Skip to main content
SpringerLink
Log in

A suggestion of a new approach to the theory of some biological periodicities

  • Published:
The bulletin of mathematical biophysics Aims and scope Submit manuscript

Abstract

Previous studies of L. Danziger and G. Elmergreen (Bull. Math. Biophysics,16, 15–21, 1954;18, 1–13, 1956) of possible biochemical periodicities in organisms assumed non-linear biochemical interaction between different metabolites, because linear systems do not lead to undamped ocsillations. They treated homogeneous systems. Later N. Rashevsky generalized their results to a more realistic case where the non-homogeneity due to the histological structure is considered. (Some Medical Aspects of Mathematical Biology, Springfield, Illinois: Charles C. Thomas, Publisher, 1964;Bull. Math. Biophysics,29, 389–393, 1967.) As long as the histological structure remains constant, the existence of sustained periodicities requires the assumption of non-linearity of biochemical interactions. If, however, the secretions of an endocrine gland affect the histological structure of the target organ, notably as in the menstrual cycle, and if there is a feed-back, the equations become non-linear and may admit sustained periodic solutions even if the purely biochemical interactions are linear.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature

  • Brown, J. H. U. and S. B. Barker. 1962.Basic Endocrinology for Students of Biology and Medicine. Philadelphia: F. A. Davis Company.

    Google Scholar 

  • Danziger, Lewis and George Elmergreen. 1954. “Mathematical Theory of Periodic Relapsing Catatonia.”Bull. Math. Biophysics,16, 15–21.

    Google Scholar 

  • —. 1956. “The Thyroid-Pituitary Homeostatic Mechanism.”Ibid.,16, 1–13.

    Google Scholar 

  • —. 1957. “Mathematical Models of Endocrine Systems.”Ibid. 19, 9–18.

    MathSciNet  Google Scholar 

  • —. 1958. “Mechanism of Periodic Catatonia.”Confinia Neurologica,18, 159–166.

    Google Scholar 

  • — and J. A. Kindwall. 1954. “Treatment of Periodic Relapsing Catatonia.”Dis. Nerv. Syst.,15, 35–43.

    Google Scholar 

  • Gjëssing, R. 1932. “Beiträge zur Kenntniss der Pathophysiologie der Katatonen Stupors.”Arch. Psychiat.,96, 319–392.

    Article  Google Scholar 

  • — 1935. “Beiträge zur Kenntniss der Pathophysiologie der Katatonen Erregung.”,Ibid,104, 355–416.

    Article  Google Scholar 

  • — 1938. “Disturbances of Somatic Functions in Catatonia with a Periodic Course and Their Compensation.”J. Ment. Sci.,84, 608–621.

    Google Scholar 

  • — 1953. “Beiträge zur Somatologie der Periodischen Katatonie.”Atch. Psychiat.,121, 191–326.

    Article  Google Scholar 

  • Hearon, John Z. 1949a. “The Steady State Kinetics of Some Biological Systems: I.”Bull. Math. Biophysics,11, 29–50.

    Google Scholar 

  • —. 1949b. “The Steady State Kinetics of Some Biological Systems: II.”Ibid.,11, 83–95.

    Google Scholar 

  • —. 1950a. “The Steady State Kinetics of Some Biological Systems: III. Thermodynamic Aspects.”Ibid.,12, 57–83.

    Google Scholar 

  • —. 1950b. “The Steady State Kinetics of Systems: IV. Thermodynamic Aspects.”Ibid.,12, 85–106.

    Google Scholar 

  • —. 1950c. “Some Cellular Diffusion Problems Based on Onsager's Generalization of Fick's Law.”Ibid.,12, 135–159.

    Google Scholar 

  • Lamport, P. 1941. “Periodic Changes in Blood Estrogen.”Endocrinology,27, 673–680.

    Article  Google Scholar 

  • Peirce, B.O. 1929.A Short Table of Integrals., Third Revised Edition, Boston, New York, Chicago: Ginn and Company.

    MATH  Google Scholar 

  • Rapoport, Anatol. 1952. “Periodicities of Open Linear Systems with Positive Steady States.”Bull. Math. Biophysics,14, 171–183.

    Google Scholar 

  • Rashevsky, N. 1930. “Sind Resonanzerscheinungen bei physikalisch-chemischen Periodizitaten moglich?”Zeitschrift für Physik,65, 556.

    Article  Google Scholar 

  • — 1960.Mathematical Biophysics. The Physico-Mathematical Foundations of Biology. 3rd Edition, 2 Volumes. New York: Dover Publications, Inc.

    Google Scholar 

  • — 1963. “Mathematical Theory of the Effects of Cell Structure and of Diffusion Processes on the Homeostasis and Kinetics of the Endocrine System with Special Reference to Some Periodic Psychoses.” InNerve, Brain and Memory Models, Norbert Wiener and J. P. Schade, Eds. Amsterdam: Elsevier Publishing Company.

    Google Scholar 

  • — 1964.Some Medical Aspects of Mathematical Biology. Springfield, Illinois: Charles Thomas, Publisher.

    Google Scholar 

  • — 1967. “Mathematical Theory of the Possible Role of Inter-Cellular Fluid and of Vascularization on Physiological Periodicities.”Bull. Math. Biophysics,29, 395–401.

    Google Scholar 

  • — 1968. “Mathematical Theory of Biological Periodicities: Formulation of then-Body Case.”Bull. Math. Biophysics,30, 735–749.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mental Health Research Institute, University of Michigan, Ann Arbor, Michigan

    N. Rashevsky

Authors
  1. N. Rashevsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rashevsky, N. A suggestion of a new approach to the theory of some biological periodicities. Bulletin of Mathematical Biophysics 30, 751–760 (1968). https://doi.org/10.1007/BF02476689

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02476689

Keywords

Search

Navigation