How Rare Is a Working Protein?

Keefe, Anthony D., and Jack W. Szostak.  “Functional proteins from a random-sequence library.”  Nature 410(6829):715–718.  2001.  A laboratory experiment by Anthony Keefe and Jack Szostak of the Massachusetts General Hospital.  They made a DNA library of 4 × 10¹⁴ independently generated random sequences, converted it by mRNA display into 6 × 10¹² purified, non-redundant proteins each carrying 80 contiguous random amino acids, and passed them over an ATP-agarose column.  Four unrelated protein families came out, and the authors estimate that roughly one in 10¹¹ random proteins has comparable ATP-binding activity.  The article uses it for the measured side of its disagreement about how common a working protein is.  Mirror:  PMC ↩ ↩

1. 1a.

   Section Results, deletion analysis:  “This analysis defines a core domain of 45 amino acids sufficient for ATP-binding.”  The same paragraph reports that affinity falls from a dissociation constant of 100 nM for the whole evolved protein to 5 mM for the 45-residue core, so the flanking residues help even though they are not needed. ↩

2. 1b.

   “Unlike other libraries that have been used in protein selections, this random region is not part of a larger structure that would otherwise tend to constrain or bias the conformation of the resulting proteins.  This library randomly samples the whole of sequence space, rather than the vicinity of a known protein.” ↩

3. 1c.

   “We therefore estimate that roughly 1 in 10¹¹ of all random-sequence proteins have ATP-binding activity comparable to the proteins isolated in this study.”  The paper's closing sentence:  “In conclusion, we suggest that functional proteins are sufficiently common in protein sequence space (roughly 1 in 10¹¹) that they may be discovered by entirely stochastic means, such as presumably operated when proteins were first used by living organisms.  However, this frequency is still low enough to emphasize the magnitude of the problem faced by those attempting de novo protein design.”  The arithmetic is a straight count: four hits in 6 × 10¹² sequences, about 6.7 × 10^-13, multiplied by ten to correct for roughly 10% folding efficiency.  The paper itself supplies the caveats the article gives: only 5–15% of the displayed protein from each winning family was active; the 100 nM K_d protein is a round-18 descendant that went through three rounds of mutagenic PCR; family B folds around a Zn²⁺ ion, and "Zinc was not added to the selection buffer, but is present at about 10 µM in mammalian blood, from which the reticulocyte lysate used for mRNA translation is prepared"; and mRNA display cannot resolve a frequency below about 1 / (library size), that is about 10^-13. ↩ ↩

Axe, Douglas D.  “Estimating the prevalence of protein sequences adopting functional enzyme folds.”  Journal of Molecular Biology 341(5):1295–1315.  2004.  Page 1300:  Axe's own rationale for the destabilised construct.  “The objective here, however, is to introduce a large number of mildly disruptive changes so as to render many side-chains suboptimal throughout the fold.  This is best achieved by introducing many changes together, without intervening selection.”  A laboratory study by Douglas Axe of the Babraham Institute in Cambridge, UK, on how rare working enzyme folds are.  He took one enzyme family, beta-lactamase, started from a weakly functional sequence that kept the fold's pattern of water-loving and water-hating residues, and randomised clusters of ten side-chains in four experiments to see which variants kept some function.  The measured rate was about one in 10⁶⁴ such sequences, and the paper gives a range from one in 10⁷⁷ to one in 10⁵³ for any domain-sized fold, so the article's one-in-10⁷⁷ figure comes from this paper and so does the range that shows how much of it rests on assumptions. ↩ ↩

1. 2a.

   Pages 1310–1311:  From the Discussion, the passage almost nobody quotes.  “A random change to a functional sequence actually has a good chance of leaving function undisturbed if very few positions are affected.  As estimated above, the likelihood of a signature-compliant substitution in the large-domain reference sequence producing a comparably functional variant is about 38%.  Since 70% of the ~1000 possible non-synonymous base changes to the reference coding sequence produce signature-compliant substitutions, about one in four random single-residue changes are functionally neutral.  The proportion would be somewhat lower under conditions requiring a higher level of function (such as those under which neutral drift normally occurs) but not so low as to preclude progressive sequence divergence by gradual accumulation of point mutations.”  Axe's thesis is specifically about the origin of new folds, which is far narrower than what the number is usually quoted for.  The headline figure is multiplied from three factors on p. 1310: his measured 10^-64, a foldability factor of 10^-10 taken from Lau and Dill's theoretical lattice model at "their least stringent folding criterion," and 10^-3 for the share of folds suited to a given task, which Axe introduces with the words "A reasonable estimate of the average proportion suited to a particular task is 0.1%."  So 10^-77 is one measurement times one theoretical number times one stated guess.  The Lau and Dill foldability figure was not checked for this article, and as far as could be established, neither side of the dispute has checked it, which makes it the most load-bearing unexamined input in the argument.  Three different quantities share this paper, 10⁶⁴, 10⁷⁷ and 10⁹⁷, and they are routinely swapped for one another downstream.  Axe states the range himself in the same paragraph:  “the proportion of all sequences of large-domain length that perform the specified function by means of any tertiary fold… is estimated to be in the range of one in 10⁷⁷ to one in 10⁵³.”  Page 1307:  Axe states his own hedges plainly.  “Simplifying assumptions will therefore always be essential for treatments of the spaces corresponding to proteins of biological significance”.  “it seems reasonable to assume that the pass rates of Table 2, when averaged, provide an upper-bound estimate of the true mean pass rate”. ↩

2. 2b.

   Page 1308:  “Reidhaar-Olsen and Sauer estimated the proportion of 92 residue sequences that form a functional λ-repressor fold to be 10^-63.  When scaled according to chain length, this gives 10^-105 as the corresponding proportion for a 153 residue fold…  As they indicated, their assumption of context independence leads to overestimation of the working proportion.”  Axe misspells the name "Reidhaar-Olsen" at this point; his reference 7 spells it correctly.  One paragraph later he writes, of Taylor et al. 2001, that their method "should provide a more accurate estimate than the earlier λ-repressor study."  Both of those sentences are Axe's own, and people who cite Axe routinely ignore both. ↩ ↩ ↩

3. 2c.

   Page 1308:  “To do this, we multiply by 10^-33, the estimated proportion of all open reading frames that encode the large-domain signature (see above, and see Materials and Methods), resulting in a figure of 10^-97.”  The 10^-97 is Axe's estimate for sequences that both carry his enzyme's fold and keep its function, as a share of all 153-residue sequences. ↩

4. 2d.

   Page 1310:  “So, if set S is about one-thousandth the size of set H (as above), then the proportion of all sequences of large-domain length that perform the specified function by means of any tertiary fold (i.e. fall within the dark portion of F) is estimated to be in the range of one in 10⁷⁷ to one in 10⁵³.” ↩

Tian, Pengfei, and Robert B. Best.  “How many protein sequences fold to a given structure?  A coevolutionary analysis.”  Biophysical Journal 113(8):1719–1730.  2017.  A computational study from the Laboratory of Chemical Physics at the US National Institutes of Health.  It fits a coevolutionary statistical model to the natural sequence family of each of ten protein domains, sets a folding cutoff from measured stabilities of mutants, checks the method against a lattice model that can be counted exactly, and estimates how many sequences fold into each structure.  The authors make no design argument;  the article uses their numbers as an independent check on how rare one particular fold is.  Mirror:  PMC ↩

1. 3a.

   Section Abstract:  “On the other hand, the relative sequence capacity, i.e., normalized by the total number of possible sequences, is an extremely tiny number and is strongly anti-correlated with the protein length.  Thus, although there may be more foldable sequences for larger proteins, it will be much harder to find them.” ↩

2. 3b.

