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)


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.


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



Akaike Information Criterion


Artificial Neural Networks


Baby Hamster Kidney


Bayesian Information Criterion


Delayed Differential Equation


Elementary Modes


Extreme Pathways


Flux Balance Analysis


Metabolic Flux Analysis


Ordinary Differential Equation


Projection to Latent Structure or Partial Least Squares


Retarded Functional Dynamic Equation


Spodoptera frugiperda


Transcription Factor


Transcription Factor A


Weighted Squares Error


Vector of concentrations of intracellular compounds


Time derivative


Dilution rate


Vectors of EMs


Parametric mathematical function


Volumetric feeding rates of glucose


Volumetric feeding rates of glutamine


Nonparametric mathematical function


Function that combines the nonparametric and parametric model


Matrix of stoichiometric coefficients


Number of data points


Stoichiometric matrix for v est


Stoichiometric matrix for v mes


Number of model parameters


Volumetric reaction kinetics


Culture volume


Vector of reaction fluxes.


Flux of baculovirus synthesis


Estimated fluxes


Estimated fluxes of the reduced model


Measured fluxes


Model inputs


Model output/Model estimate


Experimentally measured Y


Weighting factors of EMs


Parameters of the combining function h(⋅)


Specific growth rate


Time delay


Variance of the experimental data for each output Y


Nonparametric model parameters


Parametric model parameters



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).


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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

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