I see long-time commenter at Uncommon Descent, Mung, in a thread entitled Backwards eye wiring? Lee Spetner comments, asks:
How do you calculate the size of amino acid sequence space?
As this seems somewhat off-topic there, I thought I’d attempt to answer Mung’s question. I’ll try and be brief. The two most fascinating biochemicals are nucleic acids (RNA and DNA) and proteins. Proteins seem ubiquitous in cellular systems; they function as catalysts (enzymes), structural elements (keratin, collagen), signal molecules (hormones, pheromones), binding agents (antibodies). Proteins are linear sequences of amino acids joined by a condensation (called so because a molecule of water is lost) reaction forming a peptide bond. There are twenty-one amino-acids found in eukaryotes and twenty of them are directly represented in the genetic code. The special case is selenocysteine which is coded indirectly and I’ll leave that out of the calculation for the sake of simplicity.
So what number of different amino acid sequences could theoretically exist, given twenty possibilities for each aa in the polymer. I guess we shouldn’t count twenty monomers. For dimers, there are 400 possibilities. For trimers, we have have 8,000 and so on. The general formula for the number of theoretically possible different protein sequences of length 
is 
. So the answer for all possible sequences is the sum of this calculation from 
to, well, what? There are some very large proteins; titin being the largest known at around 30,000 aa’s. So I guess we should sum at least to that number.
This is a very big number indeed! I leave it as an exercise for the reader to try representing the number that results when taking the upper limit of as 30,000. 🙂
Now I’ve answered Mung’s question, would he like to enlarge on what it signifies?
ETA categories and remove tautology
ETA 2 correction not 
(hat tip Joe Felsenstein)
You have failed to show the arguments fail to accomplish the task
Computers depend on electricity. That doesn’t mean that computers are only electricity.
No but the difference is we can directly see the non-electrical components of your computer. There are no nonphysical or nonchemical cellular components. What now, are you going to try to save face by insinuating there’s invisible and immeasurable cellular components?
If you had provided a reference to where “science” had been done that determined that nature cannot produce “codes” then perhaps your words would have had meaning. But you didn’t. And they don’t.
Conclusion: Claim unproven.
LoL! Where is your science that shows mother nature can produce codes? There isn’t any so you don’t even have a claim.
How do you know that there aren’t any non-physical and nonchemical cellular components? The genetic code is nonchemical- it is physical but neither physics nor chemistry can explain it. The same goes for splicing and editing.
The difficulty in applying these large number problems is like asking “how exceptional is a Rube Goldberg machine or a Lock-and-Key system”.
There are an infinite number of ways to make Rube Golberg machines and Lock-and-Key systems. But that doesn’t make their existence highly likely. We know intuitively their synthesis without something akin to intelligent direction is hard to believe.
Some ID proponents (myself included) frame the Origin and Evolution of Life in terms analogous to the emergence of Rube Goldberg machines.
A Rube Goldberg machine can be very complex with many parts or somewhat simple. Biological systems, especially Eukaryotic animals are far more complex than is needed for mere reproduction. Darwin was horrified at the Peacock’s tail because it had the sort of excesses that were not consistent with pure survival but had lots of extravagance which one would expect Nature to select against.
So, back to the question of the amino acid sequence. There are systems in biology or chemistry that can be implemented with few parts and low specificity. By “specificity” I mean how exactly a part must be in order to be part of a system. A 30 character password for a login/password system is relatively high in specificity compared to a 2 character password.
There are systems that require a highly specified set of proteins to interact. If a there is a 30,000 amino acid protein, it has a space of 20^30,000 possible configurations. But it doesn’t mean all 30,000 have to be exactly specified for the protein to work in a system. It could be that the specificity might be that 20^1000 out of the 20^30000 will be adequately specific to work. In fact maybe 10^1000 or some number if we choose a smaller amino acid set than the standard 20.
But 10^1000 is still a huge number. Even 10^77 is a huge number (one that Doug Axe often uses).
