Journal of Molecular Evolution

, Volume 5, Issue 3, pp 199–222 | Cite as

Optimal design of feedback control by inhibition

Dynamic Considerations
  • Michael A. Savageau


The local stability of unbranched biosynthetic pathways is examined by mathematical analysis and computer simulation using a novel nonlinear formalism that appears to accurately describe biochemical systems. Four factors affecting the stability are examined: strength of feedback inhibition, equalization of the values among the corresponding kinetic parameters for the reactions of the pathway, pathway length, and alternative patterns of feedback interaction. The strength of inhibition and the pattern of feedback interactions are important determinants of steady-state behavior. The simple pattern of end-product inhibition in unbranched pathways may have evolved because it optimizes the steady-state behavior and is temporally most responsive to change. Stability in these simple systems is achieved by shortening pathway length either physically or, in the case of necessarily long pathways, kinetically by a wide divergence in the values of the corresponding kinetic parameters for the reactions of the pathway. These conclusions are discussed in the light of available experimental evidence.

Key words

Natural Selection Control Patterns Biosynthetic Pathways 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bak,T.A. (1963). Contributions to the Theory of Chemical Kinetics. New York: W.A.BenjaminGoogle Scholar
  2. Brenner,M., Ames,B.N. (1971). In: Metabolic Pathways, 3rd Ed., Vol.V, Metabolic Regulation, H.J.Vogel, ed., p.349. New York: Academic PressGoogle Scholar
  3. Creighton,T.E., Yanofsky,C. (1970). In: Methods in Enzymology, Vol.XVIIA S.P.Colowick, N.O.Kaplan, eds., p.365. New York: Academic PressGoogle Scholar
  4. Davis,B.D. (1961). Cold Spring Harbor Symposia Quant. Biol.26, 1Google Scholar
  5. Ferdinand,W. (1966). Biochem.J.98, 278Google Scholar
  6. Goodwin,B. (1963). Temporal Organization in Cells. London: Academic PressGoogle Scholar
  7. Hastings,S., Tyson,J. (1975). Biophys.J.15, 179aGoogle Scholar
  8. Hearon,J.Z. (1953). Bull.Math.Biophysics 15, 121Google Scholar
  9. Higgins,J., Frenkel,R., Hulme,E., Lucas,A., Rangazas,G. (1973). In: Biological and Biochemical Oscillators, B.Chance, E.K.Pye, A.K.Ghosh, B.Hess (eds.), p.127, New York: Academic PressGoogle Scholar
  10. Hunding,A. (1974). Biophys.Struct.Mechanism 1, 47Google Scholar
  11. Klotz,I.M., Langerman, N.R., Darnall,D.W. (1970). Ann.Rev.Biochem.39, 25Google Scholar
  12. Koshland,D.E., Neet,K.E. (1968). Ann.Rev.Biochem.37, 359Google Scholar
  13. Monod,J., Changeux,J.-P., Jacob,F. (1963). J.Mol.Biol.6, 306Google Scholar
  14. Monod,J., Wyman,J., Changeux,J.-P. (1965). J.Mol.Biol.12, 88Google Scholar
  15. Morales,M., McKay,D. (1967). Biophys.J.7, 621Google Scholar
  16. Rosen,R. (1967). Optimality Principles in Biology. London: ButterworthsGoogle Scholar
  17. Savageau,M.A. (1969). J.Theoret.Biol.25, 370Google Scholar
  18. Savageau,M.A. (1970). J.Theoret.Biol.26, 215Google Scholar
  19. Savageau,M.A. (1971). Arch.Biochem.Biophys.145, 612Google Scholar
  20. Savageau,M.A. (1974). J.Mol.Evol.4, 139Google Scholar
  21. Timothy, LaMar K., Bona,B.E. (1968). State Space Analysis: An Introduction. New York: McGraw-HillGoogle Scholar
  22. Umbarger,H.E. (1956). Science 123, 848Google Scholar
  23. Viniegra-Gonzalez,G. (1973). In: Biological and Biochemical Oscillators B.Chance, E.K.Pye, A.K.Ghosh, B.Hess, eds., p.41. New York: Academic PressGoogle Scholar
  24. Viniegra-Gonzalez,G., Martinez,H. (1969). Proc.Biophys.Soc.Abstracts 9, A210Google Scholar
  25. Walter,C.F. (1970). J.Theoret.Biol.27, 259Google Scholar
  26. Walter,C.F. (1974). J.Theoret.Biol.44, 219Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Michael A. Savageau
    • 1
  1. 1.Department of MicrobiologyThe University of Michigan Medical SchoolAnn ArborUSA

Personalised recommendations