Advertisement

The bulletin of mathematical biophysics

, Volume 34, Issue 4, pp 547–558 | Cite as

A numerical experiment on the determination of kinetic rate constants in the presence of diffusion

  • J. R. Cannon
  • Paul Duchateau
  • D. L. Filmer
Article

Abstract

Two chemicals,A andB, are allowed to diffuse together and a reaction described by
$$A + B\mathop \rightleftharpoons \limits_{K_{ - 1} }^{K_1 } C$$
is allowed to proceed. This system is described mathematically by a system of partial differential equations. A numerical procedure is presented to find the rate constants ofK 1 andK −1. A systematic analysis of the effects of errors is also presented.

Keywords

Numerical Procedure Biophysics Volume Kinetic Rate Constant Hide Periodicity Detector Slit 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature

  1. Bellman, R., B. Gluss and R. Roth. 1964. “On the Identification of Systems and the Unscrambling of Data: Some Problems Suggested by Neurophysiology.”Proc. Nat. Acad. Sci.,52, 1239–1240.MathSciNetCrossRefGoogle Scholar
  2. —, H. H. Kaginada and R. E. Kalaba. 1965. “On the Identification of Systems and the Unscrambling of Data, I. Hidden Periodicities.” —Ibid.,53, 907–910.MathSciNetCrossRefGoogle Scholar
  3. — and R. S. Roth. 1966. “Segmental Differential Approximation and Biological Systems: An Analysis of a Metabolic Process.”J. Theoret. Biol.,11, 168–176.CrossRefGoogle Scholar
  4. —, J. Jacquez, R. Kalaba and S. Schwimmer. 1967. “Quasilinearization and the Estimation of Chemical Rate Constants from Raw Limetic Data.”Math. Biosci.,1, 71–76.CrossRefGoogle Scholar
  5. Cannon, J. R. and D. L. Filmer. 1965. “Analysis of a Procedure for the Determination of Kinetic Rate Constants.”Bull. Math. Biophysics,27, 253–263.Google Scholar
  6. — and—. 1967. “The Determination of Unknown Parameters in Analytic Systems of Ordinary Differential Equations.”SIAM J. Appl. Math.,15, pp. 799–809.MATHMathSciNetCrossRefGoogle Scholar
  7. —— and N. Reiss. 1967. “A Method for the Determination of Rate Constants in Enzyme Reactions.”J. Theoret. Biol.,16, 280–293.CrossRefGoogle Scholar
  8. — and—. 1968. “A Numerical Experiment on the Determination of Unknown Parameters in an Analytic System of Ordinary Differential Equations.”Math. Biosci.,3, 267–274.Google Scholar

Copyright information

© N. Rashevsky 1968

Authors and Affiliations

  • J. R. Cannon
    • 1
  • Paul Duchateau
    • 2
  • D. L. Filmer
    • 3
  1. 1.Mathematics DepartmentUniversity of TexasAustin
  2. 2.Mathematics DepartmentUniversity of KentuckyLexington
  3. 3.Biology DepartmentPurdue UniversityLafayette

Personalised recommendations