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Is the golden ratio a universal constant for self-replication?

Yu Liu1, David J T Sumpter1

  • 1Department of Mathematics, Uppsala University, Uppsala, Sweden.

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|July 17, 2018
PubMed
Summary

The golden ratio is not a universal constant in self-replicating systems. Other algebraic numbers appear more frequently, and these ratios are transient, not constant, especially when resources are limited.

Area of Science:

  • Biophysics
  • Systems Chemistry
  • Theoretical Biology

Background:

  • The golden ratio (ϕ) is frequently observed in biological patterns and proposed as a universal constant.
  • Its connection to self-replication, including gene frequency and nucleobase ratios, has been suggested.
  • This study examines the mathematical underpinnings of self-replicating systems to verify these claims.

Purpose of the Study:

  • To investigate if chemically realistic self-replicating systems exhibit universal constants in species population ratios.
  • To determine if the golden ratio specifically governs these ratios.
  • To explore the mathematical nature of population dynamics in self-replicating systems.

Main Methods:

  • Utilizing a general framework for chemically realistic self-replicating reaction systems.

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  • Analyzing the characteristic equations governing the population dynamics of chemical species.
  • Identifying and comparing the algebraic numbers that characterize these systems.

    • Main Results:

    • Self-replicating systems are characterized by algebraic numbers, not exclusively the golden ratio.
    • Other algebraic numbers, like the 3rd lower golden ratio, appear more frequently than ϕ.
    • These population ratios represent transient behaviors under idealized infinite resource conditions.

    Conclusions:

    • The golden ratio is not a special universal constant in self-replicating chemical systems.
    • Observed ratios are transient and dependent on specific, often idealized, conditions.
    • The concept of universal constants in biological self-replication requires re-evaluation beyond simple mathematical ratios.