Skip to main content
SpringerLink
Log in

Integrative biological systems modeling: challenges and opportunities

  • Research Article
  • Published:
Frontiers of Computer Science in China Aims and scope Submit manuscript

Abstract

Most biological systems are by nature hybrids consist of interacting discrete and continuous components, which may even operate on different time scales. Therefore, it is desirable to establish modeling frameworks that are capable of combining deterministic and stochastic, discrete and continuous, as well as multi-timescale features. In the context of molecular systems biology, an example for the need of such a combination is the investigation of integrated biological pathways that contain gene regulatory, metabolic and signaling components, which may operate on different time scales and involve on-off switches as well as stochastic effects. The implementation of integrated hybrid systems is not trivial because most software is limited to one or the other of the dichotomies above. In this study, we first review the motivation for hybrid modeling. Secondly, by using the example of a toggle switch model, we illustrate a recently developed modeling framework that is based on the combination of biochemical systems theory (BST) and hybrid functional Petri nets (HFPN). Finally, we discuss remaining challenges and future opportunities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Savageau M A. Biochemical systems analysis. I. Some mathematical properties of the rate law for the component enzymatic reactions. Journal of Theoretical Biology, 1969, 25(3): 365–369

    Article  Google Scholar 

  2. Savageau M A. Biochemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation. Journal of Theoretical Biology, 1969, 25(3): 370–379

    Article  Google Scholar 

  3. Savageau M A. Biochemical Systems Analysis: A Study of Function and Design in Molecular Biology. Reading: Addison-Wesley, 1976

    MATH  Google Scholar 

  4. Voit E O. Computational Analysis of Biochemical Systems: A Practical Guide for Biochemists and Molecular Biologists. Cambridge: Cambridge University Press, 2000

    Google Scholar 

  5. Torres N V, Voit E O. Pathway Analysis and Optimization in Metabolic Engineering. Cambridge: Cambridge University Press, 2002

    Google Scholar 

  6. Kacser H, Burns J A. The control of flux. Symp. Soc. Exp. Biol., 1973, 27: 65–104

    Google Scholar 

  7. Heinrich R, Rapoport T A. A linear steady-state treatment of enzymatic chains: General properties, control and effector strength. European Journal of Biochemistry, 1974, 42: 89–95

    Article  Google Scholar 

  8. Fell D A. Understanding the Control of Metabolism. London: Portland Press, 1997

    Google Scholar 

  9. Hatzimanikatis V, Bailey J. MCA has more to say. Journal of Theoretical Biology, 1996, 182: 233–242

    Article  Google Scholar 

  10. Visser D, Heijnen J J. The mathematics of metabolic control analysis revisited. Metabolic Engineering, 2002, 4(2): 114–123

    Article  Google Scholar 

  11. Wang F-S, Ko C-L, et al. Kinetic modeling using S-systems and lin-log approaches. Biochemical Engineering Journal, 2007, 33: 238–247

    Article  Google Scholar 

  12. Goss P J E, Peccoud J. Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets. In: Proceedings of the National Academy of Sciences, 1998, 95: 6750–6755

    Article  Google Scholar 

  13. Haas P J. Stochastic Petri Nets. New York: Springer-Verlag, 2002

    MATH  Google Scholar 

  14. D’Argenio P R, Katoen J-P. A theory of stochastic systems part I: Stochastic automata. Information and Computation, 2005, 203(1): 1–38

    Article  MATH  MathSciNet  Google Scholar 

  15. Gillespie D T. A rigorous derivation of the chemical master equation. Physica A, 1992, 188: 404–425

    Article  Google Scholar 

  16. Gillespie D T. Stochastic simulation of chemical kinetics. Annual Review of Physical Chemistry, 2007, 58(1): 35–55

    Article  MathSciNet  Google Scholar 

  17. Matsuno H, Tanaka Y, et al. Biopathways representation and simulation on hybrid functional Petri net. In Silico Biology, 2003, 3: 389–404

    Google Scholar 

  18. Wu J, Voit E O. Hybrid modeling in biochemical systems theory by means of functional Petri nets. Journal of Bioinformatics and Computational Biology, 2009 (in press)

  19. Elowitz M B, Levine A J, et al. Stochastic gene expression in a single cell. Science, 2002, 297(5584): 1183–1186

    Article  Google Scholar 

  20. Blake W J, Kaern M, et al. Noise in eukaryotic gene expression. Nature, 2003, 422(6932): 633–637

    Article  Google Scholar 

  21. McAdams H H, Arkin A P. Stochastic mechanisms in gene expression. In: Proceedings of National Academy of Sciences, 1997, 94: 814–819

    Article  Google Scholar 

  22. Schnell S, Turner T E. Reaction kinetics in intracellular environments with macromolecular crowding: simulations and rate laws. Progress in Biophysics and Molecular Biology, 2004, 85: 235–260

    Article  Google Scholar 

  23. Minton A P. Molecular crowding and molecular recognition. Journal Molecular Recognition, 1993, 6: 211–214

    Article  Google Scholar 

  24. Minton A P. Molecular crowding: analysis of effects of high concentrations of inert cosolutes on biochemical equilibria and rates in terms of volume exclusion. Methods Enzymol. 1998, 295: 127–149

