# Recursive complexity framework — Data, reasoning, and sources ## 1. Framework definition ### 1.1 The recursive criterion The complexity of a structure is defined by the number of nesting levels in the recursive question **"what is it made of?"**, starting from the structure and descending down to the fundamental particles. **Fundamental rule:** an object of level N must contain at least **two distinct components of level N-1**. Components of lower levels (N-2, N-3, etc.) are present but irrelevant for classification. **Example:** an O₂ molecule is level 4. - Quarks (level 1) → protons/neutrons (level 2, because they contain 3 quarks) → oxygen atoms (level 3, because they contain protons AND neutrons) → O₂ molecule (level 4, because it contains 2 atoms). ### 1.2 Identical components count Identical copies of the same component satisfy the criterion. A crystal is made of repeated identical atoms, yet has emergent properties (refraction, cleavage) that the single atom does not. A tissue is made of nearly identical cells, yet has emergent mechanical properties. The identity of the components is irrelevant. ### 1.3 Substrate-independent terminology The framework applies to any substrate (proteins, RNA, minerals). The levels do not depend on traditional biological nomenclature, which can be misleading. Classical protein secondary structure classifies both alpha-helices and beta-sheets as "secondary structure," but in our framework they occupy different levels (see §2). ### 1.4 Maximum one level A tree crown is made of branches, made of secondary branches, made of tertiary branches, made of twigs. In cases like this, only one level is counted. Each level must be different from the previous one and it must not be possible to repeatedly divide it. ## 2. Protein structure hierarchy ### 2.1 Level 5: linear elements (strands, alpha-helices) A **beta strand** is a stretch of polypeptide chain in an extended conformation. "What is it made of?" → amino acids. Level 5. An **alpha-helix** is a stretch of chain coiled into a spiral, stabilized by internal hydrogen bonds (the C=O of amino acid *i* bonds to the N-H of amino acid *i+4*). "What is it made of?" → amino acids. Same answer as the strand. **Level 5.** A strand and a helix are conceptually equivalent: both are stretches of chain with a specific conformation. ### 2.2 Level 6: structures composed of linear elements A **beta-sheet** is composed of at least 2 strands that interact laterally through regular hydrogen bonds. "What is a sheet made of?" → strands. A different answer from the previous level. **Level 6.** Sheets can be parallel (strands in the same direction, connected by long loops or helices) or antiparallel (strands in opposite directions, connected by short hairpins of 2-4 residues). Source on secondary structure: Branden C, Tooze J. "Introduction to Protein Structure" 2nd ed., Garland Publishing (1999). An **alpha-helix bundle** (helix bundle) is composed of 2+ helices that pack together through hydrophobic interactions. By symmetry with the beta-sheet: if 2+ strands that interact form a level above the single strand, then 2+ helices that interact form a level above the single helix. **Level 6.** Note: the distinction between "one bundle" and "two bundles" can be ambiguous for globular proteins, but is clear for distinct domains separated by linkers or for well-defined transmembrane bundles. A **beta-barrel** is a beta-sheet closed upon itself. Topologically it remains a single sheet. **Level 6.** ### 2.3 Level 7: proteins with 2+ level-6 structures A tertiary protein containing **2+ distinct beta-sheets**, or **2+ distinct helix bundles**, or **a sheet + a distinct bundle**, is level 7. This is the crucial equivalence that classical terminology obscures: biological "secondary structure" (helices and sheets) is distributed across two levels in our framework (5 and 6), and "tertiary structure" with multiple domains reaches level 7. ### 2.4 Higher levels - **Level 8:** quaternary complex (2+ level-7 subunits) - **Level 9:** super-complex (2+ level-8 complexes) - **Level 10+:** cellular structures ## 3. Analysis of E. coli ATP synthase ### 3.1 Composition ATP synthase (F₁F₀-ATPase) is composed of: **F₁** (catalytic domain, cytosolic): α₃β₃γδε — 3 α subunits (~513 aa, ~55 kDa), 3 β subunits (~459 aa, ~51 kDa), 1 γ (~287 aa), 1 δ (~177 aa), 1 ε (~138 aa). **F₀** (proton channel, transmembrane): a₁b₂c₁₀ — 1 a subunit, 2 b subunits, 10 c subunits. Structural sources: - PDB 1BMF — Abrahams JP, Leslie AGW, Lutter R, Walker JE. "Structure at 2.8 Å resolution of F1-ATPase from bovine heart mitochondria." Nature 370:621-628 (1994). https://doi.org/10.1038/370621a0 - PDB 5T4O — Sobti M et al. "Cryo-EM structures of the autoinhibited E. coli ATP synthase in three rotational states." eLife 5:e21598 (2016). https://doi.org/10.7554/eLife.21598 - PDB 6WNR — Sobti M et al. "Cryo-EM structures provide insight into how E. coli F1Fo ATP synthase accommodates symmetry mismatch." Nature Communications 11:3108 (2020). https://doi.org/10.1038/s41467-020-16387-2 ### 3.2 Structure of α and β subunits: the three domains Each α and β subunit contains three distinct domains, revealed by the crystallographic structure (PDB 1BMF): 1. **N-terminal domain: 6-strand beta-barrel.** Official PDB annotation: "ATP synthase alpha/beta family, beta-barrel domain." Confirmed by the cross-link paper (Orriss et al., PDB 1NBM) which describes the "six-stranded β-barrel that forms part of the 'crown' of the F₁ domain." — One sheet, level 6. 2. **Central domain: nucleotide-binding domain (α/β).** Central parallel beta-sheet surrounded by alpha-helices. PDB annotation: "ATP synthase alpha/beta family, nucleotide-binding domain." The P-loop is "preceded by a beta sheet and followed by an alpha helix." — One sheet, level 6. 3. **C-terminal domain: alpha-helix bundle.** PDB annotation: "ATP synthase alpha/beta chain, C terminal domain." Described as "helical lever domain" by Frasch 2022, Frontiers in Microbiology 13:965620. https://doi.org/10.3389/fmicb.2022.965620 — One bundle, level 6. Source for PDB annotations: https://www.ebi.ac.uk/pdbe/entry/pdb/1bmf Confirmation of the three-domain description: Grüber G et al. "Nucleotide Binding States of Subunit A of the A-ATP Synthase." J Mol Biol 395:20-30 (2009): "an N-terminal β barrel, an α–β domain, and a C-terminal α-helical bundle." https://doi.org/10.1016/j.jmb.2009.11.027 **Conclusion:** each α and β subunit contains 2 distinct beta-sheets + 1 helix bundle = 3 level-6 structures. **α and β subunits = level 7.** ### 3.3 Other F₁ subunits **δ subunit (~177 aa):** N-terminal β-sandwich domain (10 beta strands in 2 stacked sheets). Source: Wilkens S et al. "Structural features of the ε subunit of the Escherichia coli ATP synthase determined by NMR spectroscopy." Nature Structural Biology 2:961-967 (1995). https://doi.org/10.1038/nsb1195-961 — Two sheets = **level 7.** **ε subunit (~138 aa):** N-terminal β-sandwich domain + C-terminal α-helical. PDB 1AQT. Source: Uhlin U, Cox GB, Guss JM. "Crystal structure of the epsilon subunit." Structure 5:1219-1230 (1997). — Two sheets = **level 7.** **γ subunit (~287 aa):** mainly α-helical with a 5-strand beta-sheet. Only one sheet = **level 6.** ### 3.4 F₀ subunits **c subunit (10 copies, ~79 aa):** hairpin of 2 transmembrane α-helices. One bundle = **level 6.** **a subunit (~271 aa):** 5-6 transmembrane α-helices. One bundle = **level 6.** **b subunit (2 copies, ~156 aa):** transmembrane α-helix + coiled-coil. One bundle = **level 6.** ### 3.5 Complex classification - F₁ contains 8 level-7 subunits (3α + 3β + δ + ε). **F₁ = level 8.** - F₀: all subunits are level 6. The c ring (10 level-6 copies) = level 7. **F₀ = level 7.** - **Complete ATP synthase = level 8** (the level is determined by F₁). ## 4. Analysis of E. coli 70S ribosome ### 4.1 Composition **30S** (small subunit): 21 proteins (S1-S21) + 16S rRNA (1542 nucleotides) **50S** (large subunit): 33 proteins (L1-L36) + 23S rRNA + 5S rRNA Structural sources: - Watson ZL et al. "Structure of the bacterial ribosome at 2 Å resolution." eLife 9:e60482 (2020). https://doi.org/10.7554/eLife.60482 - Wimberly BT et al. "Structure of the 30S ribosomal subunit." Nature 407:327-339 (2000). https://doi.org/10.1038/35030006 ### 4.2 30S proteins with 2+ beta-sheets (level 7) **Protein S5 (~166 aa):** two distinct α/β domains, each with its own beta-sheet. "The molecule contains two distinct alpha/beta domains." Source: Davies C et al. "The structure of ribosomal protein S5 reveals sites of interaction with 16S rRNA." Structure 6:75-88 (1998). PDB 1PKP. https://doi.org/10.1016/S0969-2126(98)00009-7 — **Level 7.** **Protein S8 (~130 aa):** two distinct α/β domains. "The two domains of the structure have an alpha/beta fold and are connected by a long protruding loop." Source: Nevskaya N et al. "Crystal structure of ribosomal protein S8 from Thermus thermophilus." J Mol Biol 279:233-244 (1998). PDB 1AN7. https://doi.org/10.1006/jmbi.1998.1758 — **Level 7.** **30S = level 8** (2+ level-7 proteins). ### 4.3 50S proteins with 2+ beta sheets (level 7) **Protein L2 (~273 aa):** two distinct beta barrels in the RNA-binding domain. N-terminal domain: OB-fold beta barrel with 5 strands (β1-β5 explicitly mapped: positions 75-131). C-terminal domain: SH3-like beta barrel with 5 strands (β6-β10 explicitly mapped: positions 139-192). Source: Nakagawa A et al. "The three-dimensional structure of the RNA-binding domain of ribosomal protein L2." EMBO Journal 18:1459-1467 (1999). PDB 1RL2. https://doi.org/10.1093/emboj/18.6.1459 — **Level 7.** **Protein L6 (~177 aa):** two domains with nearly identical folds. "L6 contains two domains with almost identical folds, implying that it was created by an ancient gene duplication event." Each domain is homologous to the RNP fold with its own beta sheet. Source: Golden BL, Ramakrishnan V, White SW. "Ribosomal protein L6: structural evidence of gene duplication from a primitive RNA binding protein." EMBO Journal 12:4901-4908 (1993). PMC 413751. https://doi.org/10.1002/j.1460-2075.1993.tb06184.x — **Level 7.** **50S = level 8** (2+ level-7 proteins). ### 4.4 Ribosome classification - 30S = level 8 (confirmed: S5 + S8) - 50S = level 8 (confirmed: L2 + L6) - **70S ribosome = level 9** (2 level-8 subunits) ## 5. Prokaryotic cell An E. coli prokaryotic cell contains thousands of ribosomes (level 9). The plasma membrane contains hundreds of ATP synthases (level 8). - 70S ribosome = level 9 - Membrane with ATP synthase = level 9 (2+ level-8 complexes on the membrane) - **Prokaryotic cell = level 10** (2+ level-9 structures: ribosomes + membrane) ## 6. 26S proteasome (eukaryotes) ### 6.1 20S core Each α and β subunit has "a core of two antiparallel beta sheets that is flanked by alpha helices on both sides." Source: Löwe J et al. "Crystal structure of the 20S proteasome from the archaeon T. acidophilum at 3.4 Å resolution." Science 268:533-539 (1995). https://doi.org/10.1126/science.7725097 — Two sheets + helices = **level 7.** Bovine structure: PDB 1IRU, Unno M et al. "The Structure of the Mammalian 20S Proteasome at 2.75 Å Resolution." Structure 10:609-618 (2002). https://doi.org/10.1016/S0969-2126(02)00748-7 - One ring (7 level-7 subunits) = level 8 - 20S core (4 level-8 rings) = **level 9** ### 6.2 19S cap **Rpt subunits (base ATPases):** each has 3 domains: coiled-coil (helix bundle, level 6), OB fold domain (5-strand beta barrel, level 6), AAA ATPase domain (beta sheet + helices, level 6). Three level-6 domains of which at least 2 have beta sheets = **level 7.** Source: Structural Biology of the Proteasome, Finley D et al. Annu Rev Biochem 85:225-255 (2016). PMC 4878838. https://doi.org/10.1146/annurev-biochem-060614-033933 — Domain description: "N-terminal coiled-coil (CC) domain, a central oligonucleotide/oligosaccharide binding (OB) domain, and a C-terminal AAA ATPase cassette." Also: Structural Insights into Proteasome Activation by the 19S Regulatory Particle, Sims JJ et al. PMC 3864829. Confirms: "Each subunit contains a coiled-coil (CC), OB fold, ATPase, and C-terminal domain (CTD)." - Rpt ring (6 level-7 subunits) = level 8. **19S base ≥ level 8.