   Section Conclusions:  “We find that more recently evolved proteins have higher SC*, which may be an advantage for initial discovery of a folded structure, but that more ancient proteins have a higher absolute SC, suggesting that evolution guides proteins toward more designable structures.” ↩

3. 3c.

   Table 1:  SC* is the share of all sequences of a domain's length that fold to its structure:  Im7 (87 residues) 1.1 × 10^-86;  titin I27 (89) 3.2 × 10^-38;  TNfn3 (90) 6.9 × 10^-39;  PDZ (94) 5.8 × 10^-50;  α-lactalbumin (123) 1.0 × 10^-121;  IFABP (131) 1.1 × 10^-111;  OmpA (171) 2.6 × 10^-126.  The three domains of 56 residues or fewer are left out here because the table's entry for one of them, the WW domain, 2.9 × 10^-24, does not match the 4.5 × 10^-22 the paper's text gives for it. ↩ ↩

Neme, Rafik et al.  “Random sequences are an abundant source of bioactive RNAs or peptides.”  Nature Ecology & Evolution 1:0127.  2017.  A laboratory experiment from Diethard Tautz's group at the Max Planck Institute for Evolutionary Biology.  They expressed a library of random 150-nucleotide inserts in E. coli and tracked each clone's share of the population over repeated growth cycles.  The positive effects it reports were disputed by Knopp and Andersson in 2018;  the article uses it as the best-known claim that random sequence is often bioactive.  Mirror:  PMC ↩

1. 4a.

   Section Abstract:  “Contrary to expectations, we find that random sequences with bioactivity are not rare.  In our experiments we find that up to 25% of the evaluated clones enhance the growth rate of their cells and up to 52% inhibit growth.” ↩

Knopp, Michael et al.  “De novo emergence of peptides that confer antibiotic resistance.”  mBio 10(3):e00837-19.  2019.  A laboratory selection from Dan Andersson's group at Uppsala University.  They expressed 5.82 × 10⁸ fully random peptides of 10 to 50 residues in E. coli and selected on aminoglycoside antibiotics, recovering three short, hydrophobic peptides that raise resistance.  The article uses it as the clearest case of a selectable benefit drawn from fully random sequence, and for what kind of benefit it is.  Mirror:  PMC ↩

1. 5a.

   Section Abstract:  “The peptides confer aminoglycoside resistance by inserting into the bacterial membrane and thereby partly reducing membrane potential and decreasing drug uptake.” ↩

2. 5b.

   Figure 1:  “The five libraries encode peptides comprised of 10 to 50 amino acids, with a total diversity of 5.82 × 10⁸.”  Section Results, Arp1-3 are small, hydrophobic membrane peptides:  “Besides the similarities in length, all peptides had a high content (80 to 86%) of hydrophobic residues”. ↩

Dryden, David T. F. et al.  “How much of protein sequence space has been explored by life on Earth?”  Journal of the Royal Society Interface 5:953–956.  2008.  Section 2, first paragraph:  The lower bound, 4×10²¹ different protein sequences tested since the origin of life, is in the same paragraph.  The paper's 10³⁴ is a generous estimate of all genes that have ever existed.  A short paper by three chemists at the University of Edinburgh that asks how much of all possible protein sequences life could have tried since it began.  It sets generous upper and lower limits for the number of organisms, genome size, mutation rate and amino acid types, and its upper limit is 4 × 10⁴³ sequences explored.  The article uses it as the generous upper bound on what life could have searched, and the paper offers it as an upper bound. ↩ ↩

1. 6a.

   Section 2, second paragraph, and abstract:  “We conclude that rather than life having explored only an infinitesimally small part of sequence space in the last 4 Gyr, it is instead quite plausible for all of functional protein sequence space to have been explored and that furthermore, at the molecular level, there is no role for contingency.”  The conclusion depends on shrinking the space by allowing reduced amino-acid alphabets.  A protein made of three kinds of amino acid is not the thing the dispute is about. ↩

2. 6b.

   Section 3, opening sentence:  The paper cites Axe 2000 and 2004 by name here.  Matlock and Swamidass, whose preprint against Durston's method is weighed in Measuring Biological Information, use the same figure of 2¹⁴⁵, which is 4×10⁴³, and read it the opposite way: "for the current alphabet of 20 amino acids and proteins with 100 or more amino acids, only an infinitesimally small proportion of protein sequences have been explored."  The difference between the two readings is entirely the alphabet-reduction assumption. ↩

Hazen, Robert M. et al.  “Functional information and the emergence of biocomplexity.”  Proceedings of the National Academy of Sciences 104(suppl. 1):8574–8581.  2007.  “In the formalism of Szostak”.  The paper credits the formalism to Szostak, so the definition develops his 2003 Nature proposal rather than coining a new one.  A paper from a December 2006 National Academy of Sciences colloquium on adaptation and complex design, by four authors at the Carnegie Institution, the University of California, Berkeley and the Massachusetts General Hospital.  It defines "functional information" as the negative logarithm of the fraction of all possible configurations that do a stated job at least to a stated degree, and tests the definition on letter sequences, artificial-life genomes and RNA aptamers.  The three conditions drawn from it, set out in the Measuring Biological Information article, are this project's summary of the paper's constraints, not the paper's own numbered list; the paper's explicit triad is n, E_x and M(E_x), stated for a letter-sequence example.  The article uses it as the mainstream definition of information, because it ties information to a stated function. ↩ ↩

1. 7a.

   The Avida figure carries two conditions that are usually dropped: it applies to sequences "with length of a magnitude of ≈10² lines" using "Avida's default set of 26 machine instructions," and the same section reports that the functional fraction "decreases with decreasing sequence length until it reaches zero for populations with sequences of a length of four machine instructions or less."  The aptamer results are Carothers's, restated here:  “They identify 11 distinct classes of GTP-binding RNAs, which are distinguished from each other both by nucleotide sequences (RNA motifs) and secondary stem-loop structures,”.  “a 10-fold increase in GTP binding strength requires ≈10 additional bits of information”.  The paper also warns that its own islands picture is a "visual simplification," since an island "may be more realistically represented by a densely interconnected network that spans all of sequence space." ↩

Durston, Kirk K. et al.  “Measuring the functional sequence complexity of proteins.”  Theoretical Biology and Medical Modelling 4:47.  2007.  “To demonstrate the relevance to functional bioinformatics, a method to measure functional sequence complexity was developed and applied to 35 protein families.”  Table 1 values run from 0 for the random-sequence and polyadenosine controls to 2,416 Fits for influenza PB2, at densities of 1.3 to 4.0 Fits per residue.  A paper by Kirk Durston and three colleagues, published in a peer-reviewed, open-access journal.  It proposes a unit called the Fit, a functional bit, that measures how much a protein family's sequences are constrained, and applies it to 35 protein families.  The article uses it because design arguments rely on this measure, and the paper is a real peer-reviewed journal article rather than a house publication. ↩ ↩

Lo Surdo, Paola et al.  “A novel ADP- and zinc-binding fold from function-directed in vitro evolution.”  Nature Structural & Molecular Biology 11:382–383.  2004.  “The crystal structure reveals a novel alpha/beta fold bound to its ligand, representing both the first protein structure derived from in vitro evolution and the first nucleotide-binding protein stabilized by a zinc ion.”  The structure was solved a second time, by NMR, in Mansy, Sheref S., et al., "Structure and evolutionary analysis of a non-biological ATP-binding protein," Journal of Molecular Biology 371 (2007): 501–513, which reports that "A series of previously described in vitro selection experiments transformed a low-affinity ancestral sequence into a stably folded, high affinity ATP binding protein structure," with twelve mutations separating the ancestor from the optimised protein.  A two-page paper from the Istituto di Ricerche di Biologia Molecolare in Pomezia, Italy, reporting the crystal structure of a randomly generated protein that binds ATP.  The article uses it because the selected protein turned out to be a fold unknown in biology, held together by a zinc ion, which is a folded binding site that came out of random sequences. ↩

Mukhopadhyay, Rajendrani.  “Close to a miracle:  researchers are debating whether function or structure first appeared in primitive peptides.”  ASBMB Today.  American Society for Biochemistry and Molecular Biology.  Sep 23, 2013.  A feature in the members' magazine of the American Society for Biochemistry and Molecular Biology on how the first proteins arose, built on interviews with Dan Tawfik, Michael Hecht, Jeffrey Skolnick, Jack Szostak and Andrei Lupas.  The article uses it for what those researchers said on record.

