THE SACRED GEOMETRY OF LIFE The Architecture of DNA

“It is obvious . . . that the complexity and variety possible in these macromolecules are beyond comprehension from the standpoint of geometric design alone.” Richard M. Tullar, in Life: Conquest of Energy, 1972

DNA is the macromolecule responsible for the genetic coding of all life. It resides in the nucleus of all cells. DNA can be thought of as the master ‘blueprint’ for life. The geometric linking that determines the shape and form of a DNA molecule involves two types of chemical bonding.

Covalent bond: A chemical bond that links two atoms together through the sharing of electrons, resulting in a stable balance of the forces of attraction and repulsion. Each atom seeks a specific subatomic arrangement and the sharing of electrons allows the completion of an unbalanced outer shell. Covalent bonds are strong bonds utilized in the construction of the helical backbone of the DNA molecule. The two opposing forces can be understood in the same light as Yin and Yang, the fundamental polarity of Creation issuing from the Tao, or fundamental unity. This polarity is reflected throughout all orders and levels of Nature. Hydrogen bond: Nitrogen and Oxygen are highly electronegative atoms, while hydrogen carries a positive charge. This electromagnetic polarity induces an attraction between hydrogen atoms and nitrogen or oxygen atoms that results in the formation of a bond. This type of bond plays a crucial role in the formation of the 3-dimensional double helical structure of the DNA molecule, linking together the chain of nucleotides. A hydrogen bond is weaker than a either a covalent bond or an ionic bond. This allows the strands to be separated with far less force than it takes to separate the covalent bonds holding the nucleotide strands together. The helical strands can separate from one another intact. This process of separation is crucial to DNA replication.

DNA is built up from components called nucleotides. Nucleotides are composed of three substructures: A deoxyribose sugar molecule, a phosphate molecule and one of four nitrogen base molecules. There are four types of nucleotide according to which one of the four nitrogenous base molecules are linked to the sugar and phosphate molecules. Nucleic acids: Covalent and hydrogen bonds are employed in the construction of the nucleic acids, RNA and DNA. They comprise a major class of organic compounds that are arranged in long polymers composed of nucleotides, the building block components of DNA. The nucleotides are built of carbon, hydrogen, oxygen, phosphorus, and nitrogen atoms. These atoms are arranged into a trinity of geometric forms linked together by a special arrangement of covalent and hydrogen bonds. The sugar molecule is a ring structure consisting of 5 carbon atoms and one oxygen atom, arranged according to the geometry of a pentagon. The nitrogeneous bases are also ring molecules consisting of carbon and nitrogen atoms, formed according to the geometry of hexagons, or to hexagons and pentagons combined. The phosphate molecule, consisting of 4 oxygen atoms linked by an atom of phosphorus arrays itself in the form of a cross with 4-fold symmetry. Geometry provides the template for the structure of the nucleotides and the key to the architecture of the DNA molecule. The sugar molecules and the phosphate molecules are linked together by covalent bonds in an alternating succession, forming a helical backbone, or strand, to which the nitrogenous bases are attached, also by covalent bonds. The sugar-phosphate strands, or chains, provide the structural support while the nitrogen base molecules, according to their arrangement, provide the genetic information.

Three components make up a nucleotide: a base molecule, a deoxyribose sugar molecule, and a phosphate molecule. The pattern of repeating nucleotides in the DNA chain determines the unique life-form. Nucleotides have a total of 4 types of nitrogen base molecules: Adenine, Cytosine, Guanine and Thymine. Adenine and Guanine are called purines. Cytosine and Thymine are called pyrimidines Purines are molecules with six-membered hexagonal rings bonded to five-membered pentagonal rings. Pyrimidines are 6-membered rings in the form of a hexagon. Purines link with pyrimidines in a specific manner. Adenine always links to Thymine and Guanine always links to Cytosine. This association is fundamental to understanding the process of DNA replication. Every cell in our bodies carries a copy of the DNA master code, inherited from the single fertilized egg that initiated our existence as individuals. Chromosomes are structures consisting of DNA, proteins and RNA. Assemblages of chromosomes form genes which provide a code or instructions for the creation of particular proteins. Human cells have a total of 46 chromosomes grouped into 23 pairs.

H

C#1

C#2

C#4

C#3

C#5

O H

Deoxyribose sugar molecule

O

The Deoxyribose sugar molecule forms itself according to the geometry of the pentagon.

KEY H – Hydrogen

C – Carbon N – Nitrogen O – Oxygen

P – Phosphorus

The atoms of carbon in deoxyribose are numbered as shown. Atom C5 is linked covalently to an oxygen atom of the phosphate cross.

C

C#1

C#2

C#4

C#3

C#5

O H

Deoxyribose 5-carbon sugar molecule

O

O

O

O

O

H

P

Phosphate molecule

Covalent bonding between deoxyribose sugar molecule and phosphate molecule

H

C#1

C#2

C#4

C#3

C#5 O

O

O

O

O

P

H

The phosphate molecule with its four oxygen atoms covalently linking deoxribose sugars molecules into a chain is called a phosphodiester bridge, or bond.

