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Modulational instability and charge localization in the Holstein-SSH model of DNA with mass impurities

R. Y. Ondoua1,2,3,*, A. Dang Koko2,3,4,†, R. Abouem A Ribama1,‡, C. B. Tabi2,5, H. P. Ekobena Fouda2,3, and J. P. Nguenang1

  • *Contact author: yanickondouar@yahoo.com
  • †Contact author: dangadamou@gmail.com
  • ‡Contact author: ribamarodrigue@gmail.com
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Phys. Rev. E 113, 024213 – Published 20 February, 2026

DOI: https://doi.org/10.1103/xc38-djk7

Abstract

This research investigates the stability of localized charge modes in a Holstein-SSH DNA model incorporating a mass impurity. By deriving a semidiscrete nonlinear Schrödinger equation through Hamiltonian formalism and the adiabatic approximation, we analyze the modulational instability to assess the impact of impurity parameters on mode stability. Analytical results reveal that impurity mass significantly influences charge localization, especially near the Brillouin zone edges, with low coupling parameters favoring localized modes and higher values promoting charge delocalization. Numerical simulations confirm that the impurity's mass and sign critically affect energy and charge localization, with negative masses acting as potential wells and positive masses inducing dispersive effects. These findings highlight the crucial role of mass impurities in modulating charge transport in DNA, offering insights for designing biomolecular and nanotechnological systems with controlled electronic properties.

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References (87)

  1. D. Tautz, Notes on the definition and nomenclature of tandemly repetitive DNA sequences, DNA Fingerprinting: State of the Science (1993), pp. 21–28.
  2. V. R. Harley, R. Lovell-Badge, and P. N. Goodfellow, Definition of a consensus DNA binding site for SRY, Nucleic Acids Res. 22, 1500 (1994).
  3. L. Wang, W. Zhou, K. Wang, S. He, and Y. Chen, Predictive value of circulating plasma mitochondrial DNA for sepsis in the emergency department: Observational study based on the Sepsis-3 definition, BMC Emerg. Med. 20, 25 (2020).
  4. A. W. Murray, How to compact DNA, Science 282, 425 (1998).
  5. M. J. Puertas and M. González-Sánchez, Insertions of mitochondrial DNA into the nucleus—effects and role in cell evolution, Genome 63, 365 (2020).
  6. D. M. Knipe, A. Prichard, S. Sharma, and J. Pogliano, Replication compartments of eukaryotic and bacterial DNA viruses: Common themes between different domains of host cells, Annu. Rev. Virol. 9, 307 (2022).
  7. R. Dwivedi, P. Prakash, B. V. Kumbhar, M. Balasubramaniam, and C. Dash, HIV-1 capsid and viral DNA integration, Mbio 15, e00212 (2024).
  8. C. Chen, W. Wang, Z. Wang, F. Wei, and X. S. Zhao, Influence of secondary structure on kinetics and reaction mechanism of DNA hybridization, Nucleic Acids Res. 35, 2875 (2007).
  9. A. Samanta, L. Baranda Pellejero, M. Masukawa, and A. Walther, DNA-empowered synthetic cells as minimalistic life forms, Nat. Rev. Chem. 8, 454 (2024).
  10. P. J. Paukstelis and N. C. Seeman, 3D DNA crystals and nanotechnology, Crystals 6, 97 (2016).
  11. A. Jaekel, P. Lill, S. Whitelam, and B. Saccà, Insights into the structure and energy of DNA Nanoassemblies, Molecules 25, 5466 (2020).
  12. X. Yan, S. Huang, Y. Wang, Y. Tang, and Y. Tian, Bottom-up self-assembly based on DNA nanotechnology, Nanomaterials 10, 2047 (2020).
  13. J. E. Deweese, M. A. Osheroff, and N. Osheroff, DNA topology and topoisomerases: Teaching a “knotty” subject, Biochem. Mol. Biol. Educ. 37, 2 (2009).
