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arxiv: 2605.07035 · v1 · submitted 2026-05-07 · 🧬 q-bio.OT · cs.ET

Recognition: 3 theorem links

· Lean Theorem

Genetic Information as a "Chord" of Chemical Oscillations: Emergence of Catalyst-RNA Systems Driven by Superposed Rhythms

Takeshi Ishida

Pith reviewed 2026-05-11 01:17 UTC · model grok-4.3

classification 🧬 q-bio.OT cs.ET
keywords modelcatalyticinternaloscillationspolymersselectionbiasbinary
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The pith

Chemical oscillations can bias binary polymer growth to establish catalytic loops and record functional sequences

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper presents a simulation of early molecular systems in which two internal chemical oscillators create rhythms that influence the choice of binary units as polymers elongate. The model incorporates protection and re-amplification of useful sequences to show that this bias produces catalytic networks and information-bearing molecules more reliably than random selection does. A reader would care because it links simple oscillating chemistry to the coupled origin of catalysis and genetic information through a concrete computational demonstration. The results hold across sensitivity tests with different random seeds.

Core claim

The central discovery is that superposing rhythms from two Lotka-Volterra oscillators during polymer elongation provides a temporal bias for 0/1 selection that enables the formation of interdependent catalyst-RNA systems, including catalytic loops, primordial tRNAs, and nucleic acids that record and amplify them, outperforming random models in loop establishment, functional molecule accumulation, polymer length, and entropy reduction.

What carries the argument

The synthesis of internal oscillations that supplies a temporal bias for monomer selection in polymer elongation, combined with mechanisms for protecting, recording, and re-amplifying functional sequences.

Load-bearing premise

That the internal oscillations generate a dependable temporal signal for biasing sequence choices and that the simplified rules suffice to protect and replicate functional sequences without degradation.

What would settle it

A direct comparison in which the oscillation bias is turned off but all other mechanisms like sequence protection and re-amplification are retained; if the catalytic loop formation rate then equals that of the random model, the role of the rhythms would be falsified.

Figures

Figures reproduced from arXiv: 2605.07035 by Takeshi Ishida.

Figure 1
Figure 1. Figure 1: Schematic overview of the model. A population of virtual protocells (e.g., 50 cells) evolves based on fitness. Each protocell contains two types of virtual monomers. While random natural polymerization and decomposition rarely produce meaningful sequences, the introduction of two internal chemical oscillators and polymerization that probabilistically synchronizes with these [PITH_FULL_IMAGE:figures/full_f… view at source ↗
read the original abstract

A central challenge in the origin of life is understanding how catalytic peptide-like polymers and information-bearing nucleic acid-like polymers emerged as an interde-pendent system. This study constructs a primordial cognitive model incorporating two internal Lotka-Volterra chemical oscillators to investigate, through simulation, whether a catalytic loop, primordial tRNAs, and nucleic acids that record and amplify them, can form through the interaction of polymers represented by binary (0/1) sequences. In this model, a mechanism was introduced where the synthesis of internal oscillations pro-vides a temporal bias for 0/1 selection during polymer elongation, while generated functional sequences are protected, recorded, and re-amplified. Simulation results demonstrated that the proposed cognitive model significantly outperformed a contrast model based on random 0/1 selection in terms of the establishment rate of catalytic loops, the accumulation of functional molecules, polymer elongation, and the reduction of Shannon entropy in sequence distribution. Furthermore, this superiority was generally maintained across sensitivity analyses, including batch calculations with different ran-dom seeds. While this study is a computational model based on abstract binary se-quences and simplified translation/replication rules rather than a direct reconstruction of life's origin, it provides a working hypothesis for the interdependent emergence of catalytic function and information retention by demonstrating that internal oscillations can bias sequence exploration within a framework linking autocatalytic networks, re-cording, and group selection. Future research must verify the generality and empirical validity of this framework by expanding monomer types, evolving into multi-oscillator systems, and establishing correspondences with compartmentalized experimental sys-tems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a primordial cognitive model incorporating two internal Lotka-Volterra chemical oscillators that supply a temporal bias for 0/1 selection during elongation of binary-sequence polymers. Functional sequences receive explicit protection, recording, and re-amplification under simplified translation/replication rules. Simulations show the model outperforms a random 0/1-selection contrast model in catalytic-loop establishment rate, functional-molecule accumulation, polymer elongation, and Shannon-entropy reduction in sequence distributions; the advantage persists across sensitivity runs with varied random seeds. The work offers a working hypothesis for the co-emergence of catalytic function and information retention via superposed rhythms.