But it is not just getting a single protein that is in question. Usually it’s many. For example we have transgenic man-made bacteria with human insulin. A human insulin is about 400 amino acids long. It’s amino acid space is 20^400, but even if we modestly assume it has some specificity of 10^100, that’s still a big number. But “having an insulin does not an insulin regulated metabolism make”. One needs additional thing like tyrosine kinase receptors, a means of regulating the insulin without killing the organism, etc.
The transgenic bacteria were intelligently designed with this human insulin molecule, but no one expects them to magically regulate their metabolism via insulin like we do. The probability calculation for a “functional” insulin is a bit meaningless if one solely looks at the number of amino acid residues needed to make a functional insulin if there isn’t the requisite machinery to utilize it. So even given that a transgenic bacteria has a head start with a proto-functional insulin, it still is a long way from being a functional insulin if the rest of the Rube Gold machine isn’t in place to utilize it.
The calculations should be approached more like calculating the improbability of the emergence of a Rube Goldberg machine of comparable complexity. No one in the ID community bothers to approach the question this way. I’ve dabbled in it but nothing rigorous.
From my viewpoint, I don’t think one needs to be hyper-rigorous to establish that biological organisms are an exceptional chemical phenomenon. I think living things are exceptional enough to warrant my belief in the miracle of life.
The problem with defining “functional” in protein space isn’t just about catalytic ability. It may be that the glyco protein complexes and the epi-proteome have some significance in all this, and that is some a reaching future research topic for the biological community.
You got me there mate. I admit, I can’t see the invisible or feel the weightless. But why stop at cells?
Maybe the keys to my apartment have nonphysical components too?
It is both. The functioning of the code is through the translation system, which begins with aminoacylation (a chemical reaction) of tRNA by aminoacyl-tRNA-synthetase.
Complementary base-pairing between mRNA and tRNA through the codon-anticodon binding is chemical. The reaction catalyzed by the ribosome is called a condensation reaction, the product is a peptide bond and water.
You mean it’s origin? If so that’s merely question-begging. If you mean it’s actual functioning in life, you’re just plainly wrong.
Same as above.
Has anyone ever said that biology is simple?
Paul Davies suggested simplicity as a possibility to explain Specified Complexity (his definition of SC, not Dembski’s). What I think he meant was that our perception of complexity was an accident of our perception. The book he wrote was “Fifth Miracle”.
I think the OOL problem is like the Rube Goldberg complexity problem.
Nothing in physics prevents 5 dominos resting on their edge on a table, but it doesn’t make the configuration highly likely without highly specified boundary conditions (i.e. an intelligent designer controlling orientation, position, velocity, etc.).
OOL has analogous challenges.
Have you any thought how an intelligent designer would or could do that?
But if the universe was full of dominoes and tables, what then?
And it does seem as if the universe is full of the basic building blocks of life as we know it. For example, Iso-propyl cyanide has been detected in a star-forming cloud 27,000 light-years from Earth.
Yes, if by intelligent designer one means a human or a little child or for that matter an adult with physics background. I’ve have an essay on the shelf that goes into the mechanics of this terms of classical coordinates.
X(t)
Y(t)
Z(t)
X'(t)
Y'(t)
Z'(t)
phi(t)
theta(t)
phi'(t)
theta'(t)
I think those are all the boundary coordinates in question. Only a small space of them will permit the domino to be stand on edge.
This has some analogy to amino-acid sequence space of a functioning protein systems. An insulin regulated metabolism is a pretty impressive Rube Goldberg machine.
A single domino would be considered specified. A cascade of such specified dominos in a Rube Goldberg machine could be qualitatively said to evidence “Specified Complexity” in Paul Davies and Leslie Orgel’s informal definition (not Dembski’s).
It doesn’t change the fact the configuration is exceptional. Is there a point you’ll deem a exceptional event miraculous? If not, if never, then even if a miracle happened, you’d never believe God did it. That’s up to you, I respect your freedom to believe or disbelieve whatever you want.
