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Open Access Methodology article

Asynchronous adaptive time step in quantitative cellular automata modeling

Hao Zhu1, Peter YH Pang2, Yan Sun1 and Pawan Dhar1*

Author Affiliations

1 Bioinformatics Institute, National University of Singapore, 30 Biopolis Street, Singapore 138671

2 Department of Mathematics, National University of Singapore, Lower Kent Ridge Road, Singapore 119260

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BMC Bioinformatics 2004, 5:85  doi:10.1186/1471-2105-5-85

Published: 29 June 2004



The behaviors of cells in metazoans are context dependent, thus large-scale multi-cellular modeling is often necessary, for which cellular automata are natural candidates. Two related issues are involved in cellular automata based multi-cellular modeling: how to introduce differential equation based quantitative computing to precisely describe cellular activity, and upon it, how to solve the heavy time consumption issue in simulation.


Based on a modified, language based cellular automata system we extended that allows ordinary differential equations in models, we introduce a method implementing asynchronous adaptive time step in simulation that can considerably improve efficiency yet without a significant sacrifice of accuracy. An average speedup rate of 4–5 is achieved in the given example.


Strategies for reducing time consumption in simulation are indispensable for large-scale, quantitative multi-cellular models, because even a small 100 × 100 × 100 tissue slab contains one million cells. Distributed and adaptive time step is a practical solution in cellular automata environment.