A 5-dimensional Numeral Series behind the Genetic Code

© Å. Wohlin

Published articles (open access):

2015-03: Journal of Theoretical Biology, Volume 369, 21 March 2015, Pages 95-109: (For a long unpublished version 2011, 51 pages, see here.)
"Numeral series hidden in the distribution of atomic mass of amino acids to codon domains in the genetic code".

 2016-11: Biomedical Genetics and Genomics,Volume 1(4) 2016:
"Numerical analysis of 3/2-relations in the genetic code and correlations with the basic series of integers 5-0." (A follow-up article.)

2021-12: Medical Research Archives, Volume 9(12), Dec 2021:
C-skeleton in the genetic code from a basic series 5 - 0, guiding valences and other numeral features in the code".

DNA-RNA: Mathematical patterns in the Genetic code

DNA is built of 4 bases G-C-T-A. When DNA is copied to RNA, the T-base is replaced by the U-base. Different triplets as "codons" of these 4 bases G-C-U-A in RNA-chains encode for the 20 "classical" amino acids that united in long strings make up all proteins. The coding system is nearly universal throughout biological life.
   Why this coding system? It's a fundamental question. A suggested view is presented in file 0 (right column) to start with.

Since the construction of DNA was discovered in 1950th, one big, old question has been if the distribution of codons to amino acids are "a frozen hazard" or may reveal some hidden logic. Hundreds of articles have been published on the subject in PubMed during decades with different approaches and theories (one review here and a selection of such articles besides references in the text is found in References), but there is still no commonly accepted answer to the question.

The 5-dimensional model, shortly presented on the site here, led to the thought that if it had any relevance, it could appear in some form on superposed levels, not least in a "main stream" development towards life and the genetic code. Here results from this research.


As said above: In spite of an immense lot of research and new knowledge during last decades there is no consensus on how to interpret the genetic code and the system for protein synthesis but a lot of quite different hypothetical aspects and approaches. To really get the faintest idea or intuitive guess on the development of a cell - and life, it's proposed here as necessary to start from general assumptions as the following ones, some of them surely shared by many, others more controversial.

a. The enormous complexity of the cell and its metabolism must be understood as an internal differentiation, through opposite forces, which implies starting from some kind of (partly) enclosed "unit", defined by a centre and an substantiated "anti-center" as a partly penetrable circumference. (This could perhaps in a first stage be some kind of metal shell - analogous to later Me-skeletons of unicellular organisms; metals representing anticenter in relation to non-metals, the main structure-building elements of life.)

b. Next, about forces, it must be assumed that all forces recognized at the level of physics (probably redefined in the future) appear on the biochemical level too, in one or another form, not just the electromagnetic one. (Naturally also aspects from quantum mechanics.)

c. Further, about dimensional conceptions on the biochemical level: To get the slightest intuitive comprehension of the biochemical complexity, it seems quite necessary to extend the dimensional analysis to higher dimension degrees (d-degrees). It would imply that aspects on structure in simple 3D-terms were integrated with other biochemical gradients of different kinds - binding and polarizing ones - as 4-dimensional vector fields, into some unified, multidimensional analysis.
   It's surely also time to leave the concept of dimensions defined only in terms of "independent" variables (already questioned in physics) and adopt a view where dimensions are deeply integrated and interdependant in dynamical processes.

d. The character of the genetic code as an information system should be closer analysed: Is it a reference system between connected complementary forms, a memory system and / or a parallel development of the same structural kind on different levels, where underlying level becomes the "memory" ... or is seen as "representing" the superposed one - or the inverse. Perhaps it's only part in a more general system of references connected with concepts as inversions, resonances, conjugates, complementary units - and relations between different, dependent d-degrees?

e. Then, about mass, mostly disregarded when the genetic code is discussed. Mass is a property not yet understood by physicists. That shouldn't be taken as a reason for regarding mass as an unimportant property for the emergence of life. Sooner, it would be extremely astonishing if not all atomic properties played essential roles at the creation.
   The main objection to reevaluate mass is surely such experiences which seem to show that some unusual isotopes don't change the studied metabolism in an established cell milieu of today.
   Smaller changes of isotopes may be possible to neglect in properties as structures and volumes of molecules, (even if they theoretically should influence gradients in mass fields, if this term is allowed),
   However, does such facts necessarily contradict a presumption that mass of common isotopes had a decisive importance at first configurations of elementary biomolecules?
   It is reasonable to assume that mass is a property of higher d-degree, representing a deeper level, than charge. (The physicists' application of the gravity concept into microcosm and quantum mechanics could be mentioned here.) If so, it would agree with dimensional views that the deeper mass level was decisive for elementary structures, while the more superficial level of charge, expressed in electron shells, becomes the relevant level in processes, in metabolism as characterized by more of released kinetic energy.
   Further, in research to find shortened ways to predict destinations and functions of proteins, mass is used as one factor besides polarity with obviously good results [1].
   About counting on ordinary isotopes, the overwhelmingly most common ones, it could also be reason for reminding of the carbon-nitrogen cycle in the sun, where it is the 3 alpha carbon and 4 alpha oxygen that make up the start and end of the fusion: 4 protons (H) giving an alpha-particles (4He).
   Some more about this matter in concluding remarks.

