Advertisement

Hybrid Modeling for Systems Biology: Theory and Practice

  • Moritz von Stosch
  • Nuno Carinhas
  • Rui OliveiraEmail author
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)

Abstract

Whereas bottom-up systems biology relies primarily on parametric mathematical models, which try to infer the system behavior from a priori specified mechanisms, top-down systems biology typically applies nonparametric techniques for system identification based on extensive “omics” data sets. Merging bottom-up and top-down into middle-out strategies is confronted with the challenge of handling and integrating the two types of models efficiently. Hybrid semiparametric models are natural candidates since they combine parametric and nonparametric structures in the same model structure. They enable to blend mechanistic knowledge and data-based identification methods into models with improved performance and broader scope. This chapter aims at giving an overview on theoretical fundaments of hybrid modeling for middle-out systems biology and to provide practical examples of applications, which include hybrid metabolic flux analysis on ill-defined metabolic networks, hybrid dynamic models with unknown reaction kinetics, and hybrid dynamic models of biochemical systems with intrinsic time delays.

Keywords

Systems biology Middle-out systems biology Hybrid modeling Hybrid semiparametric modeling Parametric/nonparametric modeling 

Abbreviations

AIC

Akaike Information Criterion

ANN

Artificial Neural Networks

BHK

Baby Hamster Kidney

BIC

Bayesian Information Criterion

DDE

Delayed Differential Equation

EM

Elementary Modes

EP

Extreme Pathways

FBA

Flux Balance Analysis

MFA

Metabolic Flux Analysis

ODE

Ordinary Differential Equation

PLS

Projection to Latent Structure or Partial Least Squares

RFDE

Retarded Functional Dynamic Equation

Sf9

Spodoptera frugiperda

TF

Transcription Factor

TFA

Transcription Factor A

WSE

Weighted Squares Error

c

Vector of concentrations of intracellular compounds

d/dt

Time derivative

D

Dilution rate

ei

Vectors of EMs

f(⋅)

Parametric mathematical function

FGlc

Volumetric feeding rates of glucose

FGln

Volumetric feeding rates of glutamine

g(⋅)

Nonparametric mathematical function

h(⋅)

Function that combines the nonparametric and parametric model

N

Matrix of stoichiometric coefficients

ND

Number of data points

Nest

Stoichiometric matrix for v est

Nmes

Stoichiometric matrix for v mes

Nω

Number of model parameters

r

Volumetric reaction kinetics

V

Culture volume

v

Vector of reaction fluxes.

vBac

Flux of baculovirus synthesis

vest

Estimated fluxes

ve

Estimated fluxes of the reduced model

vmes

Measured fluxes

X

Model inputs

Y

Model output/Model estimate

Ymes

Experimentally measured Y

λi

Weighting factors of EMs

θ

Parameters of the combining function h(⋅)

μ

Specific growth rate

τ

Time delay

\(\sigma_{Y}^{2}\)

Variance of the experimental data for each output Y

ω

Nonparametric model parameters

Ω

Parametric model parameters

Notes

Acknowledgements

The authors M. von Stosch and N. Carinhas acknowledge financial support by the Fundação para a Ciência e a Tecnologia (Ref.: SFRH/BPD/84573 and SFRH/BPD/80514).