C#5

Link to nitrogenous base molecule

H

C1

C2

C4

C3

C5

Deoxyribose 5- carbon sugar

molecule

O

Phosphate group

O

O

O

O

P

H

Covalent bonding between deoxyribose sugar molecule and phosphate molecule

KEY H – Hydrogen

C – Carbon N – Nitrogen O – Oxygen

P – Phosphorus

C#4 of deoxyribose sugar molecule

Covalent bonds

C#3 of deoxyribose sugar molecule

Organic Nitrogeneous Bases The Pyrimidines

C4

N3

N1

C2

C5

C6

H

O H

H

Cytosine Molecule

CH3

C6 C2

C5

C4

O

N3

N1

Thymine Molecule

H

H

KEY H – Hydrogen

C – Carbon N – Nitrogen O – Oxygen

P – Phosphorus

Basic hexagonal/pentagonal architecture of the purine bases adenine and guanine. These bases pair with the pyrimidine bases, thymine and cytosine, which are formed of hexagonal rings.

N9 N7

N3

N1

C4 C5

C6

C2

C8

Organic Nitrogeneous Base The Purines

Molecular formula of Adenine C5H5N5

Molecular formula of Guanine C5H5N5O

Complementary base pairing Adenine / Thiamine bonding

Two nitrogen bases are linked together by hydrogen bonds.

H

Adenine Thymine

dashed red lines = Hydrogen bonds

Hydrogen Bonds

N7

N3

N1

C8

C4

C5 C6

C2

H O

H

N

C5

C6

c4

C2

N3

N1

H

C

N9

Molecular Formula of Thymine C4H6N2O2

Molecular Formula of Adenine

C5H5N5

Molecular Formula of Cytosine C4H5N3O

Molecular Formula of Guanine

C5H5N5O

dashed red lines = Hydrogen bonds

Complementary base pairing Cytosine / Guanine bonding

N9

N7

N3

N1

C8

C4

C5 C6

C2

H

O

N3

N

H

H

H

N

O

C

C2

C4 C5

C6

N1

Cytosine Guanine

G

An example of one nucleotide, consisting of a phosphate molecule, a deoxyribose sugar molecule and one of four a nitrogenous base molecules, in this case the purine base Gaunine, all linked together by covalent bonds. Each nucleotide serves as letter in the genetic alphabet.

The nucleotides group themselves into units of three called a codon. Each codon serves as a code word for the synthesis of protein. Given that there a four unique bases arranged into groups of three, there are 64 possible combinations. (43) Combinations of these nucleotide sequences provide the codes for the formation of one of the twenty amino acids that are used in the construction of proteins, that, in turn, are the building blocks out which living organisms are constructed. The order or sequence of the nucleotides on the DNA strand determines the meaning of the genetic language that translates into amino acids. The formation of new cells in the growth of a living entity, whether worm or human being, involves the division of existing cells in a process of replication. Prior to the splitting of one cell into two, the DNA, residing in the nucleus of the cell, must divide into two, after which biochemical processes begin the construction of a new, duplicate DNA molecule out of each separated half. The DNA molecule is split apart by the action of an enzyme. “The shape of an enzyme molecule is what mainly determines its chemical function . . . The specificity of the enzyme – in other words its property of being only involved in certain reactions – is due to the specificity of the jig-saw type fitting of the components . . . into an active site on the enzyme molecule.” Francis Crick, Lifecloud: The Origin of Life in the Universe. In other words, the catalytic function of enzymes depends upon their geometry. The next image depicts a 2-dimensional representation of a sequence of four nucleotides arrayed along the helical DNA macromolecule.

+ –

C G

T

A

G C

T A

A 2-dimensional model of a section of a DNA molecule

A beautiful portrait of the DNA molecule from Wikipedia Commons. The dimensions, geometry and proportions of the molecule are of extraordinary interest to the student of Sacred Geometry and will be explored in greater depth.

Within the past several decades studies of meteorites that have fallen to Earth have revealed that they contain the building blocks of DNA in the form of the purine nucleobases, which, as we have seen, organize themselves according to the union of pentagonal and hexagonal rings. Their presence in meteorites provides powerful confirmation of the hypothesis that life originated in space and was subsequently delivered to Earth through the agency of comets and their meteoritic offspring. It demonstrates that life is cosmic in origin, and confirms that geometry is fundamental to the generation, function and propagation of life throughout the universe.

Life is Cosmic

The creation and unification of the 5 and the 6 by means of

the Vesica symbolizes the emergence of the Universe (6) and Life

(5) from the cosmic womb of creation. In the domain of counting

numbers the 5 precedes the 6, but in the realm of geometry the

6 precedes the 5, that is, the hexagon appears prior to the

pentagon in the process of geometric construction. The

pentagon is born out of the hexagon through the projection and

intersection of lines and circles, the lines representing force

vectors and the circles representing fields of force. In this

manner life is generated out of the unique pattern of matter and

energy, force and form that is present in the Cosmos.

However, it must be born in mind that the pentagon so

generated in this way is not a perfect pentagon, although for

most practical purposes the fit is close enough that the slight

deviation does not matter. On the other hand, in some cases, it

may be desirable to create a mathematically perfect pentagon,

which is precisely possible within the methods of classical

geometry and in its execution reveals a beautiful manifestation

of the Divine Proportion, or Golden Section. It could be said that

the marvelous and mysterious properties of the Divine

Proportion are a fundamental prerequisite for the emergence

and evolution of higher life forms in the Universe. The Golden

Section will be studied in great depth in future lessons.