Wednesday, 6 August 2014

how long is a piece of DNA?

Every cell in your body has 2 metres of DNA inside it. Yes, 2 metres.

This is easy to check.  Wikipedia says that one nucleotide [or base] is 0.33 nm long.  The same page also says that human have “3 billion base pairs of DNA arranged into 46 chromosomes”. However, other sites say that the 3 bn base pairs is the genomic contents of the 23 individual chromosomes.  (This demonstrates the value of checking several sites; I also checked the 0.33nm in other places.)  Since you have two copies of these chromosomes in most cells, that makes 6 bn base pairs all together.  And 0.33 nm × 6 bn = 2m.

That seems ridiculous: cells are too small to see with the naked eye, so how can there be a 2m long string of DNA inside?

Well, DNA is really really thin.  Wikipedia says the width of a DNA chain is 2.2–2.6 nm (and this number is confirmed elsewhere; you can check).  Assuming the chain is a cylinder, and taking a mid value of 2.4 nm, this gives a volume of 2m × π × (1.2 nm)2 = 9 × 10−18 m3, or (2 × 10−6 m)3, that is, a cube of side 2 microns.  That can fit in a cell, all folded up.

I’ve known this 2m fact for several years.  I’ve also known that there are over a trillion cells in the human body.  What I’d never done, until challenged by a colleague recently, was put these two together, to calculate the total length of DNA in the human body, with 2m in each of those trillion-plus cells.
Neptune: seems pretty close
in comparison
Actually, finding a value for the total number of cells is a little tricky.  I’ll go with 40 trillion.  So that makes 80 trillion metres of DNA.  That’s a huge number!  Astronomically huge. So let’s visualise it astronomically.

One astronomical unit, or AU, is the mean distance from the earth to the sun, about 150 million km, or 1.5 × 1011 m.  (I grew up knowing it as 93 million miles, but the world has changed units.)  That means you have over 500 AU of DNA in your body.  Neptune, the outermost planet, is 30 AU from the sun.  Your total DNA is nearly 10 times the diameter of the planetary solar system!

Another way to look at it.  Light travels at a speed of 3 × 108 ms−1.  Even at this colossal speed, it takes a while for light to get around the solar system: the moon is just over a light second away, and the sun is a full 8 light minutes away.  Dwarfing these, your total DNA is 3 light days long!

And yet that astronomically long piece of DNA length has a volume of 40 trillion × 9 × 10−18 m3, or 360 cm3, just about the volume of a soft drink can.  Really really really thin.

So, if anyone asks how much DNA there is in the human body, it’s 3 light days, or just over half a pint, depending how you want to measure it.

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