References

  1. 1.
    Bergold, G.H., Wellington, E.F.: Isolation and chemical composition of the membranes of an insect virus and their relation to the virus and polyhedral bodies. J. Bacteriol. 67(2), 210–216 (1954) Google Scholar
  2. 2.
    Bernal, V., et al.: Cell density effect in the baculovirus-insect cells system: a quantitative analysis of energetic metabolism. Biotechnol. Bioeng. 104(1), 162–180 (2009) CrossRefGoogle Scholar
  3. 3.
    Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford University Press, New York (1995) Google Scholar
  4. 4.
    Bocharov, G.A., Rihan, F.A.: Numerical modelling in biosciences using delay differential equations. J. Comput. Appl. Math. 125(1–2), 183–199 (2000) MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Braake, H.A.B.t.’, van Can, H.J.L., Verbruggen, H.B.: Semi-mechanistic modeling of chemical processes with neural networks. Eng. Appl. Artif. Intell. 11(4), 507–515 (1998) CrossRefGoogle Scholar
  6. 6.
    Bruggeman, F.J., Westerhoff, H.V.: The nature of systems biology. Trends Microbiol. 15(1), 45–50 (2007) CrossRefGoogle Scholar
  7. 7.
    Burnham, K.P., Anderson, D.R.: Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. Springer, New York (2002) Google Scholar
  8. 8.
    Carinhas, N., et al.: Improving baculovirus production at high cell density through manipulation of energy metabolism. Metab. Eng. 12(1), 39–52 (2010) CrossRefGoogle Scholar
  9. 9.
    Carinhas, N., et al.: Hybrid metabolic flux analysis: combining stoichiometric and statistical constraints to model the formation of complex recombinant products. BMC Syst. Biol. 5(1), 34 (2011) CrossRefGoogle Scholar
  10. 10.
    Daugulis, A.J., McLellan, P.J., Li, J.: Experimental investigation and modeling of oscillatory behavior in the continuous culture of Zymomonas mobilis. Biotechnol. Bioeng. 56(1), 99–105 (1997) CrossRefGoogle Scholar
  11. 11.
    Haerdle, W.K., et al.: Nonparametric and Semiparametric Models. Springer, Berlin (2004) CrossRefzbMATHGoogle Scholar
  12. 12.
    Haykin, S.S.: Neural Networks: A Comprehensive Foundation. Prentice Hall, New York (1999) zbMATHGoogle Scholar
  13. 13.
    Johansen, T.A., Foss, B.A.: Representing and learning unmodeled dynamics with neural network memories. In: Proc. American Control Conference (1992) Google Scholar
  14. 14.
    Kauffman, K.J., Prakash, P., Edwards, J.S.: Advances in flux balance analysis. Curr. Opin. Biotechnol. 14(5), 491–496 (2003) CrossRefGoogle Scholar
  15. 15.
    Kitano, H.: Systems biology: a brief overview. Science 295(5560), 1662–1664 (2002) CrossRefGoogle Scholar
  16. 16.
    Kramer, M.A., Thompson, M.L., Bhagat, P.M.: Embedding theoretical models in neural networks. In: Proc. American Control Conference (1992) Google Scholar
  17. 17.
    Machado, D., et al.: Modeling formalisms in systems biology. AMB Express 1(1), 45 (2011) CrossRefGoogle Scholar
  18. 18.
    Nikolov, S., et al.: Dynamic properties of a delayed protein cross talk model. Biosystems 91(1), 51–68 (2008) CrossRefGoogle Scholar
  19. 19.
    Oliveira, R.: Combining first principles modelling and artificial neural networks: a general framework. Comput. Chem. Eng. 28(5), 755–766 (2004) CrossRefGoogle Scholar
  20. 20.
    Psichogios, D.C., Ungar, L.H.: A hybrid neural network-first principles approach to process modeling. AIChE J. 38(10), 1499–1511 (1992) CrossRefGoogle Scholar
  21. 21.
    Rateitschak, K., Wolkenhauer, O.: Intracellular delay limits cyclic changes in gene expression. Math. Biosci. 205(2), 163–179 (2007) MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Rollié, S., Mangold, M., Sundmacher, K.: Designing biological systems: systems engineering meets synthetic biology. Chem. Eng. Sci. 69(1), 1–29 (2012) CrossRefGoogle Scholar
  23. 23.
    Sauro, H.M., et al.: Challenges for modeling and simulation methods in systems biology. In: Winter Simulation Conference, pp. 1720–1730 (2006) Google Scholar
  24. 24.
    Schubert, J., et al.: Hybrid modelling of yeast production processes—combination of a priori knowledge on different levels of sophistication. Chem. Eng. Technol. 17(1), 10–20 (1994) MathSciNetCrossRefGoogle Scholar