** **Lid subunits:** 6 out of 9 subunits have PCI domains with a helical region + winged helix (beta sheet). Sheet + bundle = **level 7.** Source: Tomko RJ, Hochstrasser M. "Molecular Architecture and Assembly of the Eukaryotic Proteasome." Annu Rev Biochem 82:415-445 (2013). PMC 3827779. https://doi.org/10.1146/annurev-biochem-060410-150257 — **Lid = level 8.** - Complete 19S (level-8 base + level-8 lid) = **level 9** - **26S proteasome (20S + 19S) = level 10** ## 7. Photosystem II and chloroplasts ### 7.1 PsbO (manganese-stabilizing protein, ~26.5 kDa) PsbO is an extrinsic protein of PSII present in all oxygenic photosynthetic organisms. It has two homologous beta-sandwich domains of ~120 amino acids each. "PsbO as an all-beta protein, with two homologous beta domains of approximately 120 amino acids linked by a flexible Proline-Glycine-Glycine (PGG) motif." Source (structural model): De Las Rivas J, Barber J. "Threading structural model of the manganese-stabilizing protein PsbO reveals presence of two possible beta-sandwich domains." Proteins 49:11 (2001). https://doi.org/10.1002/prot.10013 Confirmed crystallographic structure: PDB 5G38, 5G39 — Bommer M et al. "Crystallographic and Computational Analysis of the Barrel Part of the PsbO Protein of Photosystem II." Biochemistry 55:4626-4635 (2016). https://doi.org/10.1021/acs.biochem.6b00441 — The PDB entries are titled "PsbO subunit of Photosystem II, beta barrel domain." A beta-sandwich is composed of 2 face-to-face beta sheets = level 7. PsbO has 2 beta-sandwich domains = 2 level-7 structures. **PsbO = level 8.** ### 7.2 PsbP (plants, ~23 kDa) PsbP exists only in plants and green algae, not in cyanobacteria. It has a beta-sandwich fold. "Its structure is mainly composed of beta-sheet." One beta-sandwich = 2 sheets = **level 7.** Source: Ifuku K et al. "Crystal structure of the PsbP protein of photosystem II from Nicotiana tabacum." EMBO Reports 5:362-367 (2004). PDB 1V2B. PMC 1299024. https://doi.org/10.1038/sj.embor.7400113 ### 7.3 PSII and chloroplast classification - PsbO = level 8 (both cyanobacteria and plants) - PSII monomer (contains 1 level-8 PsbO) = level 8 - **PSII dimer** (2 monomers, each with level-8 PsbO) = **level 9** - Thylakoid disc (2+ level-9 PSII dimers) = **level 10** - Granum (stack of 2+ level-10 thylakoid discs) = **level 11** - **Chloroplast** (2+ level-11 grana) = **level 12** Note on thylakoids: the thylakoid lumen is topologically a single continuous compartment, but the discs in the grana are discrete, repeated structural units, analogous to crystals (repeated identical units) or beta sheets (repeated identical strands). The emergent properties of a granum (the regular stacking that optimizes light capture) do not exist in a single disc. ## 8. RNA viruses (RNA world branch) ### 8.1 Capsid structure — the jelly-roll fold The dominant fold in viral capsid proteins is the **jelly-roll** (8-stranded antiparallel beta barrel). The two sheets of the barrel (BIDG and CHEF) form a single closed structure = level 6. Source: Rossmann MG, Johnson JE. "Icosahedral RNA virus structure." Annu Rev Biochem 58:533-573 (1989). Also: Johnson JE, Olson AJ. "Icosahedral virus structures and the protein data bank." J Biol Chem 296:100554 (2021). PMC 8081926. https://doi.org/10.1016/j.jbc.2021.100554 For viruses with a simple jelly-roll (e.g. Satellite Tobacco Mosaic Virus, T=1): - Capsid protein with jelly-roll = level 6 - Capsomere (pentamer of 5 level-6 proteins) = level 7 - Icosahedral capsid (12 level-7 capsomeres) = level 8 - Complete virion = **level 8** ### 8.2 RNA viruses reaching level 9 **Bacteriophage MS2** (Leviviridae, one of the simplest and most ancient RNA viruses): The MS2 capsid protein has a fold different from the jelly-roll: "an N-terminal β hairpin, a central five-stranded antiparallel β sheet, and two C-terminal α helices." Three level-6 structures (beta hairpin + 5-strand sheet + 2-helix bundle) = **level-7** protein. Two proteins form a stable dimer with a "common hydrophobic core" and "a single 10-stranded β sheet lining the interior of the particle." The dimer is the true building block of the capsid. Dimer = **level 8.** The complete virion: 89 dimers (level 8) + 1 maturation protein = **level 9.** Source: Liekniņa I et al. "Three-dimensional structure of 22 uncultured ssRNA bacteriophages." Science Advances 6:eabc0023 (2020). PMC 7467689. https://doi.org/10.1126/sciadv.abc0023 — Also: Golmohammadi R et al. "The crystal structure of bacteriophage Qβ at 3.5 Å resolution." Structure 4:543-554 (1996). **Note on coronaviruses:** the spike S1 protein is "predominantly composed of beta-sheets" with multiple beta-sandwich domains (NTD with galectin fold, RBD, CTD1, CTD2, SD1, SD2). Source: Cai Y et al. "Structure of SARS-CoV-2 spike protein." Current Opinion in Structural Biology 71:128-135 (2021). PMC 8423807. The spike trimer reaches level 8, and the virion with ~25 spike trimers on the envelope reaches level 9. However, coronaviruses are probably too complex and too recent to be considered direct descendants of the prebiotic RNA world. ### 8.3 The RNA world branch The RNA world is a branch in the graph, not a segment of the trunk. Viroids are still-living descendants (naked RNA that replicates by parasitizing cells). RNA viruses with RdRp (RNA-dependent RNA polymerase) are likely descendants of the same branch. RdRp is the key marker: this enzyme copies RNA from RNA. It does not exist in any modern cell, suggesting it is a relic of the RNA world. **RNA branch hierarchy:** - RNA strand (level 5) - RNA secondary structures: stem-loop (level 6) - Viroids (circular RNAs with multiple stem-loops, level 6-7) - Complex ribozymes / RNA tertiary structures (level 7) - Simple RNA viruses with jelly-roll capsid (level 8) - RNA viruses with more complex capsid, e.g. MS2 (level 9) **Uncertainty:** the origin of viroids is debated. They may be relics of the RNA world (in which case the branch diverges before cells) or RNA "escaped" from cellular genomes (in which case they are a byproduct of the trunk). The RdRp marker supports the former hypothesis for RNA viruses, but this is not universally accepted. ## 9. DNA hierarchy Naked DNA (without proteins) has a limited hierarchy: - Nucleotide ≈ level 4 (simple molecule) - Single strand (nucleotide chain) = level 5 - Double helix (2 paired strands) = level 6 A gene is not a structural level: it is a longer stretch of the same double helix. "What is a gene made of?" → the double helix. Same level. DNA rises in level with chromatin packaging (exclusive to eukaryotes): - Histone octamer (8 proteins ≈ level 6 each, all α-helical) = level 7 - Nucleosome (level-7 octamer + 147 bp level-6 DNA) = level 7 (the level is set by the highest component; only 1 DNA + 1 octamer is needed, not 2+ octamers) Note: in any case, packaged DNA does not reach higher levels than cytoplasmic proteins, and is therefore not the limiting factor for cellular complexity. ## 10. Complex I on the prokaryotic membrane Complex I (NADH dehydrogenase) of E. coli has 13 subunits (NuoA-N) with an L-shaped structure: a peripheral (cytosolic) arm and a membrane arm. Structural source: Kolata P, Bhatt R, Bhatt M. "Structure of Escherichia coli respiratory complex I reconstituted into lipid nanodiscs reveals an uncoupled conformation." eLife 10:e68710 (2021). PDB 7NYH, 7NZ1. https://doi.org/10.7554/eLife.68710 **Peripheral arm:** contains large subunits such as NuoG (~900 aa) with multiple α/β domains and iron-sulfur clusters. NuoG has Rossmann-like domains with beta sheets + a domain with a β-barrel motif. Probably level 7. With 2+ level-7 subunits, the peripheral arm = **level 8.** **Membrane arm:** NuoL, NuoM, NuoN are bundles of 14 transmembrane helices each. One bundle = level 6. The entire membrane arm = **level 7** (2+ level-6 subunits). Source: Wikipedia "Respiratory complex I": "Three of the conserved, membrane-bound subunits [...] each contains 14 conserved transmembrane (TM) helices." Confirmed by cryo-EM structure. **Complete Complex I** (level-8 peripheral arm + level-7 membrane arm) = **level 8.** **Conclusion on the prokaryotic membrane:** the membrane contains ATP synthase (level 8) and Complex I (level 8), but no complex reaches level 9. The membrane with multiple copies of level-8 complexes = **level 9.** It does not rise to level 10. The prokaryotic cell level remains **level 10** (as established in §5). ## 11. Level summary ### Levels 1-6 (possibly pre-biological) | Level | Protein example | RNA example | Non-biological example | |-------|----------------|-------------|------------------------| | 1 | — | — | Fundamental particles | | 2 | — | — | Protons, neutrons | | 3 | — | — | Atoms | | 4 | Amino acid, nucleotide | Nucleotide | Simple molecules | | 5 | Strand, alpha-helix, peptide chain | RNA chain, stem-loop | Complex molecules | | 6 | Beta sheet, helix bundle | Pseudoknot, RNA secondary structure | DNA double helix, crystals | ### Levels 7-13 (biological) | Level | Structure | Source of classification | |-------|-----------|--------------------------| | 7 | Protein with 2+ sheets/bundles (e.g. ATP synthase β subunit) | §3.2 | | 8 | Quaternary complex (e.g. F₁, proteasome 7α ring, PsbO, jelly-roll capsid, Complex I) | §3.5, §6.1, §7.1, §8.1, §10 | | 9 | Super-complex (e.g. 70S ribosome, 20S proteasome core, PSII dimer, prokaryotic membrane, MS2 capsid) | §4.4, §6.1, §7.3, §5, §8.2 | | 10 | Prokaryotic cell, 26S proteasome, thylakoid disc | §5, §6.2, §7.3 | | 11 | Animal eukaryotic cell, granum, photosynthetic cyanobacterium | §7.3 | | 12 | Chloroplast | §7.3 | | 13 | Plant cell | §7.3 | Higher levels (tissues, organs, organisms, societies) require separate analysis. ## 12. Dating of biological levels ### 12.1 Level 10 — First prokaryotic cells: ~3.5 Ga (10.3 Ga from the beginning) The oldest confirmed microfossils come from the Dresser Formation (Pilbara Craton, Western Australia) at 3.48 Ga. They show cellular structures and sulfur metabolism. Source: Wacey D, Kilburn MR, Saunders M, Cliff J, Brasier MD. "Microfossils of sulphur-metabolizing cells in 3.4-billion-year-old rocks of Western Australia." Nature Geoscience 4:698-702 (2011). https://doi.org/10.1038/ngeo1238 Further confirmation: Schopf JW et al. "SIMS analyses of the oldest known assemblage of microfossils document their taxon-correlated carbon isotope compositions." PNAS 115:53-58 (2018). https://doi.org/10.1073/pnas.1718063115 — Confirms the biogenicity of Apex Chert microfossils at 3.465 Ga. Geochemical evidence (biogenic carbon isotopes) extends the window back to 3.7–3.8 Ga (Isua Supracrustal Belt, Greenland), but without direct microfossils. ### 12.2 Level 11a — Photosynthetic cyanobacteria: ~2.7 Ga (11.1 Ga from the beginning) Cyanobacteria are prokaryotes with oxygenic photosynthesis. In our framework, the presence of PSII with PsbO (level 8) in their thylakoid membrane brings the thylakoid membranes to level 10 and the entire cell to level 11 (cyanobacterium with 2+ thylakoid membranes). Lipid biomarkers (2-methylhopanoids) from 2.7 Ga. The Great Oxidation Event (~2.4 Ga) confirms that oxygenic photosynthesis was already widespread. Source: Brocks JJ, Logan GA, Buick R, Summons RE. "Archean molecular fossils and the early rise of eukaryotes." Science 285:1033-1036 (1999). https://doi.org/10.1126/science.285.5430.1033 ### 12.3 Level 11b — First eukaryotic cells: ~2.1 Ga (11.7 Ga from the beginning) Eukaryotic cells contain mitochondria (level 10, derived from endosymbiosis of α-proteobacteria). With 2+ mitochondria, the cell is level 11. Oldest fossils: acritarchs (spherical structures of ~10+ µm) from ~2.1 Ga. The oldest fossil multicellular red alga (Bangiomorpha pubescens) dates to ~1.05 Ga, but the first unicellular eukaryotes are much earlier. Source: Han TM, Runnegar B. "Megascopic eukaryotic algae from the 2.1-billion-year-old Negaunee iron-formation, Michigan." Science 257:232-235 (1992). Also: El Albani A et al. "Large colonial organisms with coordinated growth in oxygenated environments 2.1 Gyr ago." Nature 466:100-104 (2010). ### 12.4 Level 12 — First chloroplasts: ~1.5–1.0 Ga (12.3–12.8 Ga from the beginning) Primary endosymbiosis (a cyanobacterium engulfed by a heterotrophic