Significance. If the reported simulation outcomes prove robust, the paper supplies a concrete computational framework that couples autocatalytic networks, internal oscillations, and explicit recording/amplification steps, thereby generating a falsifiable hypothesis for how informational and catalytic polymers could become interdependent. The systematic sensitivity analyses with multiple random seeds constitute a methodological strength that supports reproducibility within the model's abstract setting.

major comments (2)
  1. Abstract and Results sections: the central claim of statistically significant outperformance is presented without quantitative parameter values (Lotka-Volterra rates, bias strength, protection/amplification rates), without reported effect sizes, and without description of the statistical tests used to compare the oscillator model against the random baseline. Because the headline result rests entirely on these simulation outcomes, the absence of these details prevents independent verification of robustness.
  2. Model Description and Contrast Model paragraph: it is not stated whether the random 0/1-selection contrast model receives the same protection, recording, and re-amplification rules applied to functional sequences in the oscillator model. If protection is withheld from the contrast, the reported gains in loop formation and entropy reduction cannot be attributed specifically to the temporal bias supplied by the superposed Lotka-Volterra oscillators rather than to the protection mechanism itself.
minor comments (2)
  1. Abstract: typographical line-break artifacts appear (interde-pendent, pro-vides, se-quences, re-cording); these should be removed.
  2. Methods/Implementation: the exact discrete-time update rules for the two Lotka-Volterra oscillators and the precise mapping from oscillator phase to 0/1 selection probability are not supplied; adding the governing equations or pseudocode would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which highlight important areas for improving the clarity, completeness, and verifiability of our manuscript. We address each major comment point by point below and will make the necessary revisions to strengthen the presentation of our simulation results and model description.

read point-by-point responses
  1. Referee: Abstract and Results sections: the central claim of statistically significant outperformance is presented without quantitative parameter values (Lotka-Volterra rates, bias strength, protection/amplification rates), without reported effect sizes, and without description of the statistical tests used to compare the oscillator model against the random baseline. Because the headline result rests entirely on these simulation outcomes, the absence of these details prevents independent verification of robustness.

    Authors: We agree that the abstract and results sections would benefit from greater quantitative detail to support independent verification. The specific Lotka-Volterra rates, bias strength, and protection/amplification rates are defined in the Methods section, along with the simulation parameters. We will revise the abstract and results to explicitly summarize these values, report effect sizes for the key performance metrics (catalytic loop establishment, functional molecule accumulation, polymer length, and entropy reduction), and describe the statistical tests employed (including the type of test, sample sizes from the sensitivity runs, and any multiple-comparison corrections). These additions will be incorporated without altering the core findings. revision: yes

  2. Referee: Model Description and Contrast Model paragraph: it is not stated whether the random 0/1-selection contrast model receives the same protection, recording, and re-amplification rules applied to functional sequences in the oscillator model. If protection is withheld from the contrast, the reported gains in loop formation and entropy reduction cannot be attributed specifically to the temporal bias supplied by the superposed Lotka-Volterra oscillators rather than to the protection mechanism itself.

