Concentration Robustness and Its Importance in Biology: Some More Deficiency-Oriented Theorems

  • Martin Feinberg
Part of the Applied Mathematical Sciences book series (AMS, volume 202)


This chapter is somewhat different from the surrounding ones, in which the interest is largely in network-structural conditions that confer a degree of stable behavior against composition perturbations within stoichiometric compatibility classes. The interest here is again in a kind of stability—in this case, precise maintenance of a desired concentration of a critical species—but now against composition perturbations, even very large ones, across stoichiometric compatibility classes. This chapter’s placement just after the preceding one results from its close connection to deficiency one theory. The connection will become more transparent in Part III, where we consider the common mathematics underlying both chapters.


  1. 17.
    Batchelor, E., Goulian, M.: Robustness and the cycle of phosphorylation and dephosphorylation in a two-component regulatory system. Proceedings of the National Academy of Sciences of the United States of America 100(2), 691-696 (2003)CrossRefGoogle Scholar
  2. 96.
    Goulian, M.: Robust control in bacterial regulatory circuits. Current Opinion in Microbiology 7(2), 198-202 (2004)CrossRefGoogle Scholar
  3. 114.
    Israel, K.: Monotone behavior for equilibria of dynamical systems. Ph.D. thesis, Duke University (1984)Google Scholar
  4. 121.
    LaPorte, D.C., Thorsness, P.E., Koshland, D.E.: Compensatory phosphorylation of isocitrate dehydrogenase. A mechanism for adaptation to the intracellular environment. Journal of Biological Chemistry 260(19), 10,563-10,568 (1985)Google Scholar
  5. 132.
    Nailor, J.: Behavior of equilibria in quasi-thermodynamic chemical reaction networks with mass-action kinetics. Ph.D. thesis, Duke University (1991)Google Scholar
  6. 154.
    Shinar, G., Alon, U., Feinberg, M.: Sensitivity and robustness in chemical reaction networks. SIAM Journal on Applied Mathematics 69(4), 977–998 (2009)MathSciNetCrossRefGoogle Scholar
  7. 155.
    Shinar, G., Feinberg, M.: Structural sources of robustness in biochemical reaction networks. Science 327(5971), 1389–1391 (2010)CrossRefGoogle Scholar
  8. 156.
    Shinar, G., Feinberg, M.: Design principles for robust biochemical reaction networks: What works, what cannot work, and what might almost work. Mathematical Biosciences 231(1), 39–48 (2011)MathSciNetCrossRefGoogle Scholar
  9. 159.
    Shinar, G., Milo, R., Rodriguez-Martinez, M., Alon, U.: Input-output robustness in simple bacterial signaling systems. Proceedings of the National Academy of Sciences 104(50), 19,931–19,935 (2007)CrossRefGoogle Scholar
  10. 160.
    Shinar, G., Rabinowitz, J.D., Alon, U., Papin, J.A.: Robustness in glyoxylate bypass regulation. PLoS Computational Biology 5(3), e1000,297 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Martin Feinberg
    • 1
  1. 1.Chemical & Biomolecular Engineering, The Ohio State UniversityColumbusUSA

Personalised recommendations