The larger catalogue for the whole series is on the parent page, the origin of life: the literature. Full working notes are in the research dossier
abiogenesis/research/sequence-space-and-functional-information.md.
Sources cited
On 1 October 2026 the sections on what "information" means were moved to Measuring Biological Information. The sources marked "pointer only" below are still cited here, in the short paragraphs that replaced those sections, and are worked up in full in that article's literature review.
| Source | What it is | Access | Direction |
|---|---|---|---|
| Reidhaar-Olson & Sauer 1990 | The λ-repressor randomisation, 25 positions. Their abstract stresses degeneracy; the 92-residue extrapolation to 10-63 is in the body (p. 315 by Meyer's endnote), with their own caveat that independence overestimates function. | Abstract only; the body is known through Axe 2004 p. 1308 and Meyer 2014 ch. 10 | complicates |
| Taylor, Walter, Kast & Hilvert 2001, PNAS 98:10596 | The chorismate mutase library-size calculation, routinely misread as a measured frequency. | Opened | complicates |
| Keefe & Szostak 2001, Nature 410:715 | Four ATP-binding proteins from six trillion random 80-mers; about 1 in 1011. | Opened in full | undercuts |
| Axe 2004, J Mol Biol 341:1295 | Mutational tolerance around a destabilised β-lactamase, extrapolated to "may be as low as" 1 in 1077. | Closed access; read from an archived capture of a deleted site | supports, heavily qualified |
| Lo Surdo et al. 2004 | The Keefe & Szostak winner's structure: a novel fold unknown in biology, zinc-stabilised. | Opened | undercuts |
| Hazen, Griffin, Carothers & Szostak 2007, PNAS 104:8574 | The mainstream definition of functional information, with measured examples. Pointer only, except the eleven classes of GTP-binding RNA, which this article still uses against extrapolating from one protein. | Opened in full | complicates |
| Durston, Chiu, Abel & Trevors 2007, Theor Biol Med Model 4:47 | A measure of conservation in protein families, applied to 35 of them and used by its first author in design arguments. The paper itself draws no design inference. Pointer only. | Opened in full (open access) | supports the ID argument |
| Dryden, Thomson & White 2008, J R Soc Interface 5:953 | The search-resource bound: 4 × 1021 to 4 × 1043 sequences ever explored. | Opened in full | undercuts |
| Bunn 2009, Am J Phys 77:922 | The entropy budget: sunlight pays for all of life's entropy reduction in under a year. | Opened | undercuts the second-law argument |
| Tokuriki & Tawfik 2009 | Conformational dynamism and promiscuity as routes to new folds. A review proposing, not a measurement. | Opened | complicates |
| Povolotskaya & Kondrashov 2010, Nature 465:922 | 98% of sites cannot change at any given moment; most may eventually change with compensation. | Opened | complicates, both ways |
| Matlock & Swamidass 2017 | A preprint: simulated families under zero functional constraint score like real ones on Durston's measure when they have diverged little. Durston replied in April 2017. Pointer only, and quoted in one footnote on the search-resource bound. | Opened in full | undercuts the ID measure |
| Hunt 2007 | The most detailed critique of Axe 2004: published density estimates run 10-10 to 10-63 and "Axe's work does not extend or narrow the range." | Opened | complicates |
| Gishlick, Matzke & Elsberry 2004 | Charges that Meyer "only reports the lowest extreme" of Axe's range. Partly overstated: Meyer gave the end built on the β-lactamase data he was describing, and the figure in Axe's abstract; he did drop the hedge and the range. | Opened | undercuts the ID use, partly |
| Hoyle 1981, Caltech lecture | The 747 argument in his own prose, including the clause showing he did not dispute the first step. | Opened | apologetics primary, audited |
| Shapiro 1986; Kauffman 1995 | Two hostile witnesses who reproduce the (10-20)2000 arithmetic and name its authors. | Opened | context |