  25. 25.
    Smolen, P., Baxter, D.A., Byrne, J.H.: Effects of macromolecular transport and stochastic fluctuations on dynamics of genetic regulatory systems. Am. J. Physiol., Cell Physiol. 277(4), C777–C790 (1999) Google Scholar
  26. 26.
    Sontag, E.D.: Some new directions in control theory inspired by systems biology. Syst. Biol. 1(1), 9–18 (2004) CrossRefGoogle Scholar
  27. 27.
    Su, H.T., et al.: Integrating neural networks with first principles models for dynamic modeling. In: IFAC Symposium on Dynamics and Control of Chemical Reactors Distillation Columns and Batch Processes (1992) Google Scholar
  28. 28.
    Teixeira, A., et al.: Hybrid elementary flux analysis/nonparametric modeling: application for bioprocess control. BMC Bioinform. 8(1), 30 (2007) CrossRefGoogle Scholar
  29. 29.
    Teixeira, A.P., et al.: Hybrid semi-parametric mathematical systems: bridging the gap between systems biology and process engineering. J. Biotechnol. 132(4), 418–425 (2007) CrossRefGoogle Scholar
  30. 30.
    Thompson, M.L., Kramer, M.A.: Modeling chemical processes using prior knowledge and neural networks. AIChE J. 40(8), 1328–1340 (1994) CrossRefGoogle Scholar
  31. 31.
    Tian, T., et al.: Stochastic delay differential equations for genetic regulatory networks. J. Comput. Appl. Math. 205(2), 696–707 (2007) MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Van Riel, N.A.W.: Dynamic modelling and analysis of biochemical networks: mechanism-based models and model-based experiments. Brief. Bioinform. 7(4), 364–374 (2006) CrossRefGoogle Scholar
  33. 33.
    von Stosch, M., et al.: Modelling biochemical networks with intrinsic time delays: a hybrid semi-parametric approach. BMC Syst. Biol. 4(1), 131 (2010) CrossRefGoogle Scholar
  34. 34.
    Von Stosch, M., et al.: A novel identification method for hybrid (N)PLS dynamical systems with application to bioprocesses. Expert Syst. Appl. 38(9), 10862–10874 (2011) CrossRefGoogle Scholar
  35. 35.
    Von Stosch, M., et al.: Hybrid semi-parametric modeling in process systems engineering: past, present and future. Comput. Chem. Eng. 60, 86–101 (2013) CrossRefGoogle Scholar
  36. 36.
    Walter, E., Pronzato, L., Norton, J.: Identification of Parametric Models: From Experimental Data. Springer, Berlin (1997). Original French edition published by Masson, Paris, 1994 zbMATHGoogle Scholar
  37. 37.
    Wang, Y.-C., Chen, B.-S.: Integrated cellular network of transcription regulations and protein–protein interactions. BMC Syst. Biol. 4(1), 20 (2010) CrossRefGoogle Scholar
  38. 38.
    Wang, X., et al.: Hybrid modeling of penicillin fermentation process based on least square support vector machine. Chem. Eng. Res. Des. 88(4), 415–420 (2010) CrossRefGoogle Scholar
  39. 39.
    Wellington, E.F.: The amino acid composition of some insect viruses and their characteristic inclusion-body proteins. Biochem. J. 57(2), 334–338 (1954) Google Scholar
  40. 40.
    Wellstead, P., et al.: The role of control and system theory in systems biology. Annu. Rev. Control 32(1), 33–47 (2008) CrossRefGoogle Scholar
  41. 41.
    Wiechert, W.: Modeling and simulation: tools for metabolic engineering. J. Biotechnol. 94(1), 37–63 (2002) CrossRefGoogle Scholar
  42. 42.
    Wolkowicz, G.S.K., Xia, H.: Global asymptotic behavior of a chemostat model with discrete delays. SIAM J. Appl. Math. 57, 411–422 (1997) Google Scholar
  43. 43.
    Wolkowicz, G.S.K., Xia, H., Ruan, S.: Competition in the chemostat: a distributed delay model and its global asymptotic behavior. SIAM J. Appl. Math. 57, 1281–1310 (1997) MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Moritz von Stosch
    • 1
    • 2
  • Nuno Carinhas
    • 2
    • 3
  • Rui Oliveira
    • 1
    • 2
    Email author
  1. 1.Chemistry Department, Faculty of Sciences and TechnologyUniversidade Nova de LisboaCaparicaPortugal
  2. 2.Instituto de Biologia Experimental e Tecnológica (iBET)OeirasPortugal
  3. 3.Institute of Chemical and Biological TechnologyUniversidade Nova de LisboaOeirasPortugal

Personalised recommendations