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New Generation Computing

, Volume 25, Issue 4, pp 425–441 | Cite as

Discovering Dynamic Characteristics of Biochemical Pathways using Geometric Patterns among Parameter-Parameter Dependencies in Differential Equations

  • Ryuzo Azuma
  • Ryo Umetsu
  • Shingo Ohki
  • Fumikazu Konishi
  • Sumi Yoshikawa
  • Akihiko Konagaya
  • Kazumi Matsumura
Article
  • 53 Downloads

Abstract

This paper proposes a novel approach to the analysis and validation of mathematical models using two-dimensional geometrical patterns representing parameter-parameter dependencies (PPD) in dynamic systems. A geometrical pattern is obtained by calculating moment values, such as the area under the curve (AUC), area under the moment curve (AUMC), and mean residence time (MRT), for a series of simulations with a wide range of parameter values. In a mathematical model of the metabolic pathways of the cancer drug irinotecan (CPT11), geometrical patterns can be classified into three major categories: “independent,” “hyperbolic,” and “complex.” These categories characterize substructures arising in differential equations, and are helpful for understanding the behavior of large-scale mathematical models. The Open Bioinformatics Grid (OBIGrid) provides a cyber-infrastructure for users to share these data as well as computational resources.

Keywords

Simulation Mathematical Models Pharmacokinetics Visualization Grid Computing 

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Copyright information

©  2007

Authors and Affiliations

  • Ryuzo Azuma
    • 1
  • Ryo Umetsu
    • 1
  • Shingo Ohki
    • 1
  • Fumikazu Konishi
    • 1
  • Sumi Yoshikawa
    • 1
  • Akihiko Konagaya
    • 1
  • Kazumi Matsumura
    • 2
  1. 1.Genomic Sciences CenterRIKENTsurumi-yokohamaJapan
  2. 2.Daiichi Pure Chemicals Co. Ltd.TokaiJapan

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