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Sequence motif dynamics in RNA pools

Johannes Harth-Kitzerow1,2,3,4,*, Tobias Göppel2,4, Ludwig Burger2,4, Torsten A. Enßlin1,3,4,†, and Ulrich Gerland2,4,‡

  • *Contact author: jharthki@mpa-garching.mpg.de
  • †Contact author: ensslin@mpa-garching.mpg.de
  • ‡Contact author: gerland@tum.de
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Phys. Rev. E 113, 024407 – Published 27 February, 2026

DOI: https://doi.org/10.1103/y5qv-qm7n

Abstract

In RNA world scenarios, pools of RNA oligomers form strongly interacting, dynamic systems, which enable molecular evolution. In such pools, RNA oligomers hybridize and dehybridize, ligate, and break, ultimately generating longer RNA molecules, which may fold into catalytically active ribozymes. A key process for the elongation of RNA oligomers is templated ligation, which can occur when two RNA strands are adjacently hybridized onto a template strand. Detailed simulations of the dynamics in RNA pools involve a large variety of possible sequences and reactions. Here we develop a reduced description of these complex dynamics within the space of sequence motifs. We then explore to what extent our reduced description can capture the behavior of detailed simulations that account for the full dynamics in the space of RNA strands. Towards this end, we project the dynamics into a motif space, which accounts only for the abundance of all possible four-nucleotide motifs. A system of ordinary differential equations describes the dynamics of those motifs. Its control parameters are effective rate constants for reactions in motif space, which we obtain from the rate constants for the processes underlying the full dynamics in the space of RNA strands. We find that these reduced motif space dynamics indeed capture important aspects of the informational dynamics of RNA pools in sequence space. This approach could also provide a framework to rationalize and interpret features of the sequence dynamics observed in experimental systems.

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References (33)