  14. H. D. Ou, S. Phan, T. J. Deerinck, A. Inagaki, M. H. Ellisman, and C. C. O'Shea, ChromEMT: Visualizing and reconstructing chromatin ultrastructure and 3D organization in situ, Nat. Protoc. 20, 934 (2025).
  15. J. Dekker and L. A. Mirny, The chromosome folding problem and how cells solve it, Cell 187, 6424 (2024).
  16. A. Kuzminov, Bacterial nucleoid is a riddle wrapped in a mystery inside an enigma, J. Bacteriol. 206, e00211 (2024).
  17. L. A. Loeb and K. C. Cheng, Errors in DNA synthesis: A source of spontaneous mutations, Mutat. Res. Rev. Genet. Toxicol. 238, 297 (1990).
  18. Y. Kraytsberg, A. Nicholas, P. Caro, and K. Khrapko, Single molecule PCR in mtDNA mutational analysis: Genuine mutations vs. damage bypass-derived artifacts, Methods 46, 269 (2008).
  19. A. Koren, P. Polak, J. Nemesh, J. J. Michaelson, J. Sebat, S. R. Sunyaev, and S. A. McCarroll, Differential relationship of DNA replication timing to different forms of human mutation and variation, Am. J. Hum. Genet. 91, 1033 (2012).
  20. R. A. Bharat, S. P. Prathmesh, F. Sarsu, and P. Suprasanna, Induced mutagenesis using gamma rays: Biological features and applications in crop improvement, OBM Genet. 8, 1 (2024).
  21. Y. Wang, C. Liu, C. Fang, Q. Peng, W. Qin, X. Yan, and K. Zhang, Engineered cancer nanovaccines: A new frontier in cancer therapy, Nano Micro Lett. 17, 30 (2025).
  22. J. M. Gebicki and T. Nauser, Initiation and prevention of biological damage by radiation-generated protein radicals, Int. J. Mol. Sci. 23, 396 (2021).
  23. P. Nurse, A long twentieth century of the cell cycle and beyond, Cell 100, 71 (2000).
  24. P. K. Gupta, Single-molecule DNA sequencing technologies for future genomics research, Trends Biotechnol. 26, 602 (2008).
  25. I. Pellarin, A. Dall'Acqua, A. Favero, I. Segatto, V. Rossi, N. Crestan, J. Karimbayli, B. Belletti, and G. Baldassarre, Cyclin-dependent protein kinases and cell cycle regulation in biology and disease, Signal Transduction Targeted Ther. 10, 11 (2025).
  26. R. Mukhopadhyay, S. Nath, D. Kumar, N. Sahana, and S. Mandal, Basics of the molecular biology: From genes to its function, in Genomics Data Analysis for Crop Improvement, (Springer Nature, Singapore, 2024), p. 343.
  27. K. Numata and D. L. Kaplan, Silk proteins: Designs from nature with multipurpose utility and infinite future possibilities, Adv. Mater. 37, 2411256 (2025).
  28. B. S. Chandana, S. A. Syed, S. J. Khanum, S. Abdurahman, M. N. Purohit, P. M. Vishwanath, and R. R. Achar, Structures and functions of biomolecules, Biochemical and Molecular Pharmacology in Drug Discovery (Elsevier, 2024), pp. 3–19.
  29. A. S. Giwa, N. Ali, and M. S. Akhter, Cellulose degradation enzymes in filamentous fungi, a bioprocessing approach towards biorefinery, Mol. Biotechnol. 67, 2931 (2025).
  30. M. M. Goodarzi and R. Jalalirad, Clear insight into complex multimodal resins and impurities to overcome recombinant protein purification challenges: A review, Biotechnol. Bioeng. 122, 5 (2025).
  31. J. Briggs and P. R. Panfili, Quantitation of DNA and protein impurities in biopharmaceuticals, Anal. Chem. 63, 850 (1991).
  32. R. Nian and P. Gagnon, Advance chromatin extraction enhances performance and productivity of cation exchange chromatography-based capture of immunoglobulin G monoclonal antibodies, J. Chromatogr. A 1453, 54 (2016).
  33. C. Courts, A. Gosch, and M. Rothschild, RNA analysis in forensic molecular biology, Dtsch. Aerztebl. Int. 121, 363 (2024).
