Abstract
A mathematical representation for the analysis of control mechanisms in biochemical reactions is presented. First, the theoretical concept of concentration in biological systems is developed. Then a system consisting of two functions λ and τ is constructed as a network of single output automata. The range of λ is taken to be formed by a set of twostates qualitatively different from the “repair function” Φ f of a mappingf: A→B in the stimulated Φ1 and unstimulated state Φ0. Likewise, the range of τ is formed by the set δ={f o,f 1} wheref 1 means the mappingf in its stimulated state andf o in the unstimulated one. It is demonstrated that the mathematical structure described acts as a control mechanism over thef and Φ f , so that two biochemical components,A→B, are transformed at a controlled rate. Some of the biological applications of this model are briefly examined. The Jacob-Monod model, the enzymatic adaptation phenomenon, and the “rheon unit” hypothesis are discussed within our framework. Eventually, a concrete model for the RNA-polymerase mechanism, based on the above discussion, is presented.
Similar content being viewed by others
Literature
Chance, B., D. Garfinkel, J. Higgins and B. Hess. 1960. “Metabolic Control Mechanisms.”J. Biol. Chem.,235, 2426.
Haruna, I. and S. Spiegelman. 1965. “Autocatalytic Synthesis of a Viral RNA in vitro”.Science,150, 884–886.
Jacob, F. and J. Monod. 1962. “Elements of Regulatory Circuits in Bacteria,” in Meeting of Experts on Biological Organization, Cellular and Supra-Cellular. Varenna, Italy,Biological Organization at the Cellular and Supra-Cellular Level, R. J. C. Harris, Ed. New York: Academic Press (1963), 1–24.
Kacser, H. 1962. “The Kinetic Structure of Organisms.”, 25–41.
Leng, M. and G. Felsenfeld 1966. “The Preferential Interactions of Polylysine and Polyarginine with Specific Base Sequences in DNA.”Proc. Nat. Acad. Sci.,56, 1325–1332.
Richardson, J. P. 1966. “Some Physical Properties of RNA Polymerase.”Proc. Nat. Acad. Sci.,55, 1616–1623.
Rosen, R. 1958a. “A Relational Theory of Biological Systems.”Bull. Math. Biophysics,20, 245–260.
1958b. “The Representation of Biological Systems from the Standpoint of the Theory of Categories.”20, 317–342.
1959. “A Relational Theory of Biological Systems II.”,21, 109–128.
Spiegelman, S. and I. Haruna. 1966. “A Rationale for an Analysis of RNA Replication.”Proc. Nat. Acad. Sci.,55, 1539–1554.
Von Neumann, J. 1951.The General and Logical Theory of Automata. New York: John Wiley & Sons.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Comorosan, S., Platica, O. A theoretical model for the control mechanisms in biochemical reactions. Bulletin of Mathematical Biophysics 30, 123–133 (1968). https://doi.org/10.1007/BF02476944
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02476944