A Very Intriguing Theory: Bricks and DNA?

Yesterday I began a description of arches meeting at right angles, and how this unique arrangement might possibly be found in DNA molecules, in structures known as centromeres and telomeres.  I realized today that I’ve already written about this odd masonry detour back in April, 2010.  So today I borrow from this earlier entry and expand a little, since it is a pretty interesting subject .

The system I described yesterday is some interesting geometry, I think it's fundamental and basic, and may well exist in nature. In particular, I propose that it may exist in features of DNA.

Most of you probably know that DNA is a double helix. Think of the double helix of DNA as forming a big "X". The ends of the 'x' are telomeres, the center of the 'x' is the centromere.

Centromeres are an originating site of DNA replication (copying begins here). Telomeres are a terminating site of DNA replication. It is proposed that the structures of telomeres and centromeres approximate a structure wherein a combination of four right circular cylinder sections (whose 2 axes of rotation are at right angles to each other) of radius = 1; and also of a section of a hemisphere of radius = 1.5. Here the double helix of DNA is viewed as a right circular cylinder of radius = 1.5. Cylinder sections combine (superimpose) with a spherical section through a four-fold axis of rotation. The geometry of this arrangement may create two optimal energy states simultaneously. This arrangement may be seen as a natural attempt to “square the circle.”


Background

A telomere is a region of repetitive DNA at the end of chromosomes, which protects the end of the chromosome from destruction. Derived from the Greek telos (end) and meres (part).

During cell division, the enzymes that duplicate the chromosome and its DNA can't continue their duplication all the way to the end of the chromosome. If cells divided without telomeres, they would lose the end of their chromosomes, and the necessary information it contains. (In 1972, James Watson named this phenomenon the "end replication problem.") The telomere is a disposable buffer, which is consumed during cell division and is replenished by an enzyme, the telomerase reverse transcriptase.

This mechanism usually limits cells to a fixed number of divisions, and animal studies suggest that this is responsible for aging on the cellular level and affects lifespan. Telomeres protect a cell's chromosomes from fusing with each other or rearranging. These chromosome abnormalities can lead to cancer, so cells are normally destroyed when telomeres are consumed. Most cancer is the result of cells bypassing this destruction. Biologists speculate that this mechanism is a tradeoff between aging and cancer.

I propose that the following geometry may be present in a telomere:

The centromere is a region, often found in the middle of the chromosome, involved in cell division and the control of gene expression. I propose that this geometry may be present in a centromere:

Why bother with this? Centromeres are largely responsible for cell reproduction, when centromeres malfunction genetic disease results; telomeres are largely responsible for aging. Any insight into the functionality of these structures is important to science and medicine.

Here's an interesting article on how geometry can have a direct effect on gene expression. I owe this reference to Alan Michelson, who brought it to my attention, as if to say: "maybe you're not so crazy Pete." Thanks Alan. Here's the article.

Yesterday I began trying to describe the possibility that a particular helicity of cylindrical sections meeting at right angles -into a larger sphere- may be found in structural sections of DNA known as telomeres and centromeres. To summarize this theory with images, a telomere may have a "turn-in" type structure:

A centromere may have a "turn-out" type structure, shown as:

The important aspect of this arrangement is not the individual triangular units, but the helicity and the larger spherical section of the larger assembled structure. It seems that nature is attempting to square the circle with this arrangement.

Below is a view of a telomere, looking at the end of a section of DNA, essentially looking down the "cylinder" of the double helix of DNA. The helicity of DNA changes as a chromosome replicates itself, and it seems that this helicity is what is described in those right angle intersections shown above. Here is a view of a telomere, note the quadrature, or squaring of the structure:

Below is a view of a centromere, with a view of the entire chromosome. This illustration shows how four cylinder sections intersect at a right angle. Centromere is shown as feature 2.

I propose that DNA, through telomere and centromere sites, may utilize this geometry. The ‘turn in’ corresponds to a telomere, and the ‘turn out’ to a centromere. The cylinders may be taken as base sections, or spindle poles. These arrangements may provide an intermediate energy state; somewhat analogous to a catalysis reaction.

A catalyst works by providing an alternative reaction pathway to the reaction product. The rate of the reaction is increased as this alternative route has a lower activation energy than the reaction route not mediated by the catalyst. The geometry described here is analogous to providing an alternative route with lower activation energy.

The centromere and telomere structure are similar to fullerene molecules in a few striking ways. The presence of hexagons and pentagons within the base sections is a feature the telomere shares with fullerenes. Cylinder and sphere sections are found in both centromes & telomeres and fullerenes. It is proposed that centromeres & telomeres create a lowering of thermodynamic or activation energy ‘threshold’: the same is true of fullerenes as evidenced by their existence in nature.

Currently the vast majority of genetic research is empirical, not theoretical. That is, functions of genomes are determined by seeing what effect manipulating (e.g. removing, etc.) a particular genome has on the design/function of the organism it describes. This approach disregards the geometry of DNA, and does not allow certain theoretical insights, which may otherwise be gained. Consideration of geometry may indicate thermodynamic ‘net gains’ that might point to functionality of chemical states.

