Friday, January 28, 2005
Orders of MagnitudeMolecular Biology really distorts your sense of numbers.
As a molecular biologist I deal with some truly massive numbers - and some incredibly small ones. Take a few random numbers from my lab book and you'll see a truly mind-boggling range of numbers. Take DNA for example. I was recently extracting some yeast DNA to perform a procedure called a southern blot. Speaking to the colleague who was holding my hand as I performed the procedure for the first time, I questioned how much DNA I would need.
"How much have you got?" he replied
"I've got a couple of hundred microgrammes"
"Blimey, that's shit loads, you'll have no problems".
A microgramme is one millionth of a gramme. I therefore had two hundred millionths of a gramme. That is the most DNA I have ever had, by a long shot. Normally, I regard 100 nanogrammes (100 billionths of a gramme) as loads. When I start a PCR reaction to amplify some DNA of interest, I routinely start with as little as 1 nanogramme (1 billionth of a gramme), yet the machine I use can be seeded with less than a picogramme (1 trilionth of gramme). The total genomic content of brewers yeast is about 0.9 picogramme per cell. In standard index form that's 9 times 10 to the -16 grammes or a 9 with 15 zeros between it and the decimal point.
Take the other extreme. I grow yeast cells overnight in a flask containing 50 millilitres of nutrient broth. I take a tiny pinhead of white, slimy-looking cells and add them to the broth. By the following morning I have a cloudy broth about the consistency of a strong cup of coffee with plenty of milk. If I leave them growing, by the same time the next evening I have a yellowish solution about the same consistency as tomato soup. At this point there are about 300 million individual yeast cells per millilitre. That's about 15 billion in total in a 50 ml flask. In standard index form that's 1.5 times 10 to the 10. Some coworkers use fermenters. They run them for days at a time. The largest fermenters we have on our bench hold about 2 litres. By the end of the experiment they have almost 1 billion cells per millilitre of culture times 2 litres. That's 2 x10^12 cells in total.
In just one lab book I can range from experiments involving numbers to the negative 16th power to numbers with a positve 12th power. That's 28 orders of magnitude in other words the difference between the number 1 and the number 10,000,000,000,000,000,000,000,000,000). With the sole exception perhaps of high energy particle physicists who talk about planck lengths (10^-35 metres) and in the next sentence discuss Giga Electronvolts (10^9), I doubt there are any other scientists or indeed workers whose daily vocabulary encompasses such a wide range of numbers. And where the hell else would one regard 200 millionths of a gramme as "Shitloads"?
Whilst we're on the subject, drug dealers have nothing on biological suppliers when it comes to charging lots of money for a piddling amount. In a recent TV documentary, someone claimed that a gramme of decent cocaine on the street costs about £35. I have no idea how accurate that its, but it basically puts class A drugs in the ballpark of £10's of pounds per gramme. Last week I ordered a special enzyme from a standard biological supplier. It cost the British taxpayer the princely sum of £192. This is sightly above the average cost for this class of enzymes but not so much that I took a sharp intake of breath - unfortunately it was essential that I bought this specific enzyme (I did try to get a cheaper one honest!). For your money I received a tube containing 20 microlitres (that's 20 millionths of a litre or two raindrops) of clear fluid. Assuming that 1 ml of that fluid weighs one gramme (it doesn't since it isn't pure water - but its close enough) that means that a well-known (at least to biologists) supplier of enzymes had just charged me the equivalent of £9,600 per gramme for a clear liquid.
But it gets better - that clear liquid is just glycerol to protect the enzyme when its stored in the freezer. In actual fact, the amount of enzyme (the stuff I actually want) is so small to be almost immeasurable. If I were to remove all of the liquid and weigh the enzyme, the cost for one gramme would, I estimate, exceed the entire federal budget of the United States for a year.
What a shame they can't wrap it in tinfoil and sell it on the street...
PS I would just like to point out that these companies are not duping dumb biologists into paying breathtaking amounts for something that costs pennies to make. The cost of extracting just a few molecules of this stuff, then refining it and testing it is astronomical. These companies make a healthy profit to be sure, but their profit margins are no bigger than any major food or soft drink manufacturer.
FOR YOUR PERUSAL