
Mathematics in Engineering, 2019, 1(3): 648671. doi: 10.3934/mine.2019.3.648
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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
Received: , Accepted: , Published:
Special Issues: Nonlinear models in applied mathematics
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) Nextgeneration modelbased 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/booklns.
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 modelinformed 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 timescale separation in nonlinear biochemical systems. PLoS ONE 7: e36321.
15. Hosseini I, Mac Gabhann F (2016) Mechanistic models predict efficacy of CCR5deficient 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 MichaelisMenten paper. Biochemistry 50: 8264–8269.
18. Klinke DJ, Finley SD (2012) Timescale analysis of rulebased 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) Linearinfluxexpressions 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 LinearInFluxExpressions. 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. PérezNueno 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 postgenomic 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.
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