Close examination of DNA geometry seems to have slowed immensely since Watson and Crick discovered the double helix. DNA is more than a ‘blueprint’; it is the blueprint, architect, engineer, construction worker and building inspector. It is more than these analogs; it is the actual thing itself. This appears to merit a close inspection of its structure and geometry in order to more fully understand it. If this theoretical (geometrical) approach is coupled with the knowledge gained from the empirical approach (i.e.- mapping of the human genome) then a much deeper level of understanding may be obtained.

A cell creates itself and closes itself off. It has genesis and distinction (becoming distinct, having a boundary within which it exists). This geometric model works for the combination of origin (sphere) and growth (cylinders). This is somewhat analogous to the thermodynamic conditions necessary for nucleation and growth in crystal formation. Duplication results in 2 spheres as distinct cells. The separation and distinction of 2 from 1 embodies or relates directly to the activation energy threshold.

We've had a look at one possible role of geometry, to try and show that geometry can play an important role in how things work.

Today there was an interesting article posted by Physorg.com on carbon tubes and water.  This remains a fascinating topic which merits further investigation.

I am unaware of anyone who may have stumbled across, or is investigating, or is even aware of the geometrical structure which I propose exists in the centromere and telomere structures of DNA.  I think this is worth looking at.

Arches at Ninety Degrees

Back in 2000, I had an insight into vaulted arches.  I had been developing triangular interlocking block as a masonry system, and had devised of a method for making cylinders from these triangular blocks.

A cylindrical section can be turned horizontally to create a vaulted arch, like a roman or circular or barrel vault.  

People are largely used to living in a square-cornered building or house.  There is something fundamental to the human psyche that looks to straight walls and square corners within a living space as a standard which sets people at ease.  Domes and round buildings make up a tiny fraction of habitable structures: almost all buildings have straight walls and square corners.  As you read this now, look around you at the building you are in.  I'd be willing to bet that it has straight walls and square corners.  If not, you are in a very tiny minority, living in an "alternative" structure.

It is a challenge to make a vaulted arch roof system sit atop a square cornered building.  In my own masonry approach, which uses triangular block to assemble a cylinder or arch, the triangles can be assembled to provide a helical or spiral edge.  A helix or spiral has translation and rotation, and the 'helicity' or angle of 'spiralness' can be varied.  Think of stretching a slinky: the spiral angle of translation and rotation can be varied, from shallow to steep angles of helicity.

If the translation versus rotation of a given cylindrical section is equal to the radius of the cylinder versus 90 degrees, then this helicicty can be placed atop a right-angled base.  It is thus possible to place vaulted arches atop a right-angled structure.  The right angle can be a "turn-in" as shown below, where the angle between walls is simply 90 degrees, as shown below. (taken from one of my patents)

Below is shown a structure where the vaulted arches are shown as a "turn out" where the walls meet at 270 degrees.  In the case of both a "turn-in" and a "turn-out" a gap is created between the helical edges of the abutting arches where they meet at a corner.  This gap is satisfied by a larger spherical section.  Specifically, if the arches are taken as having a raius of 1.0, then the larger spherical section that fills the gap has a radius of 1.5  (If you'd like to see these images better, just click on them to see a larger view).

This sort of arrangement provides extensive design flexibility.  One, two, three or four vaulted arches can meet at right angles to each other, merging seamlessly into a larger dome or spherical section.

This arrangement creates some very interesting possibilities far outside the realm of masonry.  Could this arrangement have something to do with the structure of DNA and the "magic" of reproduction?  We'll take a look at this next time, including a discussion of centromeres and telomeres.

Rubble and masonry

Rubble is broken stone of irregular size, shape and texture.   ‘Rubble’ derives from rubbish.  Masons make good use of this garbage.

Rubble masonry is rough, irregular unhewn building stone not laid in regular courses.  It may appear as the outer surface of a wall, or may be used to fill a wall. 

Many thick walls which appear as solid stone are commonly filled with rubble.  It is almost counter-intuitive; that a massive wall -the very symbol of solidity- is often filled with rubble.  There is much more rubble in many more exquisite masonry buildings, from The Pantheon, to cathedrals to the Taj Mahal, than most people realize.

The Great Wall of China is made mostly from rubble, which was used to fill the space between the outer bricks and below the road’s surface.

Dry stacked stone walls rely on strategically placed and compacted rubble to help bind the masonry elements together into a consolidated mass.  Good rubble will have a size distribution (big and small chunks) for space filling.  Proper use of rubble in dry stacked stone walls is an art.

Here’s to rubble.

How long will it last?

The carpenter is confident his work will last until the owner notices rot.
The painter knows a fresh coat shines.
The plumber figures those pipes won’t leak before she retires and the electrician reckons code won’t change before the decade’s out and the mason hides his smile thinking almost nothing.