  34. S. C. Tan and B. C. Yiap, DNA, RNA, and protein extraction: The past and the present, Biomed Res. Int. 2009, 574398 (2009).
  35. M. B. S. Al-Shuhaib and H. O. Hashim, Mastering DNA chromatogram analysis in Sanger sequencing for reliable clinical analysis, J. Genet. Eng. Biotechnol. 21, 115 (2023).
  36. A. Shirizadeh, M. Ebrahimpur, S. Soltani, and G. Solgi, Chemical contamination in the extracted DNA affects the results of HLA typing by the PCR-SSOP method, Mol. Biol. Rep. 52, 23 (2025).
  37. G. Lucena-Aguilar, A. M. Sánchez-López, C. Barberán-Aceituno, J. A. Carrillo-Ávila, J. A. López-Guerrero, and R. Aguilar-Quesada, DNA source selection for downstream applications based on DNA quality indicators analysis, Biopreserv. biobanking 14, 264 (2016).
  38. A. E. Basyoni, A. Atta, M. M. Salem, and T. M. Mohamed, Harnessing exosomes for targeted drug delivery systems to combat brain cancer, Cancer Cell Int. 25, 150 (2025).
  39. A. R. Arnold, M. A. Grodick, and J. K. Barton, DNA charge transport: From chemical principles to the cell, Cell chem. biol. 23, 183 (2016).
  40. K. Klepárník and P. Boček, Electrophoresis today and tomorrow: Helping biologists' dreams come true, BioEssays 32, 218 (2010).
  41. K. S. Kwok and J. C. Ellenbogen, Moletronics: Future electronics, Mater. Today 5(2), 28 (2002).
  42. D. D. Eley and D. I. Spivey, Semiconductivity of organic substances. Part 9.—Nucleic acid in the dry state, Trans. Faraday Soc. 58, 411 (1962).
  43. H. W. Fink and C. Schönenberger, Electrical conduction through DNA molecules, Nature (London) 398, 407 (1999).
  44. N. Rizan, T. Y. Shin, H. A. Tajuddin, G. Gnana kumar, and V. Periasamy, Effect of pH on the conductivity of basidiomycetes DNAs integrated within Schottky-like junctions, ChemistrySelect 5, 601 (2020).
  45. Y. Wang, Y. Xie, M. Gao, W. Zhang, L. Liu, Y. Qu, J. Wang, C. Hu, Z. Song, and Z. Wang, Electrical conductivity measurement of λ DNA molecules by conductive atomic force microscopy, Nanotechnology 33, 055301 (2022).
  46. N. Gupta, D. Kumar, A. Das, S. Sood, and B. D. Malhotra, Conductive ink-coated paper-based supersandwich DNA biosensor for ultrasensitive detection of Neisseria gonorrhoeae, Biosensors 13, 486 (2023).
  47. R. Di Felice, A. Calzolari, and H. Zhang, Towards metalated DNA-based structures, Nanotechnology 15, 1256 (2004).
  48. H. Yamada and K. Iguchi, Some effective tight-binding models for electrons in DNA conduction: A review, Adv. Condens. Matter Phys. 2010, 380710 (2010).
  49. A. Bende, F. Bogár, and J. Ladik, Model calculations of the energy band structures of double stranded DNA in the presence of water and Na ions, Solid State Commun. 151, 301 (2011).
  50. S. Sun, Y. Zhang, X. Shi, W. Sun, C. Felser, W. Li, and G. Li, From charge to spin: An in-depth exploration of electron transfer in energy electrocatalysis, Adv. Mater. 36, 2312524 (2024).
  51. R. Goobes, O. Cohen, and A. Minsky, Unique condensation patterns of triplex DNA: Physical aspects and physiological implications, Nucleic Acids Res. 30, 2154 (2002).
  52. P. Mandrekar and A. Mandal, Pathogenesis of alcohol-associated liver disease, Clin. Liver Dis. 28, 647 (2024).
  53. D. Hennig, J. F. Archilla, and J. Agarwal, Nonlinear charge transport mechanism in periodic and disordered DNA, Physica D 180, 256 (2003).