  1. F. H. C. Crick, The origin of the genetic code, J. Mol. Biol. 38, 367 (1968).
  2. L. E. Orgel, Evolution of the genetic apparatus, J. Mol. Biol. 38, 381 (1968).
  3. J. W. Szostak, The eightfold path to non-enzymatic RNA replication, J. Syst. Chem. 3, 2 (2012).
  4. P. G. Higgs and N. Lehman, The RNA world: Molecular cooperation at the origins of life, Nat. Rev. Genet. 16, 7 (2015).
  5. A. Pressman, C. Blanco, and I. A. Chen, The RNA world as a model system to study the origin of life, Curr. Biol. 25, R953 (2015).
  6. G. Leveau, D. Pfeffer, B. Altaner, E. Kervio, F. Welsch, U. Gerland, and C. Richert, Enzyme-free copying of 12 bases of RNA with dinucleotides, Angew. Chem. Int. Ed. 61, e202203067 (2022).
  7. A. Calaça Serrão, F. T. Dänekamp, Z. Meggyesi, and D. Braun, Replication elongates short DNA, reduces sequence bias and develops trimer structure, Nucleic Acids Res. 52, 1290 (2024).
  8. P. Šulc, F. Romano, T. E. Ouldridge, J. P. K. Doye, and A. A. Louis, A nucleotide-level coarse-grained model of RNA, J. Chem. Phys. 140, 235102 (2014).
  9. B. Obermayer, H. Krammer, D. Braun, and U. Gerland, Emergence of information transmission in a prebiotic RNA reactor, Phys. Rev. Lett. 107, 018101 (2011).
  10. J. Derr, M. L. Manapat, S. Rajamani, K. Leu, R. Xulvi-Brunet, I. Joseph, M. A. Nowak, and I. A. Chen, Prebiotically plausible mechanisms increase compositional diversity of nucleic acid sequences, Nucleic Acids Res. 40, 4711 (2012).
  11. H. Fellermann, S. Tanaka, and S. Rasmussen, Sequence selection by dynamical symmetry breaking in an autocatalytic binary polymer model, Phys. Rev. E 96, 062407 (2017).
  12. T. Göppel, J. H. Rosenberger, B. Altaner, and U. Gerland, Thermodynamic and kinetic sequence selection in enzyme-free polymer self-assembly inside a non-equilibrium RNA reactor, Life 12, 567 (2022).
  13. G. Laurent, T. Göppel, D. Lacoste, and U. Gerland, Emergence of homochirality via template-directed ligation in an RNA reactor, PRX Life 2, 013015 (2024).
  14. Y. J. Matsubara and K. Kaneko, Kinetic selection of template polymer with complex sequences, Phys. Rev. Lett. 121, 118101 (2018).
  15. J. H. Rosenberger, T. Göppel, P. W. Kudella, D. Braun, U. Gerland, and B. Altaner, Self-assembly of informational polymers by templated ligation, Phys. Rev. X 11, 031055 (2021).
  16. A. V. Tkachenko and S. Maslov, Spontaneous emergence of autocatalytic information-coding polymers, J. Chem. Phys. 143, 045102 (2015).
  17. A. V. Tkachenko and S. Maslov, Onset of natural selection in populations of autocatalytic heteropolymers, J. Chem. Phys. 149, 134901 (2018).
  18. S. Toyabe and D. Braun, Cooperative ligation breaks sequence symmetry and stabilizes early molecular replication, Phys. Rev. X 9, 011056 (2019).
  19. A. S. Tupper and P. G. Higgs, Rolling-circle and strand-displacement mechanisms for non-enzymatic RNA replication at the time of the origin of life, J. Theor. Biol. 527, 110822 (2021).
  20. A. S. Tupper, K. Shi, and P. G. Higgs, The role of templating in the emergence of RNA from the prebiotic chemical mixture, Life 7, 41 (2017).
  21. N. Vaidya, S. I. Walker, and N. Lehman, Recycling of informational units leads to selection of replicators in a prebiotic soup, Chem. Biol. 20, 241 (2013).
  22. K. Leu, E. Kervio, B. Obermayer, R. M. Turk-MacLeod, C. Yuan, J.-M. Luevano, Jr., E. Chen, U. Gerland, C. Richert, and I. A. Chen, Cascade of reduced speed and accuracy after errors in enzyme-free copying of nucleic acid sequences, J. Am. Chem. Soc. 135, 354 (2013).
  23. S. Rajamani, J. K. Ichida, T. Antal, D. A. Treco, K. Leu, M. A. Nowak, J. W. Szostak, and I. A. Chen, Effect of stalling after mismatches on the error catastrophe in nonenzymatic nucleic acid replication, J. Am. Chem. Soc. 132, 5880 (2010).
  24. D. T. Gillespie, A general method for numerically simulating the stochastic time evolution of coupled chemical reactions, J. Comput. Phys. 22, 403 (1976).
  25. D. T. Gillespie, Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem. 81, 2340 (1977).
  26. E. Brener, H. Levine, and Y. Tu, Mean-field theory for diffusion-limited aggregation in low dimensions, Phys. Rev. Lett. 66, 1978 (1991).
  27. E. Cohen, D. A. Kessler, and H. Levine, Fluctuation-regularized front propagation dynamics in reaction-diffusion systems, Phys. Rev. Lett. 94, 158302 (2005).
  28. T. B. Kepler and A. S. Perelson, Modeling and optimization of populations subject to time-dependent mutation, Proc. Natl. Acad. Sci. USA 92, 8219 (1995).
  29. L. S. Tsimring, H. Levine, and D. A. Kessler, RNA virus evolution via a fitness-space model, Phys. Rev. Lett. 76, 4440 (1996).
  30. J. Harth-Kitzerow, T. Göppel, L. Burger, T. A. Enßlin, and U. Gerland, Source code for Figs. 2– 11, GitHub, San Francisco (2025), https://github.com/gerland-group/SequenceMotifDynamics.
  31. J. Harth-Kitzerow, T. Göppel, L. Burger, T. A. Enßlin, and U. Gerland, Sequence motif dynamics data, Edmond, Munich (2025), https://doi.org/10.17617/3.L2WUFG.
  32. J. Harth-Kitzerow, U. Gerland, and T. A. Enßlin, MoRSAIK: Sequence motif reactor simulation, analysis and inference kit in Python, arXiv:2512.02204.
  33. J. Harth-Kitzerow, U. Gerland, and T. A. Enßlin, MoRSAIK: Sequence motif reactor simulation, analysis and inference kit in Python (Source Code), GitHub, San Francisco (2025), https://github.com/joharkit/morsaik.

Outline

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Phys. Rev. E 113, 024407– Published 27 February, 2026
  • Received 8 December 2024
  • Revised 19 December 2025
  • Accepted 22 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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