## Tuesday, July 28, 2015

### On the total length of all DNA molecules on the planet

If you were to line up all the DNA molecules from all the individuals in all the species on Earth, how long would it be? This is a kind of "Fermi question" or "Fermi problem." You should be able to estimate an answer based on what you know and reasonable assumptions.

Michael Lynch has a crude estimate in his book The Origins of Genome Architecture. Without reading the book, can you come up with an estimate of your own? Is it larger than the circumference of the Earth? Larger than the distance to Pluto? Longer than the distance to the nearest star (other than the sun) or the the center of the galaxy? Would the string of DNA molecules stretch to the nearest large galaxy (Andromeda)? Or, would it be even longer than that? In case you've forgotten everything you once knew about the structure of DNA, here's a brief refresher: The Three-Dimensional Structure of DNA.

You may assume that all of the DNA molecules are in the standard B-form with the dimensions shown in the figure.

I will not accept any answers in archaic measurement units like leagues, miles, yojana, or cubits.

John Harshman said...

A difficult estimate with lots of unknown parameters. I would like to start with something easier. Given 3 bases/nm, a diploid human cell contains around 2 meters worth of DNA. Google claims 3.7 x 10^13 cells in a human body, and I'm going to ignore erythrocytes for simplicity. So that makes 7.4 x 10^13 meters of human DNA in one individual. With a population of 7 x 10^9, let's call that 5 x 10^23 meters of DNA in the human population. Switching units for convenience, and supposing a light year to be around 10^15 meters, I get 5 x 10^8 light years of DNA, just from our species. And I think I'll stop there. It appears that all the DNA in the world must be many orders of magnitude longer than the observable universe. I sincerely hope I have made a mathematical error.

Sean Ridout said...

Your calculations look roughly correct, but the diameter of the observable universe is about 9.8*10^10 light years.

Paul McBride said...

Landenmark et al. (2015) give a lower bound estimate 5.3x10^37 bp of DNA in the biosphere, which at 0.33^09m per bp gives us 1.7x10^28 m of DNA.

Given that the universe is 8.8x10^26 metres, this leaves us with DNA spanning the equivalent of 20 universes. A dizzying prospect.

John Harshman said...

Sure, but the total human DNA is a teeny, tiny fraction of all the DNA in the world, right? Much much less than 1/200 of it, right?

Hikmet Geçkil said...

To calculate that we need to know about the genome size of all 2 millions (2e6) or so species and the number of cells in each species ofwhich about 1 million are insects. What is more daunting, we should also know the number of each of these 2 millions species on earth.

Can a logical estimate be made from the weight ratio of DNA to live material using an avarege? insects.

DAK said...

The phage biologists are fond of the saying that if we lined up tailed phages head-to-tail they'd stretch out for 200 million light years. I'll use a "guess the number of jelly beans in a jar method" and go for 10^35 km.

DAK said...

p.s

I got that number by assuming 10^30 phages (the most abundant organisms in the biosphere by a considerable margin) and assuming an average genome size of 40,000 bp (for no real reason other than it's a quarter the size of the T4 genome and assuming that accuracy is not of major importance). I worked out the length of all that DNA (ignoring the RNA genomes).and then added a few more orders of magnitude.

DK said...

My number, perfectly mindless, is that there are 10^25 more bacterial cells than eukaryotic ones. I imagine that non-human eukaryotes combine for a 10^6X of humans while having roughly the same genome size. And let's assume an average bacterial genome to be 1000X smaller than human. Finally, here are roughly 10^13 cells in the human body and 10X less that in the average eukaryote.

So, a total eukaryote+prokaryote number of bases is (3x10^9)x(10^6)x(10^12)+(3x10^9)x(10^12)x(10^25)x(10^(-3))=3x10^27+3x10^44 bp, meaning that eukaryotes actually don't matter (despite all that ocean algae and Amazon forests). If 3x10^9 is ~1 m, then 3x10^44 is ~ 10^35 m. The size of the universe is on the order of 10^27 m, so we are talking a less than a billion of Universes lined up.

The conclusion is that, anyway you slice, the number is many, many orders of magnitude more than the size of the observable Universe.

DK said...

Oh, the number above is missing number of humans, 7x10^9, bringing eukaryotic contribution much closer, 2x10^37 bp but still far away from eukaryotes. A sanity check on the overall number of >3x10^44 bp above is that it is would weight ~ 3x10^20 kg, which does not pass the check because the whole Earth is at ~ 6x10^24 kg. So it can only mean that my original bacterial estimate is about 10^6 times off. Stiil, in the end it still has to be far longer than the Universe size.