mechanism of lateral inhibition in Drosophila neurogenesis
(1) In unspecified epidermis, all the cells in a cluster initially express Delta and Notch. In this situation, Delta binds to adjacent Notch and triggers activation.
(2) By cell-to-cell interaction of Delta and Notch, a competition occurs, with one cell emerging as winner, expressing Delta strongly and inhibiting its neighbors from doing likewise.
(3) Finally, the cell (marked with dashed line, colored in pink) won the competition becomes neural cell (Delta-positive cell). On the other hand, Notch cannot be activated in the winner cell where Delta supresses Notch signaling strongly.

2 Modeling of Delta-Notch Signaling Pathway by HFPN

The Delta-Notch pathway depicted in Figure 1 is modeled by an HFPN, which includes the intracellular regulatory circuit as well as cell-to-cell interactions (Figure 6), which can construct and simulate pathway mechanisms of actions of both baseline and abnormal conditions.

In the following Figure 6, an HFPN model of the complete intracellular circuit of a single Cell #1, with interactions with adjacent Cells #2 and #13, is illustrated.
Figure 6: HFPN model of Delta-Notch signaling pathway
Each area marked with dashed line represents a cell. Continuous places represent concentrations of the molecules depicted in Figure 1. Production rates and degradation rates are assigned to the continuous transitions. When the discrete place boundary cell gets token(s), the corresponding cell becomes a boundary cell. Test arcs are used at the reactions where no substances are consumed. Inhibitory arcs are used for modeling repressive activity.

In Figure 6, When the amount of Delta in Cell #2 (Cell #13) exceeds level 1, token value is transferred from the place Notch(inactive) to the place Intermediate I. This token value is determined by the firing speed m7/200 (m8/200). To define the repression level of the processing of Intermediate I to Intermediate II, we use the following formula;

α × m2/(β × m6 + m2)           (1)

which is assigned to the transition marked with red circle. This formula describes the following two functions;
Note that the firing speed of the transition in the red can be manipulated by changing the two parameters α and β. The production rate of Delta is defined by the parameter d. The forced-expression rate of Delta can be also set to the parameter dm.

We carried out simulations of the patterning of boundary cells by using GON. Figure 7 shows the simulation model consisting of 60 cells. Each cell has the HFPN model illustrated in Figure 6.
Figure 7: 60 cells model for simulation by GON
Each cell has the HFPN model presented in Figure 6.

For representing cell-to-cell interactions, arcs are drawn from the place Delta of (up to 6) adjacent cells to the transitions between the places Notch(inactive) and Intermediate I. Since the whole HFPN model constructed in this way is very complicated and messy, it is actually difficult to monitor progress of the simulation on HFPN.

To address this issue, we wrote an XML document for GON Visualizer which realizes a model of 60 cells. In this model, the color of each cell changes according to the token value in the places which we want to observe.

3 Simulation Results

3.1 Simulation Results of Boundary Formation

With GON*, we simulated wild type and abnormal type of boundary formation, as a result, we could succeed to achieve results corresponding to experimental results. These results are following.:
simulation result experimental result (provided by Murakami Lab. of Yamaguchi Univ.)
Figure 8: Wild type of boundary formation
Figure 8 shows simulation result of wild type of boundary cell formation. Each cell corresponds to one in Figure 7. The cells colored in gray represent boundary cells (cell:25-36 in Figure 7). The color of a cell changes according to the amount of tokens of discrete place boundary cell (refer to Figure 6). The right image of Figure 8 is an experimental result corresponding to the right image of Figure 2 (two white arrows indicate boundary formation).

simulation result experimental result (provided by Murakami Lab. of Yamaguchi Univ.)
Figure 9: Forced-expression of Delta caused suppression of boundary cell differentiation
Figure 9 shows simulation result of mutant type of boundary cell formation, in which Delta is initially expressed all over the large intestine. This mutant is expressed by manipulating the value dm=30 in Figure 6. In Figure 9, no boundary cells developed since Delta's suppressive effect on Notch signaling is too strong.

simulation result experimental result (provided by Murakami Lab. of Yamaguchi Univ.)
Figure 10: Boundary cells fail to differentiate in Delta mutant embryo.
Figure 10 shows a simulation result of defective Delta. For the condition of Delta mutant, the parameter value of m8 in Figure 6 was fixed at 0, resulting in no boundary cell formation because of no cell-to-cell interaction. Eventually, the simulation result is as same as Figure 9.

simulation result experimental result (provided by Murakami Lab. of Yamaguchi Univ.)
Figure 11: Forced-expression of Delta
Figure 11 is a simulation result of forced-expression of Delta, in which a few boundary cells have formed ectopically (arrows) since the strength of Delta is weaker than Figure 9. This simulation result is obtained at the value dm=6.

simulation result experimental result (provided by Murakami Lab. of Yamaguchi Univ.)
Figure 12: Wild type of lateral inhibition
Figure 13 is a simulation result of wild type of lateral inhibition. In the left image, cells colored in red represent Delta-positive cells. Only by manipulating parameters, we could successfully achieve corresponding result with biological phenomena. The right image corresponds to Figure 4. The color of cell changes from red to gray according to the concentration of the place to which the XML document refers.

* Cell Illustrator ver.1.5

4 Parameters Used for Simulations

The parameters used for simulations described above are following.:

Boundary cell80.7490100
Lateral inhibition120.75330
Table 1: Parameters used for simulations

α and β represent the firing speed of the transition marked with red in Figure 6 in the formula (1).

In the Table 1, we choose parameter values 0.7 and 49 for α and β, respectively. Initial condition for Delta level (d) is: 0 for cells 1-36 (dorsal cells) and 10 for cells 37-60 (ventral cells). This condition represents a prepattern of Delta expression in normal large intestine, in which Delta is expressed only in the ventral cells. Simulation with this condition generated a single strand of boundary cells that are abutting ventral cells (Figure 8). For the simulation of forced expression of Delta, parameter values 53 and 60 are chosen for dm (Figure 9, 11). The condition of Delta mutant (Figure 10) is realized by removing arc from the transition where d is assigned to the place Delta (Figure 6). These results correspond well to the experimental results described above (Figures 8-11).

We also tried a simulation with an initial condition of a uniform Delta level (d = 3) for all the cells, in order to represent a situation of lateral inhibition, in which specified cells are singled out from equivalent precursors. When the parameter β was reduced to 5, a regular distribution pattern of specified cells (with a high Delta level) was obtained.

Simulation results also suggest that parameter values representing the strength of cell-autonomous suppression of Notch signaling by Delta are essential for generating two different modes of patterning: lateral inhibition and boundary formation, which could explain how a common gene regulatory network results in two different patterning modes in vivo.

The model of Delta-Notch signaling pathway of Drosophila by GON

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