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 right angles

A cylinder made of triangular bricks can be assembled with a helical edge. “Helicity” refers to translation vs. rotation: thinking of a slinky, if you stretch out the coil, you decrease the helicity. The helicity of a masonry edge can be manipulated by the shape of the triangle.


If the translation is proportional to the radius of the cylinder, and the rotation is equal to 90 degrees; then this proportioned triangle can be assembled with a helical edge that allows arches to intersect at 90 degrees.

This proportioned triangle (in this case, with independent key) looks like this:

Arches made with these blocks can be turned in, like this:

Arches can also be turned out, like this:

Note the gap between the arches where they intersect. This gap can be filled with a larger spherical section or dome. If the cylinders are considered radius 1, then the larger sphere has a radius of 1.5.

The sphere filling this section does not fill it precisely. This is the ancient problem of “squaring a circle,” a fascinating and amusing story of dedicated mathematicians pursuing a Sisyphean task. It is impossible to square a circle, and this was not proven until 1882.

This way of putting together two barrel vaults made from triangular blocks, so that they intersect at a right angle into a larger dome (also made of triangular block) creates extensive additional design flexibility. There are many ways to configure this system.

I’ll be talking about this in much detail over the next several blogs.