    Authors: We apologize for the lack of explicit statement on this point. The random 0/1-selection contrast model applies identical protection, recording, and re-amplification rules to functional sequences; the sole difference is the absence of the temporal bias from the superposed Lotka-Volterra oscillators during the 0/1 selection step in polymer elongation. We will revise the Model Description and Contrast Model paragraph to state this equivalence clearly, thereby ensuring that the reported advantages are attributable specifically to the oscillatory bias rather than the protection mechanism. revision: yes

Circularity Check

0 steps flagged

No circularity: simulation results compared to independent random control

full rationale

The paper describes a simulation in which two Lotka-Volterra oscillators supply a temporal bias for 0/1 monomer selection during polymer elongation, while separately specifying protection, recording, and re-amplification rules for functional sequences. Outcomes are evaluated against an explicit contrast model that performs random 0/1 selection. No equations, fitted parameters, or self-citations are invoked that would make the reported superiority (catalytic-loop establishment, entropy reduction, etc.) equivalent to the model's own inputs by construction. The central claim therefore rests on an external benchmark rather than on any definitional or self-referential reduction.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The model rests on numerous domain assumptions about how oscillations translate into sequence bias and how functional sequences are protected and copied; these are not derived from first principles but introduced to make the simulation tractable.

free parameters (3)
  • Lotka-Volterra oscillator parameters
    Amplitude, frequency, and coupling strengths of the two internal oscillators are required to generate the temporal bias but are not specified in the abstract.
  • selection bias strength
    The degree to which oscillator phase influences 0/1 choice during elongation is a tunable parameter that directly affects the reported performance difference.
  • protection and amplification rates
    Rates at which catalytic-loop sequences are protected from degradation and re-amplified are introduced to close the functional loop and are not derived from external data.
axioms (2)
  • domain assumption Binary (0/1) sequences can represent primordial polymers with catalytic and informational properties under simplified translation/replication rules.
    Invoked throughout the model construction to allow simulation of sequence evolution without real chemistry.
  • domain assumption Internal chemical oscillations can be treated as independent Lotka-Volterra systems whose phases provide a temporal selection bias.
    Stated as the core mechanism linking rhythms to sequence choice.

pith-pipeline@v0.9.0 · 5590 in / 1727 out tokens · 34912 ms · 2026-05-11T01:17:41.009764+00:00 · methodology

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Works this paper leans on

40 extracted references · 40 canonical work pages

  1. [1]

    Origin of life: The RNA world

    Gilbert, W. Origin of life: The RNA world. Nature 1986, 319, 618 . https://doi.org/10.1038/319618a0 https://doi.org/10.1038/319618a0

  2. [2]

    The RNA World: molecular cooperation at the origins of life

    Higgs, P.; Lehman, N. The RNA World: molecular cooperation at the origins of life. Nat Rev Genet 2015, 16, 7 –17. doi:10.1038/nrg3841. https://doi.org/10.1038/nrg3841 tRNA Hamming Distance Weights 0.005 0.01 (Ref) 0.02 0.05 Cognitive Model 93.3 % 83.3 % 73.3 % 70.0 % Number of Protocells 10 20 50 (Ref) 80 120 Cognitive Model 66.7 % 93.3 % 83.3 % 83.3 % 70...

  3. [3]

    Cell, 1982,31(1):147-157

    Kruger, K.; Grabowski, PJ.; Zaug AJ.; Sands J.; Gottschling DE.; Cech TR.; Self-splicing RNA: autoexcision and autocyclization of the ribosomal RNA intervening sequence of Tetrahymena. Cell, 1982,31(1):147-157. doi:10.1016/0092-8674(82)90414-7. https://doi.org/10.1016/0092-8674(82)90414-7

  4. [4]

    Cell, 1983, 35(3 Pt 2), 849-857

    Guerrier-Takada C.; Gardiner K.; Marsh T.; Pace N.; Altman S., The RNA moiety of ribonuclease P is the catalytic subunit of the enzyme. Cell, 1983, 35(3 Pt 2), 849-857. doi:10.1016/0092-8674(83)90117-4. https://doi.org/10.1016/0092-8674(83)90117-4

  5. [5]

    Development, Growth and Differentiation, 2023, 65(3), 167-174

    Tagami S.; Li P.; The origin of life: RNA and protein co -evolution on the ancient Earth. Development, Growth and Differentiation, 2023, 65(3), 167-174. doi:10.1111/dgd.12845. https://doi.org/10.1111/dgd.12845