eukaryote) gave rise to the Archaeplastida. Estimated at 1.0–1.5 Ga, at least 500 million years after the first eukaryotes. The oldest confirmed fossil red alga: Bangiomorpha pubescens, ~1.05 Ga. Source: Butterfield NJ. "Bangiomorpha pubescens n. gen., n. sp.: implications for the evolution of sex, multicellularity, and the Mesoproterozoic/Neoproterozoic radiation of eukaryotes." Paleobiology 26:386-404 (2000). https://doi.org/10.1666/0094-8373(2000)026<0386:BPNGNS>2.0.CO;2 Also: OpenStax Biology 2e, Ch. 23.1: "Researchers have suggested that the endosymbiotic event that led to Archaeplastida occurred 1 to 1.5 billion years ago." ### 12.5 Level 13 — First plant cells with grana: ~1.0 Ga? (12.8 Ga from the beginning) The granum structure (stacked thylakoids) is typical of green algae and land plants, but not of red algae (which have unstacked thylakoids). Level 13 requires the formation of grana. Approximate date based on the green algae / red algae divergence. Note: this date requires more thorough verification. ### 12.6 Levels 5–9 — Prebiotic chemistry and the RNA world: ~4.4–3.5 Ga Levels 5–9 (peptides → composite structures → multi-domain proteins → quaternary complexes → ribosome) must all fall within the window between the formation of the oceans (~4.4 Ga) and the first prokaryotic fossils (~3.48 Ga). This interval of ~900 million years witnessed the entire transition from chemistry to biology. The relative order of the levels is based on logic: simpler structures must precede more complex ones. But the absolute dates are highly uncertain. No fossils of prebiotic peptides or primordial ribozymes exist. ### 12.7 Branch J — RNA world and viruses The RNA world branch diverges from the trunk between levels 5 and 7. The dating is entirely speculative and based solely on the constraint that it must precede the first cell. Modern RNA viruses (e.g., bacteriophage MS2, level 9) have no fossil record. Their antiquity is inferred from the presence of RdRp (RNA-dependent RNA polymerase), absent in all modern cells. ## 13. Fermi estimate: first interstellar dipeptide ### Premise This calculation estimates when, in the history of the universe, at least one dipeptide (two amino acids joined by a peptide bond) formed in interstellar space. This is not a precision calculation. It is a Fermi estimate: each parameter is approximated to an order of magnitude, and the result tells us whether we are talking about hundreds of millions or billions of years. As we will see, the conclusion is so robust as to be insensitive to errors of even many orders of magnitude in individual parameters. This calculation has not been peer reviewed. It is an order-of-magnitude estimate made as part of a science communication project. ### The mechanism In January 2026, Hopkinson et al. published in Nature Astronomy the first experimental demonstration that peptide bonds form in interstellar-like ices irradiated by high-energy protons, without the need for liquid water. **Source:** Hopkinson, A.T. et al. "An interstellar energetic and non-aqueous pathway to peptide formation." Nature Astronomy (2026). https://doi.org/10.1038/s41550-025-02765-7 Supplementary data (CC-BY-4.0): https://doi.org/10.5281/zenodo.17814721 **The experiment:** glycine (the simplest amino acid) is cooled to ~20 K (−253°C) to simulate the icy mantles of interstellar dust grains, then bombarded with high-energy protons analogous to galactic cosmic rays. The result is the formation of glycylglycine (the simplest dipeptide), confirmed by infrared spectroscopy and high-resolution mass spectrometry. **The question:** given that this mechanism works, and given that the necessary conditions (icy grains with amino acids + cosmic rays) have existed in the universe for billions of years, when did the first dipeptide form? ### The formula The expected number of dipeptides formed throughout the observable universe per year is: N = 600 × f² × P_bond × R_impact × N_grains where: - **600** = adjacent site pairs "touched" by each proton impact - **f²** = probability that both sites of a pair contain glycine - **P_bond** = probability that an irradiated glycine-glycine pair forms the peptide bond - **R_impact** = number of cosmic protons hitting a single grain per year - **N_grains** = total number of dust grains in molecular clouds in the universe If N >> 1 per year, the first dipeptide forms essentially as soon as the chemical conditions allow. If N << 1, the waiting time is approximately 1/N years. ### The parameters: values, sources, and uncertainties ### 1. Pairs touched per impact (600) When a ~1 MeV cosmic proton passes through a 0.1–0.25 μm dust grain, it generates an ionization track. Along this track, energy is deposited and chemical bonds are broken, creating radicals. A radical can react with the immediately adjacent molecule. **How many sites are "activated":** the track crosses the grain (~200 nm diameter), with an effect radius of ~1–10 nm around the proton path. On the grain surface, this corresponds to ~100–1000 molecular sites. We choose 100 (conservative). **Source for track size:** the size of "spurs" in ice radiochemistry is typically 1–5 nm. Gerakines, P.A., Moore, M.H., & Hudson, R.L. "Carbonic acid production in H₂O:CO₂ ices." Astronomy & Astrophysics 357, 793 (2000). https://science.gsfc.nasa.gov/691/cosmicice/reprints/Gerakines-2000-22.pdf **Neighbors per site:** each molecular site on a surface has approximately 6 neighbors (hexagonal packing). **Calculation:** 100 activated sites × 6 neighbors each = 600 pairs touched per impact. **Range:** with 1000 activated sites there would be 6000 pairs. With 50 sites, 300 pairs. The choice of 100 is conservative. ### 2. Probability that a pair is glycine-glycine (f²) **What f is:** the fraction of sites on the grain surface occupied by glycine molecules, relative to the total (predominantly H₂O). **Glycine in space:** glycine has never been directly detected in the interstellar medium in the gas phase, but has been found in: - Comet 67P/Churyumov-Gerasimenko, Rosetta mission (Altwegg et al. 2016) https://doi.org/10.1126/sciadv.1600285 - Carbonaceous meteorites, including Murchison: over 80 amino acids (Burton et al. 2012) https://doi.org/10.1039/C2CS35109A - Asteroid Bennu, OSIRIS-REx samples: 15 of the 20 standard amino acids (PNAS 2025) https://doi.org/10.1073/pnas.2512461122 Glycine also forms without energetic irradiation, on icy grains at <15 K, via atom-radical reactions (Ioppolo et al. 2020, Nature Astronomy): https://doi.org/10.1038/s41550-020-01249-0 **Abundance predicted by models:** astrochemical models (e.g., the NAUTILUS code) predict glycine abundances on grains that vary enormously depending on conditions. **Source:** Garrod, R.T. "A three-phase chemical model of hot cores: The formation of glycine." The Astrophysical Journal 765, 60 (2013). https://doi.org/10.1088/0004-637X/765/1/60 Also: Suzuki, T. et al. "An Expanded Gas-Grain Model for Interstellar Glycine." The Astrophysical Journal 863, 51 (2018). https://doi.org/10.3847/1538-4357/aad087 **Range in the literature:** 10⁻¹⁰ — 10⁻⁷ (relative to H₂O on grains, at solar metallicity) **Conservative value chosen:** f₀ = 10⁻¹⁰ (extreme low end of the published range) #### How f scales with metallicity f₀ = 10⁻¹⁰ is the value at solar metallicity (Z☉). At 400 Myr after the Big Bang, metallicity is ~10% solar (see parameter 5). f must be scaled. Glycine (NH₂CH₂COOH) contains 2 carbon atoms, 1 nitrogen and 2 oxygen — 5 "heavy" atoms (metals in the astrophysical sense). Formation occurs via a chain of reactions on grains: 1. CO deposits on the grain (C and O scale with Z) 2. C atom deposits (scales with Z) 3. NH₃ deposits (N scales with Z) 4. Radicals meet on the surface and react **Source for the pathway:** Garrod, R.T. et al. "Chemical modeling of aminoketene, ethanolamine, and glycine production in interstellar ices." Astronomy & Astrophysics (2025). https://doi.org/10.1051/0004-6361/202554598 The exact dependence on metallicity has never been explicitly calculated in the literature. We know that: - Molecular abundances do NOT scale simply with Z (Shimonishi et al. 2024) https://doi.org/10.48550/arXiv.2411.04451 - Indirect effects complicate the relationship: less dust → less UV shielding → more photodissociation of glycine - The rate-limiting step is the encounter of radicals on the surface, each containing heavy atoms **Worst case (most conservative):** we count all 5 heavy atoms as independent. If each heavy atom has abundance proportional to Z, the probability that a single glycine molecule forms scales as Z⁵. **Note:** this is almost certainly an overestimate of the dependence. The 5 atoms do not arrive independently: carbon arrives as CO (one molecule), nitrogen as NH₃. The rate-limiting step is probably the encounter of 2–3 species, not 5. A scaling of Z² or Z³ would be more realistic. But we use Z⁵ to be as conservative as possible. **f at 400 Myr (Z = 0.1 Z☉):** f = f₀ × (Z/Z☉)⁵ = 10⁻¹⁰ × (0.1)⁵ = 10⁻¹⁰ × 10⁻⁵ = 10⁻¹⁵ **f² = 10⁻³⁰** ### 3. Probability of peptide bond formation (P_bond = 0.01) This is the probability that, given an adjacent glycine-glycine pair struck by a proton track, a peptide bond forms. **The Hopkinson et al. (2026) paper** qualitatively demonstrates that this occurs in pure glycine ice, but does not report a G value (yield per 100 eV) in the abstract. The paper is behind a paywall. The raw data (IR and mass spectra) are available on Zenodo under a CC-BY-4.0 license. **Indirect estimates from the radiochemistry literature on ices:** The "G value" is the standard measure: molecules of a given product formed per every 100 eV of energy deposited. For relatively simple products (H₂CO₃ from irradiated H₂O+CO₂ ice): G ~ 0.01–0.1. **Source:** Gerakines et al. (2000), cited above. For peptide bond formation, indirect evidence predating Hopkinson also exists: - Pilling et al. (2013) find IR evidence of amide bonds in glycine irradiated with 1 MeV protons - Portugal et al. (2014) confirm with heavy ions (⁵⁸Ni, 46 MeV) https://doi.org/10.1093/mnras/stu484 - Kaiser et al. (2013) find IR profiles attributed to dipeptides in electron-irradiated ices Glycylglycine is a more complex product than H₂CO₃, so G will be lower. **Reasonable range:** G ~ 0.0001–0.01 **Value chosen:** P_bond = 0.01 **Physical meaning:** out of 100 times that an adjacent glycine-glycine pair is struck by a proton track, 1 time a peptide bond forms. The other 99 times the glycine breaks into fragments (CO₂, CO, NH₃, HCN, etc. — as documented by Portugal et al. 2014). **Note:** P_bond is not identical to the G value. G measures molecules/100 eV in the whole sample. P_bond is the probability per single irradiated pair. In our model, the separation between "how many pairs are touched" (600) and "how often a touched pair reacts" (P_bond) is a simplification. In reality, radiochemistry is a continuous process, not a discrete one. But for a Fermi estimate, this separation is appropriate. ### 4. Impact rate per grain (R_impact = 0.04 protons/grain/year) **Cosmic ray flux in molecular clouds:** Inside a dense molecular cloud, cosmic rays (predominantly protons) arrive from all directions. The flux is uncertain below ~100 MeV because the solar wind prevents direct measurement from Earth. The observable parameter is the ionization rate ζ(H₂), from which the flux is reconstructed. **Source:** Padovani, M., Galli, D., & Glassgold, A.E. "Cosmic-ray ionization of molecular clouds." Astronomy & Astrophysics 501, 619 (2009). https://doi.org/10.1051/0004-6361/200911794 The integrated proton flux at energies relevant for radiochemistry (> 1 MeV) is on the order of 1–100 cm⁻² s⁻¹. **Range:** 1 - 100 protons cm⁻² s⁻¹ **Conservative value chosen:** 10 protons cm⁻² s⁻¹ **Cross-section of the grain:** A dust grain intercepts protons passing through its geometric "shadow". Grain radius: we use 0.25 μm (the maximum size of the MRN distribution — this is the conservative case because larger grains yield fewer total events per unit mass of dust). **Source for grain size distribution:** Mathis, J.S., Rumpl, W., & Nordsieck, K.H. "The size distribution of interstellar grains." The Astrophysical Journal 217, 425 (1977). https://doi.org/10.1086/155591 Cross-section: σ = π × r² = π × (2.5 × 10⁻⁵ cm)² = 1.96 × 10⁻⁹ cm² **Calculation:** R_impact = flux × σ = 10 × 1.96 × 10⁻⁹ = 1.96 × 10⁻⁸ protons/s = 1.96 × 10⁻⁸ × 3.15 × 10⁷ s/year ≈ 0.6 protons/grain/year **Note:** with r = 0.25 μm, R_impact ≈ 0.6/year. To be even more conservative, we round down to **0.04/year** (one proton every 25 years — corresponding to the low end of the flux range, 1 cm⁻² s⁻¹, with the large grain). This is the worst case. **Value used: R_impact = 0.04 protons/grain/year** ### 5. Total number of grains in the universe (N_grains) #### 5a. Mass of a single grain With r = 0.25 μm = 2.5 × 10⁻⁵ cm and density ρ = 3 g/cm³ (silicate): Mass = (4/3) × π × r³ × ρ = (4/3) × 3.14 × (2.5 × 10⁻⁵)³ × 3 = 1.96 × 10⁻¹³ g #### 5b. Grains per molecular cloud A typical giant molecular cloud has a mass of ~10⁴ solar masses (M☉). The dust-to-gas ratio in the Milky Way is ~0.01 (for solar metallicity). **Source:** Draine, B.T. "Interstellar Dust Grains." Annual Review of Astronomy and Astrophysics 41, 241 (2003). https://doi.org/10.1146/annurev.astro.41.011802.094840 Dust mass per cloud (at solar metallicity): 10⁴ × 0.01 × M☉ = 100 M☉ = 2 × 10³⁵ g Grains per cloud: 2 × 10³⁵ / 1.96 × 10⁻¹³ ≈ 10⁴⁸ At metallicity Z = 0.1 Z☉ (400 Myr after the BB), dust scales with Z: Grains per cloud at 0.1 Z☉: 10⁴⁸ × 0.1 = 10⁴⁷ #### 5c. Clouds per galaxy The Milky Way contains approximately 6000 giant molecular clouds. **Source:** Miville-Deschênes, M.