Monday, November 09, 2009

Genome Fractal Globules Globs Globulets - Jagnormously Cool ! And Merry Christmas with the Mother of All Christmas Strands.

Special greetings ( ! ! ) today to all you storage-challenged souls out there wandering in search of another closet or a better closet system. To the rest of you, a politely restrained "hello there".

Yes, I also am storage-challenged. Too much stuff, stored in linear vertical structures (stacks) with a storage retrieval system (my memory) in need of an upgrade.

So when I read the other day in Science News about the discovery that DNA appears to be stored in a fractal structure, I thought that was really really cool. But a shadow was cast over my topological joy as functional access to a linear structure within volumetric storage nudged my thoughts to the impending annual challenge- get the Christmas lights untangled.

(I) First the fractals:

See the article in Science News, Nov. 7, 2009, "New view reveals how DNA fits into cell; Map of 3-D structure of the entire human genome shows fractal folding is key," By Laura Sanders.

The work reported appears to be a very clever way to understand how linear DNA is packed ("folded") into the volume of a cell's nucleus. This is very important in order to understand the wonderful efficiencies of the transcription, replication, repair (and more) processes busily ongoing in each nucleus.

Laura Sanders' article reports:

"Cells are tidy packers, cramming DNA into nuclei to create a tangle-free, dense ball with pieces that are still accessible, researchers report October 9 in Science. The findings, based on a new three-dimensional view of the whole human genome, solve a long-standing biological mystery and may lead to a deeper understanding of how genes operate. ... a human cell’s two meters of DNA is jammed into an area about a hundredth of a millimeter wide. But researchers had been puzzled by how cells could pack the DNA, which is organized into 23 pairs of chromosomes inside the nucleus, so tightly without hopelessly tangling it and making it impossible to use." ...

"In the new study, Erez Lieberman-Aiden of Harvard University and MIT, Nynke L. van Berkum of University of Massachusetts Medical School in Worcester and colleagues developed a trick to lock pieces of neighboring DNA to each other while they were still in the nucleus. After removing the pieces and sequencing them, the researchers could calculate how close each and every piece of DNA had been to the other pieces and could reconstruct the 3-D shape of the genome."

What did they find? It appears that DNA is stored in a "fractal" structure. What does that mean? "A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole. Fractals are generally self-similar and independent of scale."

Sanders reports that the researchers found the human genome "has a highly organized structure. Small pieces of DNA fold into globs, and those globs fold into larger globs and so on. The researchers report that this “globule of globules of globules” is fractal, meaning it is organized in such a way that it has the same pattern no matter how far you zoom in. This fractal shape is “super-dense, but has no knots.”

Here is the image produced by Leonid A. Mirny, Maxim Imakaev, and reproduced in the Science News article:

This reminds me a great deal of the vast improvement in computer programming languages (e.g., introduced in the "C" programming language) that came when "go-to-less" systems (code nested inside a nest of code nested inside a nest of code nested inside ... a nest of code) - with loads of recursive functions - replaced the "spaghetti code" in the FORTRAN II that I cut my teeth on . Sometimes topology really matters.

The "knot" in the fractal would correspond to my dinosaur "GO TO" that would jump from here to there without restraint from sound organizing boundaries. The image above looks considerably more organized than some code I wrote in the stone ages. Like, debug that and have a nice day!

(II) And now the Christmas lights:

I usually try to untangle three strands, each about 25 feet long with lights about every 0.2 m (approximately 8 inches), carefully placed in a box the prior season. If I take them down, each strand is unplugged from the next so each strand is individually wound up. If my son or son-in-law takes them down, maybe the whole plugged string is tossed in the box - quickly. But it seems no matter how much care in packing the lights last year, the unpacking becomes an ugly wrestling match more often lost than won.

So how about an analogy of the DNA storage with Christmas lights? Consider a strand with four colors of lights: Amber (A=>adenine), Turquoise (T=>thymine), Coral Red (C=> cytosine), and Green (G=>guanine). But this is a special strand since it is really two "uni-strands" twisted together to form one strand so that every Amber bulb on one "unistrand" corresponds to a Turquoise bulb on the other "unistrand", while every Coral bulb on one "unistrand" corresponds to a Green bulb on the other "unistrand." The two unistrands are twisted and twisted and twisted until we get lots of twists end-to-end (call this a "helix") to correspond to the wound up structure of DNA.

It seems like this is going to be the Mother Of All Christmas Strands (MOACS), with 3 billion lights in each unistrand (corresponding to the 3 billion base-pairs in the human genome). A little math determines the coverage we can get with this strand (ignoring practical matters of blown fuses and the like). The circumference of the earth is approximately 40,000 km, that is 40,000,000 m. With a bulb-pair every 0.2 m (about 8 inches), we can get 200,000,000 bulb pairs in each circumference of the earth. Hey, this little strand of lights can circle the globe 15 times ! ! !

How about the box this thing came out of ? We have to stuff MOACS back into the box after the Christmas ham is gone. Following the globule ... glob ... globlet fractal idea and ignoring the question of linear connectivity, consider a first small cubic box 0.2m x 0.2m x0.2m (about 8 inches on a side), and assume we can store 27 bulb-pairs (27=3 cubed) in the box. Call that B1. Then form B2 as a box composed of 27 B1 boxes in a cubic 3x3x3 configuration, B3 is composed of 27 B2 boxes recursively in the same fashion, and so on. If I get the math right, the box B7 should be able to contain 10.5 billion bulb-pairs, triple the space required. B6 of course can only store 1/27 of that, or 0.39 billion bulb-pairs (only about 13% of the volume needed to hold our MOACS).

