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 AzumaEmail author
  • Ryo Umetsu
  • Shingo Ohki
  • Fumikazu Konishi
  • Sumi Yoshikawa
  • Akihiko Konagaya
  • Kazumi Matsumura


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.


Simulation Mathematical Models Pharmacokinetics Visualization Grid Computing 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Fell, D., Understanding the Control of Metabolism, Portland Press, London, 1997.Google Scholar
  2. 2.
    Palsson, B.O., Systems Biology: Properties of Reconstructed Networks, Cambridge University Press, Cambridge, 2006.Google Scholar
  3. 3.
    Hatakeyama, M., Kimura, S., Naka, T., Kawasaki, T., Yumoto, N., Ichikawa, M., Kim, J.H., Saito, K., Saeki, M., Shirouzu, M., Yokoyama, S., Konagaya, A., “A computation model on the modulation of mitogen-activated protein kinase (MAPK) and Akt pathways in heregulin-induced ErbB signaling,” Biochemical Journal, 373, pp. 451-463, 2003CrossRefGoogle Scholar
  4. 4.
    Imade, H., Mizuguchi, N., Ono, I., Ono, N. and Okamoto, M., “Gridifying: An Evolutionary Algorithm for Inference of Genetic Networks Using the Improved GOGA Framework and its Performance Evaluation on OBI Grid,” in Grid Computing in Life Science, Lecture Notes in Bioinformatics, 3370 (Konagaya, A. and Satoru K. eds.) pp. 171-186, 2005.Google Scholar
  5. 5.
    Hariparsad N, Nallani, S.C., Sane, R.S., Buckley D.J., Buckley A.R., Desai P.B., “Induction of CYP3A4 by efavirenz in primary human hepatocytes: comparison with Rifampin and Phenobarbital,” J Clin Pharmacol. 44, pp. 1273-1281, 2004CrossRefGoogle Scholar
  6. 6.
    Raymond, E., Fabbro, M., Boige, V., Rixe, O., Frenay, M., Vassal, G., Faivre, S., Sicard, E., Germa, C., Rodier, M., Vernillet, L. and Armand J.P., “Multicentre phase II study and pharmacokinetic analysis of irinotecan in chemotherapy-naïve patients with glioblastoma,” Annals of Oncology, 14, pp. 603-614, 2003.CrossRefGoogle Scholar
  7. 7.
    Garcia-Carbonero, R. and Supko J.G., “Current perspectives on the clinical experience, pharmacology, and continued development of the camptotecines,” Clinical cancer research, 8, pp. 641-661, 2002.Google Scholar
  8. 8.
    Charasson, V., Haaz, M.C. and Robert., J., “Determination of drug interactions occurring with the metabolic pathways of irinotecan,” Drug metabolism and disposition, 30, pp. 731-733, 2002.CrossRefGoogle Scholar
  9. 9.
    Kageyama, M., Namiki, H., Fukushima, H., Ito, Y., Shibata, N. and Tanada, K., “In vivo effects of cycloporin A and Ketoconazole on the pharmacokinetics of representative substrates for p-glycoprotein and cytochrome P450 (CYP) 3A in rats,” Biol pharm bull. 28, pp. 316-322, 2005.CrossRefGoogle Scholar
  10. 10.
    Mathijssen, R., van Alphen, R.J., Verweij, J., Loos, W.J., Nooter, K., Stoter, G. and Sparreboom, A., “Clinical pharmacokinetics and metabolism of irinotecan,” Clinical cancer research, 7, pp. 2182-2194, 2001.Google Scholar
  11. 11.
    Kimura, S., Ide, K., Kashihara, A., Kano, M., Hatakeyama, M., Masui, R., Nakagawa, N., Yokoyama, S., Kuramitsu, S., Konagaya, A., “Inference of S-system models of genetic networks using a cooperative coevolutionary algorithm,” Bioinformatics, 21-7, pp. 1154-1163, 2005.Google Scholar
  12. 12.
    Yamaoka, K., Nakagawa, T. and Uno, T., “Statistical moments in pharmacokinetics,” J. Pharmacokin, 6, pp. 547-558, 1978.CrossRefGoogle Scholar
  13. 13.
    Culter, D.J., “Theory of the mean absorption time, an adjunct to convolutional bioavailability studies,” J. Pharm. Pharmacol., 30, pp. 476-478, 1978.Google Scholar
  14. 14.
  15. 15.
    Ishikawa, T., Tamura, A., Saito, H., Wakabayashi, K. and Nakagawa, H., “Pharmacogenomics of the human ABC transporter ABCG2: from functional evaluation to drug molecular design,” Naturwissenschaften, 92, pp.451-463, 2005.CrossRefGoogle Scholar

Copyright information

©  2007

Authors and Affiliations

  • Ryuzo Azuma
    • 1
    Email author
  • 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

Personalised recommendations