Lamarckian Evolution of Epigenome from Open Quantum Systems and Entanglement

  • Masanari Asano
  • Irina Basieva
  • Andrei KhrennikovEmail author
  • Masanori Ohya
  • Yoshiharu Tanaka
  • Ichiro Yamato
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8369)


We develop a quantum-like (QL) model of cellular evolution based on the theory of open quantum systems and entanglement between epigenetic markers in a cell. This approach is applied to modeling of epigenetic evolution of cellular populations. We point out that recently experimental genetics discovered numerous phenomena of cellular evolution adaptive to the pressure of the environment. In such phenomena epigenetic changes are fixed in one generation and, hence, the Darwinian natural selection model cannot be applied. A number of prominent genetists stress the Lamarckian character of epigenetic evolution. In quantum physics the dynamics of the state of a system (e.g. electron) contacting with an environment (bath) is described by the theory of open quantum systems. Therefore it is natural to apply this theory to model adaptive changes in the epigenome. Since evolution of the Lamarckian type is very rapid – changes in the epigenome have to be inherited in one generation – we have to find a proper mathematical description of such a speed up. In our model this is the entanglement of different epigenetic markers.


Entanglement Open quantum systems Epigenetics Cellular evolution Neo-Lamarckism Quantum master equation Markov approximation 



This paper was finished during the visit of A. Khrennikov to the Center of Quantum BioInformatics of Tokyo University of Science, February-March 2013.


  1. 1.
    Khrennikov, A.: Ubiquitous Quantum Structures: From Psychology to Finances. Springer, Berlin (2010)CrossRefGoogle Scholar
  2. 2.
    Haven, E., Khrennikov, A.: Quantum Social Science. Cambridge Press, Cambridge (2013)CrossRefGoogle Scholar
  3. 3.
    Asano, M., Ohya, M., Khrennikov, A.: Quantum-like model for decision making process in two players game. Found. Phys. 41(3), 538–548 (2010)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Asano, M., Ohya, M., Tanaka, Yu., Khrennikov, A., Basieva, I.: On application of Gorini-Kossakowski-Sudarshan-Lindblad equation in cognitive psychology. Open. Syst. Inf. Dyn. 17, 1–15 (2010)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Asano, M., Ohya, M., Tanaka, Yu., Khrennikov, A., Basieva, I.: Dynamics of entropy in quantum-like model of decision making. J. Theor. Biol. 281, 56–64 (2011)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Asano, M., Basieva, I., Khrennikov, A., Ohya, M., Tanaka, Yu., Yamato, I.: Quantum-like model for the adaptive dynamics of the genetic regulation of E. coli’s metabolism of glucose/lactose. Syst. Synth. Biol. 6, 1–7 (2012)CrossRefGoogle Scholar
  7. 7.
    Asano, M., Basieva, I., Khrennikov, A., Ohya, M., Tanaka, Yu., Yamato, I.: Quantum-like model of diauxie in Escherichia coli: operational description of precultivation effect. J. Theor. Biol. 314, 130–137 (2012)CrossRefGoogle Scholar
  8. 8.
    Dzhafarov, E.N., Kujala, J.V.: Quantum entanglement and the issue of selective influences in psychology: an overview. In: Busemeyer, J.R., Dubois, F., Lambert-Mogiliansky, A., Melucci, M. (eds.) QI 2012. LNCS, vol. 7620, pp. 184–195. Springer, Heidelberg (2012)Google Scholar
  9. 9.
    Busemeyer, J.R., Bruza, P.: Quantum Models of Cognition and Decision. Cambridge Press, Cambridge (2012)CrossRefGoogle Scholar
  10. 10.
    Ohya, M., Volovich, I.: Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems. Springer, New York (2011)CrossRefzbMATHGoogle Scholar
  11. 11.
    Jablonka, E.J., Raz, G.: Transgenerational epigenetic inheritance: prevalence, mechanisms, and implications for the study of heredity and evolution. Q. Rev. Biol. 84, 131–176 (2009)CrossRefGoogle Scholar
  12. 12.
    Khrennikov, A.: Contextual Approach to Quantum Formalism. Springer, Berlin (2009)CrossRefzbMATHGoogle Scholar
  13. 13.
    Ogryzko, V.V.: A quantum-theoretical approach to the phenomenon of directed mutations in bacteria (hypothesis). Biosystems 43, 83–95 (1997)CrossRefGoogle Scholar
  14. 14.
    Ogryzko, V.V.: On two quantum approaches to adaptive mutations in bacteria.
  15. 15.
    McFadden, J.J., Al-Khalili, J.V.: A quantum mechanical model of adaptive mutation. Biosystems 50, 203–211 (1999)CrossRefGoogle Scholar
  16. 16.
    McFadden, J.: Quantum Evolution. Harper Collins, London (2000)Google Scholar
  17. 17.
    Donald, M.J.: A Review of Quantum Evolution. quant-ph/0101019 Google Scholar
  18. 18.
    Atmanspacher, H., Primas, H.: Epistemic and ontic quantum realities. In: Adenier, G., Khrennikov, A.Yu. (eds.) Foundations of Probability and Physics-3. Conference Proceedings, vol. 750, pp. 49–62. American Institute of Physics, Melville (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Masanari Asano
    • 1
  • Irina Basieva
    • 2
  • Andrei Khrennikov
    • 2
    Email author
  • Masanori Ohya
    • 1
  • Yoshiharu Tanaka
    • 1
  • Ichiro Yamato
    • 3
  1. 1.Department of Information SciencesTokyo University of ScienceNoda-shiJapan
  2. 2.International Center for Mathematical Modeling in Physics and Cognitive SciencesLinnaeus UniversityVäxjöSweden
  3. 3.Department of Biological Science and TechnologyTokyo University of ScienceNoda-shiJapan

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