Concentration Robustness Foundations

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


In this chapter we will discuss the mathematical foundations of theorems presented without proof in Chapter 9, the expository chapter on concentration robustness. For proof of the Deficiency One Concentration Robustness Theorem (Theorem 9.5.1), most of the work was already done in the preceding chapter; there are just a few details that remain. Again, Theorem 9.5.1 was based on work with Guy Shinar [155]. We will need to say much more about the two theorems—Theorems 9.6.1 and 9.6.6—that assert the irrelevance of certain rate constants to the robust species concentration. Finally, we will make just a few remarks about the robustness-thwarting theorems, Theorems 9.7.1 and 9.7.10. Proofs of those were provided in [154].


  1. 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
  2. 155.
    Shinar, G., Feinberg, M.: Structural sources of robustness in biochemical reaction networks. Science 327(5971), 1389–1391 (2010)CrossRefGoogle Scholar
  3. 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

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Authors and Affiliations

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

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