    Article  Google Scholar 

  25. Luby-Phelps K, Castle P E, et al. Hindered diffusion of inert tracer particles in the cytoplasm of mouse 3T3 cells. In: Proceedings of National Academy of Sciences, 1987, 84: 4910–4913

    Article  Google Scholar 

  26. Scalettar B A, Abney J R, et al. Dynamics, structure, and functions are coupled in the mitrocondrial matrix. In: Proceedings of National Academy of Sciences, 1991, 88: 8057–8061

    Article  Google Scholar 

  27. Verkman A S. Solute and macromolecule diffusion in cellular aqueous compartments. Trends in Biochemical Science, 2002, 27: 27–33

    Article  Google Scholar 

  28. Clegg J S. Properties and metabolism of the aqueous cytoplasm and its boundaries. American Journal Physiology, 1984, 246: R133–R151

    Google Scholar 

  29. Srere P, Jones M E, Matthews C K, eds. Structural and Organizational Aspects of Metabolic Regulation. New York: Alan R. Liss, 1989

    Google Scholar 

  30. Gillespie D T. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. Journal of Computation Physics, 1976, 22: 403–434

    Article  MathSciNet  Google Scholar 

  31. Qian H, Elson E L. Single-molecule enzymology: stochastic Michaelis-Menten kinetics. Biophysical Chemistry, 2002, 101–102:565–576

    Article  Google Scholar 

  32. Kuthan H. Self-organisation and orderly processes by individual protein complexes in the bacterial cell. Progress in Biophysics and Molecular Biology, 2001, 75: 1–17

    Article  Google Scholar 

  33. Hirata H, Yoshiura S, et al. Oscillatory expression of the bHLH factor Hes1 regulated by a negative feedback loop. Science, 2002, 298(5594): 840–843

    Article  Google Scholar 

  34. Monk N A. Oscillatory expression of Hes1, p53, and NF-kappaB driven by transcriptional time delays. Current Biology, 2003, 13(16):1409–1413

    Article  Google Scholar 

  35. Tian T, Burrage K, et al. Stochastic delay differential equations for genetic regulatory networks. The Journal of Computational and Applied Mathematics, 2007, 205(2): 696–707

    Article  MATH  MathSciNet  Google Scholar 

  36. Kiehl T R, Mattheyses R M, et al. Hybrid simulation of cellular behavior. Bioinformatics, 2004, 20(3): 316–322

    Article  Google Scholar 

  37. Mocek W T, Rudnicki R, et al. Approximation of delays in biochemical systems. Mathematical Biosciences, 2005, 198(2): 190–216

    Article  MATH  MathSciNet  Google Scholar 

  38. Miyano S. Cell Illustrator website. http://www.cellillustrator.com/, 2008

  39. Gardner T S, Cantor C R, et al. Construction of a genetic toggle switch in Escherichiacoli. Nature, 2000, 403: 339–342

    Article  Google Scholar 

  40. Tian T, Burrage K. Stochastic models for regulatory networks of the genetic toggle switch. In: Proceedings of the National Academy of Sciences, 2006, 103(22): 8372–8377

    Article  Google Scholar 

  41. Savageau M A, Voit E O. Recasting nonlinear differential equations as S-systems: a canonical nonlinear form. Mathematical Biosciences, 1987, 87(1): 31–113

    Article  MathSciNet  Google Scholar 

  42. Voit E O. Smooth bistable S-systems. In: Proceedings of IEEE Systems Biology, 2005, 152: 207–213

    Article  Google Scholar 

  43. Clarke E M, Grumberg O, et al. Model Checking. Cambridge: MIT Press, 1999

    Google Scholar 

  44. Nagasaki M, Yamaguchi R, et al. Genomic data assimilation for estimating hybrid functional Petri net from time-course gene expression data. Genome Informatics, 2006, 17(1): 46–61

    Google Scholar 

  45. Neapolitan R E. Learning Bayesian Networks. Prentice Hall, 2003

  46. Jiang X, Cheng D C, et al. A novel parameter decomposition approach to faithful fitting of quadric surfaces. Pattern Recognition: 27th DAGM Symposium, LNCS, 2005, 3663: 168–175

    Article  Google Scholar 

  47. Williams B C, Millar W. Decompositional, Model-based learning and its Analogy to Diagnosis. AAAI/IAAI, 1998

  48. Koh G, Teong H, et al. A decompositional approach to parameter estimation in pathway modeling: a case study of the Akt and MAPK pathways and their crosstalk. Bioinformatics, 2006, 22(14): e271–280

    Article  Google Scholar 

  49. Alves R, Savageau MA. Extending the method of mathematically controlled comparison to include numerical comparisons. Bioinformatics, 2000, 16(9): 786–798

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Bioinformatics Program, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Jialiang Wu

  2. Integrative BioSystems Institute, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Eberhard Voit

  3. The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Eberhard Voit

Authors
  1. Jialiang Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eberhard Voit
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eberhard Voit.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, J., Voit, E. Integrative biological systems modeling: challenges and opportunities. Front. Comput. Sci. China 3, 92–100 (2009). https://doi.org/10.1007/s11704-007-0011-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11704-007-0011-9

Keywords

Search

Navigation