KeithS has been requesting scientific evidence of a genuine barrier to macroevolution. The following is a condensed, non-technical summary of Dr. Douglas Axe’s paper, The Case Against a Darwinian Origin of Protein Folds. Since (i) proteins are a pervasive feature of living organisms, (ii) new proteins and new protein folds have been continually appearing throughout the four-billion-year history of life on Earth, and (iii) at least some macroevolutionary events must have involved the generation of new protein folds, it follows that if Dr. Axe’s argument is correct and neo-Darwinian processes are incapable of hitting upon new functional protein folds, then there are indeed genuine barriers to macroevolution, in at least some cases. The argument put forward by Dr. Axe is robustly quantifiable, and it is fair to say that Dr. Axe carefully considers the many objections that might be put forward against his argument. If there is a hole in his logic, then I defy KeithS to find it.
Finally I would like to thank Dr. Axe for putting his paper online and making it available for public discussion. The headings below are my own; the text is entirely taken from his paper.
Four decades ago, several scientists suggested that the impossibility of any evolutionary process sampling anything but a miniscule fraction of the possible protein sequences posed a problem for the evolution of new proteins. This potential problem – the sampling problem – was largely ignored, in part because those who raised it had to rely on guesswork to fill some key gaps in their understanding of proteins. The huge advances since that time call for a careful reassessment of the issue they raised. Focusing specifically on the origin of new protein folds, I argue here that the sampling problem remains. The difficulty stems from the fact that new protein functions, when analyzed at the level of new beneficial phenotypes, typically require multiple new protein folds, which in turn require long stretches of new protein sequence. Two conceivable ways for this not to pose an insurmountable barrier to Darwinian searches exist. One is that protein function might generally be largely indifferent to protein sequence. The other is that relatively simple manipulations of existing genes, such as shuffling of genetic modules, might be able to produce the necessary new folds. I argue that these ideas now stand at odds both with known principles of protein structure and with direct experimental evidence. If this is correct, the sampling problem is here to stay, and we should be looking well outside the Darwinian framework for an adequate explanation of fold origins.
Why the origin of new protein folds is a “search problem”
…[T]he origin of protein folds can be framed with complete generality as a search problem. Briefly, because genes encode proteins, any functional problem that can be solved with a suitable protein can be solved with a suitable gene. Therefore any functional challenge that calls for structural innovation may be thought of as posing a search problem where the search space is the set of possible gene sequences and the target is the subset of genes within that space that are suitable for meeting the challenge… The aim here will be to decide whether Darwinian mechanisms (broadly construed) can reasonably be credited with this success.
If we take 300 residues as a typical chain length for functional proteins, then the corresponding set of amino acid sequence possibilities is unimaginably large, having 20^300 (= 10^390) members… Here the point is simply that biological protein sequences are indeed members of astoundingly large sets of sequence possibilities. And by ‘astoundingly large’ we mean much more numerous than any mutation events we might postulate as having produced them. According to one estimate, the maximum number of distinct physical events that could have occurred within the visible universe, including all particles throughout the time since the Big Bang, is 10^150. Since only a minute fraction of these events had anything to do with producing new protein sequences, we can assert with confidence that there is a vast disparity between the number of distinct protein sequences of normal length that are possible, on the one hand, and the number that might have become actual, on the other. In other words, real events have provided only an exceedingly sparse sampling of the whole set of sequence possibilities.
Axe’s metaphor: Searching for a gemstone in the Sahara Desert
We will refer to this as the problem of sparse sampling, or the sampling problem, with the intent of deciding whether or not it really is a problem for the standard evolutionary model. At the very least it raises the important question of how such sparse sampling would uncover so many highly functional protein sequences. To picture the difficulty, imagine being informed that a valuable gemstone was lost somewhere in the Sahara Desert. Without more specific information, any proposal for finding the missing gem would have to come to terms with the vastness of this desert. If only an infinitesimal fraction of the expanse can feasibly be searched, we would judge the odds of success to be infinitesimally small.
What if there’s more than one gemstone?
