The Inverse Problem: Computational Algorithms and Their Efficiency with Applications to a Model of the Calvin Photosynthesis Cycle

  • Jaime Milstein
Part of the NATO Conference Series book series (NATOCS, volume 5)


The present article is concerned with the mathematical and numerical algorithms encountered in the parameter identification problem for large and complex biological systems. The primary thrust is to determine how these algorithms interact when applied to realistically complex non-linear systems. Specifically, we are concerned with the computational complexity of a model which describes the Calvin photosynthesis cycle. The cycle is described mathematically by seventeen non-linear ordinary differential equations having twenty-two undetermined parameters [Milstein, 1975]. Identifying these parameters from several sets of data constitutes the inverse problem.


Inverse Problem Calvin Cycle Nicotinamide Adenine Dinucleotide Phosphate Complex Biological System Dihydroxy Acetone Phosphate 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. A. Bassham, and G. H. Krause, “Free Energy Changes and Metabolie Regulation in State Photosynthetic Carbon Reduction,” Biochem. Biophs. Acta., 189, 1969.Google Scholar
  2. 2.
    J. H. Bremermann, “A Method of Unconstrained Global Optimization,” Math. Biosci., 9, 1 1970.CrossRefGoogle Scholar
  3. 3.
    W. S. Brown, Altran User’s Manual, Bell Laboratories, 1977.Google Scholar
  4. 4.
    C. W. Gear, Numerical Initial Value Problems In Ordinary Differential Equations, Prentice Hall, Inc., 1971.Google Scholar
  5. 5.
    J. Milstein, “Estimation of the Dynamical Parameters of the Calvin Photosynthesis Cycle Optimization and 111 Conditioned Inverse Problems,” Ph.D. Thesis, Dept. of Mathematics, University of California, Berkeley, 1975.Google Scholar
  6. 6.
    J. Milstein, “Parameter Identification of the Calvin Photosynthesis Cycle,” To appear in Journal of Mathematical Biology.Google Scholar
  7. 7.
    J. Milstein, “Error Estimates for Rate Constants of Nonlinear Inverse Problems,” In preparation, 1977.Google Scholar
  8. 8.
    J. Mosevich, “Identifying Differential Equations by Galerkin’s Method,” Math. of Comp. Vol. 31, No. 137, pp. 139–147, 1977.Google Scholar
  9. 9.
    R. Roth, and M. Roth, “Data Unscrambling and the Analysis of Inducible Enzyme Synthesis,” Math. Biosci., 5, 57, 1969.CrossRefGoogle Scholar
  10. 10.
    H. Rosenbrook, and C. Storey, Computational Techniques for Chemical Engineers, Pergamon Press, Oxford, 1966.Google Scholar
  11. 11.
    J. Swartz, “Parameter Estimation in Biological Systems,” Ph.D. Thesis, University of California, Berkeley, 1973.Google Scholar

Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • Jaime Milstein
    • 1
  1. 1.Dept. of MathematicsUniv. of Southern CaliforniaLos AngelesUSA

Personalised recommendations