Processes 2019, 7, 163
Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the
study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to
publish the results.
References
1.
Csikasz-Nagy, A. Computational systems biology of the cell cycle. Brief. Bioinform. 2009, 10, 424–434.
[CrossRef][PubMed]
2.
Pavlides, A.; Hogan, S.J.; Bogacz, R. Computational Models Describing Possible Mechanisms for Generation
of Excessive Beta Oscillations in Parkinson’s Disease. PLoS Comput. Biol. 2015, 1, e1004609. [CrossRef]
[PubMed]
3.
Zamora-Sillero, E.; Hafner, M.; Ibig, A.; Stelling, J.; Wagner, A. Efficient characterization of high-dimensional
parameter spaces for systems biology. BMC Syst. Biol. 2011, 5, 142. [CrossRef][PubMed]
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Liu, Y.; Gunawan, R. Parameter estimation of dynamic biological network models using integrated fluxes.
BMC Syst. Biol. 2014, 8, 127. [CrossRef]
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Ashyraliyev, M.; Fomekong-Nanfack, Y.; Kaandorp, J.A.; Blom, J.G. Systems biology: Parameter estimation
for biochemical models. FEBS J. 2009, 276, 886–902. [CrossRef][PubMed]
6.
Chickarmane, V.; Paladugu, S.R.; Bergmann, F.; Sauro, H.M. Bifurcation discovery tool. Bioinformatics 2005,
21, 3688–3690. [CrossRef]
7.
Li, C.; Donizelli, M.; Rodriguez, N.; Dharuri, H.; Endler, L.; Chelliah, V.; Li, L.; He, E.; Henry, A.;
Stefan, M.I.; et al. BioModels Database: An enhanced, curated and annotated resource for published
quantitative kinetic models. BMC Syst. Biol. 2010, 4, 92. [CrossRef]
8.
Choi, K.; Medley, J.K.; Cannistra, C.; Konig, M.; Smith, L.; Stocking, K.; Sauro, H.M. Tellurium: A Python
Based Modeling and Reproducibility Platform for Systems Biology. Biosystems 2018, 171, 74–79. [CrossRef]
9.
Somogyi, E.T.; Bouteiller, J.M.; Glazier, J.A.; König, M.; Medley, J.K.; Swat, M.H.; Sauro, H.M. libRoadRunner:
A high performance SBML simulation and analysis library. Bioinformatics 2015, 31, 3315–3321. [CrossRef]
10. Reich, J.G.; Selkov, E.E. Energy Metabolism of the Cell: A Theoretical Treatise; Academic Press: London, UK,
1981; p. 345.
11. Sauro, H.M.; Ingalls, B. Conservation analysis in biochemical networks: Computational issues for software
writers. Biophys. Chem. 2004, 109, 1–15. [CrossRef]
12. Sauro, H.M. Systems Biology: An Introduction to Metabolic Control Analysis; Ambrosius Publishing: Seattle,
WA, USA, 2018.
13. Storn, R.; Price, K. Differential Evolution—A Simple and Efficient Heuristic for global Optimization over
Continuous Spaces. J. Glob. Optim. 1997, 11, 341–359. [CrossRef]
14. scipy.optimize.differential_evolution—SciPy v1.1.0 Reference Guide.
Available online: https://
docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.differential_evolution.html (accessed on
5 November 2018).
15. Broyden, C.G. The Convergence of a Class of Double-rank Minimization Algorithms 1. General
Considerations. IMA J. Appl. Math. 1970, 6, 76–90. [CrossRef]
16. Fletcher, R. A new approach to variable metric algorithms. Comput. J. 1970, 13, 317–322. [CrossRef]
17. Goldfarb, D. A Family of Variable-Metric Methods Derived by Variational Means. Math. Comput. 1970,
24, 23. [CrossRef]
18. Shanno, D.F. Conditioning of Quasi-Newton Methods for Function Minimization. Math. Comput. 1970,
24, 647. [CrossRef]
19. Sauro, H.M. Systems Biology: Introduction to Pathway Modeling, 1st ed.; Ambrosius Publishing: Seattle, WA,
USA, 2017.
20. Wilhelm, T.; Heinrich, R. Smallest chemical reaction system with Hopfbifurcation. J. Math. Chem. 1995,
17, 1–14. [CrossRef]
21. Leloup, J.; Goldbeter, A. Chaos and birhythmicity in a model for circadian oscillations of the PER and TIM
proteins in drosophila. J. Theor. Biol. 1999, 198, 445–459. [CrossRef]
22. Hervagault, O.; Canu, P. Bistability and Irreversible Transitions in a Simple Substrate Cyclet; Technical Report;
University of Technology of Compiègne: Compiègne, France, 1987.