1. 10a.

   Section Where’s the starting point?:  “Hecht and colleagues made one particular library that contained more than a million polypeptide chains composed of hydrophobic and hydrophilic residues.… The investigators transformed these strains with their peptide library and found that a couple of their polypeptides were able to rescue the E. coli and let them grow on minimal medium.”  "These strains" are E. coli strains with genes for essential functions deleted. ↩

2. 10b.

   Paragraph last:  “Until that happens, the phenomenon of the rise of proteins will remain, as Tawfik says, “something like close to a miracle.””  The sentence is the author's;  the phrase in quotation marks is Tawfik's. ↩

3. 10c.

   Section If you don’t have a driver for functionality, you will not get complexity:  “We were able to select out small, single-domain proteins that did bind ATP.  But they were rare, on the order of one in 10¹¹ sequences,” says Szostak.  “Getting function from randomness is hard.”  Szostak is speaking of his 2001 experiment with Anthony Keefe. ↩

4. 10d.

   Paragraph 3:  “Once you have identified an enzyme that has some weak, promiscuous activity for your target reaction, it’s fairly clear that, if you have mutations at random, you can select and improve this activity by several orders of magnitude,” says Dan Tawfik at the Weizmann Institute in Israel.  “What we lack is a hypothesis for the earlier stages, where you don’t have this spectrum of enzymatic activities, active sites and folds from which selection can identify starting points.  Evolution has this catch-22:  Nothing evolves unless it already exists.” ↩ ↩

Meyer, Stephen C.  Darwin's Doubt: The Explosive Origin of Animal Life and the Case for Intelligent Design.  HarperOne, New York.  Paperback edition.  2014.  A book by Stephen Meyer arguing for intelligent design from the Cambrian explosion.  Its tenth chapter tells the history of protein-rarity experiments from Sauer to Axe.  The article uses it because it quotes the body of Reidhaar-Olson and Sauer's 1990 paper, which has not been read for this article.

1. 11a.

   Chapter 10, The Origin of Genes and Proteins:  “As it turns out, Sauer recognized the potential for misinterpretation of his results.  As he explained in the very paper in which he developed his quantitative estimate of rarity, “this calculation overestimates the number of functional sequences, since changes at individual positions are less likely to be independent of one another as more positions are allowed to vary.””  Meyer's endnote 3 to the chapter gives the source as Reidhaar-Olson and Sauer 1990, page 315. ↩

Reidhaar-Olson, J. F., and R. T. Sauer.  “Functionally acceptable substitutions in two alpha-helical regions of lambda repressor.”  Proteins 7:306–316.  1990.  “has been used to investigate the informational content of 25 residue positions in two alpha-helical regions of the N-terminal domain of lambda repressor.”  A 1990 laboratory study of which amino acid substitutions still give a functional protein, tested at 25 positions in two helical regions of the lambda repressor.  The article uses it because the figure of one in 10⁶³ for 92-residue sequences comes from it, as an extrapolation from 25 tested positions that the authors flag as an overestimate of function.  Spread across 92 positions, 10^-63 means a mean tolerance of about 0.21 per position, roughly four of twenty amino acids accepted per site, which fits the abstract's "wide range in tolerance." ↩

Taylor, Sean V. et al.  “Searching sequence space for protein catalysts.”  Proceedings of the National Academy of Sciences 98:10596–10601.  2001.  Page 10600, section Discussion, third paragraph:  Their own words for the quantity:  “if every position in the protein had been randomized, a library of ≈10²⁴ members would have been needed to obtain AroQ mutases.”  A caution against overstating the point: the number is built by multiplying six separately estimated factors, one of which, a factor of 10⁴ for templating effects, they flag as possibly larger.  The construct is 93 residues of a dimeric helical bundle, so a head-to-head per-residue comparison with the monomeric 92-residue λ-repressor domain is not like for like.  Section final paragraph of the Discussion:  They also call it.  “our estimate of the low frequency of protein catalysts in sequence space”.  A 2001 study from the Swiss Federal Institute of Technology in Zürich on whether enzymes can be found by searching random protein libraries.  The article uses it because the authors' figure of about 10^24 is often read as a measured rarity, when it is really the size of library that a search would need. ↩

1. 13a.

   Section final paragraph of the Discussion:  “Our estimate of the low frequency of protein catalysts in sequence space indicates that it will not be possible to isolate enzymes from unbiased random libraries in a single step.  The required library sizes far exceed what is currently accessible by experiment, even with in vitro methods.  Instead, as in natural evolution, the design of new enzymes will require incremental strategies…”  Read whole, that is a statement that one-step random search fails and stepwise search is the alternative, which is the mainstream position, not a concession to design. ↩

The article's own arithmetic.  0.38 raised to the 153rd power is 10^-64.3, and raised to the 80th power is 10^-33.6, so the 73 residues of difference account for 30.7 orders of magnitude.  0.60¹⁵³ is 10^-33.9, which is 30.3 orders above 0.38¹⁵³.  Taking those 30.7 orders and the 13 orders that rest on estimates, Lau and Dill's 10^-10 and Axe's 10^-3, out of the 66-order gap between 10^-77 and 10^-11 leaves about 22.  Scaling the whole 10^-77 to 80 residues by the ratio of lengths, the way Axe scales other studies on page 1308, gives about 10^-40 and leaves a gap of about 29 orders.  Either way, length explains about half of the disagreement and no more.² ↩

Bloom, Jesse D. et al.  “Protein stability promotes evolvability.”  Proceedings of the National Academy of Sciences 103:5869–5874.  2006.  A laboratory study from Frances Arnold's group at Caltech.  They made random-mutant libraries of a marginally stable and a stabilised version of one enzyme, cytochrome P450 BM3, under identical conditions, and screened 522 mutants of each for folding and activity.  It was not written about Axe;  the article uses it to show how much a parent protein's stability changes its tolerance of mutations.  Mirror:  PMC

1. 15a.

   Section Results:  “The overall mutation rate was 4.5 ± 0.3 nucleotide mutations per gene… As expected, mutants of the stabilized 5H6 protein were more likely than those of the 21B3 protein to fold (61% of 5H6 mutants contained at least half the folded protein of the parent versus 33% for 21B3…”  Table 1:  Table 1 gives 63% of mutations as nonsynonymous and 9% as frameshift or nonsense, so an average mutant carries about three amino-acid changes, and some are truncated. ↩

Axe, Douglas D.  “Correcting four misconceptions about my 2004 article in JMB.”  Biologic Institute, reposted by the Discovery Institute on 3 March 2016.  May 4, 2011.  Douglas Axe's blog reply to the four commonest objections to his 2004 paper, three of them from Arthur Hunt's critique, each answered with a typed-sentence analogy.  The article uses his answer to the objection that he started from a weakened enzyme.