So let's take B7 as our design box. This will leave some extra space for the hounds to get in and fetch copies of strand segments when needed. The length of one side of B1 is 0.2 m, one side of B2 is 0.2m x 3, one side of B7 is 0.2m x 3**(7-1) = 146 m, or about 160 yards. To envision that, consider a cubic box with one dimension equal to the full end-to-end field length of the Los Angeles Coliseum. Here is a photo (thanks to Wikipedia ) from the 2008 USC vs. Ohio State football game to help your imagination:

Now go that wide and that high (far above the nosebleed seats) and you have the B7 box that holds our MOACS.

Oh, we have some critical chores to accomplish with our MOACS:
First chore, we need to send in - sometimes waaaaay in - our copyists with a bag of wire and a bag of bulbs to copy good-sized chunks of the MOACS and drag the copied strand back out. These daughter-of-MOACS (DOMOACS) ministrands correspond to RNA segments copied from DNA. One problem is that the copy wire must be attached to the MOACS while the DOMOACS is being constructed. And everything gets all tangled up unless the copy hounds take in a pair of pliers to occasionally cut the MOACS while going round-and-round. Also needed is a splicing tool to put the MOACS back together again with integrity. Here is a DNA-for-dummies description of the corresponding process in transcribing RNA from DNA:
"Transcription causes a problem: the movement of the polymerase through the interwound helical DNA causes the DNA ahead of the polymerase to become tightly overwound. This would cause transcription to slow down or halt completely except that another protein, called topoisomerase, untangles the DNA. It does this by a complicated maneuver - cutting one strand of the tangled DNA, passing the uncut DNA strand through the cut strand, and then resealing the cut." (Behe, M.J., Darwin's Black Box, The Free Press, New York. 1996, p 271.) Cool, huh?

Second chore, we need to make more copies of the coliseum-sized MOACS. In the DNA world, this chore is called replication. This calls for a bag of at least 6,000,000,000 bulbs (because when the strand is separated into unistrands, another unistrand is constructed attached to each of the original-but-now-separated unistrands. I will give you dear readers just the first bit of the biochemical process analagous to our MOACS duplication job:
"DNA replication begins at a certain DNA sequence, known appropriately as an "origin of replication" and proceeds in both directions at once along the parent DNA. The first task to be tackled during replication, as for transcription, is the separation of the two parent DNA strands. This is the job of the DnaA protein. After the strands are separated, ...."
If you are anxious to read the rest of this elegant replication story, see:
Behe, M.J., Darwin's Black Box, The Free Press, New York. 1996. p. 275.


Pack, replicate, unpack, pack. Do you suppose Charles Darwin, if transported to the modern time along with his buddy dog pack:
Thomas Huxley ("Darwin's bulldog" - ),
Richard Dawkins ("Darwins Rottweiler" - ), and
Eugenie Scott ("Darwin's Golden Retriever" - )

would be able to make a duplicate copy of the MOACS described above? Well, maybe. But then let's see if they could pack all 15 earth-circumferences of it back in the coliseum-sized box. And then let's really see the smug faces fade as they try to get it back out next Christmas and untangle it. Maybe there is a corner of hell with that kind of task assigned - pack, replicate, unpack, pack, replicate, unpack .... ad infinitum. If so, I wonder who might be there.

It would be interesting to ask: "If Darwin's dog pack can pack MOACS packs. how many packs can the dog pack pack?"


"Cells are tidy packers," Ms. Sanders says.

But let's get more real and say "The Creator God is a tidy packer of cells."

There. That's better.

What can I say to any man or woman who might smugly continue to contend that accidental natural processes have formed all living things?

What can I say to one who dogmatically insists that purposeless particles, through purposeless processes, produce purposeful people?

What can I say? Nothing. Just sigh, shrug, and move on. There are others who are willing to listen. By God's mercy may they be found.

We have Christmas coming up soon - an opportunity to celebrate the incarnation (via virgin birth) of the one about whom scripture says:

"13. For He rescued us from the domain of darkness, and transferred us to the kingdom of His beloved Son,
14. in whom we have redemption, the forgiveness of sins.
15. He is the image of the invisible God, the firstborn of all creation.
16. For by Him all things were created, both in the heavens and on earth, visible and invisible, whether thrones or dominions or rulers or authorities-- all things have been created through Him and for Him.
17. He is before all things, and in Him all things hold together.
18. He is also head of the body, the church; and He is the beginning, the firstborn from the dead, so that He Himself will come to have first place in everything.
19. For it was the Father's good pleasure for all the fullness to dwell in Him,
20. and through Him to reconcile all things to Himself, having made peace through the blood of His cross; through Him, I say, whether things on earth or things in heaven.
21. And although you were formerly alienated and hostile in mind, engaged in evil deeds,
22. yet He has now reconciled you in His fleshly body through death, in order to present you before Him holy and blameless and beyond reproach--
23. if indeed you continue in the faith firmly established and steadfast, and not moved away from the hope of the gospel that you have heard, which was proclaimed in all creation under heaven, and of which I, Paul, was made a minister."

Colossians 1:13-23 (NASB)

If you read verse 13 carefully, you will see that Jesus himself is not only Savior, but also Creator. Ooooohhhhhh! So He is the one who did the pack-replicate-unpack! But He also figured out how to do it in the first place. If you are wont to use the name of Jesus in a casual or disrespectful way, bite your tongue. You have to be really careful who you diss.

May you "continue in the faith, firmly established and steadfast, and not moved away from the hope of the gospel that you have heard."

Have a blessed Christmas 2009.

Because of Jesus the Savior,

Respectfully submitted,



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