Evolutionary searches for functional proteins might seem less hopeless in some respects, though. For one, there is a highly many-to-one mapping of protein sequences onto protein functions. This means that vast numbers of comparably valuable targets (protein sequences that are comparably suitable for any particular function) are there to be found. Therefore, while it is effectively impossible to stumble upon a particular 1-in-10^390 protein sequence by chance, the likelihood of stumbling upon a particular protein function by chance will be m-fold higher, where m represents the multiplicity of sequences capable of performing that function…
Why the search space for a protein has to be very large
On the most basic level, it has become clear that protein chains have to be of a certain length in order to fold into stable three-dimensional structures. This requires several dozen amino acid residues in the simplest structures, with more complex structures requiring much longer chains. In addition to this minimal requirement of stability, most folded protein chains perform their functions in physical association with other folded chains . The complexes formed by these associations may have symmetrical structures made by combining identical proteins or asymmetrical ones made by combining different proteins. In either case the associations involve specific inter-protein contacts with extensive interfaces. The need to stabilize these contacts between proteins therefore adds to their size, over and above the need to stabilize the structures of the individual folded chains…
The ATP synthase provides an opportunity at this point to refine the connection between protein size and the sampling problem. Returning to the lost gemstone metaphor, the gem is a new beneficial function that can be provided by a protein or a set of proteins working together, and the desert is the whole space of sequence possibilities within which successful solutions are to be found. Although some of the component proteins that form the ATP synthase are at the small end of the distribution shown in Figure 1 (see Figure 3 legend), none of these performs a useful function in itself. Rather, the function of ATP production requires the whole suite of protein components acting in a properly assembled complex. Consequently, the desert is most precisely thought of as the space of all DNA sequences long enough to encode that full suite. For our purposes, though, it will suffice to picture the space of protein sequences of a length equaling the combined length of the different protein types used to form the working complex (around 2,000 residues for the ATP synthase; see Figure 3 legend).
Two possible “ways out” for neo-Darwinian evolution: either there are lots of gemstones in the desert, or the gemstones are suitably lined up, making them easy to find if the first one is located
Having shown that the problem of sparse sampling is real – meaning that cellular functions require proteins or suites of proteins that are of necessity far too large for the sequence possibilities to have been sampled appreciably – we now turn to the question of whether it is really a problem for neo-Darwinian evolution. Two possibilities for mitigating the problem need to be considered. One of these has been mentioned already. It is the possibility that the multiplicity of sequences capable of performing the requisite functions, m, might be large enough for working sequences to be found by random searches. The second possibility is that functional protein sequences might bear a relationship to one another that greatly facilitates the search. In the desert metaphor, imagine all the different gems being together in close proximity or perhaps lined up along lines of longitude and latitude. In either of these situations, or in others like them, finding the first gem would greatly facilitate finding the others because of the relationship their positions bear to one another…
Why the first neo-Darwinian solution to the sampling problem won’t work
…[W]e need to quantify a boundary value for m, meaning a value which, if exceeded, would solve the whole sampling problem. To get this we begin by estimating the maximum number of opportunities for spontaneous mutations to produce any species-wide trait, meaning a trait which is fixed in the population through natural selection (selective sweep). Bacterial species are most conducive to this because of their large effective population sizes. So let us assume, generously, that an ancient bacterial population sustained a species consisting of 10^10 individuals , passing through 10^4 generations per year. After five billion years, such a species would produce a total of 5×10^23 (=(5×10^9)x(10^4)x(10^10)) cells that happen to avoid the small-scale extinction events that kill most cells irrespective of fitness. These 5×10^23 ‘lucky survivors’ are the cells that are available for spontaneous mutation to accomplish whatever will be accomplished in the species… [A]ny adaptive step that is unlikely to appear in that number of cells is unlikely to have evolved in the entire history of the species.
In real bacterial populations, spontaneous mutations occur in only a small fraction of the lucky survivors (roughly one in 300). As a generous upper limit, we will assume that all lucky survivors happen to receive mutations in portions of the genome that are not constrained by existing functions, making them free to evolve new ones. At most, then, the number of different viable genotypes that could appear within the lucky survivors is equal to their number, which is 5 × 10^23. And again, since many of the genotype differences would not cause distinctly new proteins to be produced, this serves as an upper bound on the number of new protein sequences that a bacterial species may have sampled in search of an adaptive new protein structure.