1. 16a.

   Section Objection 3:  “The remedy is to use a different starting sequence.  Specifically, we need the starting sequence to be of the same quality that we intend to require of mutant sequences in order for them to be accepted.  Otherwise the mismatch in quality will skew our results.”  Axe's illustration is a 42-character sentence randomised seven characters at a time:  a section with two typos can be read only because the other 35 characters are perfect, so its tolerance does not carry over to the whole string. ↩

Povolotskaya, Inna S., and Fyodor A. Kondrashov.  “Sequence space and the ongoing expansion of the protein universe.”  Nature 465:922–926.  2010.  A computational study in the journal Nature about how the universe of protein sequences has been expanding over time.  The article uses it because one sentence of its abstract supports both a rarity argument and a plasticity argument, and the article quotes both halves of it. ↩

1. 17a.

   The abstract's final sentence:  “Thus, approximately 3.5 × 10⁹ yr has not been enough to reach the limit of divergent evolution of proteins, and for most proteins the limit of sequence similarity imposed by common function may not exceed that of random sequences.”  Anyone quoting the 98% figure without this sentence is quoting the paper against itself. ↩

Tokuriki, Nobuhiko, and Dan S. Tawfik.  “Protein dynamism and evolvability.”  Science 324:203–207.  2009.  “We surmise that these properties are the foundation stones of protein evolvability,”.  The words "these properties" refer to conformational dynamism and functional promiscuity.  The sentence is a proposal, so it is a legitimate citation for what the mainstream view is and not for a demonstration.  A review that proposes a view rather than reporting a measurement, which its authors frame as "an alternative, 'avant-garde view'."  The article uses it to show what the mainstream position is, that protein folds are not isolated islands, and not as a demonstration that new folds evolve easily. ↩

Axe, Douglas D.  “Extreme functional sensitivity to conservative amino acid changes on enzyme exteriors.”  Journal of Molecular Biology 301(3):585–595.  2000.  A laboratory study by Douglas Axe, then at the MRC Centre for Protein Engineering in Cambridge.  He combined conservative changes to surface residues of two unrelated enzymes, barnase and TEM-1 β-lactamase, each change harmless alone, and found that together they abolished function;  hybrids of two related β-lactamases were also all inactive.  The article uses it as the measured test of whether positions in a protein tolerate change independently of one another.

1. 19a.

   Page 585, section Abstract:  “First, highly conservative replacements of exterior residues, none of which would cause significant functional disruption alone, are combined until roughly one in five have been changed.  This is found to cause complete loss of function in vivo for two unrelated monomeric enzymes:  barnase (a bacterial RNase) and TEM-1 β-lactamase.” ↩

Gauger, Ann K., and Douglas D. Axe.  “The evolutionary accessibility of new enzyme functions: a case study from the biotin pathway.”  BIO-Complexity 2011(1):1–17.  2011.  A laboratory study by two Biologic Institute researchers, published in that institute's own journal.  They tried to give the enzyme Kbl2 the job of its structural relative BioF2 by testing 29 amino-acid changes, and found none that worked.  The article uses it as the design side's experimental case that moving between neighbouring enzyme functions takes many coordinated changes.

1. 20a.

   Page 1, section Abstract:  “After identifying and testing 29 amino-acid changes, we found three groups of active-site positions and one single position where Kbl2 side chains are incompatible with BioF2 function.… We infer from the mutants examined that successful functional conversion would in this case require seven or more nucleotide substitutions.  But evolutionary innovations requiring that many changes would be extraordinarily rare, becoming probable only on timescales much longer than the age of life on earth.” ↩

Hayashi, Yuuki et al.  “Experimental rugged fitness landscape in protein sequence space.”  PLoS ONE 1(1):e96.  2006.  A laboratory evolution experiment from Osaka University.  The authors replaced a domain of a virus coat protein with a random 139-residue segment and ran 20 rounds of random mutation and selection for infectivity, then fitted a model of the fitness landscape to the results.  The article uses it for how far selection carried a random protein and how far it fell short.  Mirror:  PMC

1. 21a.

   Page 5:  “By extrapolation, we estimated that adaptive walking requires a library size of 10⁷⁰ with 35 substitutions to reach comparable fitness.  Such a huge search is impractical and implies that evolution of the wild-type phage must have involved not only random substitutions but also other mechanisms, such as homologous recombination.” ↩

Künzel, Sven et al.  “A reassessment of positive growth effects of expressed random sequence clones in E. coli.”  bioRxiv.  Apr 10, 2026.  A preprint, not peer reviewed, from Diethard Tautz's laboratory at the Max Planck Institute for Evolutionary Biology, the group whose 2017 result it defends.  It reran competitive growth assays with 64 defined random-sequence clones alongside the vector controls its critics had used.  The article uses it for the current state of the dispute over Neme and colleagues' positive effects.

1. 22a.

   Page 1, section Abstract:  “However, these findings have been questioned, regarding potential confounding effects of the clone mixtures and a possibly negatively acting peptide expressed from the cloning vector.… Our results demonstrate that positive growth effects of random sequence clones cannot be explained by clone mixture and vector artifacts alone.” ↩

Tretyachenko, Vyacheslav et al.  “Random protein sequences can form defined secondary structures and are well-tolerated in vivo.”  Scientific Reports 7:15449.  2017.  A combined computational and laboratory study from Klára Hlouchová's group in Prague comparing random, never-selected protein sequences with natural ones for secondary structure, disorder, aggregation and toleration by E. coli.  It selected for no function.  The article uses it for what random sequence is like before any selection.  Mirror:  PMC

1. 23a.

   Section Abstract:  “We found that the overall secondary structure and physicochemical properties of random and biological sequences are very similar.  Moreover, random sequences can be well-tolerated by living cells.” ↩

Futerman, Anthony H.  “Dan Tawfik:  in memoriam.”  Inference: International Review of Science 6(2).  2021.  A memorial essay by a colleague of Tawfik's that describes his last research, on how the first proteins could have arisen from short peptides, and then questions whether chance can account for it.  The article uses it only for what Tawfik was working on.

1. 24a.

   Page 1:  “Dan was focused on this question during the last years of his life.”  "This question" is, in the essay's preceding sentence, how to explain the emergence of functional proteins or protein domains in abiotic scenarios. ↩

Miller, Brian, and Casey Luskin.  “Defending Douglas Axe on the Rarity of Protein Folds.”  Science and Culture Today.  Discovery Institute.  Nov 29, 2023.  The Discovery Institute's restatement, verbatim:  “Axe studied the beta-lactamase enzyme in E. coli and found that the likelihood of a chance sequence of 153 amino acids generating the stable, functional fold needed for the larger domain in that enzyme was as low as 1 in 10⁷⁷.”  Three edits away from Axe's abstract, all consequential: the measured number is 10^-64 and applies to signature-consistent sequences already carrying the fold's hydropathic pattern; "may be as low as" is a bound, not a measurement; and "performing a specific function" has become "functional," which converts a claim about one nominated enzyme activity into a claim about functionality in general.  And, quoting the Discovery Institute's own peer-reviewed paper, verbatim:  “For example, Axe (2000, 2004)'s work on the larger beta-lactamase protein domain indicates that only 1 in 10⁷⁷ sequences are functional — astonishingly rare indeed.”  For fairness, Axe himself reports the range in print, in Douglas D. Axe, "The case against a Darwinian origin of protein folds," BIO-Complexity 2010, no. 1 (2010): 1–12.  “The reported range is one in 10⁷⁷ (based on data from the more complex beta-lactamase fold;  ℓ = 153) to one in 10⁵³ (based on the data from the simpler chorismate mutase fold, adjusted to the same length:  ℓ = 153).”  The compression is downstream of Axe.  A blog post, dated 29 November 2023, by two senior fellows of the Discovery Institute's Center for Science and Culture, Brian Miller and Casey Luskin, defending Douglas Axe's protein-rarity work.  The site, formerly called Evolution News, restates Axe's result more strongly than Axe does, and the article uses it to show how the figure travels into the intelligent-design movement's own writing. ↩

Axe, Douglas D.  “The case against a Darwinian origin of protein folds.”  BIO-Complexity 2010(1):1–12.  2010.  A review by Douglas Axe in the Biologic Institute's own journal, arguing that Darwinian searches cannot find new protein folds.  The article uses it for Axe's own account of where the two ends of his 2004 range come from.

