# Probability of a single protein forming by chance

The amino acids are the building blocks of the proteins right? At each one of these sites, how many possible amino acids could be part of a growing protein? Do you know this from the biology that there are 20 possible protein-forming amino acids. So you’ve got a one in 20 chance at each site. To get two sites, how many possible combinations do you have? 20 x 20 = 400. If then you go to three sites, how many possible combinations? 20 x 20 x 20 = 8000. Now 8000 x 20 = 160,000 and we’re only to four. So there’s a vast number of possibilities. You’ve got a one in twenty times one in twenty times one in twenty times one in twenty, going out however many sites you have for amino acids. So in a chain of amino acids that’s just 10 sites long, you’re already got 20 to the power of 10 possible combinations. That’s 10 trillion possibilities. But most proteins, even modest ones, short proteins are 100 to 150 amino acids. The average-length proteins may be 300 to 400-length amino acids. Can you see what’s going to happen to these exponential numbers as far as the number of possible ways of combining the amino acids? Let’s take a protein of 150 amino acids in length. That’s a very modest, not real big one. We’ll do that same calculation. We’ve got 150 sites with 20 possibilities at each site, 20 to the 150th power. Convert that to base 10, that’s 10 to the 195th power. We can’t even begin to grasp how many combinations that is. You know there’s only 10 to the 80th elementary particles – protons, neutrons, electrons in the whole observable universe. You’re getting some idea of the scope of these numbers.

We know that not every single amino acid combination is functional, but we also know that many of them are, so there’s a big question: If you’re just kind of trying to assess how likely is it that we’d find a protein by chance with all the amino acids in that prebiotic soup interacting with each other for say billions of years – that’ll give it a lot of time – how likely is it that we’d ever get a protein to arise by chance? Imagine you’re looking for red marbles in a jar of blue marbles. To know the odds of finding a red marble, you want to know something about the ratio. Is it 1 out of 1000 or is 500 out of 1000? It makes a difference, doesn’t it? I have a colleague who’s been interested in the whole question of whether or not life could arisen by chance for a long time. His name is Doug Axe. He’s a molecular biologist. He did his Phd at Caltech. He worked for 14 years at Cambridge University and he wanted to find out how common or how rare are the functional sequences of amino acids among the big space of all the possible amino acids there are. And he chose to work on a protein of about 150 amino acids to start to get an answer to this question. Now what he did is he found that there were indeed many combinations that produced functional proteins but he also found out that the ratio was very very small. Essentially what he was asking was this: For every protein that forms a function, how many combinations of amino acids are there? You get the idea he’s trying to get that marbles to marbles ratio. You know this is like the the red marbles we want and the blue ones that we don’t. And he came up with a really amazing number and it’s 10 to the 74th power. Now that seems a little less scary because we just looked at this great big number but this is still an enormously small probability. In other words, if you think of all the amino acids that there could be as a big haystack and you start searching around for the functional ones, the ratio of functional ones to non-functional ones is like 1 to 10 to the 74th. That’s the ratio. So finding a functional protein by chance just on this calculation you can see is going to be easy or hard? Pretty hard.

We’re going to start putting up some numbers on the board. Just to get the amino acids sequenced properly, you’ve got an odds of about 1 in 10 to the 74th.

But there’s other probabilistic hurdles that have to be overcome. If you want to build a protein, we know from chemistry that you have to attach the amino acids together with what’s called a peptide bond. In nature, peptide bonds occur with about a one in two frequency. Half the bonds that form between amino acids are peptide bonds and half aren’t. But if you get any bonds forming that aren’t peptide bonds, you can’t form a protein. To form a protein 150 amino acids long, you’ve got a one in two chance at each site of getting the correct type of linkage. So you’ve got one in two times one in two to the what power? Close to 150. Since we got linkages we have 149 but call it 150. So another huge exponential problem to overcome. It turns out that one in two to the 150th is equal is the same number as 10 to the 45th. Now we’ve got two incredibly improbable things that we’ve got to overcome to build a functional protein by chance alone.

One more problem when you’re building proteins: amino acids come in two flavors – there’s a left-handed flavor and a right-handed flavor. They’re called optical isomers, not flavors, and the left-handed version is the only kind that can be used in building proteins. Get even one right-handed amino acid in there and your protein won’t fold properly. So you got another probabilistic hurdle to overcome. You’ve got a one and two chance at each site again out to the 150th power. 2 to 150th power is 10 to the 45th. The odds of building even a short functional protein by chance alone is…Remember how you do this in math you can add the exponents if you’re multiplying exponential numbers. The number is 164. Can anyone get their mind around a number that big? There’s only 10 to the 80th elementary particles in the entire universe. There’s only 10 to the 16th seconds since the big bang. There’s only 10 to 139th total events since the beginning of the universe. You’re starting to get the understanding of why people are very skeptical that the chance hypothesis is going to do the job. You may have heard just the opposite. Has anyone ever gotten in a discussion with you about the origin of life and said “it happened by chance.” Do you hear that? This happens to me, I”ll be lecturing in hostile university environments and I’ll get done and somebody’s wants to argue with me about the probabilities and I just shut the discussion down because I say no serious scientist thinks this is the way it happened. It’s always going to be more probable that it didn’t happen by chance than it did. And with that kind of reasoning, you realize it’s time to move on and look at some other options.