  54. C. B. Tabi, A. Mohamadou, and T. C. Kofané, Modulational instability of charge transport in the Peyrard–Bishop–Holstein model, J. Phys.: Condens. Matter 21, 335101 (2009).
  55. H. Ngoubi, G. H. Ben-Bolie, and T. C. Kofané, Charge transport in a DNA model with solvent interaction, J. Biol. Phys. 44, 483 (2018).
  56. H. Ngoubi, G. H. Ben-Bolie, and T. C. Kofané, Delocalized charge through the DNA with microscopic effect, Eur. Phys. J. Plus 137, 166 (2022).
  57. H. Ngoubi, I. Sali, A. Mvogo, G. H. Ben-Bolie, and T. C. Kofané, Multi-exciton transfer in a biomolecular system, Nonlinear Dyn. 112, 3887 (2024).
  58. A. Dang Koko, C. B. Tabi, H. P. Ekobena Fouda, and T. C. Kofané, Discrete charge patterns in a Holstein-SSH DNA lattice, Int. J. Quantum Chem. 115, 34 (2015).
  59. D. Belobo Belobo and A. Dang Koko, Bright solitary waves as charge transport in DNA: A variational approximation, Biopolymers 111, e23346 (2020).
  60. S. M. Rayhanul Islam, S. M. Yiasir Arafat, and M. Inc, Exploring novel optical soliton solutions for the stochastic chiral nonlinear Schrödinger equation: Stability analysis and impact of parameters, J. Nonlinear Opt. Phys. Mater. 34, 2450009 (2025).
  61. U. Younas, J. Muhammad, H. F. Ismael, M. A. S. Murad, and T. A. Sulaiman, Optical fractional solitonic structures to decoupled nonlinear Schrödinger equation arising in dual-core optical fibers, Mod. Phys. Lett. B 39, 2450378 (2025).
  62. S. Abbagari, A. Houwe, L. Akinyemi, and S. Y. Doka, Soliton interaction and nonlinear localized waves in one-dimensional nonlinear acoustic metamaterials, Physica D 476, 134591 (2025).
  63. D. Mahmoud, S. Abdoulkary, L. Q. English, and A. Mohamadou, Propagation of acoustic solitons in a nonlinear left-handed transmission line, Wave Motion 139 103597 (2025).
  64. E. M. Zayed, B. M. Saad, A. H. Arnous, and Y. Yildirim, Novel solitary wave solutions in a generalized derivative nonlinear Schrödinger equation with multiplicative white noise effects, Nonlinear Dyn. 113, 7139 (2025).
  65. D. Chou, H. U. Rehman, A. Amer, and M. S. Osman, Optical soliton dynamics of the conformable nonlinear evolution equation in Bose-Einstein condensates, Rend. Lincei. Sci. Fis. Nat. 35, 1065 (2024).
  66. M. M. Khater, S. H. Alfalqi, and A. Vokhmintsev, Dynamic behavior of solitons in nonlinear Schrödinger equations, Sci. Rep. 15, 4101 (2025).
  67. D. Chevizovich, D. Michieletto, A. Mvogo, F. Zakiryanov, and S. Zdravković, A review on nonlinear DNA physics, R. Soc. Open Sci. 7, 200774 (2020).
  68. A. Zafar, K. K. Ali, M. Raheel, N. Jafar, and K. S. Nisar, Soliton solutions to the DNA Peyrard–Bishop equation with beta-derivative via three distinctive approaches, Eur. Phys. J. Plus 135, 726 (2020).
  69. T. Shafique, M. Abbas, A. Mahmood, F. A. Abdullah, A. S. Alzaidi, and T. Nazir, Solitary wave solutions of the fractional Peyrard Bishop DNA model, Opt. Quantum Electron. 56, 815 (2024).
  70. S. Nawaz, M. O. Ahmed, M. Z. Baber, E. Bittaye, and M. W. Yasin, Explicit solitary wave structure for the stochastic resonance nonlinear Schrödinger equation under Brownian motion with dynamical analysis, Sci. Rep. 15, 31817 (2025).