1. 26a.

   Page 6:  “The reported range [25] is one in 10⁷⁷ (based on data from the more complex beta-lactamase fold;  ℓ = 153) to one in 10⁵³ (based on the data from the simpler chorismate mutase fold, adjusted to the same length:  ℓ = 153).” ↩

Meyer, Stephen C.  “The origin of biological information and the higher taxonomic categories.”  Proceedings of the Biological Society of Washington 117(2):213–239.  2004.  A review essay by Stephen Meyer, director of the Discovery Institute's Center for Science and Culture, arguing that the Cambrian animals needed new genes and proteins that mutation and selection could not supply in the time available.  The article uses its summary of Axe 2004, which is the passage Axe's critics answered.

1. 27a.

   Section Novel Genes and Proteins:  “On the basis of these experiments, Axe has estimated the ratio of (a) proteins of typical size (150 residues) that perform a specified function via any folded structure to (b) the whole set of possible amino acids sequences of that size.  Based on his experiments, Axe has estimated his ratio to be 1 to 10⁷⁷.  Thus, the probability of finding a functional protein among the possible amino acid sequences corresponding to a 150-residue protein is similarly 1 in 10⁷⁷.” ↩

Gishlick, Alan et al.  “Meyer's Hopeless Monster.”  The Panda's Thumb.  Aug 24, 2004.  A critical review of a 2004 paper by Stephen Meyer on the origin of biological information, posted on the blog The Panda's Thumb.  The critics of record for Axe 2004 are Gishlick, Matzke and Elsberry, and Arthur Hunt.  It was the first to point out that Axe's paper gives a range, one in 10⁷⁷ to one in 10⁵³, and that Meyer's summary gives only one end.  The article quotes that charge and finds it partly overstated, because the end Meyer gave is the one built on the enzyme he was describing.

1. 28a.

   Section Of Text and Peptides:  “Meyer only reports the lowest extreme.  One in 10⁵³ is still a small number, but Meyer apparently didn't feel comfortable mentioning those 24 orders of magnitude to his reader.” ↩

Hunt, Arthur.  “Axe (2004) and the evolution of enzyme function.”  The Panda's Thumb.  Jan 14, 2007.  “Also, many thanks are due to Douglas Axe, who graciously helped me with early drafts of this essay.”  Axe confirmed the exchange in his 2011 reply: "In August of 2004 I received an email inquiry from plant biologist Art Hunt.  He had written a draft for a blog piece aimed at reviewing a research article of mine…  His summary of the experiments I reported in the JMB paper was largely correct, though his understanding of my analysis was off in several respects" (Axe, Douglas D., "Correcting Four Misconceptions about my 2004 Article in JMB," Biologic Institute, 4 May 2011; reposted by the Discovery Institute, 3 March 2016, at https://scienceandculture.com/2016/03/in_response_to/).  “Axe's work does not extend or narrow the range.”  Axe's 2011 reply answers Hunt's objection to the weakened starting enzyme on its own terms:  the starting sequence must meet the same bar as the mutants, or the untouched positions prop up the randomised cluster and inflate its tolerance.  The stability measurements of Bloom and colleagues in 2006 show how large that propping-up effect is, and they do not settle how far Axe's per-residue figure would move.  A blog essay of 14 January 2007 by the plant biologist Arthur Hunt, the most detailed published critique of Axe 2004.  Its own footnote establishes an unusual provenance: Axe helped with early drafts.  The essay gives the context for the number: published estimates of the density of functional sequences run from about 10^-10 to 10^-63.  The article takes its account of Axe's method from this essay, because the paper itself is closed access. ↩

Matlock, Matthew K., and S. Joshua Swamidass.  “Evolution and Functional Information.”  bioRxiv.  Mar 5, 2017.  A preprint posted to bioRxiv in 2017 that has not been peer reviewed and has no journal version, which is a real limit on its weight.  Both authors work at Washington University School of Medicine.  Its simulations of protein families with no function find that their sequence alignments still score high, and the authors use this to argue that the alignment measure is a poor estimate of functional information.  Swamidass is a computational biologist, an IVP Academic author, a Veritas Forum speaker and the founder of Peaceful Science, which is worth knowing before anyone reads this as an anti-religious argument.  Durston replied to it on 5 April 2017 in Evolution News; the reply, and how the exchange scores, are in Measuring Biological Information.  The article uses it because it is the decisive technical objection to Durston's method. ↩

“Nature, volume 294, issue 5837.”  Nature 294(5837).  Nov 12, 1981.  Page 105:  The page itself states:  “Nature volume 294, page 105 (1981).”  The table of contents of this issue of Nature, dated 12 November 1981, read item by item to test a citation of a Hoyle article.  There is no article by Hoyle in it, and none titled "Hoyle on evolution."  The article uses it to show that the citation to a Hoyle article in this issue is wrong.  The article that occupies page 105 is a news story, not by Hoyle: Vera Rich, "Albanian development: Hoxha looks ahead," Nature 294 (1981): 105, https://www.nature.com/articles/294105a0. ↩

Creation Ministries International.  Hoyle on Origin of Life.  Nov 17, 2011.  Verbatim, the page attributes the figure to:  “—Sir Fred Hoyle, as quoted by Lee Elliot Major, 'Big enough to bury Darwin'.  Guardian (UK) education supplement, Thursday August 23, 2001.”  That Guardian piece is an obituary round-up published three days after Hoyle died on 20 August 2001.  Its sidebar, headed "Hoyleisms: A selection of quotes from the great man," has six pull-quotes; five are unsourced, and the sixth is attributed only to Hoyle's novel Element 79, with no book, paper, page or date attached to any of them.  The Guardian text reads "one to a number with 40,000 naughts after is", a plain typographical error; the CMI version silently corrects it to "after it."  The same Guardian article states Hoyle's conclusion: "Nor did Hoyle think this was a random process.  He argued it was the handiwork of a super-intelligent civilisation wishing to 'seed' planet Earth."  A Creation Ministries International web page, dated 17 November 2011, that attributes the "40,000 noughts" figure to the astronomer Fred Hoyle, but gives as its only source a 2001 Guardian education supplement and no publication by Hoyle.  The article uses it to show that the figure has no traceable origin in Hoyle's own work. ↩

Major, Lee Elliot.  “Big enough to bury Darwin.”  Guardian education supplement.  Aug 23, 2001.  A roughly 700-word obituary feature in the Guardian's education supplement, published three days after Hoyle died on 20 August 2001.  The quotation attributed to Hoyle appears only in an unsourced pull-quote box, not in the body of the piece.  The article uses it because Creation Ministries International sources its Hoyle figure to this piece rather than to Hoyle. ↩

Shapiro, Robert.  Origins: A Skeptic's Guide to the Creation of Life on Earth.  Summit Books, New York.  1986.  Page 127.  A 1986 book by Robert Shapiro that argues for a metabolism-first origin of life throughout.  Shapiro sets out the calculation in order to reject it.  The article uses it as one of two hostile witnesses who set out the same calculation and name its authors. ↩

