Reconstructing chemical reaction networks: data mining meets system identification

ABSTRACT

We present an approach to reconstructing chemical reaction networks from time series measurements of the concentrations of the molecules involved. Our solution strategy combines techniques from numerical sensitivity analysis and probabilistic graphical models. By modeling a chemical reaction system as a Markov network (undirected graphical model), we show how systematically probing for sensitivities between molecular species can identify the topology of the network. Given the topology, our approach next uses detailed sensitivity profiles to characterize properties of reactions such as reversibility, enzyme-catalysis, and the precise stoichiometries of the reactants and products. We demonstrate applications to reconstructing key biological systems including the yeast cell cycle. In addition to network reconstruction, our algorithm finds applications in model reduction and model comprehension. We argue that our reconstruction algorithm can serve as an important primitive for data mining in systems biology applications.

REFERENCES

• 1: A. Arkin, P. Shen, and J. Ross. A Test Case of Correlation Metric Construction of a Reaction Pathway from Measurements. Science, Vol. 277(5330):1275--1279, Aug 1997.
• 2: U.S. Bhalla. Understanding Complex Signaling Networks through Models and Metaphors. Progress in Biophysics and Molecular Biology, Vol. 81(1):45--65, Jan 2003.
• 3: F. Bromberg, D. Margaritis, and V. Honavar. Efficient Markov Network Structure Discovery using Independence Tests. In Proceedings of the Sixth SIAM International Conference on Data Mining. SIAM Press, 2006.
• 4: Peter N. Brown , Alan C. Hindmarsh , Linda R. Petzold, Using Krylov methods in the solution of large-scale differential-algebraic systems, SIAM Journal on Scientific Computing, v.15 n.6, p.1467-1488, Nov. 1994 [doi>10.1137/0915088]
• 5: K.C. Chen, L. Calzone, F.R. Csikasz-Nagy, F.R. Cross, B. Novak, and J.J. Tyson. Integrative Analysis of Cell Cycle Control in Budding Yeast. Molecular Biology of the Cell, Vol. 15:3841--3862, Aug 2004.
• 6: Scott D. Cohen , Alan C. Hindmarsh, CVODE, a stiff/nonstiff ODE solver in C, Computers in Physics, v.10 n.2, p.138-143, March/April 1996
• 7: A. Csikasz-Nagy, D. Battogtokh, K.C. Chen, B. Novak, and J.J. Tyson. Analysis of a Generic Model of Eukaryotic Cell Cycle Regulation. Biophys. J., Vol. 90:4361--4379, 2006.
• 8: A.V. Karnaukhov and E.V. Karnaukhova. System Identification in Biophysics: A New Method based on Minimizing Square Residuals. Biofizika, Vol. 49(1):88--97, 2004.
• 9: A.V. Karnaukhov, E.V. Karnaukhova, and J.R. Williamson. Numerical Matrices Method for Nonlinear System Identification and Description of Dynamics of Biochemical Reaction Networks. Biophysical Journal, Vol. 92:3459--3473, 2007.
• 10: Steffen Klamt , Ernst Dieter Gilles, Minimal cut sets in biochemical reaction networks, Bioinformatics, v.20 n.2, p.226-234, January 2004 [doi>10.1093/bioinformatics/btg395]
• 11: E. Klipp, R. Herwig, A. Kowald, C. Wierling, and H. Lehrach. Systems Biology in Practice. Wiley-VCH, May 2005.
• 12: S.L. Lauritzen. Graphical Models. Oxford University Press, 1996.
• 13: W. Marwan, A. Wagler, and R. Weismantel. A Mathematical Approach to Solve the Network Reconstruction Problem. Mathematical Methods in Operations Research, Vol. 67:117--132, 2008.
• 14: M.R. Maurya, S.J. Bornheimer, V. Venkatasubramanian, and S. Subramaniam. Reduced-order Modelling of Biochemical Networks: Application to the GTpase-Cycle Signalling Module. IEE Systems Biology, Vol. 152(4):229--242, Dec 2005.
• 15: J. Ross, I. Schreiber, and M.O. Vlad. Determination of Complex Reaction Mechanisms: Analysis of Chemical, Biological, and Genetic Networks. Oxford University Press, Nov 2005.
• 16: W. Sha, J. Moore, K. Chen, A.D. Lassaletta, C.-S. Yi, J.J. Tyson, and J. Sible. Hysteresis drives Cell-cycle Transitions in Xenopus laevis Egg Extracts. PNAS, Vol. 100(3):975--980, Feb 2003.
• 17: J.J. Tyson. Modeling the Cell Division Cycle: cdc2 and Cyclin Interactions. PNAS, Vol. 88(16):7328--7332, Aug 1991.
• 18: J.J. Tyson, K.C. Chen, and B. Novak. Sniffers, Buzzers, Toggles and Blinkers: Dynamics of Regulatory and Signaling Pathways in the Cell. Current Opinion in Cell Biology, Vol. 15(2):221--231, Apr 2003.
• 19: C.H. Wiggins and I. Nemenman. Process Pathway Inference via Time Series Analysis. Experimental Mechanics, Vol. 43(3):361--370, Sep 2003.

INDEX TERMS

Primary Classification:
  H. Information Systems
  H.2 DATABASE MANAGEMENT
      H.2.8 Database applications
          Subjects: Data mining

Additional Classification:
  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
      I.2.6 Learning
          Subjects: Induction

General Terms:
Algorithms, Experimentation, Measurement

Keywords:
graphical models, markov networks, network reconstruction, ordinary differential equations, systems biology