Very roughly how many water molecules would you guess there are in a single cell? Within a couple of orders of magnitude?
I got it quite wrong.
I got it quite wrong.
I guessed off-hand “a billion” which I think was just my brain’s way of saying “wow, a really big number!”
But it’s WAY too small.
But it’s WAY too small.
There’s a bunch of different numbers you can find on the web. Some of them are definitely way off. But there’s a wide range of values that seem reasonable (to me) because cells vary in size over several orders of magnitude.
You can do a Fermi estimate based either on mass (which didn’t occur to me, but several tweeps did it that way!) or based on volume. en.wikipedia.org/wiki/Fermi_pro…
A water molecule is roughly 3Å (I remembered this!). An Å is 10^-10m (I remembered this too!) How big is a cell? (I didn’t remember this, if I ever knew!) 10μ is too small and 100μ is too big (although for a Fermi estimate, but might be reasonable).
So call it 30μ, i.e. 3*10^-5. Then the ratio of linear dimensions is 10^5, or volumetrically 10^15. But water isn’t the whole of the cell, so less than that. Maybe 10^14. This is larger than most numbers I found on the web, but not way off.
Several tweeps did estimates based on total mass of human body divided by the number of cells, and came up with similar numbers. I wouldn’t have thought of that approach!
I think my original guess was dumb in an interesting way. 10^9 is the cube of only 10^3. Would it be reasonable for a cell to be 10^3 water molecules across? If you think about all the stuff that’s crammed into a cell, made of proteins, and proteins are WAY bigger—no, not 10^3.
The lesson for me is that cubing numbers makes them grow faster than I realized at a gut level. “Polynomial algorithms are fast!” is not so true for O(n^3).
Apparently there are on the order of 10^8 protein molecules per cell, which sounds like an awful lot until you take the cube root, to get a few hundred, which seems plausible if you think of all the organelles, made of protein, that have to fit in there.
