Summary
This article is concerned with the determination of kinetic parameters of the Calvin photosynthesis cycle which is described by seventeen nonlinear ordinary differential equations. It is shown that the task requires dynamic data for several sets of initial conditions. The numerical technique is based upon an algorithm for non-linear optimization and Gear's numerical integration scheme for stiff systems of differential equations. The sensitivity of the parameters to noise in the data is tested with a method adapted from Rosenbrook and Storey. A preliminary set of parameters has been obtained from a preliminary set of experimental data. The numerical methods are then tested with synthetic data derived from these parameters. The mathematical model and the results obtained in the simulation are used as an aid in designing new experiments.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Banks, H. T.: Modeling and Control in the Biomedial Sciences. Springer Lecture Notes Vol. 6. Berlin, Heidelberg, New York 1975
Bassham, J. A., Calvin, M.: The path of carbon in photosynthesis. Prentice Hall, Englewood Cliffs, New Jersey 1957
Bassham, J. A., Krause, G. H.: Free energy changes and metabolic regulation in state photosynthetic carbon reduction. Biochem. Biophys. Acta, 189, 207 (1969)
Bassham, H. A.: Control of photosynthetic carbon metabolism. Science, 172, 526 (1971)
Bassham, J. A.: Gerri Levine and John Forder III. Photosynthesis in vitro: Achievements of high rates. Plant Sci. Ltrs., 2, 15 (1974)
Bellman, R., Kalaba, R.: Quasilinearization and non-linear boundary-value problems. New York: American Elsevier 1965
Bremermann, J. H.: A method of unconstrained global optimization. Math. Biosi. 9, 1 (1970)
Bremermann, H. J.: Complexity of automata brains and behavior. In: Physics and Mathematics of the Nervous System (M. Conrad, W. Guttinger, M. Dal Cin, eds.) Biomathematics Lecture Notes, Vol. 4, Heidelberg: Springer Verlag 1974
Bremermann, H. J.: Complexity and transcomputability, in: The Encyclopaedia of Ignorance, Vol. 1, Physical Sciences (R. Duncan, M. Weston-Smith eds.) Oxford: Pergamon Press Ltd. 1977
Brown, W. S.: Altran User's Manual. Bell Laboratories (1973)
Garfinkel, D.: Simulation of glycolitic systems, In: concepts and models of biomathematics (F. Heimmets ed.) Dekker, N.Y. 1969
Garfinkel, D.: Computer applications to biochemical kinetics, A Rev. Biochem. 39, 473 (1970)
Garfinkel, D., Frenkel, R., Garfinkel, L.: Simulation of the detailed regulation of glycolysis in a heart supernatant preparation, Comput. Biomed. Res. 2, 31 (1968)
Garfinkel, D., Hess, B.: A detailed computer model of the glycolitic pathway in ascites cells, J. Biol. Chem. 239, 71 (1964)
Gear, C. W.: Numerical initial value problems in ordinary differential equations. Prentice Hall, Inc. 1971
Heimmets, F.: Concepts and models of biomathematics. New York: Dekker 1969
Hemker, H., Hess, B.: Analysis and simulation of biochemical systems. Febs, North Holland, American Elsevier 1972
Himmelblau, D. M.: Determination of rate constants for complex kinetic models. Ind. Eng. Chem. Fundam. 6, 539 (1967)
Jensen, R. G., Bassham, J. A.: Photosynthesis by isolated chloroplasts. Light activation of the carboxylation reaction, Biochem. Biophys. Acta 153, 227 (1968)
Milstein, J.: Global Optimization by Weighted Random Directions and Interpolating Schemes. To appear
Milstein, J.: Estimation of the dynamical parameters of the Calvin photosynthesis cycle optimization and ill conditioned inverse problems. Ph.D. thesis, Berkeley: University of California 1975
Milstein, J.: Error estimates for rate constants of non-linear inverse problems, SIAM Journal of Applied Mathematics 35, 3 (1978)
Roth, R., Roth, M.: Data unscrambling and the analysis of inducible enzyme synthesis. Math. Biosci. 5, 57 (1969)
Rosenbrook, H., Storey, C.: Computational techniques for chemical engineers. Oxford: Pergamon Press 1966
Squire, W.: A simple integral method for system identification. Math. Biosci. 10, 145 (1971)
Swartz, J.: Parameter estimation in biological systems, Ph.D. thesis, University of California at Berkeley 1973
Swartz, J., Bremermann, J. H.: Discussion of parameter estimation in biological modelling: Algorithms for estimation and evaluation of the estimates. J. Math. Biology 1, 241 (1975)
Tanner, R.: Estimating kinetic rate constants using orthogonal polynomial and Picard's iteration method, Ind. Eng. Chem. Fundam. 11, 1 (1972)
Tanner, R.: Identification, hysteresis, and discrimination in enzyme kinetic models, A.I.Ch.E., 18, 385 (1972)
Yesley, W. G., Pollard, E. C.: J. Theoretical Biology, 7, 485 (1964)
Zeitz, Stanley: Cell cycle kinetics modeling and optimal control theory in the service of cancer chemotherapy. Ph.D. dissertation. Dept. of Math. University of California Berkeley 1976. (Available from Dept. of Math.)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Milstein, J., Bremermann, H.J. Parameter identification of the calvin photosynthesis cycle. J. Math. Biology 7, 99–116 (1979). https://doi.org/10.1007/BF00276924
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00276924