## The cell nucleus and its DNA on a human scale – IV

At this point our parts catalogue of the 150 foot nucleus contains just 15,000,000 feet of double stranded DNA and water.  No proteins to copy DNA into RNA or DNA, or to repair it or to mush it down (the subject of this post).  In our blown up model nucleus,  DNA is a cylinder 20 Angstroms (3/8 of an inch) thick.  The thickness of each base of DNA is 1/16th of an inch.  For how I arrived at these numbers see the first post in the series.  You can visualize DNA at this level of magnification as two strands of linguini wrapped around each other every 10/16ths of an inch forming a right handed helix (which I’m never sure how to draw).

What do you do with this much linguini?  Well, an Italian friend (uncle Tom) showed me how to eat it properly by using a spoon to curl it around a fork.

So does the cell.  Except that fork is a set of 8 proteins (called histones) packed together.  When the DNA is wrapped around it, the particle is called a nucleosome.  How big is it?  How much DNA is wrapped around the 8 histones of each nucleosome?  Not very much, just 147 nucleotides in about 1.7 complete turns (around the nucleosome — recall that the two strands of DNA wrap around each other every 10 nucleotides or so).  The turns around the proteins of the nucleosome form a left handed helix (as opposed to the right handed turns of the double helix).

How big is the nucleosome?  Voet && Voet (Biochemistry 3rd Ed. p. 1424) gives the diameter at 110 Angstroms and the thickness at 60 Angstroms.  Trying to visualize this means that given 20 Angstroms = 3/8 of an inch, means that the nucleosome is just over 1 inch high and just over 2 inches wide.

The net effect is to shorten the overall length of DNA.  Well, by just how much? 147 nucleotides is about 147 1/16ths of an inch or about 9 inches long.  Molecular Biology of the Cell (5th Ed) says that we have 30,000,000 nucleosomes per nucleus, which if you multiply it out is more than the 3.2 billion base pairs we have. But the 3.2 is the size of half the genome as we have two copies of each chromosome.  Recall that we decided not to wait while the grounds crew pumped in the other 15,000,000 feet, (see the second post in the series).

Going from 9 inches to just over an inch is roughly a 10-fold compaction of DNA.  But we’ve got to compact DNA down by a factor of 100,000.  Why? Because the DNA in our cells, if stretched out is 1 meter long, while our nuclei are only 10 millionths of a meter (10 microns) in diameter.  We still have a factor of 10,000 to account for.

Before going on to higher levels of chromosomal organization think a bit about what the nucleosome looks like.  The 1.7 turns of DNA are pretty close to each other.  From top to bottom the nucleosome is just over an inch, but DNA in our model is 3/8 of an inch thick.  Not much room between the turns.   Also, there isn’t any room to speak of between the DNA and the histone core of the nucleosome, as I’ve described it (more on this in future posts).  Wikipedia says that there are over 120 direct protein DNA interactions (probably salt bridges and hydrogen bonds) and ‘several hundred’ water mediated protein DNA interactions.

Voet has the mass of the nucleosome core particle (8 proteins + 150 nucleotides of DNA) at 205 kiloDaltons.  So how fast does it move? Recall from the last post that at 80 Farenheit (27 Celsius) something with a molecular mass of 100 kiloDaltons moves at 9 meters/second, while something with a mass 10 times that moves at 2.7 meters/second.  So the nucleosome has plenty of time to travel all over the nucleus (if it were free, but it isn’t).  Even with binoculars sitting in the stands we couldn’t see the nucleosomes zooming about, but we certainly could if we got close to the sphere.

DNA nucleosomal compaction potentially introduces another problem. Although the DNA has been shortened by the nucleosome, it takes up more volume.  What is the volume of a cylinder 110 Angstroms wide and 60 Angstroms tall?  It’s pi * 5.5 * 5.5 * 6.0 cubic nanoMeters or 570 cubic nanoMeters.  We know how much volume 147 nucleotides of double stranded DNA takes up — it’s pi * 1 * 1 * 147 * .34 cubic nanoMeters  = 156 (the .34 is the 3.4 Angstrom thickness of a given nucleotide).  In the second post of the series, I calculated that even assuming two copies of each chromosome, the DNA occupied 6.28 cubic microns of a 523 cubic micron nucleus. Assuming most DNA is found in nucleosomes (and given 30,000,000 nucleosomes/nucleus over half of it is) we have to multiply the 6.28 by 570/156 obtaining 23 cubic microns taken up by DNA bundled into nucleosomes in a 523 cubic micron nucleus — still plenty of room. (But we have not accounted for proteins manipulating the DNA — copying it, repairing it, etc. etc.).

While this blog is mostly about chemistry, it’s time to pause and think of what must happen to untangle  the 30,000,000 feet of linguini into each of the 46 chromosomes. Then the cell must pair chromosome #1 with chromosome #1 (not with any other), chromosome #2 with chromosome #2, etc. etc.  Then it must line them up on the meiotic (not mitotic) spindle so each daughter cell gets one member of each pair.  No wonder 30% of conceptions are thought to be spontaneously aborted because of chromosomal abnormalities (not 30% of clinical pregnancies, these abortions happen very early on before a woman realizes that she has conceived).

Even worse, think about duplicating each of the two strands of DNA on each chromosome (bringing the total to 60,000,000 feet of linguini), lining up all 46 chromosomes on the mitotic plate, splitting the chromosomes so that each daughter cell gets the correct 30,000,000 feet in the trillion or so cells that make us up. What’s miraculous is that we’re here at all, not that we get sick.   Such thoughts helped me deal with the Godawful stuff a neurologist sees (and I saw it for 38 years). Molecular biology as psychotherapy (or religion if you look at it that way).

Finally, people have been screwing around for over 30 years trying to figure out the next level of compaction of DNA (which must exist in some form to fit all the DNA into the nucleus).  They have found something called the 30 nanoMeter fiber.  Therein hangs a tale, and some scientific philosophizing, but that’s for the next post.

Here’s a link to the next post in the series

https://luysii.wordpress.com/2010/04/22/the-cell-and-its-nucleus-on-a-human-scale-v/