Integrated biological systems modeling: challenges and opportunities
Integrated biological systems modeling: challenges and opportunities
Jialiang WU1, Eberhard VOIT2,3()
1. Department of Mathematics, Bioinformatics Program, Georgia Institute of Technology, Atlanta, GA 0332, USA; 2. Integrative BioSystems Institute, Georgia Institute of Technology, Atlanta, GA 30332, USA; 3. The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology, tlanta, GA 30332, USA
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.
. Integrated biological systems modeling: challenges and opportunities[J]. Frontiers of Computer Science in China, 2009, 3(1): 92-100.
Jialiang WU, Eberhard VOIT. Integrated biological systems modeling: challenges and opportunities. Front Comput Sci Chin, 2009, 3(1): 92-100.
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 doi: 10.1016/S0022-5193(69)80026-3
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 doi: 10.1016/S0022-5193(69)80027-5
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 doi: 10.1111/j.1432-1033.1974.tb03318.x
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 doi: 10.1006/jtbi.1996.0160
10
Visser D, Heijnen J J. The mathematics of metabolic control analysis revisited. Metabolic Engineering , 2002, 4(2): 114-123 doi: 10.1006/mben.2001.0216
11
Wang F-S, Ko C-L, . Kinetic modeling using S-systems and linlog approaches. Biochemical Engineering Journal , 2007, 33: 238-247 doi: 10.1016/j.bej.2006.11.002
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 doi: 10.1073/pnas.95.12.6750
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 doi: 10.1016/j.ic.2005.07.001
15
Gillespie D T. A rigorous derivation of the chemical master equation. Physica A , 1992, 188: 404-425 doi: 10.1016/0378-4371(92)90283-V
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) doi: 10.1142/S0219720009004047
19
Elowitz M B, Levine A J, . Stochastic gene expression in a single cell. Science , 2002, 297(5584): 1183-1186 doi: 10.1126/science.1070919
20
Blake W J, Kaern M, . Noise in eukaryotic gene expression. Nature , 2003, 422(6932): 633-637 doi: 10.1038/nature01546
21
McAdams H H, Arkin A P. Stochastic mechanisms in gene expression. In: Proceedings of National Academy of Sciences , 1997, 94: 814-819 doi: 10.1073/pnas.94.3.814
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 doi: 10.1016/j.pbiomolbio.2004.01.012
23
Minton A P. Molecular crowding and molecular recognition. Journal Molecular Recognition , 1993, 6: 211-214 doi: 10.1002/jmr.300060410
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 doi: 10.1016/S0076-6879(98)95038-8
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 doi: 10.1073/pnas.84.14.4910
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 doi: 10.1073/pnas.88.18.8057
27
Verkman A S. Solute and macromolecule diffusion in cellular aqueous compartments. Trends in Biochemical Science , 2002, 27: 27-33 doi: 10.1016/S0968-0004(01)02003-5
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 doi: 10.1016/0021-9991(76)90041-3
31
Qian H, Elson E L. Single-molecule enzymology: stochastic Michaelis-Menten kinetics. Biophysical Chemistry , 2002, 101-102: 565-576 doi: 10.1016/S0301-4622(02)00145-X
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 doi: 10.1126/science.1074560
34
Monk N A. Oscillatory expression of Hes1, p53, and NF-kappaB driven by transcriptional time delays. Current Biology , 2003, 13(16): 1409-1413 doi: 10.1016/S0960-9822(03)00494-9
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 doi: 10.1016/j.cam.2006.02.063
36
Kiehl T R, Mattheyses R M, . Hybrid simulation of cellular behavior. Bioinformatics , 2004, 20(3): 316-322 doi: 10.1093/bioinformatics/btg409
37
Mocek W T, Rudnicki R, . Approximation of delays in biochemical systems. Mathematical Biosciences , 2005, 198(2): 190-216 doi: 10.1016/j.mbs.2005.08.001
38
Miyano S. Cell Illustrator website. http://www.cellillustrator.com /, 2008
39
Gardner T S, Cantor C R, . Construction of a genetic toggle switch in Escherichiacoli. Nature , 2000, 403: 339-342 doi: 10.1038/35002131
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 doi: 10.1073/pnas.0507818103
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 doi: 10.1016/0025-5564(87)90035-6
42
Voit E O. Smooth bistable S-systems. In: Proceedings of IEEE Systems Biology , 2005, 152: 207-213 doi: 10.1049/ip-syb:20050063
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 doi: 10.1093/bioinformatics/btl264
49
Alves R, Savageau MA. Extending the method of mathematically controlled comparison to include numerical comparisons. Bioinformatics , 2000, 16(9): 786-798 doi: 10.1093/bioinformatics/16.9.786