Non-sequitur. The functioning of the code does not explain how it arose via physicochemical processes nor how it is guided by those processes.
OMagain,
The earth is full of the building blocks of Stonehenge. By your “logic” Stonehenge should be considered as a geological formation.
And this thread was going so well. Alan and I having a nice polite conversation.
I vow to try not to be an asshole. (The walto rule.)
You are welcome to think whatever you want.
How has such thinking played out in the past?
I don’t claim it does, so there’s no non-sequitur there.
That is exactly what it explains. The function of the code is the translation system in operation, which is only and entirely a chain of chemical reactions between structurally complementary, electromagnetically reacting molecules.
I don’t claim that this functioning in and of itself explains how the code originated. But that is entirely besides the point I set out to argue for: That when a simple prokaryotic cell divides it “creates” a new life through nothing but physicochemical processes. I have now argued for it, and I have given a reference in support of it from a university-level textbook in molecular cell biology.
Your response has been to either just declare, for no apparent reason, that I’m wrong. Or to somehow insinuate that there’s something “unknown” about cell division which, presumably, you think leaves enough doubt about the point of contention that I cannot claim what I do.
Then I gave an argument by analogy that showed you have no particular reason to think there’s something non-physical or non-chemical about cell division you could also not erect in the same ad-hoc fashion about anything at all. A sort of reductio ad absurdum. You could say the same about a computer. Just because you understand all these things about how computers work doesn’t mean there’s not still some yet-to-be-discovered nonchemical and nonphysical component to computers. But what a silly way to argue. Or to even think. Where does it stop? You could just sit here and declare that nothing at all is EVER sufficiently explained through physics or chemistry, because it’s still concievable there’s some sort of “immaterial” component, or non-lawful behavior associated with it.
Molecules behave differently to stones. By your “logic” there is no difference in behaviour at any scale, which is demonstrably untrue.
What configuration?
stcordova,
I think there are fundamental issues with the ‘God did it’ alternative. If we think a particular configuration cannot arise ‘naturally’, a God might (for argument’s sake) know what configuration would work, but I see a conceptual problem in getting that configuration built out of these highly reactive components. You don’t want the energetic cascade to start working until everything is in place, and it is very hard to stop that happening. As Mike Elzinga repetitiously pointed out here, physics is not scale invariant, and our imaginings of bolting together relatively inert components or program instructions at our scale do not translate to the molecular scale.
One can of course imbue God with whatever properties it takes to overcome this issue – indeed you espouse the view that entire dimorphic populations and ecosystems of working multicellular organisms were assembled quickly enough to prevent thermodynamic gradients being followed in the ‘undesirable’ way. But personally I find that unsatisfactory, and I tend towards the view that whatever probabilistic restrictions there may be were overcome by the number of trials and the total volume of the ‘test-tube’ (which is not restricted to this planet – we simply live where a ‘hit’ occurred). Of course, we have no idea what the probabilities even are. But it’s a reasonably safe bet it is not even remotely deducible from polymer spaces – especially a polymer which, IMO, is a secondary component of Life.
The problem occurs when you try to assert the designer/constructor is less than omnipotent and omniscient.
I’m not sure what it means to say that something is a miracle. If you base it merely on how “unlikely” it is, how could you ever know? Unlikely things happen very rarely, likely things happen often. And there’s an infinity of gradations between the most likely and the least likely to happen. Now you come along and declare that, somewhere around extremely improbable, it shifts from being an unlikely natural thing, to a supernatural and miraculous thing. Where precisely? And more importantly, why? It seems to me you’d have to set up some cut-off line beyond which events that happen are suddenly “miraculous”, but where to put it? It would be totally arbitrary.
The issue isn’t that I can’t imagine discovering some event that I would attribute to the actions of a godlike being. I certainly can. For example if it was discovered that asking a specific god using a specific prayer consistently produced fully regrown limbs from amputees, well above a level expected by chance, then I think the best explanation for that would be that there really was a god (the god being prayed to).
Why is it exceptional, what do you even mean by that? And why does that “exceptionality” require a different kind of explanation?