  71. E. M. Boon and J. K. Barton, Charge transport in DNA, Curr. Opin. Struct. Biol. 12, 320 (2002).
  72. D. W. Kang, J. H. You, and L. B. Li, The effect of hydrogen bond breaking defect on charge transport in a DNA molecular device, Physica B 407, 184 (2012).
  73. A. Alvarez, F. R. Romero, J. F. R. Archilla, J. Cuevas, and P. V. Larsen, Breather trapping and breather transmission in a DNA model with an interface, Eur. Phys. J. B 51, 119 (2006).
  74. C. L. Gninzanlong, F. T. Ndjomatchoua, and C. Tchawoua, Forward and backward propagating breathers in a DNA model with dipole-dipole long-range interactions, Phys. Rev. E 102, 052212 (2020).
  75. S. Flach and K. Kladko, Moving discrete breathers? Physica D 127, 61 (1999).
  76. J. F. Zhao, S. Zhou, X. F. Fang, and H. Zhang, Managment of nonautonomous breather molecules and rogue waves in plasma physics, Chaos, Solitons Fract. 195, 116277 (2025).
  77. R. A. A. Ribama, M. Youssoufa, R. Y. Ondoua, Z. I. Djoufack, and J. P. Nguenang, Influence of next-nearest neighbor interactions on the dynamics of discrete energy transport within neuronal microtubules, Chaos, Solitons Fract. 198, 116538 (2025).
  78. F. Schindler, V. B. Bulchandani, and W. A. Benalcazar, Nonlinear breathers with crystalline symmetries, Phys. Rev. B 111, 064312 (2025).
  79. J. Cuevas, F. Palmero, J. F. R. Archilla, and F. R. Romeo, Moving discrete breathers in Klein-Gordon chain with impurity, J. Phys A: Math. Gen. 35, 10519 (2002).
  80. R. Y. Ondoua and D. Belobo Belobo, Solitary waves dynamic for Davydov α-helical protein model: Effects of localized and periodic inhomogeneities, Phys. Rev. E 102, 062414 (2020).
  81. R. Y. Ondoua, C. B. Tabi, H. P. Ekobena, A. Mohamadou, and T. C. Kofané, Discrete energy transport in the perturbed Ablowitz-Ladik equation for Davydov model of α-helix proteins, Eur. Phys. J. B 85, 318 (2012).
  82. Z. I. Djoufack, R. Abouem A Ribama, and J. P. Nguenang, Impurity-impurity and impurity- breather interactions combined with energy localization in a quantum 1D Klein-Gordon chain, Chaos, Solitons Fract. 168, 113208 (2023).
  83. M. Youssoufa, O. Dafounansou, M. Inc, S. Rezapour, Alim, and A. Mohamadou, Traveling waves, chaos and solitons in a cubic-quintic nonlinear optical media, Comput. Appl. Math. 44, 119 (2025).
  84. L. Yang and T. Yi, Bright and dark small amplitude nonlinear localized modes in a quantum one-dimensional Klein–Gordon chain, Chin. Phys. B 17, 3841 (2008).
  85. R. A. A. Ribama, Z. I. Djoufack, and J. P. Nguenang, Breather-impurity interactions and modulational instability in a quantum 2D Klein–Gordon chain, Eur. Phys. J. B 95, 86 (2022).
  86. R. Abouem A Ribama, Z. I. Djoufack, and J. P. Nguenang, Scattering of impure mode and self-trapping phenomenon in a 1D quantum diatomic Klein–Gordon chain containing a mass defect, Eur. Phys. J. Plus 139, 193 (2024).
  87. R. Abouem A Ribama, Z. I. Djoufack, and J. P. Nguenang, Effects of nonlinear coupling parameters on the formation of intrinsic localized modes in a quantum 1D mixed Klein-Gordon/Fermi-Pasta-Ulam chain, Physica D 473, 134556 (2025).

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Phys. Rev. E 113, 024213– Published 20 February, 2026
  • Received 29 September 2025
  • Accepted 3 February 2026
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