Abstract
Some consequences of Onsager's, generalization of Fick's law are examined. It is found thatmetabolized solutes may flow continually against their concentration gradients.Inert solutes may exist in a higher or lower concentration inside of the cell than in the medium thus appearing to be accumulated or excluded. The magnitudes of such concentration differences are dependent upon the rates of metabolism of metabolized solutes. Alteration of these rates mayfurther increase the concentration disparity by causing inert solute to flow from a low to a high concentration. Due to the mutual dependence, demanded by Onsager's law, of the diffusion currents, the rates ofchemically independent reactions are mutually dependent. This so calledcoupling by diffusion implies that:The rate of metabolism of a given substrate is influenced by the rates of metabolism of metabolically unrelated substrates. Furthermore, the presence, in the medium, of aninert solute to which the membrane is permeable will influence the rates of concentration-dependent reactions in the cell. The spatial distribution of a catalyst in the diffusion field within the cell is examined. The general effect of including heat flow and thermal diffusion in the cellular diffusion problems is briefly pointed out.
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Literature
Aitken, A. C. 1948.Determinants and Matrices, Fifth Edition. New York: Interscience Publishers.
Bloch, I. 1944 “A Theory of Membrane Permeability.”Bull. Math. Biophysics,6, 85–92.
Casimir, H. B. 1945. “On Onsager's Principle of Microscopic Reversibility.”Rev. Mod. Phys.,17, 343–356.
Davis, H. S. and G. S. Crandall. 1930. “The Role of the Liquid Stationary Film in Batch Absorption of Gases. I. Absorption Involving no Irreversible Chemical Reactions.”Jour. Am. Chem. Soc.,52, 3757–3769.
Danielli, J. F. 1942.Cytology and Cell Psysiology. Chapter III. (Ed. G. Bourne.) Oxford: Clarendon Press.
Eckart, C. 1940b. “The Thermodynamics of Irreversible Processes: II. Fluid Mixtures.”Phys. Rev.,58, 269–275.
Frank, J. and J. E. Mayer. 1947. “An Osmotic Diffusion Pump.”Arch. Biochem.,14, 297–313.
Harned, H. S. 1947. “The Quantitative Aspects of Diffusion in Electrolytic Solutions.”Chem. Rev.,40, 461–522.
Hearon, J. Z. 1949. “The Steady State Kinetics of Some Biological Systems: I.”Bull. Math. Biophysics,11, 29–50.
— 1950a. “The Steady State Kinetics of Some Biological Systems: III. Thermodynamic Aspects.”Bull. Math. Biophysics,12, 57–83.
— 1950b. “The Steady State Kinetics of Some Biological Systems: IV. Thermodynamic Aspects.”Bull. Math. Biophysics,12, 85–106.
Horton, W. S. 1948. “Temperature Lag and Chemcial Kinetics.”Jour. Phys. Collid Chem.,52, 1129–1136.
Lamm, O. 1947. “On a Generalization in the Diffusion Theory.”Jour. Phys. Chem.,51, 1063–1078.
Landahl, H. 1942. “A Kinetic Theory of Diffusion Forces, in Metabolizing Systems.”Bull. Math. Biophysics,4, 15–26.
Leaf, B. 1946. “Phenomenological Theory of Transport Processes in Fluids.”Phys. Rev.,70, 748–758.
Meixner, J. 1942. “Reversble Bewegungen von Flüssigkeiten und Gasen.”Ann. Phys.,41, 407–425.
Morales, M. F. 1944. “On a Possible Mechanism for Biological Periodicity.”Bull. Math. Biophysics,6, 65–70.
Onsager, L. 1931a. “Reciprocal Relations in Irreversible Processes: I.”Phys. Rev.,37, 495–526.
— 1931b. “Reciprocal Relations in Irreversible Processes: II.”Phys. Rev.,38, 2265–2279.
— and R. M. Fuoss. 1932. “Irreversible Processes in Electrolytes. Diffusion Conductance and Viscous Flow in Arbitrary Mixtures of Strong Electrolytes.”Jour. Phys. Chem.,36, 2689–2778.
— 1945. “Theories and Problems of liquid diffusion.”Ann. N. Y. Acad. Sci.,46, 241–265.
Rashevsky, N. 1948.Mathematical Biophysics. Second Edition: Chicago: University of Chicago Press.
— 1949. “A Note on The Diffusion Drag Foreces.”Bull. Math. Biophysics,11, 9–13.
Rosenberg, T. 1948. “On Accumulation and Active Transport in Biological Systems.”Acta Chem. Scand.,2, 14–33.
Roughton, F. J. 1941. “A Method of Allowing for the Influence of Diffusion in Manometric Measurements of Certain Rapid Biochemical Reactions.”Jour. Biol. Chem.,141, 129–145.
Young G. 1938. “Theory of Diffusion Forces in Metabolizing Systems.”Growth,2, 160–180.
— 1939. “On the Mechanics of Viscous Bodies and Elongation of Ellipsoidal Cells.”Bull. Math. Biophysics,1, 31–46.
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Hearon, J.Z. Some cellular diffusion problems based on Onsager's generalization of Fick's law. Bulletin of Mathematical Biophysics 12, 135–159 (1950). https://doi.org/10.1007/BF02478250
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DOI: https://doi.org/10.1007/BF02478250