Let us suppose for a moment, then, that protein sequences that produce new functions by means of new folds are common enough for success to be likely within that number of sampled sequences. Taking a new 300-residue structure as a basis for calculation (I show this to be modest below), we are effectively supposing that the multiplicity factor m introduced in the previous section can be as large as (20^300)/(5×10^23), or 10^366. [Recall that 20^300 is about 10^390 – VJT.] In other words, we are supposing that particular functions requiring a 300-residue structure are realizable through something like 10^366 distinct amino acid sequences. If that were so, what degree of sequence degeneracy would be implied? More specifically, if 1 in 5×10^23 full-length sequences are supposed capable of performing the function in question, then what proportion of the twenty amino acids would have to be suitable on average at any given position? The answer is calculated as the 300th root of 1/(5×10^23), which amounts to about 83%, or 17 of the 20 amino acids. That is, by the current assumption proteins would have to provide the function in question by merely avoiding three or so unacceptable amino acids at each position along their lengths.
No study of real protein functions suggests anything like this degree of indifference to sequence…
The second neo-Darwinian solution: Shortcuts to new folds?
The possibility yet to be examined is that functional protein sequences might bear a relationship to one another that allows spontaneous mutations to discover new functional protein folds much more readily than wholly random sampling would. The simplest way for this to occur would be if all functional sequences, regardless of what their functions are, happen to be much more similar to each other than a pair of random sequences would be. In other words, suppose there were a universal consensus sequence that typified all biological proteins, with functional diversity caused by minor deviations from that consensus. The effect of such a universal correlation between sequence and function would be to concentrate all the useful protein sequences within a tiny region of sequence space, making searches that start in that region much more likely to succeed.
Localized searches of this kind are known to work in some cases… The problem comes when we attempt to generalize this local phenomenon. Although there are definite correlations between the various kinds of functions that proteins perform and the respective fold structures used to perform them, and these structural correlations often imply sequence correlations as well, it is simply not the case that all functional folds or sequences are substantially alike. Consequently, while local searches may explain certain local functional transitions, we are left with the bigger problem of explaining how so many fundamentally new protein structures and functions first appeared.
To get an idea of the scale of this problem, consider that the SCOP classification of protein structures currently has 1,777 different structural categories for protein domains, the basic units of folded protein structure… [N]o model of protein origins can be considered satisfactory without accounting for the origin of this great variety of domain folds.
In fact, although the sampling problem has here been framed in terms of protein chains, it could equally be framed in terms of domains. Since domains are presumed to be the fundamental units of conserved structure in protein evolution , the question of whether functional sequences are confined to a small patch of sequence space is best addressed at the domain level. And it turns out that domain sequences are not confined in this way…
It therefore seems inescapable that considerable distances must be traversed through sequence space in order for new protein folds to be found. Consequently, any shortcut to success, if it exists, must work by traversing those distances more effectively rather than by shortening them.
A third neo-Darwinian possibility: proteins are made up of small reusable modules, which a search can easily discover
The only obvious possibility here is that new folds might be assembled by recombining sections of existing folds [40-42]. If modular assembly of this kind works, it would explain how just one or two gene fusion events might produce a new protein that differs substantially from its ‘parents’ in terms of overall sequence and structure. Of course, probabilistic limitations would need to be addressed before this could be deemed a likely explanation (because precise fusion events are much less likely than point mutations), but the first question to ask is whether the assumed modularity is itself plausible.
To examine this further, we begin by considering what this kind of modularity would require. If it is to be of general use for building up new folds, it seems to require that folds be divisible into more or less self-contained structural components that can be recombined in numerous ways, with each combination having a good chance of producing a well-formed composite structure. Two physical criteria would have to be met for this to be true. First, the sequence specificity for forming these components must be internal to the components themselves (making their structures self-contained), and second, the interactions that hold neighboring components together to form composite structures must be generic in the sense of lacking critical dependence on the particulars of the components.
