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The kinetics of linear systems with special reference to periodic reactions

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Abstract

It is shown on the basis of (1) conservation of mass, (2) positive concentrations, and (3) the principle of detail balancing that periodic reactions cannot occur in a closed system described bylinear differential equations. The matrix,A, of the rate equations must be such that |A|=0,a ij>0 fori≠j,a ii<0, andVAV −1=B, whereV is diagonal andB is symmetric. These properties ofA imply that the latent roots are real and non-positive and that neither catalysis nor inhibition can be described bylinear equations. It is further shown that periodic reactions cannot occur in anopen system for which the matrix associated with the chemical reactions has the above properties and in which thesimple law of diffusion is obeyed. The relation of these results to Onsager's reciprocal relations and to previous work on periodic and cyclic chemical reactions is discussed. The utility of certain of these results for the treatment of isotope kinetics is indicated.

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Authors and Affiliations

  1. Oak Ridge National Laboratory, Oak Ridge, Tennessee

    John Z. Hearon

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  1. John Z. Hearon
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Additional information

A portion of this work was performed while the author was in the Department of Physiology, University of Chicago, and was supported by a grant from the Dr. Wallace C. and Clara A. Abbott Memorial Fund.

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Hearon, J.Z. The kinetics of linear systems with special reference to periodic reactions. Bulletin of Mathematical Biophysics 15, 121–141 (1953). https://doi.org/10.1007/BF02476377

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