In a paper titled “Autocatalytic Sets of Proteins” [9
], Kauffman has proposed a theory of peptide self-organization that specifically excludes residue-by-residue recognition. The theory is mathematical in nature, but I will try to explain the central idea without going into mathematical detail. Kauffman envisages a system in which the input consists of an aqueous solution of a mixture of amino acids. He assumes that amino acids are capable of reacting together spontaneously to form peptides and that peptides can undergo spontaneous hydrolysis at any internal amide bond. Kauffman also assumes that there is a small probability, P
, that a randomly chosen peptide will catalyze the ligation of any two other randomly chosen peptides. He next considers how likely it is that a randomly chosen set of peptides of length M
can be formed from monomers and arranged to yield a closed cycle, where closure means that each peptide catalyzes the formation of the next peptide in the cycle from one or more pairs of smaller peptides. Closure, importantly, also requires that the peptides of the cycle and their subsequences collectively catalyze the specific synthesis of the components of the cycle from amino acids.
It is obvious that if P is small, the probability of closing the cycle with a randomly chosen set of peptides must be very small, and gets smaller as the number of peptides in the cycle increases. Nonetheless, Kauffman shows that as M gets larger, the number of possible choices of random sets of peptides increases faster than the probability decreases that any one such set will form a closed cycle. Consequently, as M increases, it must eventually reach a value for which the existence of a closed cycle is virtually certain. This proof establishes that, given any value of P, it is always possible to write down on paper a cycle of peptides that is closed in the sense envisaged by Kauffman. The minimum value of M required to make the existence of a closed cycle probable, of course, depends on the assumed value of P, and would also depend on the number of different amino acids in the mixture. Kauffman assumes throughout his illustrative examples that there are just two amino acids, A and B, but the theory could be generalized to mixtures of an arbitrary number of amino acids.
Kaufmann takes it for granted that if it is possible to write down on paper a closed peptide cycle and a set of catalyzed ligations leading from monomeric amino acids to the peptides of the cycle, then that cycle would self-organize spontaneously and come to dominate the chemistry of a reaction system. This, as I will discuss below, is unlikely because peptide molecules do not have the properties that Kauffman assigns to them. I will illustrate the difficulties in the context of the system of two amino acids, A and B, but I have also explored a number of alternative systems with different numbers of amino acids or with inputs of random families of short peptides, and I find that they all encounter similar or more severe difficulties. Before beginning the discussion of the core of the theoretical argument, it is necessary to clear up a few misunderstandings concerning the thermodynamics of peptide bond formation.
Kauffman assumes that, in sufficiently concentrated solution, the naturally occurring amino acids or some subset of them would condense spontaneously to form a mixture of long peptides in substantial yield. In practice, this would not happen. The mistaken conclusion arises in part from assuming a value of 1.2 kcal/mol for the free energy of hydrolysis of a peptide bond, rather than a value of about 2.4 kcal/mol, as suggested by recent experiments [24
]. A more serious misunderstanding concerns the effect on peptide bond formation of replacing a 1 M solution of a single amino acid by a solution of a mixture of amino acids. Kaufmann's conclusions would only be true if each amino acid in the mixture was present at a concentration of 1 M. If the total concentrations of the different amino acids sums to 1 M, as is assumed in his model, the replacement of a single amino acid by a mixture of amino acids would not result in a substantial increase in the amounts of long peptides formed.
These misunderstandings are not fatal for the theory, but they do require a reformulation of the proposed experiment. The reaction mixture must contain, in addition to amino acids, a coupling agent that provides the free energy needed to drive peptide bond formation. This does not affect the mathematical argument, but adds to the difficulty of proposing a relevant prebiotic system to which the mathematical treatment might apply. However, similar difficulty arises for all theories of the origin of life that involve the formation of polypeptides or polynucleotides. It could only be avoided by proposing a series of monomers, such as aminoaldehydes, that polymerize spontaneously, but the difficulty of finding a prebiotic synthesis of suitable monomers then becomes severe.
One can restate Kauffman's claim simply as follows: if a solution containing two amino acids—for example a mixture of l
-arginine and l
-glutamic acid or of l
-alanine and l
-histidine—is allowed to reach a steady state in which spontaneous or peptide-catalyzed hydrolysis of pre-existing peptide bonds is balanced by the uphill formation of new peptide bonds, a cycle involving peptides of substantial length will come to dominate the chemistry of the solution. The calculated length of the peptide constituents of the cycle, of course, depends on the assumed value of P
, the probability that a randomly chosen triplet of peptides is a “catalytic triplet,” and on a number of other details of the model. Kauffman suggests that a value of P
equal to or greater than 10−9
is likely and that a value of M
no greater than 13 would then follow. Here I will discuss the likelihood that a cyclic steady state of this kind could be stable, but I will not attempt the much more difficult task of discussing the way in which a cycle of this kind might become established. I will assume that P
and that M
is consequently 10, as suggested in Table 2 of Kauffman's paper [9
Ghadiri and his coworkers have demonstrated experimentally that peptide cycles of the type envisaged in Kauffman's theory are possible. They first showed that peptides of length 32 that have been carefully designed to self-associate to form stable coiled-coils will facilitate the ligation of their N-terminal and C-terminal subsequences. This shows that the self-replication of peptides is possible [25
]. In later work they demonstrated the self-organization of networks of ligation reactions when more than two carefully designed input peptides are used [26
]. These findings, however, cannot support Kauffman's theory unless the prebiotic synthesis of the specific 15mer and 17mer input peptides from monomeric amino acids can be explained. Otherwise, Ghadiri's experiments illustrate “intelligent design” of input peptides, not spontaneous self-organization of polymerizing amino acids. This takes us to the core of the problem: do sets of peptides of length approximately ten exist that have the ability to constitute a cycle and, even more importantly, could they and their subsequences specifically catalyze their own formation from a mixture of amino acids?