f. Looking for an eventual guiding principle behind emergence of the code, where could it be found? If it isn't regarded as an invention from heaven, it's unavoidable to look for the guiding principle somewhere else, most naturally expressed in the singular atoms themselves.
   Hence, we could suspect that the atoms themselves - with their underlying relations in the fusion processes - should serve as microcodes for cellular life and the principles guiding it. Those principles should probably be found in their internal configurations, also deeper in their nuclei and on a higher level in their spectral lines?

g. Finally, about numbers in general, it's hard to see why numeral series as such should be regarded as special exceptions when appearing in Nature. Different elements are regarded as characterized by numbers of units (u) and on a molecular level by protons equivalent with electrons and their relation to the "octet rule". Since all matter - as well as radiation - is quantified, it shouldn't be too strange to find underlying arithmetical relations behind the structuring principles in the genetic code.
   Most scientists in the field may perhaps feel inconvenient with this idea, regarding it too abstract for any practical work. However, since pure mathematics has led to deeper understanding of nature on the level of physics and astronomy, why shouldn't it in biochemistry?
   In fact, such number series could be compared with structure drawings for buildings, revealing mutual relations between later, stepwise materialized structures. Or perhaps more resemble the principal scheme for the working processes, the logistics? Just the way of Nature to organize itself.
   After all, the numeral series behind the periodic system didn't "exist" - in any recognizable form - in the first materialized Universe after Big Bang.

Rather few contributions to interpretation of the genetic code have paid attention to number regularities as it seems (among references chiefly [2 and 3] but also in one aspect [4]). Recently, according to reference [5], it has been shown that the human genome as a whole single strand is of a fractal kind regarding frequency of codons.
   Since long ago it's observed that features of Fibonacci number series and the golden section appear in Nature. (Below it's shown that such series show up also in mass analysis of the genetic code.)
   There are more general and recognized numeral series: One very simple example is the valences of the central structuring elements in the genetic code: P - C - N - O - H with valences 5 - 4 - 3 - 2 - 1. (A suggestion here is that numbers also could refer to d-degrees or to dimensional steps, presumably as fractals, with the same patterns reappearing on different levels of evolution.)
   Another essential example is the 2x2-series (x = 5 - 0), 50 - 32- 18 - 8 - 2, behind the periodic system, with intervals defining number of electrons in the different orbitals, the orbitals p, d, f also occupying increasing d-degrees in their orientation. It's natural to assume that the arrangement of electron shells have correspondences in the atomic nuclei, responsible for most of the atomic mass.
   A third example is the formulas for spectral lines of hydrogen, where differences between inverted squares of integers as n = 1, 2, 3, 4 and m = 2,3,4, 3,4,5 etc. times a constant give the wavelengths.
   Quotients between wavelengths (n = 2, m = 5, 4, 3) in the Balmer series times 102 happen to give the mass numbers of U- and A-bases too (112 and 135) and approximately the G-base (151,2), which could awake some suspicions...* (Quotients as a kind of phase waves? Alleged not to carry any information!)

Fig 1-1: From Balmer series for spectral lines of hydrogen:

  (C-base eventually later developed to give two pairs?
  Last  term in c. = 1/9,  x 1000, = 111,1. C-base = 111 )

To Table of amino acids and first observations.

© Åsa Wohlin
Individual research
E-mail: a.wohlin@u5d.net


Links and Notes

Table 24 amino acids (ams)
R-chains, A, Z, N

- ways of writing -

Background model

Files here:

0. Amino acids and codon bases.
Why this coding system?

All these files gathered
in one document, word,
124 p.

All these files in 3 documents, pdf:
Section I, files 0-11

Section II, files 12-16
Section III, files 17-22
Discusssion, References in section III

To 17 short files.
- partly other material -

The 17 files as one document,


An earlier version (2007)
with more material
on the same subject, 73 pages



Latest updated: