Abstract
Systems biology aims at an understanding of increasingly large and complex cellular systems making use of computational approaches, e.g. numerical simulations. The size and complexity of the underlying biochemical reaction networks call for methods to speed up simulations and/or dissect the biochemical network into smaller subsystems which can be studied independently. Both goals can be achieved by so-called complexity reduction algorithms. However, existing complexity reduction approaches for biochemical reaction networks are mostly based on studying the steady state behavior of a system and/or are based on heuristics. Given the fact that many complex biochemical systems display highly nonlinear dynamics and that this dynamics plays a crucial role in the functioning of the organism, a new methodology has to be developed. Therefore, we present a new complexity reduction method which is time-dependent and suited not only for steady states, but for all possible dynamics of a biochemical system. It makes use of the evolution of the different time–scales in the system, allowing to reduce the number of equations necessary to describe the system which is speeding up the computation time. In addition, it is possible to study the way different variables/metabolites contribute to the reduced equation system which indicates how strongly they interact and couple. In the extreme case of variables decoupling in a specific state, the method allows the complete dissection of the system resulting in subsystems that can be studied in isolation. The whole method provides a systematic tool for an automated complexity reduction of arbitrary biochemical reaction networks. With the aid of a specific example, the oscillatory peroxidase-oxidase system, we show that coupling of time–scales depends heavily on the specific dynamics of the system. Therefore, neither computational improvement nor systematic understanding can be achieved by studying these aspects solely under steady state conditions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Kitano, H.: Computational systems biology. Nature 420, 206–210 (2002), References therein
Kauffman, K.J., Pajerowski, J.D., Jamshidi, N., Palsson, B.O., Edwards, J.E.: Description and analysis of metabolic connectivity and dynamics in the human red blood cell. Biophys. J. 83, 646–662 (2002)
Price, N.D., Reed, J.L., Papin, J.A., Famili, I., Palsson, B.O.: Analysis of metabolic capabilities using singular value decomposition of extreme pathway matrices. Biophys. J. 84, 794–804 (2003)
Schuster, S., Pfeiffer, T., Moldenhauer, F., Koch, I., Dandekar, T.: Exploring the pathway structure of metabolism: decomposition into subnetworks and application to Mycoplasma pneumoniae. Bioinformatics 18, 351–361 (2002)
Holme, P., Huss, M., Jeong, H.: Subnetwork hierarchies of biochemical pathways. Bioinformatics 19, 532–538 (2003)
Berridge, M.J., Bootman, M.D., Lipp, P.: Calcium - a life and death signal. Nature 395, 645–648 (1998)
Petty, H.R., Worth, R.G., Kindzelskii, A.L.: Imaging sustained dissipative patterns in the metabolism of individual cells. Phys. Rev. Lett. 84, 2754–2757 (2000)
Duysens, L.N.M., Amesz, J.: Fluorescence sprectrophotometry of reduced phosphopyridine nucleotide in intact cells in the near-ultraviolet and visible region. Biochim. Biophys. Acta 24, 19–26 (1957)
Frenkel, R.: Control of reduced diphosphopyridine nucleotide oscillations in beef heart extracts.I. Effect of modifiers of phosphofructokinase activity. Arch. Biochem. Biophys. 125, 151–156 (1968)
Scheeline, A., Olson, D.L., Williksen, E.P., Horras, G.A., Klein, M.L., Larter, R.: The peroxidase-oxidase oscillator and its constituent chemistries. Chem. Rev. 97, 739–756 (1997)
Bronnikova, T.V., Fed’kina, V.R., Schaffer, W.M., Olsen, L.F.: Period-doubling bifurcations and chaos in a detailed model of the peroxidase-oxidase reaction. J. Phys. Chem. 99, 9309–9312 (1995)
Okino, M.S., Mavrovouniotis, M.L.: Simplification of mathematical models of chemical reaction systems. Chem. Rev. 98, 391–408 (1998)
Tomlin, A.S., Turanyi, T., Pilling, M.J.: Mathematical tools for the construction, investigation and reduction of combustion mechanisms. In: Pilling, M.J. (ed.) Low Temperature Combustion and Autoignition, pp. 293–437. Elsevier, Amsterdam (1997)