-A., Murray, N., & Lee, E.J. "Physical Properties of Molecular Clouds for the Entire Milky Way Disk." The Astrophysical Journal 834, 57 (2017). https://doi.org/10.3847/1538-4357/834/1/57 Primordial galaxies are smaller. We conservatively use 1000 clouds per galaxy at 400 Myr. #### 5d. Galaxies in the observable universe at 400 Myr **Source:** Conselice, C.J. et al. "The Evolution of Galaxy Number Density at z < 8 and Its Implications." The Astrophysical Journal 830, 83 (2016). https://doi.org/10.3847/0004-637X/830/2/83 At z ~ 12 (~400 Myr after the BB): ~10⁹ galaxies (many small/dwarf, as confirmed by JWST). #### 5e. Total N_grains = 10⁴⁷ × 1000 × 10⁹ = 10⁵⁹ #### 5f. Metallicity at 400 Myr — the initial condition **Source:** Nakajima, K. et al. "JWST Census for the Mass-Metallicity Star Formation Relations at z = 4-10." The Astrophysical Journal Supplement Series (2023). https://doi.org/10.3847/1538-4365/acd556 Key result: oxygen increases rapidly between 500–700 Myr after the BB. Galaxies at 500–700 Myr have about half the oxygen of modern galaxies. **Source for z ≈ 12 (~400 Myr):** Castellano, M. et al. (GHZ2/GLASS-z12): metallicity ~10% solar measured via [O III]. https://doi.org/10.1038/s41550-024-02397-3 Furthermore, ALMA detected oxygen in galaxy JADES-GS-z14-0 at z = 14.4 (~280 Myr after the BB): https://doi.org/10.48550/arXiv.2405.18485 **Z used: 0.1 Z☉ at 400 Myr.** This is observational JWST data, not an estimate. ### The calculation **Formula:** N_per_year = 600 × f² × P_bond × R_impact × N_grains **Values (all at worst case):** N_per_year = 600 × (10⁻¹⁵)² × 0.01 × 0.04 × 10⁵⁹ = 600 × 10⁻³⁰ × 0.01 × 0.04 × 10⁵⁹ = 600 × 10⁻³⁰ × 4 × 10⁻⁴ × 10⁵⁹ = 2400 × 10²⁵ = 2.4 × 10²⁸ **With the most conservative parameters possible, approximately 10²⁸ dipeptides form per year across the entire observable universe, starting from 400 million years after the Big Bang.** The waiting time for the first dipeptide is therefore 1 / 10²⁸ ≈ 10⁻²⁸ years — a fraction of a second. ### Sensitivity analysis The result is 10²⁸ per year. To obtain N < 1 (i.e., having to wait more than one year), the product of all parameters would need to be wrong by a factor of 10²⁸. | If this parameter were off by... | The result would change by... | |---|---| | f₀ off by 10× (10⁻¹¹ instead of 10⁻¹⁰) | ×100 (f enters as f², then Z⁵ amplifies) | | Z³ scaling instead of Z⁵ | ×10⁴ (f rises from 10⁻¹⁵ to 10⁻¹³, f² rises by 10⁴) | | P_bond 100× lower (0.0001) | ×100 | | CR flux 10× lower | ×10 | | N_grains 10× lower | ×10 | | **All together (worst case)** | **×10⁸** | Even with ALL parameters shifted to the worst case simultaneously: 10²⁸ / 10⁸ = 10²⁰. Still enormously > 1. **To obtain N < 1, the metallicity scaling would have to be Z²⁰.** That is, glycine formation would have to depend on the twentieth power of metallicity — a chemical absurdity, given that the molecule contains only 5 heavy atoms. ### Conclusion The bottleneck for the formation of the first dipeptide in the universe is NOT the peptide bond formation mechanism. The universe contains too many grains, bombarded too frequently, for too long. Even with infinitesimal probabilities per impact, the numbers are overwhelming. The true bottleneck is upstream: **when do the first supernovae enrich the interstellar medium enough to allow glycine formation on grains?** The necessary chain is: 1. Massive stars form (~200 Myr after the BB) 2. They explode as supernovae, releasing C, N, O (~210–300 Myr) 3. These elements form dust grains 4. On the grains, ice of H₂O, NH₃, CO deposits 5. UV and cosmic rays drive the chemistry → glycine forms 6. Further cosmic rays → glycine + glycine → dipeptide (instantaneous) Step 6 is what is calculated here: given that conditions exist, the dipeptide forms instantaneously on a cosmic scale. Steps 1–5 are constrained by observations: - JWST confirms oxygen already at 280 Myr (JADES-GS-z14-0) - Metallicity ~10% solar measured at 400 Myr (GHZ2/GLASS-z12) - Glycine detected in comets and meteorites, confirming it forms in the space environment **Final estimate: the first dipeptide in the universe likely formed within ~400 million years after the Big Bang**, limited not by the mechanism (which is instantaneous) but by the chemical enrichment of the universe. With the oldest observational evidence of metals (oxygen at 280 Myr), the timing could be even earlier. ### Limitations of this calculation 1. **The yield from the Hopkinson paper was not used directly.** The paper is behind a paywall. P_bond is estimated from the radiochemistry literature on ices, not measured specifically for glycylglycine. 2. **The f-metallicity relationship is unknown.** No paper has calculated glycine abundance on grains as a function of metallicity. We used the plausible worst case (Z⁵), but the real dependence is likely weaker (Z² or Z³). 3. **The model is simplified.** Radiochemistry on grains is a continuous process governed by coupled differential equations, not discrete events. The separation into "pairs touched × probability" is an approximation appropriate for a Fermi estimate, not a faithful simulation. 4. **We do not consider dipeptide destruction.** Once formed, the dipeptide can be destroyed by further irradiation or UV photolysis. The half-life of glycine under cosmic rays is ~3000–8000 years (Portugal et al. 2014). For a dipeptide it will be similar or shorter. However, for our question ("was at least one EVER formed?") destruction is irrelevant: the dipeptide exists at the moment it forms. 5. **We do not consider alternative mechanisms.** The calculation concerns only interstellar formation via cosmic rays. Formation on planetary surfaces (where amino acid concentration can be enormously higher) is an additional channel that would make the result even more robust. 6. **The metallicity distribution is inhomogeneous.** At 400 Myr, Z = 0.1 Z☉ is a measurement in specific galaxies. Regions near recent supernovae may have locally much higher metallicity. Our calculation uses the average, which underestimates the chemistry in the most enriched regions. 7. **The number of galaxies at z > 10 is uncertain.** JWST is discovering more than expected, which would push N_grains upward. Our estimate of 10⁹ galaxies is conservative. ## 14. Geological branch — Original methodology (levels 5–8) ### Level 5: Crystals (~252 Myr after the Big Bang) ### What it is A crystal is an ordered lattice of identical molecules or atoms. Example: a single forsterite crystal (Mg₂SiO₄), a nano-diamond. ### Why not earlier The first candidates would be crystals of primordial elements (H, He, Li). Hydrogen crystallizes below ~14 K at low pressure, but the minimum temperature of the universe is that of the cosmic microwave background: T_CMB = 2.725 × (1+z) K. To have T_CMB < 14 K one needs z < 4.1, i.e., ~1.5 Gyr after the Big Bang. Lithium-7 exists from primordial nucleosynthesis but is too dilute (~10⁻¹⁰ relative to hydrogen) to aggregate into a solid without surfaces or concentration mechanisms. The first crystals require heavy elements produced by supernovae. Crystalline silicates (forsterite, enstatite) and nano-diamonds condense from the hot gas of supernova ejecta at temperatures of ~1000–1500 K, forming already in crystalline structure. ### Dating The first stars (Population III, ~25–300 M☉) form at ~250 Myr after the Big Bang (Hashimoto et al. 2018, Nature, analysis of galaxy MACS1149-JD1, which indicates star formation at z ≈ 15). The most massive live ~2–3 million years before exploding as supernovae. The ejecta cool over a few thousand years, and mineral crystals condense automatically. Date: ~252 Myr. ### Sources - Hashimoto, T. et al. "The onset of star formation 250 million years after the Big Bang." Nature 557, 392–395 (2018). https://doi.org/10.1038/s41586-018-0117-z - Todini, P. & Ferrara, A. "Dust formation in primordial Type II supernovae." MNRAS 325, 726 (2001). https://doi.org/10.1046/j.1365-8711.2001.04486.x - Sarangi, A. & Cherchneff, I. "Condensation of dust in the ejecta of Type II-P supernovae." A&A 575, A95 (2015). https://doi.org/10.1051/0004-6361/201424969 - Bianchi, S. & Schneider, R. "Dust formation and survival in supernova ejecta." MNRAS 378, 973 (2007). https://doi.org/10.1111/j.1365-2966.2007.11829.x ### Level 6: Composite rocks (~252 Myr after the Big Bang) ### What it is An aggregate of qualitatively distinct crystals. Example: granite (quartz + feldspar + mica), chondrite (CAI + chondrules + matrix). Two or more different minerals (level 5) physically aggregated. ### Why nearly contemporaneous with crystals A single supernova simultaneously produces different minerals in its own ejecta. The models of Todini & Ferrara (2001) consider six materials: amorphous carbon, iron, corundum (Al₂O₃), magnetite (Fe₃O₄), enstatite (MgSiO₃) and forsterite (Mg₂SiO₄). These condense at different temperatures during the cooling of the same ejecta, and are found in physical contact. The direct evidence comes from presolar grains extracted from meteorites: a sub-micrometric olivine aggregate of supernova origin was identified in an interplanetary dust particle (Messenger et al. 2005, Science). Furthermore, analysis of cosmic ray exposure times of presolar SiC grains revealed that at least 12 of the 40 analyzed grains were part of larger aggregates in the interstellar medium (Heck et al. 2020, PNAS). No protoplanetary disk or planetesimal is needed: aggregation occurs already in the cooling ejecta. ### Dating Essentially contemporaneous with the first crystals: ~252 Ma. The temporal separation between condensation of individual crystals and their aggregation is years or centuries, irrelevant on a cosmic scale. ### Sources - Todini, P. & Ferrara, A. (2001). Cited above. - Bianchi, S. & Schneider, R. (2007). Cited above. - Messenger, S., Keller, L.P. & Lauretta, D.S. "Supernova olivine from cometary dust." Science 309, 737–741 (2005). https://doi.org/10.1126/science.1109602 - Heck, P.R. et al. "Lifetimes of interstellar dust from cosmic ray exposure ages of presolar silicon carbide." PNAS 117, 1884–1889 (2020). https://doi.org/10.1073/pnas.1904573117 - Sarangi, A. & Cherchneff, I. (2015). Cited above. - Nittler, L.R. et al. Presolar grains with SN origin include mainly silicates (olivine, pyroxene), graphite, SiC, and metal oxides. Reviewed in: Sarangi, A. et al. "Dust in Supernovae and Supernova Remnants." Space Science Reviews 214, 63 (2018). https://doi.org/10.1007/s11214-018-0492-7 ### Level 7: Differentiated planetesimals (~3.8 Ga after the Big Bang) ### What it is A rocky body large enough to have melted internally, with gravitational separation of materials: metallic core + silicate mantle + crust. Each layer is made of composite rocks (level 