| Morowitz, McLean v. Arkansas testimony | "somewhat deceptive," and unscientific because deceptive. | Opened via a Wayback capture | undercuts the ID use |
| Yockey 2005, Kitzmiller filing | The repudiation of creationism and intelligent design, the 1985 letter to Thaxton, and his idiosyncratic use of "materialism." | Opened in full from the library | undercuts the ID use |
| Morris 1976, Entropy and Open Systems | The creationist second-law argument in its strongest form. | Opened | apologetics primary, audited |
| Thaxton, Bradley & Olsen 1984 | "it is thermodynamically possible to develop complex living forms," in the founding intelligent-design book. | Opened | undercuts the second-law argument |
| Sarfati 2011, CMI | "they should refrain from claiming that organic evolution contradicts the Second Law." | Opened | undercuts, from inside the movement |
| Gitt 1996 | Theorems 4, 9 and 10, exactly as numbered. Pointer only. | Opened | apologetics primary, audited |
| Carter 2011, CMI | "The phrase, 'Mutations cannot create new information' is almost a mantra among some creationists, yet I do not agree." Pointer only. | Opened | undercuts, from inside the movement |
| Sarfati 2006, CMI, "Arguments we think creationists should NOT use" | The wording the ministry recommends in place of "there are no beneficial mutations." Pointer only. | Opened | complicates |
| Axe 2000, J Mol Biol 301:585 | Conservative surface changes, each harmless alone, combined until one residue in five changed: function lost in barnase and TEM-1 β-lactamase. | Opened in full (library PDF; the text layer prints "fi" as "®") | supports |
| Axe 2010, BIO-Complexity 2010(1) | Axe's own account of his 2004 range, p. 6: 10-77 from beta-lactamase data, 10-53 from chorismate mutase scaled to the same length. | Opened in full | context |
| Axe 2011, "Correcting Four Misconceptions" | Axe's reply to Hunt: the starting sequence must meet the same bar as the mutants (Objection 3). | Opened in full | supports Axe's method |
| Bloom, Labthavikul, Otey & Arnold 2006, PNAS 103:5869 | 4.5 nucleotide mutations per gene; 61% of mutants of a stabilised P450 fold against 33% of a marginal one. Whole-gene fractions, not per-residue tolerances. | Opened in full (PMC text) | complicates, both ways |
| Futerman 2021, Inference 6(2) | Memorial of Tawfik; used only for his last research focus. Futerman's own probability argument (1 in 10040 with 100 candidate amino acids) is not used: it computes one exact sequence, which no model proposes. | Opened in full | context |
| Gauger & Axe 2011, BIO-Complexity 2011(1) | Kbl2 to BioF2 conversion would need seven or more nucleotide changes. | Opened in full | supports |
| Hayashi et al. 2006, PLoS ONE 1:e96 | A random 139-residue domain improved by selection, then stalled; reaching wild type "requires a library size of 1070." | Opened in full | supports, with the authors' recombination caveat |
| Knopp et al. 2019, mBio 10:e00837-19 | Three of 5.82 × 108 random peptides raise aminoglycoside resistance by membrane insertion that lowers membrane potential. | Opened in full | undercuts "random sequence is inert"; complicates the scale of function |
| Künzel et al. 2026, bioRxiv preprint | Tautz laboratory reassessment: the vector effect is real but does not explain the gains of a subset of random clones. Not peer reviewed. | Opened in full | undercuts, provisionally |
| Meyer 2004, Proc Biol Soc Wash 117:213 | Meyer's own summary of Axe 2004: correct definition ("a specified function via any folded structure"), 1 in 1077 given without range or hedge, closing sentence widened to "a functional protein." | Opened in full (Discovery Institute reprint) | apologetics primary, audited |
| Meyer 2014, Darwin's Doubt, ch. 10 | Quotes Reidhaar-Olson & Sauer's own caveat from their p. 315. | Opened in full (library text) | context |
| Mukhopadhyay 2013, ASBMB Today | On-record remarks: Tawfik's "catch-22" and "something like close to a miracle"; Szostak's "Getting function from randomness is hard"; Hecht's binary-patterned proteins rescuing E. coli knockouts. | Opened in full | supports the narrow claim; Hecht complicates |