Lam, S.H., Goussis, D.A.: The CSP method for simplifying kinetics. Int. J. Chem. Kinet. 26, 461–486 (1994), References therein
Maas, U., Pope, S.B.: Simplifying chemical reaction kinetics: Intrinsic low-dimensional manifolds in composition space. Combustion and Flame 88, 239–264 (1992)
Davis, M.J., Skodje, R.T.: Geometric investigation of low-dimensional manifolds in systems approaching equilibrium. J. Chem. Phys. 111, 847–859 (1999)
Skodje, R.T., Davis, M.J.: Geometrical simplification of complex kinetic systems. J. Phys. Chem. A 105, 10356–10365 (2001)
Roussel, M.R., Fraser, S.J.: Invariant manifold methods for metabolic model reduction. Chaos 11, 196–206 (2001)
Valorani, M., Goussis, D.A.: Explicit time-scale splitting algorithm for stiff problems: auto-ignition of gaseous mixtures behind a steady shock. J. Comput. Phys. 169, 44–79 (2001)
Schmidt, D., Blasenbrey, T., Maas, U.: Intrinsic low-dimensional manifolds of strained and unstrained flames. Combustion Theory and Modelling 2, 135–152 (1998)
Correa, C., Niemann, H., Schramm, B., Warnatz, J.: Reaction mechanisms reduction for higher hydrocarbons by the ILDM method. Proc. Comb. Inst. 28, 1607–1614 (2001)
Voet, D., Voet, J.G.: Biochemistry. Wiley, New York (1990)
Agarwal, P.K., Billeter, S.R., Ravi Rajagopalan, P.T., Benkovic, S.J., Hammes-Schiffer, S.: Network of coupled promoting motions in enzyme catalysis. Proc. Natl. Acad. Sci. 99, 2794–2799 (2002)
Segel, L.A., Slemrod, M.: The Quasi-steady state assumption: a case study in perturbation. SIAM Review 31, 446–477 (1989)
Heinrich, R., Schuster, S.: The regulation of cellular systems. Chapman and Hall, New York (1996)
Reder, C.: Metabolic control theory: a structural approach. J. Theor. Biol. 135, 175–201 (1988)
Deuflhard, P., Heroth, J.: Dynamic dimension reduction in ODE models. In: Scientific Computing in Chemical Engineering, pp. 29–43. Springer, Berlin (1996)
Golub, G.H., van Loan, C.F.: Matrix computations, 3rd edn. Johns Hopkins University Press, Baltimore (1996)
Golub, G.H., Wilkinson, J.H.: Ill-conditioned eigensystems and computation of the Jordan canonical form. SIAM review 18, 578–619 (1976)
Deuflhard, P., Nowak, U.: Extrapolation Integrators for Quasilinear Implicit ODEs. In: Large Scale Scientific Computing. Progress in Scientific Computing, vol. 7, pp. 37–50. Birkhäuser, Boston (1987)
Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Sorensen, D.: LA-PACK Users’ Guide, 3rd edn. SIAM, Philadelphia (1999)
Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical recipes in FORTRAN 77, 2nd edn. Cambridge University Press, Cambridge (1993)
Thompson, D.R., Larter, R.: Multiple time-scale analysis of two models for the peroxidase-oxidase reaction. Chaos 5, 448–457 (1995)
Hauser, M.J.B., Kummer, U., Larsen, A.Z., Olsen, L.F.: Oscillatory dynamics protect enzymes and possibly cells against toxic intermediates. Faraday Discuss. 120, 215–227 (2001)
Amit, A., Kindzelskii, A.L., Zanoni, J., Jarvis, J.N., Petty, H.R.: Complement deposition on immune complexes reduces the frequencies of metabolic, proteolytic, and superoxide oscillations of migrating neutrophils. Cell. Immunol. 194, 47–53 (1999)
Klann, E., Robertson, E.D., Knapp, L.T., Sweat, J.D.: A role for superoxide in protein kinase C activation and long-term potentiation. J. Biol. Chem. 273, 4516–4522 (1998)
Carafoli, E., Santella, L., Brance, D., Brini, M.: Generation, control, and processing of cellular calcium signals. Crit. Rev. Biochem. Mol. Biol. 36, 107–260 (2001)
Olson, D.L., Williksen, E.P., Scheeline, A.: An experimentally based model of the Peroxidase-NADH biochemical oscillator: an enzyme-mediated chemical switch. J. Am. Chem. Soc. 117, 2–15 (1995); Biol. 36, 107–260 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Zobeley, J., Lebiedz, D., Kammerer, J., Ishmurzin, A., Kummer, U. (2005). A New Time-Dependent Complexity Reduction Method for Biochemical Systems. In: Priami, C. (eds) Transactions on Computational Systems Biology I. Lecture Notes in Computer Science(), vol 3380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32126-2_7
Download citation
DOI: https://doi.org/10.1007/978-3-540-32126-2_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25422-5
Online ISBN: 978-3-540-32126-2
eBook Packages: Computer ScienceComputer Science (R0)