Kauffman, Stuart A.  At Home in the Universe: The Search for the Laws of Self-Organization and Complexity.  New York: Oxford University Press.  1995.  Chapter 2:  “the authors concede a probability of 1 in 10²⁰.  But now the coup de grace:  to duplicate a bacterium, it would not suffice to create a single enzyme.  Instead, it would be necessary to assemble about 2,000 functioning enzymes.  The odds against this would be 1 in 10²⁰ … or 1 in 10^40,000.”  “Since you are reading this book, and I am writing it, something must be wrong with the argument.”  A general book on self-organisation and complexity by Stuart Kauffman.  In its second chapter he reproduces Robert Shapiro's account of the odds of building a bacterium, names Shapiro as its source, and gives his own verdict, which follows immediately.  The article uses it to show that the calculation is an old one, and that Kauffman himself judged it wrong. ↩

Hoyle, Fred.  “The Universe: Past and Present Reflections.”  Engineering and Science 45(2):8–12.  Nov 1981.  Pages 10–11:  “If amino acids were linked at random, there would be a vast number of arrangements that would be useless in serving the purposes of a living cell.  When you consider that a typical enzyme has a chain of perhaps 200 links and that there are 20 possibilities for each link, it's easy to see that the number of useless arrangements is enormous, more than the number of atoms in all the galaxies visible in the largest telescopes.  This is for one enzyme, and there are upwards of 2000 of them, mainly serving very different purposes.  So how did the situation get to where we find it to be?  This is, as I see it, the biological problem — the information problem.”  Page 11:  His conclusion, p. 11.  “So try as I would, I couldn't convince myself that even the whole universe would be sufficient to find life by random processes — by what are called the blind forces of nature. …  Rather than accept the fantastically small probability of life having arisen through the blind forces of nature, it seemed better to suppose that the origin of life was a deliberate intellectual act.  By 'better' I mean less likely to be wrong.”  An essay by the astronomer Fred Hoyle, published in November 1981 in a Caltech magazine written for general readers.  Hoyle argues that a random assembly of amino acids would almost never give a working enzyme, and that the origin of life was therefore a deliberate intellectual act rather than a product of blind chance.  The article quotes his enzyme passage and his answer to the gradualist view. ↩

1. 36a.

   Page 11:  Hoyle dismissing the gradualist alternative calls it deceitful, but he accepts that the first, simpler enzymes could be found by chance; his objection is to the environment that would have to drive the later changes.  “It's easy to frame a deceitful answer to it. Start with much simpler, much smaller enzymes, which are sufficiently elementary to be discoverable by chance;  then let evolution in some chemical environment cause the simple enzymes to change gradually into the complex ones we have today.  The deceit here comes from omitting to explain what is in the environment that causes such an evolution.” ↩

Parker, Gary.  “The Origin of Life: DNA and Protein.”  Creation: Facts of Life.  Answers in Genesis.  2006.  A creationist article on the origin of life, published by Answers in Genesis in 2006 as part of Creation: Facts of Life.  The same organization's article by David Menton, "The Origin of Life," first published in 1993, gives a different provenance for the Hoyle material: "a recent address at Cal Tech."  Parker gives "'Hoyle on Evolution,' Nature (November 12, 1981)" instead, and the two also disagree about whether the speaker was Hoyle alone or Hoyle with Wickramasinghe.  No Hoyle article appears in the Nature issue that Parker cites, and Hoyle did publish the argument himself, in his 1981 Caltech lecture.  The article uses it because these two sources give incompatible provenances for the same Hoyle material, and a quotation with three provenances has none. ↩

1. 37a.

   Parker's page, verbatim:  “Both were surprised by their results.  Hoyle called himself an agnostic, and, in the same article, Wickramasinghe said he was an atheistic Buddhist who 'was very strongly brainwashed to believe that science cannot be consistent with any kind of deliberate creation.'”  He also states his own purpose plainly:  “not, of course, to suggest that they are creationists who would endorse all my views”.  which is more careful than most uses of this material downstream of him. ↩

Morowitz, Harold J.  “Testimony for the plaintiffs.”  McLean v. Arkansas Board of Education, 494–513.  Dec 1981.  Pages 500–501:  “Q:  Now, you have been explaining why the creation science dual model approach to the teaching of origins of life on this planet is unscientific.  Is there any other aspect of the creation science treatment of the origins of life on this planet that is similarly unscientific?  A:  Well, I find the use of probabilistic arguments to be somewhat deceptive. …  To do the probabilistic calculations, we would have to know all the kinetic and mechanistic details by which the processes have come about…  We are simply lacking the information to do the calculations now, so to present them on the basis of the random model is somewhat deceptive.  Q:  Is it also in your view unscientific?  A:  Since deception is unscientific, the answer to that is yes.”  Morowitz spent his career arguing the opposite of what his number is used for.  His own preface to Energy Flow in Biology (Academic Press, 1968), p. vii, reads: "I have rejected the prebiological notion of 'historical accident' as a kind of know-nothingness which renders further study impossible."  Testimony given for the plaintiffs at the McLean trial in December 1981 by the biophysicist Harold Morowitz, who was asked about creationist probability arguments.  He calls them somewhat deceptive, and says that makes them unscientific.  The article uses it because the one-in-10^339,999,866 figure is attributed to Morowitz, and this testimony shows what he thought of such arguments.  The exchange, from the transcript: ↩

1. 38a.

   The 1-in-10^339,999,866 figure was not computed by Morowitz.  James F. Coppedge did the subtraction, in Evolution:  Possible or Impossible? (Grand Rapids:  Zondervan, 1973), ch. 14, p. 235, and Coppedge's own page says so.  The quoted passage is Coppedge's:  “Under 'equilibrium' conditions (the stable state reached after initial reactions have balanced), the probability of such a fluctuation during earth's history would be 10¹³⁴ in 10^340,000,000 for a minimal cell.  This would be 1 chance in 10^339,999,866.”  His footnote 17 reads:  “Harold J. Morowitz, Energy Flow in Biology (New York:  Academic Press, 1968), p. 99.”  Morowitz's Table 4-14 on that page gives the equilibrium probability of a 10^-14 g cell arising as a thermal fluctuation in an ocean of monomers as 10^-3.4×108⁸ 3.4 × 10⁸ = 340,000,000, and 340,000,000 − 134 = 339,999,866, so the derivation checks exactly.  What Morowitz was calculating is an equilibrium thought experiment: heat a pellet of E. coli to about 10,000 °C to destroy its chemical state, cool it, and ask what fraction of the equilibrium ensemble is alive, a construction meant to show that equilibrium is the wrong frame for thinking about life. ↩

Yockey, Hubert P.  “Dr. Hubert Yockey's answer to FTE amicus brief.”  Kitzmiller v. Dover Area School District (court filing).  Nov 16, 2005.  Yockey is describing the Foundation for Thought and Ethics' misreading of two paragraphs on p. 24 of his own paper, paragraphs he says.  “used sarcasm to point out that the origin of life isn't just building blocks and the laws of physics and chemistry any more than a message in language results from having all the letters of the alphabet and rules of grammar.  (The missing ingredient needed for the origin of living matter is the genome, not Intelligent Design.)”  Note the construction: the passage design advocates quote approvingly is one Yockey wrote sarcastically, and he says so.  He also rejects the FTE's claim that his work.  “suggested how to quantify information in long-chain protein molecules and DNA so that we can identify the patterns characteristic of intelligence,”.  calling it "wrong."  A reply filed in the Kitzmiller v. Dover case by Hubert Yockey, an information theorist, answering an amicus brief from the Foundation for Thought and Ethics.  The Foundation was the publisher of The Mystery of Life's Origin, which is why Yockey was answering it.  The article uses it because Yockey rejects intelligent design in it, and because the same filing limits his earlier endorsement of Thaxton's book. ³⁹: section: numbered objection 1. ↩

1. 39a.