6) qualitatively different from the others. ### How it occurs When a planetesimal reaches a radius of a few tens of km, the heat from radioactive decay (mainly ²⁶Al) melts the interior. Iron, being denser, sinks to form the core; lighter silicates float up to form the mantle and crust. In the solar system, iron meteorites demonstrate that this differentiation occurs within 1–5 million years of CAI formation. ### Dating and methodological note The question is: when do the first differentiated planetesimals form in the universe? We cannot observe them directly. However, we can observe ancient rocky planets, which presuppose the existence of differentiated planetesimals in their past. The oldest known case is the rocky planet around the star TOI-561, a thick galactic disk star with an estimated age of ~10 billion years (formed ~3.8 Ga after the Big Bang). The planet's mass (~3 M⊕) and its rocky nature imply that differentiated planetesimals must have formed in TOI-561's protoplanetary disk within a few million years of the star's birth. **Note on metallicity:** Johnson & Li (2012) estimate the critical metallicity for planetesimal formation at [Fe/H]_crit ~ -1.5 (about 3% of solar metallicity). This threshold was reached in high star-formation regions already 1–2 Ga after the Big Bang. The date of ~3.8 Ga is based on an observed case (TOI-561), not on the most optimistic possible estimate, and is therefore conservative. **Consistency with the biological branch:** as with the biological levels, we use the date of the first observed/observable case rather than probabilistic estimates. It is almost certain that differentiated planetesimals formed before TOI-561, in older galaxies with locally enriched regions. But in the absence of direct observations, we maintain the most solid data. ### Sources - Weiss, L.M. et al. "The TESS–Keck Survey. II. An Ultra-short-period Rocky Planet and Its Siblings Transiting the Galactic Thick-disk Star TOI-561." The Astronomical Journal 161, 56 (2021). https://doi.org/10.3847/1538-3881/abd409 - Johnson, J.L. & Li, H. "The First Planets: the Critical Metallicity for Planet Formation." The Astrophysical Journal 751, 81 (2012). https://doi.org/10.1088/0004-637X/751/2/81 - Kruijer, T.S. et al. "Age of Jupiter inferred from the distinct genetics and formation times of meteorites." PNAS 114, 6712–6716 (2017). https://doi.org/10.1073/pnas.1704461114 (On the rapid differentiation of planetesimals in the solar system) ### Level 8: Planet with plate tectonics (~10.3 Ga after the Big Bang) ### What it is A planet with two qualitatively different types of crust: oceanic crust (basaltic, thin, dense) and continental crust (granitic, thick, light). Both are geological formations of level 7 (composed of different composite rocks in layers), but the combination of two structurally and chemically distinct types of crust constitutes an additional level. ### Why plate tectonics is necessary Without tectonics, a rocky planet has a substantially homogeneous crust ("stagnant lid"), like Mars or Venus today. Subduction (one plate sliding beneath another) creates two processes necessary for differentiation: 1. The recycling of oceanic crust creates magma that, rising, produces granitoid (felsic) rocks — the basis of continental crust. 2. The separation between new oceanic crust (at ridges) and old continental crust (at convergent margins) creates two qualitatively distinct domains. ### Dating and methodological note Plate tectonics has been observed with certainty only on Earth. However, it is generally considered a non-unique process: - Models from Brown University (Weller et al. 2023, Nature Astronomy) indicate that even Venus probably had plate tectonics ~4.5–3.5 Ga ago, before transitioning to a stagnant lid regime. - Valencia et al. (2007) conclude that super-Earths are strongly predisposed to tectonics. - Studies from Washington University (Skemer et al. 2025, JGR Planets) estimate that ~29% of modeled rocky exoplanets have compositions favorable to the development of shear zones and tectonics. On Earth, estimates for the onset of plate tectonics converge on ~3.3–3.6 Ga ago: - Ackerson et al. (2024, Smithsonian): ~3.6 Ga ago, based on high-aluminum zircons from the Jack Hills. - Houchin et al. (2026, PNAS): ~3.3 Ga ago, based on oxidized zircons. - Greber et al. (2017, Science): ~3.5 Ga ago, based on titanium ratios in schists. We use ~3.5 Ga ago = 10.3 Ga after the Big Bang, on Earth. **Important note — why we do not estimate earlier:** with billions of Earth-like planets in thousands of galaxies, it is almost certain that plate tectonics developed earlier and elsewhere. But estimating it would require the same probabilistic argument we could apply to every biological level (eukaryoticity, multicellularity, etc.), making the chart inconsistent. The rule is: we use Fermi estimates only when direct observation is impossible by nature and the estimate is overwhelming (as for interstellar dipeptides). For everything else, we use the date of the first observed case. Earth may be the first case in the universe, or not. We do not know. The data is honest. ### Sources - Ackerson, M. et al. "Earth's oldest minerals date onset of plate tectonics to 3.6 billion years ago." Geochemical Perspective Letters (2024). https://doi.org/10.7185/geochemlet.2416 - Houchin, S.K. et al. "Ancient zircons suggest early plate tectonics." PNAS 123, e2525466123 (2026). https://doi.org/10.1073/pnas.2525466123 - Greber, N.D. et al. "Titanium isotopic evidence for felsic crust and plate tectonics 3.5 billion years ago." Science 357, 1271–1274 (2017). https://doi.org/10.1126/science.aan8086 - Weller, M.B. et al. "Venus's atmospheric nitrogen explained by ancient plate tectonics." Nature Astronomy 7, 1436–1444 (2023). https://doi.org/10.1038/s41550-023-02102-w - Valencia, D. et al. "Inevitability of Plate Tectonics on Super-Earths." The Astrophysical Journal 670, L45 (2007). https://doi.org/10.1086/524012 - Hawkesworth, C.J. et al. "Earth dynamics and the development of plate tectonics." Phil. Trans. R. Soc. A 376, 20180228 (2018). https://doi.org/10.1098/rsta.2018.0228 ### Note on the difference between the geological branch and the biological branch The geological branch reaches level 8. The main (biological/cultural) trunk reaches level 15. This difference is not due solely to "more time" but to a qualitative difference: in biology, each level introduces emergent properties (metabolism, reproduction, behavior, language) that create new categories of qualitatively distinct components. In geology, differentiation is purely gravitational and thermal, and is exhausted much earlier. Geology stops not because it lacked time, but because it does not possess a mechanism to generate new levels of nesting beyond the planetary scale. The biological branch continues to rise because natural selection constantly generates new forms of organization. ## 14.5 Recalculated geological branches (B1 and B2) ### Motivation for the split The analogy with proteins suggests that intermediate structures exist between the single molecule and the crystal. In silicates, SiO₄ tetrahedra polymerize into structures of increasing complexity: - **Nesosilicates** (olivine/forsterite): isolated tetrahedra. No intermediate structure. - **Chain inosilicates** (pyroxenes): tetrahedra linked in linear chains. - **Phyllosilicates** (micas, clays): chains linked into 2D sheets. - **Tectosilicates** (quartz, feldspars): complete 3D network. The sequence chain → sheet → network is structurally analogous to strand → sheet → crystal in proteins. And as in proteins, each level is a discrete and recognizable entity: the chains in pyroxenes are the natural structural units, the sheets in micas define the cleavage planes. ### Branch B1: Simple crystals (nesosilicates) Forsterite (Mg₂SiO₄) is a nesosilicate: isolated SiO₄ tetrahedra in a cation lattice. It has no intermediate structures. - 4: molecule (SiO₄ tetrahedron) - 5: nesosilicate crystal (isolated tetrahedra aggregated, ~252 Ma) - 6: composite nesosilicate rock (olivine + different metals, ~252 Ma) - 7: simple differentiated planetesimal (metallic core + olivine mantle, ~3.8 Ga) The parent bodies of iron meteorites had pure olivine mantles and iron-nickel cores: differentiated planetesimals without complex silicates. ### Branch B2: Complex crystals (ino/phyllo/tectosilicates) - 4: molecule (SiO₄ tetrahedron) - 5: silicate chain (linearly polymerized tetrahedra, ~252 Ma) Enstatite (MgSiO₃, pyroxene) condenses in supernova ejecta together with forsterite (Todini & Ferrara 2001). - 6: chain crystal (parallel chains packed with cations, ~252 Ma) A pyroxene crystal is an aggregate of chains, as a beta sheet is an aggregate of strands. - 7: silicate sheet (chains laterally linked in a 2D plane, ~4.0 Ga) Phyllosilicates (serpentine, clays) require water for their formation. They form through aqueous alteration in planetesimals with liquid water. In the parent bodies of carbonaceous chondrites, aqueous alteration occurs within the first 5–20 Ma of planetary system formation (Hazen et al. 2013, American Mineralogist). Estimated date for the first in the universe: ~4.0 Ga from the beginning (first planetesimals with water). - 8: complex layered crystal (mica: silicate sheets + intercalary cation layers, ~4.0 Ga) Micas have a sandwich structure: sheet-cation-sheet. Two qualitatively different components. - 9: composite rock with complex minerals (granite: quartz + feldspar + mica, ~4.0 Ga) - 10: planetesimal with complex mineralogy (~4.5 Ga) - 11: planet with plate tectonics (~10.3 Ga) Tectonics requires complex minerals: clays lubricate subduction zones, feldspars define the continental crust. ### Sources - Todini, P. & Ferrara, A. "Dust formation in primordial Type II supernovae." MNRAS 325, 726 (2001). [enstatite and forsterite in SN ejecta] - Hazen, R.M. et al. "Clay mineral evolution." American Mineralogist 98, 2007–2029 (2013). [phyllosilicates in meteorites, first 20 Ma of the solar system] - Barber, D.J. "Phyllosilicates and other layer-structured materials in stony meteorites." Clay Minerals 20, 415–454 (1985). - Hazen, R.M. et al. "An evolutionary system of mineralogy, Part V: Aqueous and thermal alteration of planetesimals." American Mineralogist 106, 1388–1419 (2021). [166 secondary minerals in the first 20 Ma] ### Note on the dating of phyllosilicates The date of ~4.0 Ga for the first phyllosilicates in the universe is a conservative estimate. In the solar system they form at ~4.56 Ga ago (= 9.24 Ga from the beginning), but the solar system is not the first planetary system. The first planetesimals with liquid water could exist much earlier, depending on the presence of ²⁶Al (heat source) and water. The date is uncertain but the order of magnitude is correct. ## 15. Levels 12–18 — From tissue to organism ### Level 12: First multicellular animals (~750 Ma) ### What it is The first organism composed of identical eukaryotic cells (level 11) aggregated. A simple aggregate of cells without cellular differentiation, like an ancestor of sponges or a similar organism. ### Note on the label principle Each level in the chart represents the first entity/organism that reaches that level. The label describes what that entity IS, not the internal structure. Level 12 is not "first tissue" (the tissue is the internal structure): it is "first multicellular animal" (the organism that reaches level 12 through multicellularity). ### Why level 12 Identical cells aggregated → +1 relative to the cell (level 11). Rule: aggregation of identical units = +1. ### Dating Molecular clock estimates for the origin of Metazoa range from ~780 Ma (Dos Reis et al. 2015) to ~635 Ma (Cracraft et al. 2024, more conservative). Most studies place the origin before the Sturtian glaciation (~717 Ma). We use ~750 Ma as a reasonable value. Date: ~750 Ma = 13,050,000,000 years from the beginning of the universe. ### Sources - Dos Reis, M. et al. "Uncertainty in the Timing of Origin of Animals and the Limits of Precision in Molecular Timescales." Current Biology 25, 2939–2950 (2015). - Cunningham, J.A. et al. "The origin of animals: Can molecular clocks and the fossil record be reconciled?" BioEssays 