A favorite argument of creationists against the abiotic origin of life is the unlikeliness of complex biomolecules assembling at random out of base materials. They frequently focus on proteins and give the example of a 100 amino acid protein. They way they present it, you have 100 amino acids that have to assemble in exactly the right manner to form this protein. Since there are 20 natural amino acids (sort of) that gives 20^100 possible combinations. That's 1.26 * 1 with a hundred and thirty zeros behind it. 1.26E130 is a lot of combinations. If you tried one combination per second, you'd be checking them for about 4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 years. (4*10^123.) Needless to say, this would be a grand blow against the argument for abiotic genesis of life. Except for the false premise.
For each protein, there is only one set of amino acids that works.
This is fairly obviously false. Most proteins have many different forms among a population. In fact, for most proteins, the majority of the amino acids are filler. They help determine the 3d shape of the molecule, but could be replaced by other amino acids. In fact, the active sites on a protein (which are more picky, but still not entirely static) are only a small segment of the total amino acids in a given protein.
(Also, you wouldn't have to use all 20 amino acids for your initial form. After all, most life uses 20 amino acids, and there are rather a lot more possible amino acids out there, and working from the assumption that the origin of life required the presence of pre-built proteins, all sorts of other amino acids would have been present in the potential mix. Many wouldn't have been included in the end product from blind chance, and once you have a replicator of some sort, other amino acids may have been excluded as more efficient builds popped out. I'll try to do the power of replicators + selection thing later. It might be a while.)
Let's pretend that 20% of our protein is essential to its function. Also, let's keep all 20 amino acids on the table.
That means that we have 20 amino acids and 20 slots to fill. We'll, for the sake of making the math easy, assume that there is only one combination of amino acids that will work to make our protein. Furthermore, we aren't requiring each amino acid to be used, we are just throwing them all into the pool to play with. There are 20^20 combinations of amino acids. That's 1.08*10^24 different combinations. Still a damned big number. But we are talking about a planet. That's a damned big area.
We count small, numerous things like atoms, photons, electrons, molecules, and such in a unit called moles. One mole is close enough to 6.0*10^23 objects. This number is very very large, but then the things we talk about in moles are very very very small. A mole of Hydrogen molecules (H2) weighs about 2 grams. Amino acids are a good deal larger than a pair of hydrogen atoms though, with an average weight of 145 g per mole (as an aside, we have a special name for a mole of generic photons. An einstein. Not important, but fun.)
If we take one mole of each of our 20 amino acids (that's about 3 kg, or one small lean cat in a blender worth of amino acids. Not much for a place the size of a planet, but enough to demonstrate my point.) and let them combine in sets of 20 at a rate of 1 time per year per molecule (I just want to give them a fair shake, reaction rates are usually much higher.) That's 1.08*10^24/6.02*10^23 or 174.8 years. The Earth finished coalescing about 4.5-5 billion years ago, we'll say 4.5. We keep finding earlier and earlier signs of life, down to something like 4.2 or 4.3 billion years ago now. Worst case scenario, that is .2 billion years. or 200,000,000 years. Let's say that things were too busy for the first hundred million of those years what with the cooling down of the crust and the rocks from space mixing things up energetically, that means we only have time for about our molecule to pop up 500,000 times. Assuming that in all world, there is only one mole of each amino acid in conditions that would allow them to combine. (This goes equally well for other complex biomolecules, and in most cases, requiring that 20% be exactly right? Overkill.)
(Note: the evidence on the exact timing of the origin of life is still coming in. I've heard everything from 3.5 bya (those nice Australian rocks) to 4.3 bya which on further consideration seems like a rough time to come about, what with the space rocks falling on the planet like burny explody rain. So if we take the 3.5 bya date and compare it to the end of the early bombardment (approximately 3.8-3.9 bya) we still have a lot of time on our hands.
*edit* My brother pointed out that I was off by a power of ten on the size of a mole. It is 10^23 not 10^22. So some numbers got smaller (number of years per successful active site) and some got bigger (number of times the protein could have happened in 100,000,000 years.) Thanks Lloyd.
*edit* Fixed some spacing and spelling errors, clarified a point or two, added more asides. There's always more asides. Kept the cat.