You are alive and for rather obvious reasons that feels exceptional to you. Great, but so what? Why does that demand a different kind of explanation you would not accept for, say, the Mt. Everest?
Look at it this way. There is only one Mt. Everest in the entire universe. Think about how many atoms Mt. Everest is made of, how they are all arranged exactly the way they are into the shape it has. All it’s cracks, faults, peaks, valleys, whatever countless miniscule surface features, texture, hardness etc. etc. Every cubic millimetre of that entire mountain from it’s core and foundation to it’s surface and peak everywhere in it’s total occupied volume. Made of billions of tonnes of rock, which consists of atoms, incomprehensible numbers of atoms arranged into it’s particular shape and structure. Any one particular atom could be in a different place. Any imaginable different place. But they aren’t, they’re part of the Mt. Everest, and not just arbitrarily, but they each have some particular and exact position. Litterally unique. Chance can’t have produced it, it’s too unlikely.
Are we now to believe the Mt. Everest was intentionally designed. Are we now to believe the universe was made with the specific intent of making the Mt. Everest?
Notice how you can make the exact same argument for anything that exists. Any particular rock, or leaf, or cloud, mountain, body of water, is exactly the way it is. The odds that anything would happen to be exactly like the way it is, sometime before it formed, is incalculably improbable.
Rumraket,
Exceptional means something in many scientific discourses. In the field of mathematics it means sigmas from expectation.
In regards to physical structures exceptional means components (bricks, atoms, whatever) are arranged in a way that not consistent with physical expectation in the face of uncertainty. i.e. 500 fair coins 100% heads, 100 dominos standing on their edge, RNAs floating around after millions of years even though some have half-lives as short as hours in a cytoplasmic type context, DNAs floating around after millions of years even though they have half-lives of 521 years give or take, homochiral amino acids after millions of years even though they have half lives of hundreds to thousands of years.
The 3 chemical classes I listed (RNA, DNA, amino acids) have half lives that point to expected configurations (namely unsuitability for life). If that is the case, life is not expected in general to spontaneously assemble from the non-living state. For that to happen it would be an exceptional event. We know this experimentally since non-living things stay non-living without outside intervention. No known exceptions.
So for life to emerge from an initial condition of non-life, it would be an exceptional vs. ordinary event. You disagree? 🙂
stcordova,
You really would need more information about how long it took, relative to those half-lives, to know how many trials it might take from some starting state. Clearly, there is expected to be some non-equilibrium primordial state towards which and away from which ‘random’ processes were pushing. If they get there, and manage to sustain at least an approximate level of replication, that replication itself forms a hedge against entropy, with exponentially increasing returns in security.
Two more points: a half-life is only a point on a curve, and half-lives are extremely sensitive to the specific environment in which a molecule finds itself. You need to know a lot more about the territory before you can declare it non-navigable on probabilistic grounds.
I didn’t say absolutely non-navigable, it is obviously exceptional. If it weren’t very exceptional we’d have seen an exception by now in our labs.
How exceptional will something have to before one accepts it is a miracle? It’s an educated guess because to solve the problem rigorously one has to be aware of all facets of the universe, maybe certainty beyond Heisenberg to get the exact figure.
It is a relatively known fact we shouldn’t expect DNAs to float around forever. RNA is a brittle molecule. If you need special environmental conditions to preserve RNAs then, that leans more toward an exceptional set of circumstances.
Here are some basics, for starters the temperatures have to be in a relatively narrow range relative to the range of temperatures found in the universe. Most of the matter in the universe (say 99%) is in the plasma state, not solid or liquid state. One needs a few basic chemicals to get things going and that in the right sustained temperature range.
So just for starters, life with an DNA-RNA-protein replication cycle needs an exceptional environment. We don’t expect algorithmically controlled metabolisms to emerge in plasmas in space or in stars.
