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The bulletin of mathematical biophysics

, Volume 31, Issue 4, pp 775–787 | Cite as

Some conditions for sustained oscillations in biochemical chains with feedback inhibition

  • H. D. Landahl
Article

Abstract

A chain ofn reactions is considered in which the last substance inhibits the production of the first with degreep, p being the order of the inhibition. Maintained oscillations are possible for certain values of the parameters under the following conditions: (1) If there is no time delay, then there must be at least three compartments (n=3) and either the degree of inhibition is sufficiently large (p>8 forn=3) or there must be enzymatic removal from the first compartment, in which casep≥1. (2) If there are time delays, but there is no enzymatic removal, the degree of the inhibition must be greater than or equal to 2 for any value ofn. (3) If there is a time delay in addition to enzymatic removal, one compartment with simple first order inhibition is sufficient. Conditions on the parameters necessary for maintained oscillations are given for many of the cases discussed.

Keywords

Time Delay Vortex Point Biochemical System Constant Input Sustained Oscillation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© N. Rashevsky 1968

Authors and Affiliations

  • H. D. Landahl
    • 1
  1. 1.Department of Biochemistry and BiophysicsUniversity of California at San FranciscoSan FranciscoUSA

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