  6. [6]

    Journal of Systematics and Evolution

    Saad NY., A ribonucleopeptide world at the origin of life. Journal of Systematics and Evolution. 2018, 56(1), 1-13. doi:10.1111/jse.12287 https://doi.org/10.1111/jse.12287

  7. [7]

    Evolutionary Steps in the Emergence of Life Deduced from the Bottom -Up Approach and GADV Hypothesis (Top - Down Approach)

    Ikehara, K. Evolutionary Steps in the Emergence of Life Deduced from the Bottom -Up Approach and GADV Hypothesis (Top - Down Approach). Life 2016, 6, 6. https://doi.org/10.3390/life6010006

  8. [8]

    Ikehara, K., Towards Revealing the Origin of Life: Presenting the GADV Hypothesis, Springer, 2021, ISBN : 978-3030710866

  9. [9]

    Proceedings of the National Academy of Sciences of the United States of America

    Schimmel P.; Giegé R.; Moras D.; Yokoyama S., An operational RNA code for amino acids and possible relationship to genetic code. Proceedings of the National Academy of Sciences of the United States of America . 1993 , 90(19), 8763-8768. doi:10.1073/pnas.90.19.8763. https://doi.org/10.1073/pnas.90.19.8763

  10. [10]

    Journal of Molecular Evo- lution

    Yarus M.; Widmann JJ.; Knight R., RNA-amino acid binding: a stereochemical era for the genetic code. Journal of Molecular Evo- lution. 2009, 69, 406-429. doi:10.1007/s00239-009-9270-1. https://doi.org/10.1007/s00239-009-9270-1

  11. [11]

    , The origin of the genetic code: theories and their relationships, a review

    Di Giulio M. , The origin of the genetic code: theories and their relationships, a review. Biosystems, 2005, 80(2), 175-184. doi:10.1016/j.biosystems.2004.11.005. https://doi.org/10.1016/j.biosystems.2004.11.005

  12. [12]

    Philosophical Transactions of the Royal Society B: Biological Sciences

    Suga H.; Hayashi G.; Terasaka N., The RNA origin of transfer RNA aminoacylation and beyond. Philosophical Transactions of the Royal Society B: Biological Sciences. 2011, 366(1580), 2959-2964. doi:10.1098/rstb.2011.0137. https://doi.org/10.1098/rstb.2011.0137

  13. [13]

    Nature Chemical Biology

    Ishida S.; Terasaka N.; Katoh T.; Suga H., An aminoacylation ribozyme evolved from a natural tRNA-sensing T-box riboswitch. Nature Chemical Biology. 2020, 16(6), 702-709. doi:10.1038/s41589-020-0500-6. https://doi.org/10.1038/s41589-020-0500-6

  14. [14]

    Naturwissenschaften 1971, 58(10), 465–523

    Eigen, M., Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften 1971, 58(10), 465–523. https://doi.org/10.1007/BF00623322

  15. [15]

    Nicolis, G.,; Prigogine, I., Self-organization in non-equilibrium systems. Wiley. 1977. ISBN 978-0471024019

  16. [16]

    A principle of natural self -organization

    Eigen M.; Schuster P., The hypercycle. A principle of natural self -organization. Part A: Emergence of the hypercycle. Naturwis- senschaften, 1977, 64(11), 541-565. doi:10.1007/BF00450633. https://doi.org/10.1007/BF00450633

  17. [17]

    https://www.mdpi.com/2075-1729/12/10/1580

    Ishida,T., Emergence Simulation of Biological Cell -like Shapes Satisfying the Conditions of Life Using a Lattice -Type Multiset Chemical Model, LIFE, 2022, 12(10), 1580. https://www.mdpi.com/2075-1729/12/10/1580

  18. [18]

