Integrated biological systems modeling: challenges and opportunities

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.

Keywords

biochemical systems theory / Petri net / hybrid modeling / hybrid functional Petri net / toggle switch / canonical modeling / stochastic delay

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

[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

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

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

[5] Torres N V, Voit E O. Pathway Analysis and Optimization inMetabolic Engineering. Cambridge: Cambridge University Press, 2002

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

[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

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

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

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

[11] Wang F-S, Ko C-L, . Kinetic modeling using S-systems and linlog approaches. Biochemical Engineering Journal, 2007, 33: 238-247

[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

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

[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

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

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

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

[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, . Stochastic gene expression in a single cell. Science, 2002, 297(5584): 1183-1186

[20] Blake W J, Kaern M, . Noise in eukaryotic gene expression. Nature, 2003, 422(6932): 633-637

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

[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

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

[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

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

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

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

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

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

[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

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

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

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

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

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

[36] Kiehl T R, Mattheyses R M, . Hybrid simulation of cellular behavior. Bioinformatics, 2004, 20(3): 316-322

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

[38] Miyano S. Cell Illustrator website. 2008

[39] Gardner T S, Cantor C R, . Construction of a genetic toggle switch in Escherichiacoli. Nature, 2000, 403: 339-342

[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

[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

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

[43] Clarke E M, Grumberg O, . Model Checking. Cambridge: MIT Press, 1999

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

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

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

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

[48] Koh G, Teong H, . 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

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

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