(the closer we get... the better we look...?)

from Dan Winter, 6/13/2000 (reprint of academic Article on Golden Ratio in DNA) url: ../beautygenes ,

In the below note, some very helpful documentation on perfect PHI Golden Ratio embedding in the structure of DNA, AND THE HINT THAT PERHAPS EVOLVING AWARENESS / CONSCIOUSNESS / SELF-REFERENCE IN THE HUMAN GENOME, MAY CORRELATE TO A CLOSER APPROACH TO ACTUAL PHI EMBEDDING IN DNA GEOMETRY ! (fig 4, bottom)

It is curious to note that the Mathematics and Structural Chemistry academic view expressed in this article, while acknowledging a probable profound meaning to PHI Golden Ratio embedding in DNA, (for its pure beauty), fails entirely to consider the recursive wave heterodyning , or pure constructive wave interference (implosion), implications of that geometry! (superconductivity, superluminal cascading, ensoulment, inPHIknit multiple connectedness, the grail idea in DNA by perfect scale invariant compressibility as waveform...etc..) ( pictorial discussions at: ../magneticx , ../superDNA )

below reprinted from, THE QUEST FOR PHI, (Wayne) London Research, (London, Wayne. The Spiritual And Healing Aspects Of The Classical Seven Path Labyrinth: A Work In Progress. Vermont. London Research, 1998.), 139 Main St., Brattleboro, VT 05301, (SECTION 1: 13)

originally? Elsever Science Publishers, Amsrerdam .., 1986

by D. Harel, R. Unger and J. L Sussman

* With Apologies to Watson and Crick..

D. Harel and R.Unger are at the Department of Applied Mathematics, and Joel L. Sussman is at the Department of Structural Chemistry, The Weizmann Institute of Science, Rehovot 76100, Isreal.

An interpretation of the particular proportions of DNA as found In the Watson--Crick double helix model is suggested. It is based on the classcal, highly aesthetical concept known as the Golden Ratio. Specifically, it is shown that in B-DNA both pitch / diameter and diameter / offset are exrrernely close to the Golden Ratio. Here, pitch is the helical repeat, and offset refers to the vertical distance that forms the minor groove.

We wish to suggest an interpretation of the panicular proportions of DNA as found In the Watson--Crick double helix model This interpretation has 'novel features which are of considerable historical, theological, mathematical and, above all, aesthetical interest.

The Watson--Crick model, generally referred to as the double helix, consists of two helical chains coded round the same axis. These chains (excluding the bases) are related by a dyad perpendicular to the helix axis; thus the two chains are antiparallel (see Fig. I).

Fig I Golden Ratio in DNA.

(PHI as Golden Ratio, or approximately 1.61803398....)

There have been many attempts of biological and chemical nature to explain why this particular structure is the one DNA abides by. In our opinion, these explanations are not wholly satisfactory for various reasons. We believe that a definitive, universally acceptable, historically rooted and highly intuitive interpretation should exist for the particular structure and proportions of this most profound and fundamental molecule.

We wish to put forward a radically different interpretation of the structure for the salt of cleoxyribose nucleic acid. This interpretation is concerned with the internal dimensionality and proportions of the double helix; it can be thought of as involving two of the most appealing branches of human intellect, mathematics and art, both coded round the same axis, that of divine aesthetics.

We submit that DNA is structured as it is mainly for aesthetic reasons and support this claim with the use of the Golden Ratio, a concept going back to ancient times. The Golden Ratio, denoted (Greek symbol Phi - inserted here) is an irrational number. like "PI". which expresses a fundamental ratio that is almost as common as PI and has the habit of appearing when least expected. The geometrical meaning of PHI is seen from the line segments of Fig. 2.

The horizontal length of the rectangle has been divided into two parts, A and B. such that the ratio of B to A is the same as that of A to A + B, the length of the entire line. In each case the ratio can easily be shown to be given by:

There is little doubt that the Ancient Greeks were familiar with the Golden Ratio and it was used by some of their architects and sculptors. parnicularly in the structure of the Parthenon (see Fig. 3a).

In fact the name PHI was originally given by the American mathematician Mark Barr in the early 1900s in memory of the famous Greek sculptor Phidias who often used the Golden Ratio in his work (ref.2.).

