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Module Decomposition and Integration Method Optimizes
A Large-Scale Cell Cycle Model
Daichi Nitta1
Hiroyuki Kurata1
[email protected] [email protected]
1
Department of Bioscience and Bioinformatics, Kyushu Institute of Technology,
Iizuka, Fukuoka 820-8502, Japan
Keywords: CADLIVE, dynamic simulation, systems biology, budding yeast, cell cycle, GA
1 Introduction
Major objectives of systems biology are to build molecular interaction networks and to predict or
understand their dynamics at the molecular interaction level. It is necessary to estimate the unmeasured
values of many kinetic parameters for mathematical modeling. Genetic algorithms (GAs) is one of the most
efficient method for estimation of the values of kinetic parameters, but large-scale models such as a budding
yeast cell cycle model have too many parameters for ordinary GAs to optimize efficiently. To circumvent this
problem, we propose a novel evolutionary method based on module decomposition and integration. The
large-scale cell cycle model is decomposed into 5 modules. After the optimization of each module, the
modules are integrated together and the resultant full model is optimized as multi-objective problems.
2 Method and Results
2.1 Construction of the Cell Cycle Modael
Using CADLIVE we drew the budding yeast
cell cycle map, as shown in Figure 1.
CADLIVE describes not only reactions but
also various events such as budding, DNA
replication start, spindle formation, and
chromatin separation. This map is one of the
most sophisticated images for the whole
system of the yeast cell cycle [1]. To estimate
the kinetic parameter values in this map using
genetic algorithms (GAs) efficiently, we
decompose it into 5 modules; G1 phase
module, S phase (budding) module, S phase
(DNA synthesis) module, G2-M phase module,
M phase checkpoint module as shown in Fig 1.
Figure 1: A budding yeast cell cycle map. (1) G1
phase, (2) S phase (budding), (3) S phase (DNA
synthesis), (4) G2-M phase, (5) M phase
checkpoint.
2.2 Dynamic Model
Regulator-reaction equations are converted into
the differential and algebraic equations using
the two-phase partition method (TPP). A flow for the conversion from the creation of a network to a dynamic
model is performed using CADLIVE [2][3][4]. In simulation of the budding yeast cell cycle, the dynamic
model consists of 76 algebraic equations, 40 differential equation, and 116 variables.
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2.3 Optimization
We optimized the 5 modules with GAs separately and
assumed the top 4 parameter sets in every module as the
candidates of optimum solutions, thereby obtaining the
assembled model (full model) with 1024 (= 45) parameter
sets. We simulated the full model with every candidate
parameter set as the initial values for optimization, as shown
in Figure 2, to explore the parameter set that best satisfies the
experimental data. Since there are various experimental data,
the multi-objective GAs (MOGA) are employed. The time
course data for the best solution are shown in Figure 3,
demonstrating that the cell cycle repeats every 150 minutes
[5].
3 Discussions
We estimate the values of kinetic parameters of a large-scale
cell cycle model. The optimization method based on module
decomposition and integration is effective in
optimizing the large-scale biochemical networks.
Cell cycle networks have been extensively
studied, as it closely relates the elucidation of the
molecular mechanisms for cancer cells or general
cell growth. The developed mathematical model
contributes to advances in the studies of cancer
development or systems biology.
Figure 2: Image of integration
References
[1] Katherine C. Chen, Attila Csikasz-Nagy, Bela
Gyorffy, John Val, Bela Novak, and John J.,
Tyson, Kinetic Analysis of a Molecular Model
of the Budding Yeast Cell Cycle, Molecular
Biology of the Cell, 11:369-391, 2000.
Figure 3: The result of simulation
[2] Kurata, H., Inoue, K., Maeda, K., Masaki, K., Shimokawa, Y., Quanyu Zhao, Extended CADLIVE: a
novel graphical notation for designing a biochemical network map that enables computational pathway
analysis, Nucleic Acids Res, 35(20):e134, 2007.
[3] Kurata, H., Masaki, K., Sumida, Y., Iwasaki, R., CADLIVE Dynamic Simulator: Direct Link of
Biochemical Networks to Dynamic Models, Genome Res., 15: 590-600, 2005.
[4] Kurata, H., Matoba, N., Shimizu, N., CADLIVE for constructing a large-scale biochemical network
based on a simulation-directed notation and its application to yeast cell cycle, Nucleic Acids Res.31:
4071-4084, 2003.
[5] Yamamichi, S., Kurata, H., A large-scale dynamic simulation of the cell cycle network, Proceedings of
7th Asia-Pacific Biochemical Engineering Conference, Jeju Island, Korea, SYS2-05, 2005.
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