    Ishida,T., A constructive chemical oscillator model demonstrates the emergence of homeostasis before genetic information through active inference, Discov Life 56, 2 (2026) https://doi.org/10.1007/s11084-026-09723-x

  19. [19]

    J R Soc Interface, 2013; 10 (86): 20130475

    Friston K., Life as we know it. J R Soc Interface, 2013; 10 (86): 20130475. https://doi.org/10.1098/rsif.2013.0475

  20. [20]

    Hordijk, W., Autocatalytic Sets: From the Origin of Life to the Economy, BioScience, 2013, vol. 63, no. 11, pp. 877 –881, doi: 10.1525/bio.2013.63.11.6. https://academic.oup.com/bioscience/article-lookup/doi/10.1525/bio.2013.63.11.6

  21. [21]

    Systematic and Applied Microbiology

    Wächtershäuser G., Pyrite Formation, the First Energy Source for Life: a Hypothesis. Systematic and Applied Microbiology. 1988, 10(3), 207-210. doi:10.1016/S0723-2020(88)80001-8. https://doi.org/10.1016/S0723-2020(88)80001-8

  22. [22]

    Huber C.; Wächtershäuser G., Peptides by Activation of Amino Acids with CO on (Ni,Fe)S Surfaces: Implications for the Origin of Life. Science. 1998, 281(5377), 670-672. doi:10.1126/science.281.5377.670. https://doi.org/10.1126/science.281.5377.670

  23. [23]

    Chen, C.; Li, J., Recent advances in coacervate protocells from passive catalysts to chemically programmable systems, Commu- nications Chemistry, 2026, vol. 9, art. no. 76, doi: 10.1038/s42004-026-01937-4. 33 of 34 https://www.nature.com/articles/s42004-026-01937-4

  24. [24]

    Matsuo, M.; Kurihara, K., Proliferating coacervate droplets as the missing link between chemistry and biology in the origin s of life, Nature Communications, 2021, vol. 12, no. 1, art. no. 5487, doi: 10.1038/s41467-021-25530-6. https://doi.org/10.1038/s41467-021-25530-6

  25. [25]

    Kauffman, S. A., Autocatalytic sets of proteins, Journal of Theoretical Biology, 1986,Vol.119, Issue 1, , Pages 1 -24, https://doi.org/10.1016/S0022-5193(86)80047-9 https://www.nature.com/articles/s41467-021-25530-6

  26. [26]

    A.; Roli, A., Is the emergence of life and of agency expected?, Phil

    Kauffman, S. A.; Roli, A., Is the emergence of life and of agency expected?, Phil. Trans. R. Soc. B, 2025, vol. 380, no. 1 936, p. 20240283, doi: 10.1098/rstb.2024.0283. https://royalsocietypublishing.org/doi/10.1098/rstb.2024.0283

  27. [27]

    Hordijk, W.; Steel, M., Autocatalytic Networks at the Basis of Life’s Origin and Organization, Life, 2018, vol. 8, no. 4, p . 62, doi: 10.3390/life8040062. https://www.mdpi.com/2075-1729/8/4/62

  28. [28]

    Hordijk, W.; Steel, M., Detecting autocatalytic, self -sustaining sets in chemical reaction systems. J. Theor. Biol. 2004, 227, 451 –

  29. [29]

    (doi:10.1016/j.jtbi.2003.11.020) https://doi.org/ doi:10.1016/j.jtbi.2003.11.020

  30. [30]

    doi: 10.26434/chemrxiv.7895891.v1

    Hou, L.; Dueñas-Diez, M.; Srivastava, R.; Perez-Mercader, J., Flow Chemistry Controls Both Self -Assembly and the Entrapped Oscillatory Cargo in Belousov -Zhabotinsky Driven Polymerization -Induced Self -Assembly, ChemRxiv, 2019. doi: 10.26434/chemrxiv.7895891.v1. https://chemrxiv.org/doi/full/10.26434/chemrxiv.7895891.v1

  31. [31]

    M., Oscillations, travelling fronts and patterns in a supramo- lecular system, Nature Nanotech, 2018, vol