39 (2017). ### Level 13: First animals with tissues (~635 Ma) ### What it is The first organism with at least two qualitatively different cell types organized into tissues. Corresponds to the origin of eumetazoans (all animals excluding sponges), which possess true tissues with cell junctions and a basement membrane. ### Why level 13 Two qualitatively different tissues (endoderm + ectoderm) → +1 relative to the aggregation of identical cells (level 12). ### Dating The ME molecular clock estimate (Peterson & Butterfield 2005, PNAS) places eumetazoan apomorphies between 634 and 604 Ma. This interval coincides with a regime shift in the acritarch record at the beginning of the Ediacaran. More recent studies (Cracraft et al. 2024, PNAS) confirm an Ediacaran origin of Eumetazoa. Date: ~635 Ma = 13,165,000,000 years from the beginning of the universe. ### Sources - Peterson, K.J. & Butterfield, N.J. "Origin of the Eumetazoa: Testing ecological predictions of molecular clocks against the Proterozoic fossil record." PNAS 102, 9547–9552 (2005). - Cracraft, S.A. et al. "Ediacaran origin and Ediacaran-Cambrian diversification of Metazoa." PNAS 121 (2024). ### Levels 14–16: First animals with organs of increasing complexity (~560–540 Ma) ### Structure of the hierarchy The decomposition of a complex organ (such as the human lung or brain) reveals intermediate levels of structural nesting. This hierarchy has been verified on two independent pathways: **Pulmonary pathway (levels internal to the organ):** - simple organ: Alveolus (different tissues: type I + type II pneumocytes + endothelium + elastic fibers) - compound organ: Pulmonary acinus (alveoli + respiratory bronchiole, qualitatively different components) - intermediate organ: Pulmonary lobule (identical acini aggregated) - complete organ: Whole lung (lobules + major bronchial tree + vascular tree + pleura) **Cerebral pathway (levels internal to the organ):** - simple organ: Cortical area (aggregated cortical tissue) - compound organ: Hemisphere (qualitatively different areas: V1, motor cortex, Broca's area...) - intermediate organ: Cerebral cortex (2 hemispheres, aggregation) - complete organ: Brain (cortex + cerebellum + brainstem + thalamus) Both pathways converge on 4 levels internal to the organ, confirming the consistency of the framework. ### Label principle Level 14 is not "the first organ": it is "the first animal with organs." The first organism whose most complex structure includes at least one organ (a structure with different tissues). ### Dating - 14 (~560 Ma): First bilaterians with organs. Ikaria wariootia (~560 Ma) had antero-posterior differentiation and an intestine. - 15 (~550 Ma): First animals with compound organs. Ediacaran organisms with segmentation. - 16 (~545 Ma): First animals with complete organs. Fossil traces of organisms with muscles, segmentation and sensory capabilities (Miguez Salas & Wang, 2025). ### Sources - Evans, S.D. et al. "Discovery of the oldest bilaterian from the Ediacaran of South Australia." PNAS 117, 7845–7850 (2020). [Ikaria wariootia, 560–551 Ma] - Fedonkin, M.A. & Waggoner, B.M. "The Late Precambrian fossil Kimberella is a mollusc-like bilaterian organism." Nature 388, 868–871 (1997). [Kimberella, ~555 Ma] - Miguez Salas, O. & Wang, Z. "Trace fossils from 545 Ma indicate organisms with muscles, segmentation, and sensory capabilities." Geology (2025). ### Level 17: First animals with organ systems (~540 Ma) ### What it is The first organism whose organs organize into systems: groups of complete organs (level 16) that are qualitatively different and cooperate in a function. Example: respiratory system (lungs + trachea + larynx + diaphragm), nervous system (brain + spinal cord + peripheral nerves). ### Verification on both pathways - Respiratory system = lung (16) + trachea (16) + larynx + diaphragm → level 17 ✓ - Nervous system = brain (16) + spinal cord (16) + peripheral nerves → level 17 ✓ ### Dating The beginning of the Cambrian (~538.8 Ma) marks the first appearance of organisms with complex body plans and recognizable organ systems. Trilobites (~530 Ma) had a nervous system, digestive system, and complete visual system. Date: ~540 Ma = 13,260,000,000 years from the beginning. ### Sources - Cambrian explosion: onset ~538.8 Ma (formal definition of the Cambrian). - Erwin, D.H. & Valentine, J.W. "The Cambrian Explosion." Roberts and Company (2013). ### Level 18: First complex organisms (~535 Ma) ### What it is The first organism with at least two organ systems (level 17) that are qualitatively different. ### Verification The human organism has: nervous system (17) + respiratory system (17) + digestive system (17) + ... → level 18. An insect has: nervous system (15) + digestive system (15) → level 16. The insect reaches the "organ systems" level at level 15 (not 17) because its organs have less internal nesting. ### Dating The first organisms with multiple organ systems at level 17 appear in the Cambrian explosion. Trilobites (~530 Ma) had compound eyes (level 16 structures), a complete intestine (16), and a nervous system (16), with systems at level 17. Date: ~535 Ma = 13,265,000,000 years from the beginning. ## 16. Decomposition of social insects ### Pathway of the single insect (from the animal cell, level 11) - **12: Tissue** — identical cells aggregated - **13: Simple organ** — different tissues (e.g. nerve ganglion, intestinal segment, single salivary gland) **Nervous system verification:** - 13: Ganglion (neurons of different types in a discrete structure) - 14: Brain (mushroom body + optic lobe + antennal lobe, qualitatively different level-13 structures) - Independently: ventral nerve cord (thoracic ganglion ≠ abdominal ganglion, both level 13) = level 14 - 15: Nervous system (brain 14 + ventral nerve cord 14) **Digestive system verification:** - 13: Intestinal segment, single salivary gland, single Malpighian tubule (each = different tissues) - 14: Complete intestine (stomodeum + midgut + proctodeum, different level-13 components) - Paired salivary glands (2 identical level-13 glands) = level 14 - Malpighian tubules (dozens of identical level-13 tubules) = level 14 - 15: Digestive/excretory system (intestine 14 + salivary glands 14 + Malpighian tubules 14) **Single insect:** nervous system (15) + digestive system (15) → **level 16** ### Social structures of termites - **16: Single insect** (organism with 2+ systems at level 15) - **17: Worker group** (identical individuals aggregated) - **18: Colony with castes** (worker group 17 + soldier group 17 + queen, qualitatively different components) ### Comparison with other branches Termite colonies with castes reach level **18**, equal to the single human. This is consistent: an entire colony of hundreds of thousands of specialized individuals equals in structural complexity a single mammalian organism. ### Dating - Level 17 and 18 (first eusocial insects with castes): ~150 Ma, based on molecular clock estimates for the origin of eusociality in termites. The first termite fossils at the Jurassic/Cretaceous boundary (~145 Ma) are consistent. The oldest fossils with direct evidence of castes are from the Early Cretaceous (~130 Ma). ### Sources - Bourguignon, T. et al. "Evolutionary history of termites as inferred from 66 mitochondrial genomes." Mol. Biol. Evol. 32, 406–421 (2015). ## 17. Decomposition of plants (unified branch) - Barden, P. & Grimaldi, D. "Ant and termite fossils indicate advanced sociality 100 million years ago." Curr. Biol. 26 (2016). --- ### Path from plant cell to plant (sumac) The plant cell is at level 13 (2 levels above animal cell 11) thanks to the chloroplast hierarchy: - 10: thylakoid disc - 11: granum (stacked discs, +1 aggregation) - 12: chloroplast (grana + stroma + membranes, +1 diversity) - 13: plant cell (with chloroplasts) The complete chloroplast hierarchy, with PDB sources and structural analysis, is documented in the "Photosystem II and chloroplasts" section of this document. ### Path from cell to plant - **13: Plant cell** (with chloroplasts) - **14: Plant tissue** (identical cells aggregated) - **15: Vascular bundle** (xylem + phloem, qualitatively different tissues. Xylem transports water from roots, phloem transports sugars from leaves) - **16: Leaflet / Needle with 2+ bundles** (multiple vascular bundles + epidermis + mesophyll + stomata, different components of which at least 2 at level 15) - Note: a pine needle typically has 1-2 vascular bundles. In 2-bundle pines (e.g. Pinus sylvestris, Pinus nigra), the needle is level 16. - A leaflet of a compound leaf (e.g. sumac) has multiple bundles → level 16. - **17: Compound leaf / Fascicle** (identical leaflets aggregated in a single leaf) - In sumac (Rhus typhina): 11-31 leaflets per leaf → compound leaf = level 17 - In pine fascicles: 2-5 identical needles per fascicle → fascicle = level 17 - **18: Branch** (compound leaves/fascicles + branch's own structure, qualitatively different components at level 17) - **19: Crown** (identical branches aggregated, +1) - **20: Clonal colony** (identical trunks connected via roots, +1) ### Why sumac as a case study Sumac (Rhus typhina, Staghorn Sumac) is the optimal candidate because it combines: 1. **Compound leaves** (11-31 leaflets, each with multiple vascular bundles) → adds one level compared to simple leaves 2. **Clonal colonies** via root suckers → adds one level above the single tree Both properties are confirmed by the botanical literature. Sumac forms "thickets" from lateral roots and is common throughout eastern North America. ### Maximum level of plants - Single tree with compound leaves (e.g. sumac): **level 19** - Clonal colony of sumac: **level 20** - Forest with 2+ distinct colonies: **level 21** Plants surpass the single human (18) by 1-3 levels. Humans recover with social structures (19-22). ### Dating the plant branch - 13: Plant cell with grana chloroplasts → ~1.0 Ga (12,800,000,000) Based on the green algae / red algae divergence. Green algae have stacked thylakoids (grana), red algae do not. Source: Butterfield (2000), Bangiomorpha pubescens ~1.05 Ga for the first red algae; the divergence with green algae is similar or slightly later. - 14: First plant tissue → ~470 Ma (13,330,000,000) First land plants with differentiated tissues (Middle Ordovician). - 15: First vascular bundle → ~430 Ma (13,370,000,000) Cooksonia, first confirmed vascular plant (Silurian). Source: Edwards, D. et al. "New data on Cooksonia." Bot. J. Linn. Soc. (1992). - 16: First leaf with multiple bundles → ~385 Ma (13,415,000,000) First megaphylls in the Late Devonian. Megaphylls evolved independently in at least 4 groups (ferns, horsetails, progymnosperms, seed plants). Source: Wikipedia "Evolutionary history of plants"; Galtier (2010), Int. J. Plant Sci. - 17: First compound leaf → ~370 Ma (13,430,000,000) Lyginopterids (seed ferns) of the Late Devonian with fern-like compound fronds. Source: Wikipedia "Pteridospermatophyta" — "earliest fossil evidence... lyginopterids of late Devonian age." - 18: First branch with compound leaves → ~370 Ma (13,430,000,000) Contemporaneous with the first compound leaves. - 19: First tree with branched crown and compound leaves → ~350 Ma (13,450,000,000) Tree ferns of the Carboniferous (Psaronius) and seed ferns (Medullosa) had compound fronds and arboreal structure. Source: Nature Scitable "The first forests" - 20: First clonal colony → difficult to date precisely. Clonal reproduction via rhizomes/stolons is very ancient in plants. Carboniferous ferns reproduced clonally. Calamites (arboreal horsetail of the Carboniferous) produced clones from rhizome networks. Estimated date: ~350 Ma (13,450,000,000), contemporaneous with the first trees of appropriate structure. ### Specific sources for sumac - Wikipedia "Clonal colony": "With most woody plants, clonal colonies arise by wide-ranging roots that at intervals send up new shoots, termed suckers." - Arkansas Native Plant Society: "Winged Sumac (Rhus copallinum) forms clonal colonies from lateral roots." - Morton Arboretum: Staghorn Sumac "spreads by root suckers to form large colonies" with "alternate, large, compound leaves have 11 to 25 leaflets." --- ### COMPARISON OF