What I said, I think is well within the scientific mainstream, life is an exceptional phenomenon from typical initial conditions. Maybe there is life throughout the universe, just like there are many buildings in a city. Abundance is not evidence against life’s exceptional properties. It could well-be testament of some extra-ordinary sets of events.
You mean like Spiegelman’s monster? No. But I’m just pointing out, replication is not a panacea for evolution of more deeply integrated Rube Goldberg machinery. Salt crystals replicate. Autocatalytic reactions “replicate” (like the Ghadiri peptides). Doesn’t mean we expect them to have more Rube Goldberg complexity with future replications. If anything, natural selection selects against more complexity.
Even Michael Lynch points out complex replicators (aka multicellular animals) don’t compete well against simpler ones. That principle is extensible to simple replicators, and the Spiegelmann experiment should be informative that the claim you asserted:
is a little suspect as far as evolving more replicators, and is dubious whether the replication can be self-sustaining since one needs a special environment to make it feasible.
Finally, I think many underestimate the importance of the cytoplasmic chemistry in the origin of life. We barely understand the significance of glycoprotein complexes and the difficulty of evolving interactome cascades. When Ventner made artificial life, he had to use pre-existing cytoplasmic machinery. Ventner nor anyone on the planet is able to synthesize a cytoplasm from scratch and put it in the right interactome state. I think the problem of a DNA-RNA-protein replicator requires much more machinery in place simultaneously than you think.
A mere RNA autocatalytic replicator has to have the capacity to evolve. The Spiegelmann monster highlights the problem that simpler replicators are favored in the short term over more complex ones.
Sure, more complex ones will survive in a much more diverse environment if they exist, but selection can’t select toward non-existent complex traits.
Rumraket,
Then you don’t have a point. You lose.
That is only an opinion.
What a joke- molecules make up stones
stcordova,
Sorry, but that is really shaky reasoning! What total volume of reaction mixture, total time, or possible environmental/physico-chemical combinations do you think have been represented by the entirety of OoL research to date, as a proportion of that available on the actual planet (and all other planets in the universe)? And given that a single replicator molecule is all that is fundamentally required, how sensitive do you think techniques would have to be to detect it, compared to the sensitivities available to date?
stcordova,
I addressed exactly that point already; it doesn’t become more forceful on repetition!
[eta: I realise you may not have seen it]
Using your logic, the advent of a being that can perform miracles must be more unlikely than those miracles themselves.
So however unlikely OOL might be, adding another layer that has to be explained makes it more unlikely, not less. So you are not actually helping yourself with these arguments.
stcordova,
In that very specific selective environment. Effectively, Spiegelman’s Monster represents the kind of selective milieu available to parasites, which have all metabolites provided and a premium placed on rapid growth. It’s not a universal situation.
Ah, but if the onlooker only sees the repetition then Sal appears to have made a point that was not rebutted. And, frankly, that’s all they seem to care about – appearances.
That is not true. We have auto catalytic replicators that went nowhere. I mentioned two: Spiegelmann’s monster and the Ghadiri peptide. What you stated was possibly a necessary, but not sufficient condition. I pointed out, simple replicators may not be evolvable to more complex ones anyway!
With respect specifically to RNAs, I’m not saying anything that is outside the mainstream. I cite this paper:
http://www.biologydirect.com/content/7/1/23
The author offers some responses, but the bottom line is that he adds more specialized conditions for the RNA world to remain a viable hypothesis, and more conditions means more exceptional rather than general circumstances.
He even proposes proteins co-evolving with RNAs! Why not also add co-evolving DNAs to boot and add a little more and you have an EVERYTHING-FIRST model, which is indistinguishable from an event of miraculous special creation.
Which is why I asked you “what configuration”. You must have something in mind, or how do you know it’s improbable to the point of near-miracle?
Understood. The behaviour of molecules and stones is identical in all circumstances. Thanks for your input, it’s been most useful.