   Section numbered objection 1:  Yockey is describing the Foundation for Thought and Ethics' misreading of two paragraphs on p. 24 of his own paper, paragraphs he says.  “used sarcasm to point out that the origin of life isn't just building blocks and the laws of physics and chemistry any more than a message in language results from having all the letters of the alphabet and rules of grammar.  (The missing ingredient needed for the origin of living matter is the genome, not Intelligent Design.)”  Note the construction: the passage design advocates quote approvingly is one Yockey wrote sarcastically, and he says so.  He also rejects the FTE's claim that his work.  “suggested how to quantify information in long-chain protein molecules and DNA so that we can identify the patterns characteristic of intelligence,”.  calling it "wrong." ↩ ↩

2. 39b.

   Page 5:  “In a letter to Dr. Thaxton dated 13 March 1985, I wrote, 'With regard to Creationism, I have no trouble with the conclusions in your book [The Mystery of Life's Origin, which is primarily about why the chance and self-organization theories of the origin of life are not valid].  They are well reasoned and they are supported by the scientific evidence.'”  The bracketed gloss is Yockey's own, and it is the limit he places on the endorsement.  Anyone citing Yockey against intelligent design owes the reader this letter, and anyone citing the letter owes the reader his repudiation of intelligent design in the same filing. ↩

3. 39c.

   In the filing:  “Whenever I refer to materialism, I am referring to the dialectical materialism of Marxism-Stalinism.”  He goes on to argue that self-organization scenarios.  “are founded on the Marxist-Stalinist philosophical belief, called dialectical materialism, in the 'Law of the Transformation of Quantity into Quality.'”  That is an idiosyncratic and historically contestable framing, and it is why his attacks on "materialism" cannot be read as attacks on naturalism in the ordinary sense. ↩

Morris, Henry M.  “Entropy and Open Systems.”  ICR Impact (40).  Oct 1, 1976.  An essay by Henry Morris, founder and president emeritus of the Institute for Creation Research, in its ICR Impact series, published in October 1976.  It argues that the Second Law of Thermodynamics rules out evolution, and that the usual reply, that the earth is an open system, does not answer the argument.  The article uses it because Morris made this argument the centerpiece of creationist thermodynamics, and because his replacement for the open-system reply is a design argument, not a thermodynamic one. ↩

1. 40a.

   Morris's own restated law, in full:  “If either the information program or the converter mechanism is not available to that 'open' system, it will not increase in order, no matter how much external energy surrounds it,”.  followed by.  “what is the information code that tells primeval random particles how to organize themselves into stars and planets, and what is the conversion mechanism that transforms amoebas into men?”  He closes:  “The only adequate cause of the initial order and complexity of the universe must have been an omniscient Programmer.”  That is a design argument written in thermodynamic vocabulary, not a consequence of the second law, and it should be argued on its own terms. ↩

Bunn, Emory F.  “Evolution and the second law of thermodynamics.”  American Journal of Physics 77:922–925.  2009.  “We conclude that the entropy reduction required for life on Earth is far less than |ΔS_life| ∼ 10⁴⁴ k.”  “If we compare this value with the rate of entropy production due to sunlight in Eq. (3), we find that the second law, in the form of Eq. (1), is satisfied as long as the time required for life to evolve on Earth is at least Δt = … ∼ 10⁷ s, or less than a year.  Life on Earth took four billion years to evolve, so the second law of thermodynamics is safe.”  Bunn's paper is a correction of Styer's, which he says rested on.  “an unjustified and probably incorrect assumption.”  Two physicists arguing about how to do the sum, and both conclude there is no conflict.  A short physics paper by Emory Bunn of the University of Richmond that puts a number on the entropy argument against evolution.  It counts the entropy that sunlight delivers to Earth, compares it with a generous upper bound on the order life needed, and finds the sunlight pays that bill in under a year, while life took four billion years.  It corrects Daniel Styer's 2008 article (American Journal of Physics 76: 1031–1033), and the article uses it as the quantitative answer to the second-law argument.  Mirror:  arXiv ↩

Thaxton, Charles B. et al.  The Mystery of Life's Origin: Reassessing Current Theories.  Philosophical Library, New York.  1984.  Chapter 8:  The passage that opens with the atoms and molecules, quoted in part:  “atoms and molecules… individually obey the laws”.  “In Chapter 7 it has been shown that energy and/or mass flow through a system can constrain it far from equilibrium, resulting in an increase in order.  Thus, it is thermodynamically possible to develop complex living forms, assuming the energy flow through the system can somehow be effective in organizing the simple chemicals into the complex arrangements associated with life.”  “Without a doubt, the atoms and molecules which comprise living cells individually obey the laws of chemistry and physics, including the laws of thermodynamics.  The enigma is the origin of so unlikely an organization of these atoms and molecules.”  Chapter 9:  “We found it to be a reasonable explanation for doing the chemical and thermal entropy work, but clearly inadequate to account for the configurational entropy work of coding (not to mention the sorting and selecting work).  We have noted the need for some sort of coupling mechanism.”  A 1984 book by Charles Thaxton, Walter Bradley and Roger Olsen on the origin of life, which the article calls the founding book of the intelligent design movement on this subject.  Its chapters 7 to 9 ask whether energy flow can do the chemical, thermal and coding work needed to build DNA and protein, and its summary of the three-chapter treatment says it can do the chemical and thermal work but that the coding work needs some sort of coupling mechanism.  In chapter 8 it opens by conceding the physics.  This is the 1984 text; the 2020 revised edition, published by Discovery Institute Press, carries new material by Stephen Meyer, James Tour, Guillermo Gonzalez, Brian Miller and Jonathan Wells, was never obtained, and nothing here is a statement about it.  The article uses it because the book's concession on the physics is not its real claim: its real claim is about coupling, not entropy bookkeeping, and it should be argued in the language of chemistry. ↩

1. 42a.

   Chapter 8:  The three work terms they compute.  Chemical work, quoting Morowitz:  “the chemical work, or average increase in enthalpy, for macromolecule formation in living systems is 16.4 cal/gm.”  Thermal entropy work, again from Morowitz:  “the average decrease in thermal entropy that occurs during the formation of macromolecules of living systems in 0.218 cal/deg-gm or 65 cal/gm at 298°K.”  Their own configurational term, for a 100-residue protein:  “-TΔS_c = … = 15.8 cal/gm”.  and for the DNA of E. coli:  “-TΔS_c = … = 2.39 cal/gm.”  Read together, these terms show that by their own calculation the coding work is the smallest of the three for a protein, about a sixth of the total.  For a bacterial genome it is 2.39 cal/gm against 65 cal/gm of thermal entropy work, a factor of twenty-seven smaller.  Whatever is hard about making a coded polymer, the energy budget of the coding is not it.  Anyone citing this book for "the thermodynamic cost of information" has misread it. ↩