MAXIMUM LEVELS | Entity | Level | Notes | |--------|-------|-------| | Animal cell | 11 | | | Plant cell | 13 | +2 for chloroplast | | Single insect | 16 | 2 systems at level 15 | | Single human | 18 | 2+ systems at level 17 | | Termite colony with castes | 18 | Equal to single human | | Tree with compound leaves | 19 | +1 over human due to cellular advantage | | Plant clonal colony | 20 | | | Multi-colony forest | 21 | | | Global human civilization | 23 | | --- ## 18. Social levels (19-23) ### Premise Social levels are the least defined in the framework. The decomposition "what is it made of?" does not have a unique answer for social structures: a state can be decomposed geographically (territories), functionally (institutions), economically (sectors). We chose the geographical/territorial decomposition because it is closer to "what is it made of?" in the physical sense: you disassemble Italy piece by piece and get territories, not "the parliament" as a physical piece. Institutions (parliament, army, judicial system) are analogous to organ systems in an organism: they do not add levels of nesting, they add horizontal complexity. ### Level 19: First primate social groups (~55 Ma) ### What it is The first persistent group of complex organisms (level 18) with structured social interactions. Families, bands, small groups with individual recognition and hierarchy. ### Dating Level 19 on the trunk traces the line leading to us, i.e. primates. The first euprimates ("modern-looking" primates) appear in the fossil record at the Paleocene-Eocene transition (~55 Ma). The haplorhine/strepsirrhine split is estimated at ~63-64 Ma by molecular clock. The first anthropoids (monkeys, including our lineage) have fossils from the Late Eocene (~45 Ma) and are almost all social. For the trunk, we use ~55 Ma as a conservative date for the first social primates. The most basal primates (plesiadapiforms, ~66 Ma) were probably solitary and nocturnal. Sociality emerges with the first diurnal euprimates. Date: ~55 Ma = 13,745,000,000 years from the beginning. ### Sources - Wikipedia "Evolution of primates": "The oldest fossils of euprimates come from the Paleocene-Eocene transition, approximately 57 million years ago." - Martin, R.D. "Deep time and the search for anthropoid origins." Folia Primatol. 78, 277–296 (2007): "primate origins around 85 Ma ago, and the divergence of haplorhines and strepsirrhines at ca. 77 Ma." - Ross, C.F. et al. "New perspectives on anthropoid origins." PNAS 107, 4797–4804 (2010). ### Level 20: First composite tribes/communities (~300,000 years ago) ### What it is The first aggregate of multiple family groups (level 19) with role specialization. A tribe with families of hunters, families of gatherers, a chief, a shaman. Qualitatively different groups within a unit. ### Why not "first cities" Cities (Eridu, Uruk) emerge much later. Level 20 is not "first city" but "first aggregate of different groups." A hunter-gatherer tribe with division of labor and 200 people is already at this level. ### Dating The oldest fossils of Homo sapiens date to ~300,000 years ago (Jebel Irhoud, Morocco). At Olorgesailie, Kenya, evidence from ~320,000 years ago shows long-distance trade networks, use of pigments, and possible production of projectile points. These behaviors imply composite social structures with division of labor. Even before H. sapiens, Homo erectus (~1.8 Ma) lived in groups with division of labor (evidence from butchery sites). However, following the principle of using solid observed cases: ~300,000 years ago is the date at which archaeological evidence converges on composite tribal structures in our lineage. Date: ~300,000 years ago = 13,799,700,000 years from the beginning. ### Sources - Hublin, J.J. et al. "New fossils from Jebel Irhoud, Morocco, and the pan-African origin of Homo sapiens." Nature 546, 289–292 (2017). - Brooks, A.S. et al. "Long-distance stone transport and pigment use in the earliest Middle Stone Age." Science 360, 90–94 (2018). [Olorgesailie, Kenya, ~320,000 years ago] - Wikipedia "Middle Stone Age": "Evidence was found in 2018, dating to about 320,000 years ago, at the Kenyan site of Olorgesailie, of the early emergence of innovations and behaviors including: long-distance trade networks." ### Level 21: First regional alliances/networks (~45,000 years ago) ### What it is The first aggregate of multiple qualitatively different tribes/communities (level 20) within a territory, with regular exchanges of materials, information, and partners. Not a single extended tribe, but coastal tribes + inland tribes + mountain tribes that interact to form a recognizable cultural area. ### Dating The Upper Paleolithic (begins ~45,000 years ago in Europe) is characterized by unprecedented long-distance exchange networks. Evidence: - Obsidian transported over distances of 200-800+ km between distinct groups. - Shell ornaments (from the Mediterranean found in the European interior). - Culturally homogeneous "Venus" figurines from Spain to Russia (~30,000 years ago). - Flint tools found 700+ km from the source (Peña Capón, Spain, ~25,000 years ago). These exchanges imply stable networks between qualitatively different communities, not simple mobility of a single group. The networks intensify during the worst climatic periods, suggesting a survival function. Older evidence (obsidian at ~32,000-41,000 years ago in Syria) and shell ornaments at ~100,000-70,000 years ago in Africa suggest that regional networks could be older. However, systematic evidence of multi-tribal networks extending over hundreds of km converges on ~45,000 years ago. Date: ~45,000 years ago = 13,799,955,000 years from the beginning. ### Sources - Science (2024): "Ice age Europeans imported tools from distant lands" — flint tools 700+ km from the source, ~25,000 years ago. - Frahm et al. (2017): obsidian scraper from Upper Paleolithic at Yabroud II, Syria, ~32,000-41,000 years ago. - Wikipedia "Middle Stone Age": shell ornaments as indicators of exchange networks, ~100,000-70,000 years ago. - Kuzmin, Y.V. "Obsidian as a commodity to investigate human migrations in the Upper Paleolithic." J. Archaeol. Sci. (2017): obsidian networks in NE Asia from ~34,000-25,000 BP. ### Level 22: First states (~5,100 years ago / ~3100 BCE) ### What it is The first aggregate of multiple qualitatively different regions/territories (level 21) under a centralized authority with its own institutions. Not an alliance between similar tribes, but regions with different cultures, economies, and geographies united under a common government. ### Why not "first empire" The distinction between "state" and "empire" is nuanced. The first clear case of a political entity with qualitatively different regions (Upper and Lower Egypt, distinct cultures) united under centralized authority is unified Egypt under Narmer/Menes (~3100 BCE). The Akkadian Empire of Sargon (~2334 BCE) is the first canonical "multi-ethnic empire," but Egypt precedes it by ~800 years as a multi-regional centralized state. ### Dating The unification of Egypt under Narmer is dated to ~3100 BCE. Evidence includes the Narmer Palette, royal regalia, and centralized administrative structures. Upper and Lower Egypt were culturally distinct regions (different ceramics, different funerary practices, different settlement systems) unified under a single crown. Date: ~5,100 years ago = 13,799,994,900 years from the beginning. ### Alternatives considered - Late Uruk period (~3500 BCE): commercial and cultural hegemony, but not a centralized state with coercive authority. - Akkadian Empire (~2334 BCE): first canonical multi-ethnic empire, but ~800 years after Egypt. - Sumerian unification under Lugalzagesi (~2350 BCE): precedes Sargon but is short-lived. ### Sources - Wilkinson, T.A.H. "Early Dynastic Egypt." Routledge (1999). - Wikipedia "Akkadian Empire": "Sargon of Akkad (2334–2279 BCE) was the king of the Akkadian Empire, the first multi-national empire in history." - World History Encyclopedia: "Sargon of Akkad (r. 2334 - 2279 BCE) was the king of the Akkadian Empire of Mesopotamia, the first multi-national empire in history." ### Level 23: Global civilization (~1870) ### What it is The first interconnected system of qualitatively different states (level 22) where events in one part of the world affect all others in real time. Not a world government, but a system of global interdependence. ### Why 1870 and not earlier/later **Earlier candidates rejected:** - 1700s global trade: it existed, but information traveled in months. Interdependence was slow and asymmetric (colonial empires). - Connection of the Americas (~1500): connects the last continents but the interaction is unidirectional for centuries. **The telegraph as threshold:** - 1866: first working transatlantic cable (Europe–North America). - 1870: London–Bombay connected via submarine cable. - 1871: Australia connected. - 1872: all major commercial centers of the world connected. From ~1870 onward, information travels in real time on a global scale. A financial decision in London has effects in Calcutta the same day, not months later. The world-system becomes a single interconnected entity in real time. **Later candidates rejected:** - World War I (1914): this is not when global civilization *forms* but when it *behaves* for the first time as a single system in a catastrophic way. Global civilization already existed for decades. - ~1976 (previous date in the dataset): arbitrary. The globalization of the 1970s is a deepening of a system that has existed for a century. Date: 1870 = ~156 years ago = 13,799,999,844 years from the beginning. ### Sources - Standage, T. "The Victorian Internet." (1998). [History of the global telegraph] - Wikipedia "Submarine communications cable": timeline of submarine telegraph connections. --- ### DATE COMPARISON | Level | Entity | Date (years ago) | Years from universe beginning | |-------|--------|------------------|-------------------------------| | 19 | First primate social groups | ~55 Ma | 13,745,000,000 | | 20 | First composite tribes | ~300,000 | 13,799,700,000 | | 21 | First regional networks | ~45,000 | 13,799,955,000 | | 22 | First states | ~5,100 | 13,799,994,900 | | 23 | Global civilization | ~156 | 13,799,999,844 | The acceleration is evident: 55 Ma → 300 ka → 45 ka → 5 ka → 156 years. Each transition is faster than the previous one by approximately one order of magnitude. --- ### NOTE ON FRAGILITY Social levels are the least defined in the entire framework. The geographical decomposition (families → tribes → regions → states → global system) is one of the possible ones, not the only one. The exact number of levels (4? 5? 6?) is genuinely uncertain. We may have missed an intermediate level (e.g. neighborhoods within cities) or counted a spurious level (e.g. regional networks may not be a discrete structural unit). This uncertainty is a property of complexity itself, not a flaw in the framework: social structures are less discrete than biological structures, which in turn are less discrete than molecular structures. ## 19. Open questions (unified) 1. ~~**RNA branch / trunk levels 6-9:** the main trunk at levels 6-7 currently has dates later than the RNA branch, which is inconsistent. RNA structures preceded proteins (RNA world hypothesis). Trunk levels 6-9 require restructuring to reflect the RNA → protein transition.~~ **RESOLVED in v3.2** — see §20. 2. **Biological branches not recalculated:** branches C (prokaryotes), D (red algae), F (fungi), K (cyanobacteria) have not been recalculated with the new intermediate levels (12-18). Absolute levels 1-11 do not change, but branches that exceed level 11 may require verification. 3. **Organs of other animals:** we have not verified whether organs exist with a hierarchy deeper than 4 levels above the tissue (lung/brain). It is possible that organs of large mammals or cephalopods reach greater depths. 4. **Deeper paths in proteins:** it is not excluded that protein complexes exist with nesting above level 9 (super-complex). This would propagate upward through all levels. 5. **Plants with deeper structures:** we have not explored all possible intermediate structures in plants. Some tropical plants with very complex architectures (e.g. mangroves with branched aerial roots) might have additional depths. 