## The cell and its nucleus on a human scale – II

The grounds crew has finished pumping in the 15,000,000 feet of linguini into the 150 foot sphere sitting on the 50 yardline.  The head groundskeeper is coming our way.  He tells us will have to come back because they aren’t done if we want the exercise to be realistic.  Think what else they have to do before you look at the next paragraph.

The 15,000,000 feet covers all 3 billion bases (3 gigaBases) of the human genome.  But being human, we have a backup just to be sure.  We have two of each chromosome in our nuclei (if you’re a woman).  Males have two of the 22 nonSex chromosomes and an X and Y, women have two of their X chromosomes.  This means 30,000,000 feet of linguini, bringing the space occupied by it up to 6.28 cubic microns, in the 523 cubic micron nucleus.  The adventurous can figure out what this means in cubic feet in the sphere, but the ratio will be the same.   Do we want the high priced spread?   This would be the set of chromosomes just before the nucleus is to divide, where each strand of the double helix of each chromosome has been copied — bringing the total amount of linguini up to 60,000,000 feet.  We tell him to just bring in the second set and we’ll be back.

2 Days later.

We’re back in the grandstand 75 feet up at eye level with the equator of the sphere.  What can we see?  A la Clinton it depends on what you mean by see. The smallest wavelength of visible light is 4000 Angstroms (4 * 10^3 * 10^-10 meters) = 400 nanometers (400 x 10^-9 meters) = .4 microns or 4% of our 10 micron sphere. To see an object, we throw light at it, and the object alters the trajectory of the light wave.  To do so the object must be of the same size as the wavelength of the light wave.  This means that we can’t see anything closer together than .04 * 150 = 6 feet apart on or in the sphere.  Light of wavelength 6 feet will pass over the linguini like a gentle ocean swell passing over a swimmer. Parenthetically, this is why a century ago the brain wasn’t thought to be made of cells.  The neurons and glia are plastered so close together that visible light couldn’t see the boundaries between them.  You can also imagine why light microscopists had such a hard time seeing what was going on.

Well, we’re going to use visible light to look at our 150 foot sphere, and 3/8 of an inch (the thickness of the linguini) is a lot bigger than .4 microns (which is .0004 milliMeters), so we can probably see the linguini (if we use high powered binoculars) and if the strands of linguini stick together enough.  Why are some of the strands of linguini likely to be close together?  Think a bit before reading the next paragraph.

Even though the strands account for only 6% or so of the sphere’s volume, they can be at most 150 feet long before hitting the edge of the sphere, and we’ve got 15,000,000 feet of the stuff.  So there have to be at least 100,000 150 foot lengths of it in the nucleus (and probably a lot more) so it has to curl back on itself.  Well, the genome is chopped up into 23 different chromosomes (24 if you count the X and Y as separate).  This doesn’t help much as even the smallest (chromosome #21) contains 47 megaBases.  Each base is 1/16 of an inch (roughly) so there are 192 per foot.  So chromosome #21 is 244,792 feet long or 46 miles long.  Something must be done.  That’s for next time.

Here’s a link to the next paper in the series
https://luysii.wordpress.com/2010/03/31/the-cell-nucleus-and-its-dna-on-a-human-scale-iii/

• Sacha Nelson  On December 12, 2013 at 12:32 am

Though I get less out of the translation to human dimensions, the calculations at the nuclear level have important mechanistic implications. In fact, I found your blog by looking for just such calculations.

A key question is how much is this linguini waving around? But to constrain this better (no pun intended) it is important to include the other elements of the nucleus. E.g. how much volume do the histones take up? There are other abundant nuclear proteins (e.g. Mecp2 a methyl DNA binding protein is present at near histone levels in neurons at least). There are all the transcripts (transcriptome of a cell is approximately known and there are some estimates of the fraction that is in the nucleus) though estimating the volume of these might be more difficult given the vagaries of RNA structure.

The question is how much room to move around is there? A key unknown is how much of the genome is tightly compacted vs. in a euchromatic state–but this can also be expressed as a variable, given a certain euchromatic/heterochromatic ratio what is the room left for the free linguini to wave around looking for meatballs to play with?

• luysii  On December 12, 2013 at 11:56 am

It isn’t the linguini that needs to move around around, but rather the proteins binding to it. I really should finish up the series because I’ve got the numbers.

Speaking of moving linguini, you should look at another post –https://luysii.wordpress.com/2011/04/10/would-a-wiring-diagram-of-the-brain-help-you-understand-it/

particularly since that’s what your lab seems to be involved in. There is a great review of the constantly changing ion channel composition of even a single synapse in the 30 October Neuron. I’ve been involved in other things, and have meant to write a post on Heraclitus (you can’t step into the same river twice) and the brain.