The number PHI appears in Renaissance an, including works of da Vinci and others, and is rumoured to be the basis of the segmentation of a well-built human body; first finger joint to second, second to both. hand to lower arm, lower arm to hand +lower arm, and so on, culminating in navel upwards to navel downwards and navel downwards to whole body. This particular observation strengthens one's feeling that the proportions of DNA should similarly be based on PHI.

That the structure of a double helix is in itself one of immense beauty goes without saying; we concentrate here on the local dimensions of the type-B double helix, which appears to be the most common form of DNA in chromatin, ref 3. It is easy to conceive of a double helix of uncomely proportions, but it is difficult to imagine that one which was unpleasant to behold would be chosen to carry the genetic code. Given that DNA is to be structured as a right-handed double helix, there are three crucial diamensions that essentially determine its final form: the external width (diameter) of the double helix, the length of its period (i.e. the pitch, or the height of a representative 'slice'), and the verical offset of one helix from the other, which forms the minor groove.

The novel feature of our interpretation of Watson and Crick's structure is the manner in which these three basic dimensions are held together by the rule of the Golden Ratio. Specifically we have found that the ratio of the height to the width, and the ratio of the width to the offset are always very close to PHI (see Figs I and 3). In particular, since the ratio between height and offset is responsible for the unequal sizes of the major and minor grooves of B-DNA, we might say that the ratio between the grooves themselves is golden (or PHI) too.

Although the crystal structure of a B-DNA dodecamer has been refined to high resolution, it is too short and irregular to accurately estimate the pitch, diameter and offset of the DNA molecule as a whole. However the most recent and best refined X-ray fibre studies of long chains of B-DNA, ref 5 (re-refined by Arnott, S. and Chandrasekaran, R., personal communication 1982) yield ratios of 1.6031 and 1.538, respectively, or approximately 1 and 5% less than PHI.

Beauty Improves over Time (!?...DNA MOVING TOWARD PHI EMBEDDING over time?)

Moreover, both ratios seem to converge on PHI as time proceeds (Fig. 4) in contrast, in the less frequently occurring forms of DNA, i.e. A-DNA and Z DNA, the ratios are further from PHI. as shown in Table 1.

Currently available X-ray data on DNA are insufficient for a rigorous test of our interpretation of the structure. At far as we can tell. however, our interpretation is smoothly compatible with the experimental data (and is getting better with time*), but it must be regarded as unproven until it has been checked against more exact results. Our 99 and 95% fits, in other words, are only the starting point ...

It has not escaped our notice that the specific interpretation we have postulated immediately suggests a possible motto for the copying mechanism of the genetic material:

Beauty is in the genes of the beholder.

Acknowledgement
This work was supported in part by grant from the H.Gutwirth fund to JLS.

*Note added in proof , In fact, just 7 years after the Watson Crick model was proposed Langridge et al(ref.10) built a DNA model with ratios of height/width = 1.63, and width/offset = 1.51.

References

I Watson, J. D. and Crick, F. H. C. (1953) Nature 171,737-738

2 Gardner. M. (1959, Sci. Am. 200.128-134

3 Richmond, T. J.. Finch, J. T., Rushton. B. Rhodes ' D. and Mug. A. (1984) Nature 311, 532-537

4 Wing. R., Drew, H., Takano, T., Broka. C. Tanaka, S.. hakura. K. and Dickerson, R. E (1980) Nature 297, 755 -758

5 Amon, S.. Chandraseliaran, R., Birdsall. D L., Leslie, A. G. W. and Ratliff. R. L. (1980 Nature 293, 743-745

6 Crick, F. H. C. and Watson. J. D. (1954) Proc Roy. Soc. A223, 80-96

7 Arrion, S., Dover, S. D. and Wonacott, A. J(1969) Acta Crystallogr. B25. 2192-2206

9 Arnott S. and Hukins, D. W. L. (1972 Biochem. Biophys. Res. Comm. 47.1504-1509

9 Wang. A. H-J., Ouigley, G. J., Kolpak. F. J Crawford, J. L.. van Boom, 1. H.. van dc Matel.G.and Rich.A. , Nature282., 680-686

10 Langiridge, R.. Marvin, D. A.. Seeds, W. E. Wilson. U. R.. Hooper. C. W., Wilkins. M. U F. and Hamilton. L. D. (1960) J. Mol. Biol 2? 38-64