Both explicit and implicit assumptions of the peptide cycle theory present difficulties. The most obvious concerns the assumed value of P, coupled with the assumed specificity of the ligation reactions. In the illustrative example, P is explicitly assumed to have a value in the range of 10−6–10−9 for catalyzed ligations, and it is implicitly assumed that catalysis is negligible for ligation reactions that are not involved in the cycle. Sufficiently efficient catalysis could possibly be demonstrated for peptides rich in histidine, for example, because histidine is an imidazole derivative and imidazole derivatives are often excellent general acid–base catalysts. In fact, any peptide containing enough histidine residues might catalyze indiscriminate peptide ligation, so P could approach unity. In that case, Kauffman's criteria would be met because any set of two or more peptides of length M containing histidine could be synthesized from amino acids and written as a closed cycle. However catalysis of this kind would increase the rate at which all peptides accumulate, but would not lead to self-organization. Instead, it would support a faster synthesis of a complex, nonorganized mixture of peptides. Clearly, self-organization requires catalysis that is not only sufficiently efficient but also sufficiently sequence-specific.
The catalytic properties of enzymes are remarkable. They not only accelerate reaction rates by many orders of magnitude, but they also discriminate between potential substrates that differ very slightly in structure. Would one expect similar discrimination in the catalytic potential of peptides of length ten or less? The answer is clearly “no,” and it is this conclusion that ultimately undermines the peptide cycle theory. One must therefore consider the discrimination that would be needed to make the cycle theory plausible and then explain why short peptides are extremely unlikely to exhibit the necessary catalytic specificities.
I take as an example a peptide cycle that is composed of five decamers because this seems to be the type of cycle that Kauffman envisages. Then the complete self-organized system for the operation of the cycle and the synthesis of its constituents from monomeric amino acids can only include the five decamer sequences, ten nonamer subsequences, 15 octamer sub-sequences, and so on for all subsequences down to the dimers. The task that this set of potential catalysts must achieve, in addition to the operation of the cycle, is the synthesis of the 45 specific peptide bonds needed to create a set of five decamers of the required sequences. The side reactions that must be avoided or at least minimized are all ligation reactions that lead to products outside the cycle. What kind of peptides could have such remarkable catalytic specificity?
The specificity of protein catalysis is dependent on the stable three-dimensional structures of enzymes and enzyme-substrate complexes. Highly specific catalytic activity could only be expected from short peptides if they, too, adopted stable structures either alone or in association with potential substrates. In fact, short peptides rarely form stable structures, and when they do, the structures are only marginally stable. The synthesis of a decapeptide that would catalyze the ligation in the correct order of two particular pentapeptides out of a mixture of ten pentapeptides that are required to form the five cycle components, while failing to bring about any of the other possible ligations, would present an extremely difficult challenge to peptide chemistry. It seems certain that the additional requirement that this peptide should also catalyze specifically many of the reactions leading from amino acids to the pentamer precursors of the decamers of the cycle could never be met. Of course, the decamers need not be formed only from pairs of pentamers, but the difficulties are no less severe for more complex synthetic networks.
There are a number of possible ways in which this difficulty might be circumvented, but none seems relevant to the origin of life. Perhaps the members of “catalytic triplets” are not randomly distributed among peptide triplets but are strongly dependent on some generic feature of the sequences. Suppose, for example, that all peptides with a repeating (AB)n (where n = 1, 2, 3, …) sequence catalyze the addition of an A reside to a peptide terminating in B or the addition of a B residue to a peptide terminating in A, but never catalyze the addition of A to A, or B to B. Then alternating AB peptides might indeed come to dominate the reaction products formed from A and B. This does not seem very useful in the context of molecular evolution, nor is it clear that any peptides formed from potentially prebiotic amino acids would show the required specificity. More complex proposals along these lines need to be supported by experimental evidence or compelling theoretical arguments based on the known properties of amino acids and peptides. Claims that they exist cannot be taken seriously without support from experimental or theoretical chemistry.
A different and more interesting class of solutions to the problem might depend on finding very short peptides that adopt stable conformations either through self-association or through association with a structured surface. Recent work on the x-ray structures of amyloids provides a relevant background [27
]. Peptides as short as tetramers, for example the peptide Asn-Asn-Gln-Gln, form long fibrils. These stable structures are formed by the very close packing of pairs of identical ß sheets. The sheets associate together along the fiber axis by hydrogen bonding. There is already evidence that amyloid fibrils formed by longer peptides will catalyze the ligation of subsequence peptides to form more of the full-length peptide, a form of self-replication [28
]. It is not impossible that some amyloid fiber based on a very short peptide, say a tetramer, would catalyze its own extension from a mixture of activated amino acids. Even if such systems exist, their relevance to the origin of life is unclear. It is unlikely, therefore, that Kauffman's theory describes any system relevant to the origin of life.