19
Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the
study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to
publish the results.
References
1.
Csikasz-Nagy, A. Computational systems biology of the cell cycle. Brief. Bioinform. 2009, 10, 424–434.
[CrossRef][PubMed]
2.
Pavlides, A.; Hogan, S.J.; Bogacz, R. Computational Models Describing Possible Mechanisms for Generation
of Excessive Beta Oscillations in Parkinson’s Disease. PLoS Comput. Biol. 2015, 1, e1004609. [CrossRef]
[PubMed]
3.
Zamora-Sillero, E.; Hafner, M.; Ibig, A.; Stelling, J.; Wagner, A. Efficient characterization of high-dimensional
parameter spaces for systems biology. BMC Syst. Biol. 2011, 5, 142. [CrossRef][PubMed]
4.
Liu, Y.; Gunawan, R. Parameter estimation of dynamic biological network models using integrated fluxes.
BMC Syst. Biol. 2014, 8, 127. [CrossRef]
5.
Ashyraliyev, M.; Fomekong-Nanfack, Y.; Kaandorp, J.A.; Blom, J.G. Systems biology: Parameter estimation
for biochemical models. FEBS J. 2009, 276, 886–902. [CrossRef][PubMed]
6.
Chickarmane, V.; Paladugu, S.R.; Bergmann, F.; Sauro, H.M. Bifurcation discovery tool. Bioinformatics 2005,
21, 3688–3690. [CrossRef]
7.
Li, C.; Donizelli, M.; Rodriguez, N.; Dharuri, H.; Endler, L.; Chelliah, V.; Li, L.; He, E.; Henry, A.;
Stefan, M.I.; et al. BioModels Database: An enhanced, curated and annotated resource for published
quantitative kinetic models. BMC Syst. Biol. 2010, 4, 92. [CrossRef]
8.
Choi, K.; Medley, J.K.; Cannistra, C.; Konig, M.; Smith, L.; Stocking, K.; Sauro, H.M. Tellurium: A Python
Based Modeling and Reproducibility Platform for Systems Biology. Biosystems 2018, 171, 74–79. [CrossRef]
9.
Somogyi, E.T.; Bouteiller, J.M.; Glazier, J.A.; König, M.; Medley, J.K.; Swat, M.H.; Sauro, H.M. libRoadRunner:
A high performance SBML simulation and analysis library. Bioinformatics 2015, 31, 3315–3321. [CrossRef]
10. Reich, J.G.; Selkov, E.E. Energy Metabolism of the Cell: A Theoretical Treatise; Academic Press: London, UK,
1981; p. 345.
11. Sauro, H.M.; Ingalls, B. Conservation analysis in biochemical networks: Computational issues for software
writers. Biophys. Chem. 2004, 109, 1–15. [CrossRef]
12. Sauro, H.M. Systems Biology: An Introduction to Metabolic Control Analysis; Ambrosius Publishing: Seattle,
WA, USA, 2018.
13. Storn, R.; Price, K. Differential Evolution—A Simple and Efficient Heuristic for global Optimization over
Continuous Spaces. J. Glob. Optim. 1997, 11, 341–359. [CrossRef]
14. scipy.optimize.differential_evolution—SciPy v1.1.0 Reference Guide.
Available online: https://
docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.differential_evolution.html (accessed on
5 November 2018).
15. Broyden, C.G. The Convergence of a Class of Double-rank Minimization Algorithms 1. General
Considerations. IMA J. Appl. Math. 1970, 6, 76–90. [CrossRef]
16. Fletcher, R. A new approach to variable metric algorithms. Comput. J. 1970, 13, 317–322. [CrossRef]
17. Goldfarb, D. A Family of Variable-Metric Methods Derived by Variational Means. Math. Comput. 1970,
24, 23. [CrossRef]
18. Shanno, D.F. Conditioning of Quasi-Newton Methods for Function Minimization. Math. Comput. 1970,
24, 647. [CrossRef]
19. Sauro, H.M. Systems Biology: Introduction to Pathway Modeling, 1st ed.; Ambrosius Publishing: Seattle, WA,
USA, 2017.
20. Wilhelm, T.; Heinrich, R. Smallest chemical reaction system with Hopfbifurcation. J. Math. Chem. 1995,
17, 1–14. [CrossRef]
21. Leloup, J.; Goldbeter, A. Chaos and birhythmicity in a model for circadian oscillations of the PER and TIM
proteins in drosophila. J. Theor. Biol. 1999, 198, 445–459. [CrossRef]
22. Hervagault, O.; Canu, P. Bistability and Irreversible Transitions in a Simple Substrate Cyclet; Technical Report;
University of Technology of Compiègne: Compiègne, France, 1987.
19