OMagain,
To be fair he had trouble with water | Ice | Steam.
stcordova,
And therefore don’t count. I was careful about that word fundamentally There are likely to be many false starts, stuttering replicators whose net exponent over the long term was less than 1, even if they copied a couple of times or more. Nonetheless, if all Life descends from a single replicating sequence, that is all that is fundamentally required – that replicating sequence, or one of equivalent capacity. You need to know how improbable that is. And if you had that, or an equivalent, in your reaction mixture, how would you know? Say you have a billion random oligonucleotides, and 8 of them are 3rd generation copies of an exponential replicator, do you think recent techniques are good enough to spot them?
For no particular reason though. The Spiegelman Monster is not strictly a replicator, and it has very particular conditions of ‘life’ that favour shortness. You can’t draw wide-reaching lessons from it.
The evidence says that you and yours have trouble with that.
Wow, OM makes a claim it can’t support, gets exposed and turns into a churl.
Allan Miller,
Allan, your position can’t even get to Spiegelman’s monster. You can’t get molecular replicators capable of Darwinian evolution.
As for probabilities, well seeing that yours doesn’t have any actual evidence nor a methodology, that is all we have to try to judge the claims of your position.
stcordova,
These are not unchallengeable. Also published in Biology Direct, I give you this, which addresses several of these issues in a readable and not entirely serious style, from the title on in.
Claim: The behavior of molecules and rocks are different.
Counter-Claim: What a joke- molecules make up stones
Conclusion: ?????????????
If it truly exponential and unmitigated in ability to grow exponentially, yes, but if prevented from growing exponentially even though it has the capcacity, no.
In any case that doesn’t detract from the point that 1 in a billion is an exceptional configuration. The more trials needed the more exceptional a phenomenon is.
If one grants that, you can’t draw the converse, that longer more complicated replicators will be necessarily favored either.
I don’t think anyone believes one can just have a pot of random RNAs, DNA, and proteins and they’ll spontaneously evolve complex replication cycles. They have to be in an exceptional state to replicate, namely the living state. It’s the Humpty Dumpty problem.
You seem to think the universe can provide enough trials to overcome exceptional odds. Even granting that, the emergence of DNA-RNA-protein replication must proceed from an exceptional set of events. If not all at once, then a series of highly fortuitous events.
I don’t think I’m saying anything that isn’t acknowledged by the OOL community.
Doesn’t get much worse than that — comparing RNA OOL researchers to creationists. Ouch.
Frankie,
Of course it can. Take one Sol Spiegelman. Take one Qbeta bacteriophage … ah, you mean my position can’t account for Sol Spiegelman! Curses! And ID has a precise explanation of the method by which one accounts for Sol Spiegelman! I am indeed undone!
Well, Behe made similar arguments.
Don’t you see how absurd this is? You are willing to grant that life can evolve, but only if what it evolved from is already alive?
And if you did have “a pot of random RNAs, DNA, and proteins” what do you suppose would happen? And say the pot was the size of a planet and you had billions of years? Would nothing at all happen? Literally nothing? Not a single, “interesting” thing in all that time? I’d re-read that Behe court transcript.
Seen any signs of alien life recently? The problem you have is if god made the universe for life, then he’s doing a fairly bad job of it. So far, just the one planet out of billions. And who knows how many more we’ll never even see as they are outside of our light-cone? You think that god created life on Earth? Well, what about the rest of it? Why not there also?
stcordova,
It needs building blocks. Unless you know you are likely to have it, you are not likely to have set the experimental conditions up to allow it. Your original point remains refuted – you think that an equivalent amount of effort has been expended in labs for us to reach the robust conclusion that Life on Earth is ‘exceptional’, which is clearly unsupportable. Or rather, ‘unexceptional’ is anything that occurs at detectable levels within about a couple of swimming pools’ worth of reagents. Most OoL work is involved in establishing plausible parameters for partial systems, not building hopeful crucibles of Living Systems.
No. A winning lottery ticket is ‘exceptional’ according to that, yet it happens most weeks.
You surely haven’t had time to read the whole of the Bernhardt piece? He discusses the direct attack by Kurland. Sure, there are those who deprecate the RNA World. Stop cherry picking! Read both sides.