Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Equilibria and control of metabolic networks with enhancers and inhibitors

1 Center for Computational and Integrative Biology, Rutgers Camden. Camden NJ USA
2 Joseph and Loretta Lopez chair professor of Mathematics

Special Issues: Nonlinear models in applied mathematics

Linear-In-Flux-Expressions (briefly LIFE) methodology models metabolism by using correlations among fluxes of metabolic networks and reducing the number of model parameters. These correlations are calculated for an equilibrium state and developed to include tools from the fields of network flows, compartmental systems, Markov chains, and control theory. LIFE methodology was developed with pharmacology simulators in mind, and the present study advances this goal, by focusing on the control of metabolic networks and inclusion of enhancers and inhibitors. We consider two control problems on metabolic networks: 1. The optimization of intakes from the outside environment to drive the system to a desired state, and 2. The inclusion of inhibitors and enhancers and their optimization. Simulations are included to test the approach on these more complex networks.
  Figure/Table
  Supplementary
  Article Metrics

References

1. Allen R, Rieger TR, Musante CJ (2016) Efficient generation and selection of virtual populations in quantitative systems pharmacology models. CPT Pharmacometrics Syst Pharmacol 5: 140–146.    

2. Allerheiligen SRB (2010) Next-generation model-based drug discovery and development: Quantitative and systems pharmacology. Clin Pharmacol Ther 88: 135–137.    

3. Biggs N (1993) Algebraic Graph Theory, volume 67. Cambridge university press.

4. Bressan A, Piccoli B (2007) Introduction to Mathematical Control Theory, Philadelphia: American Institute of Mathematical Sciences.

5. Bullo F (2018) Lectures on Network Systems, with contributions by J. Cortes, F. Dorfler and S. Martinez, Kindle Direct Publishing, 0.96 edition. Available from: http://motion.me.ucsb. edu/book-lns.

6. Castiglione F, Piccoli B (2006) Optimal control in a model of dendritic cell transfection cancer immunotherapy. Bull Math Biol 68: 255–274.    

7. Castiglione F, Piccoli B, (2007) Cancer immunotherapy, mathematical modeling and optimal control. J Theor Biol 247: 723–732.    

8. Caughman JS, Veerman J (2006) Kernels of directed graph Laplacians. Electron J Comb 13: R39.

9. Cinlar E (2013) Introduction to Stochastic Processes, Courier Corporation.

10. Feinberg M, Horn FJ (1974) Dynamics of open chemical systems and the algebraic structure of the underlying reaction network. Chem Eng Sci 29: 775–787.    

11. Ford LR, Fulkerson DR (1956) Maximal flow through a network. Can J Math 8: 399–404.    

12. Friedrich C (2016) A model qualification method for mechanistic physiological QSP models to support model-informed drug development. CPT Pharmacometrics Syst Pharmacol 5: 43–53.    

13. Grundy SM, Stone NJ, Bailey AL, et al. (2018) 2018 AHA/ACC/AACVPR/AAPA/ABC/ACPM/ADA/AGS/APhA/ASPC/NLA/PCNA Guideline on the Management of Blood Cholesterol: A report of the american college of cardiology/american heart association task force on clinical practice guidelines. J Am Coll Cardiol.

14. Gunawardena J (2012) A linear framework for time-scale separation in nonlinear biochemical systems. PLoS ONE 7: e36321.    

15. Hosseini I, Mac Gabhann F (2016) Mechanistic models predict efficacy of CCR5-deficient stem cell transplants in hiv patient populations. CPT pharmacometrics Syst Pharmacol 5: 82–90.    

16. Jacquez JA, Simon CP (1993) Qualitative theory of compartmental systems. SIAM Rev 35: 43–79.    

17. Johnson KA, Goody RS (2011) The original Michaelis constant: Translation of the 1913 Michaelis-Menten paper. Biochemistry 50: 8264–8269.    

18. Klinke DJ, Finley SD (2012) Timescale analysis of rule-based biochemical reaction networks. Biotechnol Prog 28: 33–44.    

19. Maeda H, Kodama S, Ohta Y (1978) Asymptotic behavior of nonlinear compartmental systems: Nonoscillation and stability. IEEE Trans Circuits Syst 25: 372–378.    

20. McQuade ST, Abrams RE, Barrett JS, et al. (2017) Linear-in-flux-expressions methodology: Toward a robust mathematical framework for quantitative systems pharmacology simulators. Gene Regul Syst Biol 11: 1–15.

21. McQuade ST, An Z, Merrill NJ, et al. (2018) Equilibria for large metabolic systems and the life approach, In: 2018 Annual American Control Conference (ACC), 2005–2010.

22. Merrill NJ, An Z, McQuade ST, et al. (2018) Stability of metabolic networks via Linear-In-Flux-Expressions. arXiv:1808.08263.

23. Mirzaev I, Gunawardena J (2013) Laplacian dynamics on general graphs. Bull Math Biol 75: 2118–2149.    

24. Palsson B (2015) Systems Biology. Cambridge: Cambridge university press.

25. Pérez-Nueno VI (2015) Using quantitative systems pharmacology for novel drug discovery. Expert Opin Drug Discov 10: 1315–1331.    

26. Rogers M, Lyster P, Okita R (2013) NIH support for the emergence of quantitative and systems pharmacology. CPT Pharmacometrics Syst Pharmacol 2: e37.    

27. Schmidt BJ, Casey FP, Paterson T, et al. (2013) Alternate virtual populations elucidate the type I interferon signature predictive of the response to rituximab in rheumatoid arthritis. BMC bioinf 14: 1–16.

28. SorgerPK, Allerheiligen SR, Abernethy DR,et al. (2011) Quantitativeandsystemspharmacology in the post-genomic era: New approaches to discovering drugs and understanding therapeutic mechanisms. An NIH white paper by the QSP workshop group, 1–48, NIH Bethesda.

29. Xia W, Cao M (2017) Analysis and applications of spectral properties of grounded laplacian matrices for directed networks. Automatica 80: 10–16.    

© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved