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Hybrid Modeling for Systems Biology: Theory and Practice

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Large-Scale Networks in Engineering and Life Sciences

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.

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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

e i :

Vectors of EMs

f(⋅):

Parametric mathematical function

F Glc :

Volumetric feeding rates of glucose

F Gln :

Volumetric feeding rates of glutamine

g(⋅):

Nonparametric mathematical function

h(⋅):

Function that combines the nonparametric and parametric model

N :

Matrix of stoichiometric coefficients

N D :

Number of data points

N est :

Stoichiometric matrix for v est

N mes :

Stoichiometric matrix for v mes

N ω :

Number of model parameters

r :

Volumetric reaction kinetics

V :

Culture volume

v :

Vector of reaction fluxes.

v Bac :

Flux of baculovirus synthesis

v est :

Estimated fluxes

v e :

Estimated fluxes of the reduced model

v mes :

Measured fluxes

X :

Model inputs

Y :

Model output/Model estimate

Y mes :

Experimentally measured Y

λ i :

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

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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).

Author information

Authors and Affiliations

  1. Chemistry Department, Faculty of Sciences and Technology, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal

    Moritz von Stosch & Rui Oliveira

  2. Instituto de Biologia Experimental e Tecnológica (iBET), 2780-157, Oeiras, Portugal

    Moritz von Stosch, Nuno Carinhas & Rui Oliveira

  3. Institute of Chemical and Biological Technology, Universidade Nova de Lisboa, 2780-157, Oeiras, Portugal

    Nuno Carinhas

Authors
  1. Moritz von Stosch
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  2. Nuno Carinhas
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  3. Rui Oliveira
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Corresponding author

Correspondence to Rui Oliveira .

Editor information

Editors and Affiliations

  1. Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany

    Peter Benner

  2. Institute for Automation Engineering (IF, Otto-von-Guericke University Magdeburg, Magdeburg, Germany

    Rolf Findeisen

  3. Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Sachsen-Anhalt, Germany

    Dietrich Flockerzi

  4. Max Planck Inst Dynamics Complex Tech, Magdeburg, Sachsen-Anhalt, Germany

    Udo Reichl

  5. Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Sachsen-Anhalt, Germany

    Kai Sundmacher

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von Stosch, M., Carinhas, N., Oliveira, R. (2014). Hybrid Modeling for Systems Biology: Theory and Practice. In: Benner, P., Findeisen, R., Flockerzi, D., Reichl, U., Sundmacher, K. (eds) Large-Scale Networks in Engineering and Life Sciences. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-08437-4_7

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