Sarfati, Jonathan.  Thermodynamics and evolution.  Creation Ministries International.  2011.  “I have yet to see the calculations involving either heat transfer or Boltzmann microstates involved for natural selection.  Until creationists can do that, they should refrain from claiming that organic evolution contradicts the Second Law;  a trite appeal to 'things become more disordered according to the Second Law' is inadequate.”  “I tend not to use entropy arguments at all for biological systems.”  “I must admit that I hardly ever refer to the second law, although as a Ph.D. physical chemist I am well qualified to do so.  Without meaning to brag, if I don't use it, then few people should;  instead, concentrate on the information argument.”  “Origin of first life is different, since natural selection can't occur without two or more self-reproducing entities”.  He carves out the origin of life as a different case.  That is fair, but the carve-out is no longer a second-law argument; it is the information argument, and he says so in the same breath.  Sarfati holds a PhD in physical chemistry and is Creation Ministries International's house scientist, which is what gives this concession its force.  The article uses it because it is a concession from Creation Ministries International's own physical chemist.  This is a different page from the 2006 "Answers to Critics" article by Sarfati, cited elsewhere in the article, which does defend thermodynamic arguments "when done properly."  Both are live; the two are five years apart and this later page is the concession. ↩

Sarfati, Jonathan.  The Second Law of Thermodynamics: Answers to Critics.  Creation Ministries International.  Feb 12, 2006.  “Open systems still have a tendency to disorder. There are special cases where local order can increase at the expense of greater disorder elsewhere. …  The open systems argument does not help evolution.  Raw energy cannot generate the specified complex information in living things.  Undirected energy just speeds up destruction.”  “I suggest that thermodynamic arguments are excellent when done properly, and the 'open systems' canard is anticipated.  Otherwise I suggest concentrating on information content.”  The two other ministry pages on the same argument are Creation Ministries International's "Arguments we think creationists should NOT use," which lists only "The 2nd Law of Thermodynamics began at the Fall," and Answers in Genesis's "Arguments to Avoid," which likewise lists only the Fall version.  Both retire only the theological version.  Answers in Genesis maintains a separate page arguing that the second law does tell against evolution.  A web article, published 12 February 2006, by Dr Jonathan Sarfati for Creation Ministries International, which replies to readers who say the second law does not apply to Earth, because the sun pours energy into it.  The page opens by quoting a reader's open-system objection and answers it.  It holds that raw energy does not build order, and grants that local order can rise only in special cases such as crystals and programmed machinery.  The article uses it because it shows the ministry defending the scientific form of the argument, not only the theological one. ↩

Sewell, Granville.  “WITHDRAWN: A second look at the second law.”  Applied Mathematics Letters.  Jan 26, 2011.  The publisher's page for Granville Sewell's article.  It was available online from 26 January 2011 as an article in press, then withdrawn after it had been accepted for publication.  The page carries Elsevier's standard withdrawal notice, which gives no reason and no body text.  The article uses it because the page still carries only that boilerplate.  The notice's disjunction, "at the request of the author(s) and/or editor," is the template's, not a statement about this case.  Rodin's 25 February email, which the article quotes, is known from a Retraction Watch report of 16 March 2011 that reproduces it from its publication on Antievolution.org. ↩

Applied Mathematics Letters.  “Editor's note.”  Applied Mathematics Letters 24(11):1968.  2011.  The journal's editor's note, published in volume 24, apologising to Sewell for withdrawing his article.  The text comes from Retraction Watch, a professional science-journalism site that is not a party to the dispute and prints the note in full.  It is a second-best source, and that is stated plainly: the publisher's own copy is paywalled.  The withdrawal was not because of any errors or technical problems found by the reviewers or editors, but because the editor concluded that the content was more philosophical than mathematical and so out of scope for a technical journal.  The note gives the submission, acceptance and withdrawal dates, and points readers to Sewell's own copy of the accepted text at math.utep.edu. ↩

Retraction Watch.  “Elsevier apologizes for Applied Mathematics Letters retraction, pays author's legal fees.”  Retraction Watch.  Jun 8, 2011.  “Elsevier, the publisher of Applied Mathematics Letters, which retracted a paper questioning the second law of thermodynamics earlier this year, will issue an apology and pay $10,000 in legal fees.”  Retraction Watch then contacted Elsevier, which would not confirm or deny that there had been a settlement; the report says "who wouldn't confirm or deny that there had been a settlement."  “The study will not be reinstated.”  A Retraction Watch post reporting that the publisher would apologise to Granville Sewell and pay $10,000 in legal fees.  The chain of custody should be read carefully: Retraction Watch attributes the story to John West at the Discovery Institute's blog, which broke it, so the figure comes from an interested party.  The settlement itself is not public.  The article uses it because the fee figure is unconfirmed by the publisher, and the article says so rather than printing it flat.  The report opens, verbatim: ↩

Gitt, Werner.  “Information, science and biology.”  Journal of Creation 10(2):181–187.  1996.  A paper by Dr Werner Gitt, first printed in August 1996 in what was then called the CEN Technical Journal, arguing that information is a third fundamental quantity beside matter and energy.  It sets out five hierarchical levels that information must show (statistics, syntax, semantics, pragmatics and apobetics) and a set of theorems, and the article uses it because Gitt's theorems put the conclusion inside the definitions.  Its theorems 4, 9 and 10 are the statements the article's claim rests on.  The paper is not peer reviewed outside a creationist journal, but the strong half of what Gitt wants is available from a hostile witness without the circularity: Koonin and Novozhilov, in a mainstream review that Measuring Biological Information cites with its page, write of "a dreary vicious circle" at the heart of the origin of the coding principle and call it "perhaps, the most formidable problem of all evolutionary biology." ↩

Carter, Robert W.  “Can mutations create new information?”  Journal of Creation 25(2):92–98.  2011 (edition of 2025).  “It depends on what you mean by 'new' and 'information'.”  This is the page's own standfirst.  It is part of the claim and must not be cut.  “In the same way that species are not static, neither are genomes…”  The body of Carter's article opens with these words.  The sentence this article quotes from him is therefore not his opening sentence; it begins the second body paragraph.  An article by Robert Carter, who holds a doctorate in marine biology, first printed in August 2011 in the Journal of Creation and posted online by Creation Ministries International on 28 October 2011, updated 21 February 2025.  CMI describes him as a senior scientist and speaker for CMI-USA whose current research for them is human genetics, and the article does not call him a geneticist.  It argues that the slogan "mutations cannot create new information" depends on what "new" and "information" mean, and that the examples offered as evidence for evolution all involve something breaking.  The article uses it because its concession, that mutations can create new varieties, comes from inside the movement, and the concession carries weight because he writes for the movement, not because of the degree. ↩

1. 49a.

   Section Conclusions:  The full set of conclusions is the strongest form of the argument available.  “There are no known examples of the types of information-gaining mutations necessary for large-scale evolutionary processes”.  “In fact, it looks like all examples of gain-of-function mutations, put in light of the long-term needs of upward evolutionary progress, are exceptions to what is needed, because every example I have seen involves something breaking”.  “Mutations can create new varieties of old genes, as can be seen in white-coated lab mice, tailless cats, and blue-eyed people.  But damaging mutations cannot be used to vindicate molecules-to-people evolution.”  He also notes that "not all new traits are caused by mutation." ↩

Sarfati, Jonathan.  Arguments we think creationists should NOT use.  Creation Ministries International.  Feb 7, 2006.  “This is not true, since some changes do confer an advantage in some situations.  Rather, we should say, 'We have yet to find a mutation that increases genetic information in ways needed for microbes-to-man evolution to be feasible.'”  The word is "genetic information," not "information," and the page is CMI's rather than Answers in Genesis's.  Both details are commonly got wrong.  A web page by Dr Jonathan Sarfati for Creation Ministries International that lists arguments the ministry advises creationists to drop.  CMI published it on 7 February 2006 and maintains it as a living document, and the article uses it for the ministry's own reformulation of the mutation argument, which no longer says that mutations cannot add information. ↩