The immediate problem is that the first criterion tends to be met only at the level of a complete fold – a folding domain. Important structural features are certainly discernible at lower levels, the most ubiquitous of these being the regular chain conformations known as the alpha helix and the beta strand (secondary structure being the term for these repetitive patterns in local chain structure). But these only find stable existence in the context of larger fold structures (tertiary structure) that contain them. That is, the smallest unit of protein structure that forms stably and spontaneously is typically a complete globular assembly with multiple, layered elements of secondary structure. Smaller pieces of structure can have some tendency to form on their own, which is important for triggering the overall folding process , but the highly co-operative nature of protein folding  means that stable structure forms all at once in whole chunks – domains – rather than in small pieces. Consequently, self-contained structural modules only become a reality at the domain level, which makes them unhelpful for explaining new folds at that level…
The binding interfaces by which elements of secondary structure combine to become units of tertiary structure are predominantly sequence dependent, and therefore not generic. This presents a major challenge for the idea of modular assembly of new folds, at least as a general explanation… As we will see next, several studies demonstrate that proteins with substantially different amino acid sequences (roughly 50% amino acid identity or less) fail to show part-for-part structural equivalence even if they are highly similar in terms of overall structure and function. Since the modularity hypothesis assumes a much more demanding sense of structural equivalence (where modules retain their structure even when moved between proteins that differ radically in terms of overall structure and function) the failure of the less demanding sense seems to rule that hypothesis out…
With no discernible shortcut to new protein folds, we conclude that the sampling problem really is a problem for evolutionary accounts of their origins. The final thing to consider is how pervasive this problem is. How often in the history of life would new phenotypes have required new protein folds? Or, narrowing that question, how much structural novelty do metabolic innovations appear to have required in the history of bacteria? Continuing to use protein domains as the basis of analysis, we find that domains tend to be about half the size of complete protein chains (compare Figure 10 to Figure 1), implying that two domains per protein chain is roughly typical. This of course means that the space of sequence possibilities for an average domain, while vast, is nowhere near as vast as the space for an average chain. But as discussed above, the relevant sequence space for evolutionary searches is determined by the combined length of all the new domains needed to produce a new beneficial phenotype…
Summary: the gemstone metaphor revisited
…We have used a picture of gems hidden in a vast desert at various points in our discussion in order to illustrate the challenge. Now that we have estimated the relevant fractions it may be helpful to return to this picture. Imagine that the search for gems is conducted by specifying sample points as mathematically exact geographic coordinate pairs (longitude and latitude). Sampling then consists of determining whether a gemstone rests at any of these specified points. A target the size of a grain of sand amounts to about one part in 10^20 of a search space the size of the Sahara, which is above the feasibility threshold of one part in 5 × 10^23. So under favorable circumstances a Darwinian search would be capable of locating a sand-grain-sized gemstone in a Sahara-sized search space. As mentioned above, the ability to accomplish a search on this scale is clearly of some practical significance.
But as a generator of new protein folds, it turns out to be decidedly insignificant. Extending our desert picture, imagine that the top surface of every grain of sand in the Sahara has a miniature desert of its own resting upon it – one in which the entire Sahara is replicated in minute detail. We may call the sub-microscopic sand in these miniature deserts level-1 sand, referring to the fact that it is one level removed from the real world (where we find level-0 sand). This terminology can be applied to arbitrarily small targets by invoking a succession of levels (along the lines of De Morgan’s memorable recursion of fleas). In terms of this picture, the sampling problem stems from the fact that the targets for locating new protein folds appear to be much smaller than a grain of level-0 sand. For example, the target that must be hit in order to discover one new functional domain fold of typical size is estimated to cover not more than one ten-trillionth of the surface of a single grain of level-1 sand. Under favorable circumstances a Darwinian search will eventually sample the grain of level-0 sand on which the right grain of level-1 sand rests, but even then the odds of sampling that level-1 grain are negligible, to say nothing of the target region on that grain. And the situation rapidly deteriorates when we consider more relevant targets, like beneficial new phenotypes that employ (typically) several new protein structures. In the end, it seems that a search mechanism unable to locate a small patch on a grain of level-14 sand is not apt to provide the explanation of fold origins that we seek.
Clearly, if this conclusion is correct it calls for a serious rethink of how we explain protein origins, and that means a rethink of biological origins as a whole.
Readers will observe that the foregoing argument made by Dr. Axe has nothing to do with the argument made in his and Dr. Ann Gauger’s subsequent paper, The Evolutionary Accessibility of New Enzyme Functions: A Case Study from the Biotin Pathway. Even if the argument in that paper were invalid, as KeithS claims, the above argument would still stand as a genuine barrier to macroevolution.