But you can’t just extrapolate like that from one function to another. Some functional sequences are extremely abundant in sequence space, some are much more rare. In fact on this very website in another thread we have Bill Cole say:
“The evolutionists smoke and mirrors game is to show a single protein and say that is representative of all proteins.”
We noted the irony there, I will do so again here.
The total sequence space for a protein 70 amino acids in length is approximately 10^91. That means there are more functional cytochrome c sequences(of any size), than there are possible sequences of L=70.
So of course it matters. But obviously not every sequence in that L=70 space will then be a cytochrome c, that doesn’t follow. But it does highlight an issue with looking exclusively at sequence space of a given length. Which I will try to highlight below. It also highlights an issue with these estimates for the total number of functional sequences, as they are based on extrapolations from known functional proteins.
So the core of the protein may be the same in both proteins. and even if not we are still talking about 70 aa compare with 100. so i dont think that it will change the chance so much. remember that a tipical protein is much longer than 100 aa.
This is where we run into an issue with looking exclusively at proteins of some specific length, like 100 amino acids.
If there are 10^93 functional cytochrome cs, and we restrict sequence space to sequences of (say) length 80, then approximately one in every ten million sequences could be a functional cytochrome c.
Why?
Sequence space for L=100 is approximately 10^130. 10^130/10^93 = 10^37
So, the odds of finding a functional cytochrome c just by arbitrarily picking a 100 aa sequence is approximately 1 in 10^37. That’s the number you came up with above, for 100 aa space.
But what happens for 80 aa space?
Sequence space for L=80 is approximately 10^104. 10^104/10^93 = 10^7.
So moving from 100 amino acid to 80 amino acid sequence space potentially increases the odds of finding a functional cytochrome c by thirty orders of magnitude.
Moving down to 70 amino acid sequence space we get total sequence space of approximately 10^91. That’s FEWER sequences than there are total cytochrome cs. If we just looked exclusively at 70 aa space we would have to paradoxically conclude all sequences in 70 aa space are functional cytochrome cs. That obivously can’t be the case.
Now, the problem here is that we don’t know how functional cytochromes are distributed in sequences space in relation to size. It could be that most of the functional cytochrome cs are found in the 80-90 range, or the 90-100 range, or 100-120, or the 60-70 range. We simply don’t know, so you simply cannot pick a length, calculate the total size of sequence space, and then divide that space by the estimated total number of functional cytochromes to get a probability of obtaining one. It is logically not possible when you don’t know the relationship between size and density of function.