Both (ID) Intelligent Designer supporters and creationists are prone to use an arbitrary length of protein and calculate a probability of it happening at random. They use what appears to be a reasonable residue length but they forget that “protein” is not a measure of length but the term used for these polypeptides that we find in living things. Their mathematics is usually the number of amino acids in life today (20) raised to the power of the residue length. All very reasonable sounding if we ignore the probability of occurrence of each residue. As an added bonus they tally up the total number of proteins in a modern cell to come up with an even bigger number. It seems to be a competition to find the most improbable number with a race to get past Dembski’s Universal Probability Bound which is about 1 in 10150 but equally the probability of the sequence of heads or tails information content of a bag of 500 coins being shoved into a coin counter at random is also 1 in 10150 so you have to be careful how you use this number.
They don’t bother trying to use the (approx) 30,000 amino acid Titin and they don’t try using the Trp-cage which “is a 20-residue miniprotein, which is believed to be the fastest folder known so far.” ? http://www.pnas.org/content/100/23/13280
Titin would be silly to use (it is made up of many protein domains so to stretch the ID argument they would have to calculate the probability of the protein domains) but the 20 residues of the Trp-gage means their maths won’t work out too well. That’s the smallest we know of – it is possible there are others in nature that are smaller.
As proteins are a polypeptide that are formed from a nucleic acid using a spontaneous chemical action their calculating the probability of an arbitrary length protein without calculating the probability of the nucleic acid makes their calculation pointless other than telling us that life probably didn’t form that way i.e. 300 residue polypeptides did not spontaneously pop into existence at random.
What ID and creationists hope to show is a gap that a random process with natural selection can’t cross. So the question is – are there smaller functional polypeptides to fill this gap ? Yes there is; a “designed molecule” (called CLN025) that is a 10 amino acids long seems to be stable – http://pubs.acs.org/doi/pdf/10.1021/ja8030533 I know the ID supporters will leap on “designed molecule” like dogs to a bone but using the same calculation of random probability that ID supporters use for CLN025 is showing that the problem landscape isn’t as vast as ID people make it out to be. Given this was derived from another 10 residue protein called Chignolin what this work is doing is showing that rather than being a irreducible gap to leap to modern life length proteins there is in all probability a continuum of proteins and functionality. Thus it is reasonable to say that early life forms could have spontaneously formed and co-evolved functional polypeptides that we would reasonably call proteins and it is unreasonable to use the ID/irreducible complex argument that proteins must be better than ‘x’ length of residues.