The bulletin of mathematical biophysics

, Volume 15, Issue 1, pp 15–21 | Cite as

Nonlinear diffusion in metabolic systems

  • John Z. Hearon


Some general properties of the solution of the diffusion equation are deduced for the steady-state, spherically symmetric system. On the basis of these developments some results of N. Rashevsky (Bull. Math. Biophysics,11, 15, 1949) are discussed and the results of a previous investigation (Hearon,Bull. Math. Biophysics,12, 135, 1950b) are extended to more general conditions. In particular these extensions apply to the flow of a soluteagainst its concentration gradient, the nonzero gradient of an inert metabolite, and theaccumulation or exclusion of an inert metabolite in a metabolic system.


Biophysics Volume Metabolic System Nonlinear Diffusion Constant Sign Symmetric System 
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  1. Hearon, J. Z. 1950a. “The Steady State Kinetics of Some Biological Systems: IV. Thermodynamic Aspects.”Bull. Math. Biophysics,12, 85–106.Google Scholar
  2. — 1950b. “Some Cellular Diffusion Problems Based On Onsager's Generalization of Fick's Law.”Ibid.,12, 135–59.Google Scholar
  3. Onsager, L. 1945. “Theoreies and Problems of Liquid Diffusion.”Ann. N.Y. Acad. Sci.,46, 241–65.Google Scholar
  4. Rashevsky, N. 1949. “Note On A Case of Non-Linear Diffusion.”Bull. Math. Biophysics,11, 15–17.MathSciNetGoogle Scholar
  5. Reid, A. T. 1951. “On the Diffusion of Metabolic Intermediates.”Bull. Math. Biophysics,13, 31–37.Google Scholar

Copyright information

© The University of Chicago Press 1953

Authors and Affiliations

  • John Z. Hearon
    • 1
  1. 1.Department of PhysiologyThe University of ChicagoUSA

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