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. 2017 Sep 21;11(Suppl 4):80.
doi: 10.1186/s12918-017-0455-8.

Modeling and analysis of the Delta-Notch dependent boundary formation in the Drosophila large intestine

Fei Liu  1   2 , Deshun Sun  3 , Ryutaro Murakami  4 , Hiroshi Matsuno  4
Affiliations

Modeling and analysis of the Delta-Notch dependent boundary formation in the Drosophila large intestine

Fei Liu et al. BMC Syst Biol. .

Abstract

Background: The boundary formation in the Drosophila large intestine is widely studied as an important biological problem. It has been shown that the Delta-Notch signaling pathway plays an essential role in the formation of boundary cells.

Results: In this paper, we propose a mathematical model for the Delta-Notch dependent boundary formation in the Drosophila large intestine in order to better interpret related experimental findings of this biological phenomenon. To achieve this, we not only perform stability analysis on the model from a theoretical point of view, but also perform numerical simulations to analyze the model with and without noises, the phenotype change with the change of Delta or Notch expression, and the perturbation influences of binding and inhibition parameters on the boundary formation.

Conclusions: By doing all these work, we can assure that our model can better interpret the biological findings related to the boundary formation in the Drosophila large intestine.

Keywords: Boundary formation; Delta-Notch signaling pathway; Drosophila large intestine; Local stability analysis; Perturbation analysis; Simulation validation.

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Figures

Fig. 1
Fig. 1
An illustration of the Drosophila hindgut. a Boundary cells form one-cell-wide domains bilaterally (arrows) between dorsal and ventral domains of the large intestine. b A diagram of the hindgut domains in the wild-type Drosophila embryo, adapted from [3]
Fig. 2
Fig. 2
A diagram of the Delta-Notch signaling pathway in boundary cell formation of the large intestine. This pathway shows the interaction of two neighboring cells, which is adapted from [1]
Fig. 3
Fig. 3
Diagram for the experimental result of the boundary formation of the Drosophila large intestine. (a): Wild-type, (b1) to (b2): over-expression of Notch with decreasing Delta background, and, (c1) to (c2): over-expression (decreasing) of Notch with fixed Delta background. Each filled circle is a boundary cell. D means the dorsal domain and V the ventral domain. This diagram is made according to [1, 4, 13]
Fig. 4
Fig. 4
The model for one cell. In this model, only two species, Delta (D) and Notch are considered. Notch can be in inactive state (N) or active state (A)
Fig. 5
Fig. 5
A two-dimensional lattice for the model. The mathematical model proposed in this paper works on the two-dimensional lattice, which defines a patch of a tissue
Fig. 6
Fig. 6
A simulation plot at λ=0. In this plot, the simulation traces of D 1 (N 1, A 1) and D 2 (N 2, A 2) overlap
Fig. 7
Fig. 7
A simulation plot at λ>0. In this plot, the simulation traces of D 1 (N 1, A 1) and D 2 (N 2, A 2) overlap
Fig. 8
Fig. 8
Deterministic simulation results. a Wild-type: λ N=0 and λ=9, b over-expression of Notch: λ N=0.008 and λ=9, and, c over-expression of Notch: λ N=0.1 and λ=9
Fig. 9
Fig. 9
Two random simulation runs at λ N=0.0005 and λ=0.3. The noises are randomly sampled from [−5·10−4,5·10−4]
Fig. 10
Fig. 10
Perturbation influence of parameter a. The considered disturbance intensities are: ε=10−7, ε=10−6, ε=10−5 and ε=10−4, respectively
Fig. 11
Fig. 11
Perturbation influence of parameter b. The considered disturbance intensities are: ε=0.01, ε=0.05, ε=0.1 and ε=0.2, respectively
Fig. 12
Fig. 12
Perturbation influence of parameters f 1 and f 2. The considered disturbance intensities are: ε=0.001, ε=0.005, ε=0.01 and ε=0.02, respectively
Fig. 13
Fig. 13
Two simulation runs for parameter a with a perturbation intensity ε=10−6. All the parameters take the values given in Fig. 8b
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References

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