| Neme et al. 2017, Nat Ecol Evol 1:0127 | Up to 25% of random 50-codon clones raised growth and up to 52% lowered it in E. coli. The positive half is disputed. | Opened in full (PMC manuscript) | undercuts, disputed |
| Tian & Best 2017, Biophys J 113:1719 | Coevolution-based count of sequences folding to ten natural domains: shares of 10-38 to 10-86 at 87–94 residues and 10-111 to 10-126 at 123–171. Table 1's WW-domain entry disagrees with the text by a factor of about 150. | Opened in full (PMC) | supports the rarity of any one fold |
| Tretyachenko et al. 2017, Sci Rep 7:15449 | Random sequences resemble natural ones in secondary structure and are well tolerated; no function selected. | Opened in full | complicates |
| The Sewell documents | The Elsevier withdrawal page, the editor's note via Retraction Watch's transcript, and the Discovery Institute's account of the settlement. | Wayback raw capture; the editor's note is paywalled and quoted from a transcript | context |
Considered and not used
- Wong et al. 2023, the proposed "law of increasing functional information." Cited here until 1 October 2026. It moved with the definitional sections and is now cited, from its full text, in Measuring Biological Information.
- Lau & Dill's lattice model, the source of the 10-10 foldability term inside Axe's calculation. Not opened. As far as this research could establish, nobody on either side of a thirty-year argument has gone back and checked it, and it carries ten of the seventy-seven orders of magnitude.
- Knopp & Andersson 2018, "No beneficial fitness effects of random peptides" (Nat Ecol Evol 2:1046, doi 10.1038/s41559-018-0585-4). Closed access, not opened. The article describes its argument through Künzel et al. 2026's account and does not quote it. Tautz & Neme's 2018 reply (doi 10.1038/s41559-018-0586-3) is likewise closed and not used.
- Weisman 2022, "The origins and functions of de novo genes: against all odds?" (J Mol Evol, open access). Considered as a review of the random-sequence debate; the PMC download returned an empty page and it was not needed once the primaries were read.
- Skolnick and Lupas in Mukhopadhyay 2013. Their remarks (random compact structures already have ligand-binding pockets; function before structure) are relevant to origins but not to the density question, and are not used.
- Hoyle & Wickramasinghe's own book, the ultimate source of the 1040,000 arithmetic. Never read here, which is why no version of the figure is printed.
- The Guardian education supplement of 23 August 2001. Obtained. The quotation is not in its argument; it sits in an unsourced pull-quote box headed "Hoyleisms."
- Coppedge 1973. The actual source of the Morowitz number. His own page states that he did the subtraction, which is all this article needs.
- Wolpert's published rejection of the intelligent-design use of the no-free-lunch theorem, and Häggström's Biology and Philosophy reply. Neither is on disk, and the article makes no no-free-lunch argument in consequence.
- Meyer's Signature in the Cell beyond the passages already audited. Handled in the parent article.
Open questions
- Somebody should check the Lau and Dill foldability term. It is the least-examined number in the most-quoted calculation in this field.
- Whether any published experiment measures the density of catalytic function in unbiased sequence space. Keefe and Szostak measured binding; Axe measured tolerance. Neither is the quantity everyone argues about.
- Axe 2004 remains closed access. The copy this project read is an archived capture of a deleted personal site, which is a fragile provenance for a load-bearing citation.
Whether the Durston measure has been defended in print against the Matlock and Swamidass simulation.Answered on 1 October 2026. Durston replied in Evolution News on 5 April 2017 ("On the Astonishing Improbability of Protein Families") and posted a five-page review. Both are in the source library and are weighed in Measuring Biological Information. The earlier search missed them.