    Leira-Iglesias, J.; Tassoni, A.; Adachi, T.; Stich, M.; Hermans, T. M., Oscillations, travelling fronts and patterns in a supramo- lecular system, Nature Nanotech, 2018, vol. 13, no. 11, pp. 1021–1027, doi: 10.1038/s41565-018-0270-4. https://www.nature.com/articles/s41565-018-0270-4

  32. [32]

    -F.; Zhang, X., Dissipative Supramolecular Polymerization Powered by Light, CCS Chem, 2019, vol

    Yin, Z.; Song, G.; Jiao, Y.; Zheng, P.; Xu, J. -F.; Zhang, X., Dissipative Supramolecular Polymerization Powered by Light, CCS Chem, 2019, vol. 1, no. 4, pp. 335–342,doi: 10.31635/ccschem.019.20190013. http://www.chinesechemsoc.org/doi/10.31635/ccschem.019.20190013

  33. [33]

    R.; Runikhina, S

    Ter Harmsel, M.; Maguire, O. R.; Runikhina, S. A.; Wong, A. S. Y.; Huck, W. T. S.; Harutyunyan, S. R., A catalytically ac tive oscillator made from small organic molecules, Nature, 2023, vol. 621, no. 7977, pp. 87–93, doi: 10.1038/s41586-023-06310-2. https://www.nature.com/articles/s41586-023-06310-2

  34. [34]

    A.; Rossi, F., Transport -driven chemical oscillations: a review,Phys

    Budroni, M. A.; Rossi, F., Transport -driven chemical oscillations: a review,Phys. Chem. Chem. Phys.,2024, vol. 26, no. 47, pp. 29185–29226, doi: 10.1039/D4CP03466J. https://xlink.rsc.org/?DOI=D4CP03466J

  35. [35]

    Damer, B.; Deamer, D., The Hot Spring Hypothesis for an Origin of Life, Astrobiology, 2020, vol. 20, no. 4, pp. 429 –452, doi: 10.1089/ast.2019.2045. https://journals.sagepub.com/doi/full/10.1089/ast.2019.2045

  36. [36]

    N., Wet-dry cycles cause nucleic acid monomers to polymerize into long chains, Proc

    Song, X.; Šimonis, P.; Deamer, D.; Zare, R. N., Wet-dry cycles cause nucleic acid monomers to polymerize into long chains, Proc. Natl. Acad. Sci. U.S.A., 2024, vol. 121, no. 49, p. e2412784121, doi: 10.1073/pnas.2412784121. https://pnas.org/doi/10.1073/pnas.2412784121

  37. [37]

    Segré, D.; Ben-Eli, D.; Lancet, D., Compositional genomes: prebiotic information transfer in mutually catalytic noncovalent as- semblies, Proc. Natl. Acad. Sci. U.S.A., 2000, vol. 97, no. 8, pp. 4112–4117, doi: 10.1073/pnas.97.8.4112. https://pnas.org/doi/full/10.1073/pnas.97.8.4112

  38. [38]

    Parrondo, J. M. R. ; Horowitz, J. M.; Sagawa, T., Thermodynamics of information, Nature Physics, 2015, vol. 11, pp. 131 –139, 2015, doi: 10.1038/nphys3230. https://www.nature.com/articles/nphys3230

  39. [39]

    8, Issue 14, pp

    Marsaglia,G., Xorshift RNGs, Journal of Statistical Software, 2003, Vol. 8, Issue 14, pp. 1-6, DOI: 10.18637/jss.v008.i14 https://doi.org/10.18637/jss.v008.i14

  40. [40]

    J., The Origin and Nature of Life on Earth: The Emergence of the Fourth Geosphere

    Smith, E.; Morowitz, H. J., The Origin and Nature of Life on Earth: The Emergence of the Fourth Geosphere. Cambridge Univer- sity Press. 2016, ISBN: 978-1107121881 34 of 34 Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual au- thor(s) and contributor(s) and not of MDPI and/or th...