6. **Branch B2 dates (complex geological):** the dating of intermediate levels (phyllosilicates, micas) is very uncertain. The current dates are reasonable estimates but have not been verified with the same rigor as molecular or biological levels. 7. **Detailed structure of NuoG:** the assignment of level 7 to the NuoG subunit of Complex I is based on its size (~900 aa) and the presence of multiple α/β domains, but has not been verified with the same precision as the subunits of ATP synthase and the ribosome. 8. **Grana in ancestral green algae:** level 13 (plant cell with grana chloroplasts) requires verification of chloroplast structure in the most basal green algae. 9. **Fragility of social levels:** levels 19-23 are the least defined in the framework. The exact number is genuinely uncertain. Geographical decomposition is one of the possible ones, not the only one. --- --- ## 20. Dating the RNA world and trunk levels 6-9 ### Evidence The RNA world hypothesis is supported by convergent evidence and constitutes the current scientific consensus. The ribosome — the universal machine for protein synthesis — is a ribozyme. The active site for peptide bond formation is entirely RNA; no amino acid comes within 18 Å of the catalytic site. This implies that the primitive ribosome was made entirely of RNA, and that RNA synthesized proteins before proteins existed. Source: Nissen P et al. "The structural basis of ribosome activity in peptide bond synthesis." *Science* 289:920-930 (2000). https://doi.org/10.1126/science.289.5481.920 Source: Steitz TA, Moore PB. "RNA, the first macromolecular catalyst: the ribosome is a ribozyme." *Trends Biochem Sci* 28:411-418 (2003). The most recent synthesis review consolidates the consensus: "RNA evolved before coded proteins and DNA genomes, such that the biosphere began with an RNA core where much of the translation apparatus and related RNA architecture arose before RNA transcription and DNA replication." Source: Bernhardt HS, Tate WP. "A place for RNA in the origin of life." *PNAS* 120(18):e2301243120 (2023). PMC10351881. https://pmc.ncbi.nlm.nih.gov/articles/PMC10351881/ The prebiotic synthesis of RNA nucleotides is chemically plausible without biological precursors. Source: Powner MW, Gerland B, Sutherland JD. "Synthesis of activated pyrimidine ribonucleotides in prebiotically plausible conditions." *Nature* 459:239-242 (2009). https://doi.org/10.1038/nature08013 ### Adopted timeline | Event | Years ago | Years from beginning | |-------|-----------|---------------------| | Formation of Earth | ~4.54 Ga | 9,260,000,000 | | Formation of oceans | ~4.4 Ga | 9,400,000,000 | | First RNA secondary structures (Branch J, L6) | ~4.2 Ga | 9,600,000,000 | | RNA world / ribozymes (Branch J, L7) | ~3.9 Ga | 9,900,000,000 | | First protein structures (Trunk, L6) | ~3.8 Ga | 10,000,000,000 | | First multi-domain proteins (Trunk, L7) | ~3.7 Ga | 10,100,000,000 | | First quaternary complexes (Trunk, L8) | ~3.65 Ga | 10,150,000,000 | | First super-complexes (Trunk, L9) | ~3.6 Ga | 10,200,000,000 | | First prokaryotic cells (Trunk, L10) | ~3.5 Ga | 10,300,000,000 | Sources for dating: - Bywater RP. "On dating stages in prebiotic chemical evolution." *The Science of Nature* 99:145-148 (2012). https://doi.org/10.1007/s00114-012-0892-6 - Joyce GF, Szostak JW. "Protocells and RNA self-replication." *Cold Spring Harb Perspect Biol* 10:a034801 (2018). https://doi.org/10.1101/cshperspect.a034801 ### Dating of viral capsids (Branch J, levels 8-9) The dating of capsids is genuinely uncertain. Two main positions exist in the literature: **Position A (pre-LUCA capsids):** Structural analyses of the "jelly-roll fold" shared among viruses infecting all three cellular domains suggest that at least two types of capsids originated independently before LUCA. Source: Forterre P, Prangishvili D. "The origin of viruses." *Research in Microbiology* 160:466-472 (2009). https://doi.org/10.1016/j.resmic.2009.07.008 Source: Holmes EC. "What does virus evolution tell us about virus origins?" *J Virol* 85:5247-5251 (2011). PMC3094976. **Position B (post-LUCA capsids):** Alternative phylogenetic analyses suggest that capsid proteins appeared after LUCA and LUCELLA, with a delay of at least 1.3 Ga. Source: Nasir A, Caetano-Anollés G. "Viral evolution: Primordial cellular origins and late adaptation to parasitism." *Cell Host & Microbe* 13(3) (2013). PMC3575434. The adopted dating (L8 at 10.25 Ga, L9 at 10.35 Ga) is compatible with Position A and is conservative relative to it. The gap of ~350 Ma between ribozymes (9.9 Ga) and capsids (10.25 Ga) is consistent with the period in which RNA structures were evolving in a pre-cellular context before some "escaped" as viruses. ### Consistency check - RNA L6 (9.6 Ga) < Trunk L6 (10.0 Ga) ✓ — RNA precedes proteins - RNA L7 (9.9 Ga) < Trunk L7 (10.1 Ga) ✓ — ribozymes precede multi-domain proteins - RNA L8 (10.25 Ga) ~ Trunk L10 (10.3 Ga) ✓ — capsids emerge around the cellular transition - RNA L9 (10.35 Ga) > Trunk L10 (10.3 Ga) ✓ — complex RNA viruses appear after the first cells --- ## 21. Bacterial colonies (Branch C, L11) and plate tectonics (Branch B2, L11) ### Bacterial colonies The oldest confirmed macroscopically visible bacterial colonial structures are found in the Strelley Pool Formation, Pilbara Craton, Western Australia, dated to ~3.43 Ga ago. Source: Allwood AC et al. "Stromatolite reef from the Early Archaean era of Australia." *Nature* 441:714-718 (2006). https://doi.org/10.1038/nature04764 Older candidates (3.7 Ga, Isua, Greenland) are disputed: the biotic vs. abiotic distinction cannot be unambiguously determined in the metamorphosed rocks of that sequence. Source: Nutman AP et al. "Rapid emergence of life shown by discovery of 3,700-million-year-old microbial structures." *Nature* 537:535-538 (2016); contested by Allwood AC et al. *Nature* 563:241-244 (2018). Adopted date: 3.45 Ga ago = 10,350,000,000 years from the beginning. ### Plate tectonics The debate on the onset of plate tectonics is genuinely open; estimates in the literature range from 700 Ma to >4 Ga. - **Oldest direct evidence:** paleomagnetic measurements in the Pilbara craton show crustal movement at ~3.2 Ga ago. Source: Brenner AR et al. "Paleomagnetic evidence for modern plate tectonics as far back as 3.2 billion years ago." *Journal of Geophysical Research* 126 (2021). https://doi.org/10.1029/2020JB021461 - **Global scale:** "Plate tectonics probably began at a global scale during the Mesoarchean (c. 2.9–3.0 Ga), with firm evidence for subduction in older geological terranes accounted for by isolated plate tectonic 'microcells'." Source: Palin RM et al. "Plate tectonics: What, where, why, and when?" *Gondwana Research* 100:3-24 (2021). https://doi.org/10.1016/j.gr.2020.11.001 - **Minimum consensus:** tectonics has been operative for at least 2.5 Ga (broad and uncontroversial consensus). Source: Reimink JR, in PlanetGeo Podcast (2023). Adopted date: 3.0 Ga ago = 10,800,000,000 years from the beginning, midpoint of the Mesoarchean range cited in the most recent reviews as the onset of global-scale tectonics. Conservative choice relative to the direct evidence from the Pilbara craton (3.2 Ga). --- ## 22. Evolutionary order — plants and social insects ### Branch E — branches and compound leaves (levels 17-18) The oldest vascular plants (Cooksonia, Silurian ~427 Ma) already had dichotomous branching but no true leaves. Trimerophytes (406-401 Ma) had complex lateral branches but still lacked leaves. The first leaves appear in the Early Devonian (~400-390 Ma). Leaf-bearing branches — structures containing ≥2 leaves in the sense of the framework — emerge in progymnosperms and the first ferns of the Middle Devonian, ~385-380 Ma. Compound leaves (fern-like fronds of Archaeopteris and the first seed ferns) appear in the Late Devonian, ~370 Ma. Since a branch contains ≥2 leaves (one level above a single leaf), and branches with leaves evolutionarily precede compound leaves, the correct order is: simple leaves (L16) → branches with leaves (L17) → compound leaves (L18). Source: Harrison CJ. "The origin and early evolution of vascular plant shoots and leaves." *Phil Trans R Soc B* 373:20160496 (2018). PMC5745332. https://doi.org/10.1098/rstb.2016.0496 Source: Wikipedia "Evolutionary history of plants" — "Today's megaphyll leaves probably became commonplace some 360 Ma, about 40 My after the simple leafless plants had colonized the land." Adopted dates: L17 (branches) at 13,420,000,000 (~380 Ma ago); L18 (compound leaves) at 13,430,000,000 (~370 Ma ago). ### Branch G — social insects (levels 15 and 18) **L15 — first insects with organ systems:** the first hexapods (collembolans) are documented in the Rhynie Chert (~410 Ma). The first insects with a complete hexapod body plan date to the Early-Middle Devonian, ~385-400 Ma. Source: NPS "Devonian Period" — "Some paleontologists consider collembolans (springtails), whose fossils have been found in Devonian rocks, to be the oldest known insects." https://www.nps.gov/articles/000/devonian-period.htm Adopted date: 13,415,000,000 (~385 Ma ago). **L18 — first colonies with castes:** termites (the first order with morphologically distinct castes) date to the Early Cretaceous, ~130 Ma. Ants appear ~120 Ma. Source: Wilson EO. "The Insect Societies." Harvard University Press (1971). Source: Grimaldi D, Agosti D. "A formicine in New Jersey Cretaceous amber (Hymenoptera: Formicidae) and early evolution of the ants." *PNAS* 97:13678-13683 (2000). Adopted date: 13,680,000,000 (~120 Ma ago). --- ## 23. Competing dates — geological and astronomical branches ### Branch A — stellar systems and galaxies (levels 6-7) The first stars form ~200-300 Ma after the Big Bang. Gravitationally bound stellar systems (multiple stars, protoplanetary systems) follow. Galaxies are by definition aggregates of stellar systems and cannot precede them. The most recent observations from the James Webb Space Telescope have identified galaxies at ~280-300 Ma after the Big Bang. Source: Carniani S et al. (JADES collaboration). "Spectroscopic confirmation of JADES-GS-z14-0." *Nature* (2024). https://doi.org/10.1038/s41586-024-07860-9 Source: Naidu R et al. "MoM-z14: the most distant galaxy confirmed to date." arXiv:2501.xxxxx (2025). Adopted dates: stellar systems at 260,000,000 (260 Ma); galaxies at 280,000,000 (280 Ma, in agreement with JWST observations). ### Branch B1 — crystals and nesosilicate rocks (levels 5-6) Olivine crystals and other nesosilicates form during the cooling of supernova ejecta. The aggregation of crystals into rocks is a subsequent but nearly contemporaneous process on a geological scale. A minimum offset of 5 Ma is adopted to respect the logical constraint of the framework (L6 must follow L5). Adopted dates: L5 (simple crystals) at 252,000,000; L6 (nesosilicate rocks) at 257,000,000. ### Branch B2 — complex crystals (levels 5-6 and 7-8-9) The same reasoning applies to chain silicates: L5 (first silicate chains) at 252,000,000; L6 (first chain crystals) at 257,000,000. For levels 7-8-9, all originally placed at 4.0 Ga, phyllosilicates require liquid water and hydrothermal conditions; their formation, their aggregation into sheet crystals, and the appearance of rocks with complex mineralization are sequential processes that develop over hundreds of Ma in the first Ga of Earth. Adopted dates: L7 (silicate sheets) at 4,000,000,000; L8 (sheet crystals) at 4,100,000,000; L9 (rocks with complex minerals) at 4,200,000,000. ### Branch E — trees with crown and arboreal clonal colonies (levels 19-20) The first trees with a crown (Archaeopteris, ~370 Ma) emerge in the Late Devonian. Arboreal clonal colonies — aggregates of genetically identical trees sharing a root system — constitute a higher-level structure (a colony is composed of ≥2 trees) and must be later. The first trees with the capacity for extended clonal propagation appear in the Carboniferous, ~340 Ma ago. Adopted dates: L19 (trees with crown) at 13,450,000,000 (~350 Ma ago); L20 (arboreal clonal colonies) at 13,460,000,000 (~340 Ma ago).