Biological Oscillations

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Biological Oscillations

• Using the Goodwin Oscillator
• as a model of negative feedback
• J. Watrous
• Biology Department
• St. Josephs University
• July, 2008

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• The Goodwin oscillator model is used to describe
  and analyze the behavior of simple negative
  feedback systems like the one shown above. The
  model assumes a constant supply of DNA and
  substrate while the amounts of mRNA, enzyme and
  product will change with time. As the amount of
  product increases, it signals a decrease in mRNA
  production.

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Modeling Equations

• Three equations are needed. Both DNA and
  substrate concentrations are assumed to be at
  much greater concentrations than mRNA, the enzyme
  machinery and the product made.

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mRNA Production

• A Michaelis-Menton type equation is used to
  describe mRNA production along with a term that
  accounts for any breakdown of nucleic acid.
• dm/dt ((D/(k(pq))) - am
• Because the product is in the denominator, as it
  increases, it will reduce any increase in mRNA.

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Enzyme Production

• The level of enzymatic activity is a function of
  two terms the amount produced from mRNA and the
  amount broken down.
• de/dt bm - ce

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Product produced

• The product produced depends on the substrate
  available (assumed to be in excess), the reaction
  is dependent on the enzyme produced and any
  product breakdown.
• dp/dt de - (np/(kp)

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Sample output using Madonna

• The output shows a segment of the simulation
  using a set of parameter values where
  oscillations can be observed.
• Parameter value plots can be constructed to see
  the role each plays in the simulation and to
  maximize the amount of product made.

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References

• Goodwin, B. 1965. Oscillatory behavior in
  enzymatic control processes. In Advances in
  Enzyme Regulation 3 425.
• Murray, J.D. Mathematical Biology. 1989.
  Springer-Verlag
• Biochemical Regulation 2008 obtained
  from http//mcb.berkeley.edu/courses/mcb137/exerc
  ises/Biochemistry.pdf