Asynchronous adaptive time step in quantitative cellular automata modeling

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Abstract

Background

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.

Results

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.

Conclusions

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.

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Most cited references 18

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Analysis of optimality in natural and perturbed metabolic networks.

Daniel Segrè, Dennis Vitkup, George Church (2002)

An important goal of whole-cell computational modeling is to integrate detailed biochemical information with biological intuition to produce testable predictions. Based on the premise that prokaryotes such as Escherichia coli have maximized their growth performance along evolution, flux balance analysis (FBA) predicts metabolic flux distributions at steady state by using linear programming. Corroborating earlier results, we show that recent intracellular flux data for wild-type E. coli JM101 display excellent agreement with FBA predictions. Although the assumption of optimality for a wild-type bacterium is justifiable, the same argument may not be valid for genetically engineered knockouts or other bacterial strains that were not exposed to long-term evolutionary pressure. We address this point by introducing the method of minimization of metabolic adjustment (MOMA), whereby we test the hypothesis that knockout metabolic fluxes undergo a minimal redistribution with respect to the flux configuration of the wild type. MOMA employs quadratic programming to identify a point in flux space, which is closest to the wild-type point, compatibly with the gene deletion constraint. Comparing MOMA and FBA predictions to experimental flux data for E. coli pyruvate kinase mutant PB25, we find that MOMA displays a significantly higher correlation than FBA. Our method is further supported by experimental data for E. coli knockout growth rates. It can therefore be used for predicting the behavior of perturbed metabolic networks, whose growth performance is in general suboptimal. MOMA and its possible future extensions may be useful in understanding the evolutionary optimization of metabolism.

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Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors.

Birgit Schoeberl, Claudia Eichler-Jonsson, Ernst Gilles … (2002)

We present a computational model that offers an integrated quantitative, dynamic, and topological representation of intracellular signal networks, based on known components of epidermal growth factor (EGF) receptor signal pathways. The model provides insight into signal-response relationships between the binding of EGF to its receptor at the cell surface and the activation of downstream proteins in the signaling cascade. It shows that EGF-induced responses are remarkably stable over a 100-fold range of ligand concentration and that the critical parameter in determining signal efficacy is the initial velocity of receptor activation. The predictions of the model agree well with experimental analysis of the effect of EGF on two downstream responses, phosphorylation of ERK-1/2 and expression of the target gene, c-fos.

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Kinetic analysis of a molecular model of the budding yeast cell cycle.

Béla Novák, Jiann-Chu Chen, B Győrffy … (1999)

The molecular machinery of cell cycle control is known in more detail for budding yeast, Saccharomyces cerevisiae, than for any other eukaryotic organism. In recent years, many elegant experiments on budding yeast have dissected the roles of cyclin molecules (Cln1-3 and Clb1-6) in coordinating the events of DNA synthesis, bud emergence, spindle formation, nuclear division, and cell separation. These experimental clues suggest a mechanism for the principal molecular interactions controlling cyclin synthesis and degradation. Using standard techniques of biochemical kinetics, we convert the mechanism into a set of differential equations, which describe the time courses of three major classes of cyclin-dependent kinase activities. Model in hand, we examine the molecular events controlling "Start" (the commitment step to a new round of chromosome replication, bud formation, and mitosis) and "Finish" (the transition from metaphase to anaphase, when sister chromatids are pulled apart and the bud separates from the mother cell) in wild-type cells and 50 mutants. The model accounts for many details of the physiology, biochemistry, and genetics of cell cycle control in budding yeast.

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Author and article information

Journal

Journal ID (nlm-ta): BMC Bioinformatics

Title: BMC Bioinformatics

Publisher: BioMed Central (London )

ISSN (Electronic): 1471-2105

Publication date Collection: 2004

Publication date (Electronic): 29 June 2004

Volume: 5

Page: 85

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

Article

Publisher ID: 1471-2105-5-85

DOI: 10.1186/1471-2105-5-85

PMC ID: 459211

PubMed ID: 15222901

SO-VID: 0f5231ca-2599-4020-9285-f1f70c5fd39e

Copyright © Copyright © 2004 Zhu et al; licensee BioMed Central Ltd. This is an Open Access article: verbatim copying and redistribution of this article are permitted in all media for any purpose, provided this notice is preserved along with the article's original URL.

Asynchronous adaptive time step in quantitative cellular automata modeling

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Abstract

Background

Results

Conclusions

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Most cited references 18

Analysis of optimality in natural and perturbed metabolic networks.

Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors.

Kinetic analysis of a molecular model of the budding yeast cell cycle.

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