Virtual
Simulation ofDrosophila
Drosophila

Koji Kyoda 1323Leg Formation

Hiroaki Kitano 23

kyoda@mt.cs.keio.ac.jp
1Pro ject:kitano@csl.sony.co.jp

Department of Computer Science, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223, Japan.
Sony Computer Science Laboratory, Inc., 3-14-13 Higashi-Gotanda, Shinagawa-ku,Tokyo 141, Japan.
Systems Biology Group, Kitano Symbiotic Systems Pro ject, ERATO, JST., 6-31-15
6A, Jingu-Mae, Shibuya-ku, Tokyo 150, Japan.

1 Introduction
Historically, Drosophila has been an extremely popular animal for molecular and developmental biology. There is a substantial accumulation of genetic and cytological knowledge and detailed analysis
for the organism. The formation of leg, wing, eye, and other structures from imaginal discs is particularly interesting as these discs undergo dramatic changes in structure. Leg formation in Drosophila
is especially important not only for Drosophila research but also vertebrate development research, as
they may share some common mechanisms in forming limb axes.
The goal of this paper is to reproduce the patterns of gene expressions observed in actual leg discs,
and propose a biologically faithful model in the light of recent of molecular biology studies, involving
gene regulation and axis determination in the Drosophila leg disc.

2 Modeling and DesignThe leg disc of this simulation has more than 1,000 cells which are approximated as spheres andarranged as a circle. We have implemented eight major genes and their regulations involved in theformation of the Drosophila leg disc. In the simulation, we de ned four processes: transcription,translation, protein di usion and protein decay. We unify these processes with the following equation
[1].
@Ui
@t

Uitxy::::= Di@2@x

2+@2@y!

Ui

2concentration of protein itime
position on x axis
position on y axis

DifUg+ f (U) 0 g 1 Ui
::::

(1)

di usion constant
protein production function
concentration vector
degradation rate (g = 0:1)

Currently we hand-optimize the binding anity, protein di usion constant value, etc. In the future
we hope to use an optimization algorithm to determine ideal parameter setting for the simulator.
The system is composed of the Leg, Cell, Gene and Protein classes. Each cell in this system
contains a list of proteins. First, the system checks whether a protein is secretable. If the protein
secretable, the amount of di using protein is calculated in comparison with the protein concentrationin the adjacent cells by the Di usion Engine. Second, the Reaction Engine calculates the amount ofprotein which is produced from genes through transcription and translation in the presence of activatorand repressor protein concentrations.
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Figure 1: A Screen Dump of the Leg Simulator.

3 Results
The simulator successfully reproduces the expression patterns for the genes involved and the localization patterns of their products. Fig. 1 shows simulated patterns for the genes ci, hh, en, wg, dpp, dll,
dac, al. These results agree well with experimental biological data.

4 Summary and Conclusions
In this paper, we present a simulation system for leg formation, simulating the genes interactions
involved. We use this simulator to investigate a mathematical framework of leg formation which isotherwise well-founded from a molecular perspective. Particularly, we focus on the formation of theexpression patterns of dpp, wg, dll, dac, al, en, hh and ci genes, which are involved in the developmentof the third instar Drosophila leg disc. Our results support the theory that the coaxial patterns ofgene expressions of al, dll and dac in the leg disc are formed by two chemical gradients of wg and dpp
products [2].

Acknowledgements
This work was carried out under the Virtual Drosophila Project [3]. We would like to thank to Dr.
Mario Tokoro at Keio University for his useful advice. We also want to express our thanks to Dr.
Tetsuya Kojima at Tokyo University for providing useful comments.

References[1] Hamahashi, S. and Kitano, H., Simulation of Drosophila Embryogenesis, In Proceedings of theSixth International Conference on Arti cial Life, 151{160, 1998.
[2] Lecuit, T. and Cohen, S.M., Proximal-distal Axis Formation in the Drosophila Leg, Nature,388:139{145, 1997.
[3] Kitano, H., Hamahashi, S., Kitazawa, J., Takao, K., and Imai, S., Virtual Biology Laboratories:
A New Approach of Computational Biology, In Proceedings of Fourth European Conference onArti cial Life, 274{283, 1997.
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