Abstract
This chapter is devoted to a model of the epigenetic cellular evolution based on the mathematical formalism of open quantum systems. We emphasize that, although in this book we restrict our QL-modeling to the epigenetic evolution, it is clear that the structure of the model allows it to be extended to describe evolution of biological organisms in general. We restrict the model to epigenetics, since here we can use a closer analogy with quantum mechanics and mimic behavior of a cell as behavior of a quantum particle. In general, we have to take into account cell death (annihilation in quantum terminology) and birth (creation). Mathematically, such a model is more complicated. One of the basic quantum information constructions used in this chapter is entanglement of quantum states. Our evolutionary model is based on representation of the epigenetic state of a cell as entanglement of various epigenetic markers.
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Notes
- 1.
Such kind of natural selection is performed not on the cellular, but on the molecular level.
- 2.
Mathematically, it is characterized by approaching a steady state solution of the quantum master equation (Sect. 2.4).
- 3.
- 4.
As was already emphasized, our model treats all possible sources of CEI and their interrelations in the universal framework by extracting fundamental features of information processes leading to CEI.
- 5.
Quantum jump (leap) is a jump of an electron from one quantum state to another within an atom. Quantum jumps were invented by Einstein, who postulated that electrons in an atom can absorb and emit electromagnetic energy only by discrete portions, which later were called photons. Thus, opposite to classical systems, electron energy cannot change continuously.
- 6.
As in Sect. 8.2.3, we proceed under the assumption that the time scale constant \(\gamma \) was set as \(\gamma =1.\) If we take \(\gamma \) into account, then the formula for the jump-probability takes the form: \(P_{\mathrm {jump}} = p \vert c_{0} \vert ^{2} \frac{\delta t}{\gamma }.\) Hence, the smallness of the jump duration is relative to the time scale of evolution.
- 7.
Depending on the biological context, it is always possible to select a few epimutations of the main importance. Hence, the number \(k_{g}\) need not be very large. We state again that our model is operational. It need not be very detailed.
- 8.
What is beyond such a global (“nonlocal”) structure of state update? This is the separate question that can be ignored in the operational approach. However, biologists may want to have some picture of what happens beyond the operational description. Our picture is that gene expressions in genome are strongly correlated; these correlations can be nonlocal in the purely classical field manner: strongly correlated waves, including electromagnetic and chemical waves, in a cell. However, we state again that we shall proceed in the purely operational framework. Hence this classical wave picture for QL entanglement, see [22–27] need not be taken into account (and, moreover, it may be wrong). We state again that a model of brain functioning based on the representation of information by purely classical electromagnetic waves was elaborated in [28–30].
- 9.
We state once again that it has nothing to do with nonlocality of hidden variables.
References
Jablonka, E., Raz, G.: Transgenerational epigenetic inheritance: prevalence, mechanisms, and implications for the study of heredity and evolution. Q. Rev. Biol. 84, 131–176 (2009)
Asano, M., Ohya, M., Khrennikov, A.: Quantum-like model for decision making process in two players game. Found. Phys. 41(3), 538–548 (2010)
Asano, M., Ohya, M., Tanaka, Y., Khrennikov, A., Basieva, I.: On application of Gorini-Kossakowski-Sudarshan-Lindblad equation in cognitive psychology. Open. Syst. Inf. Dyn. 17, 1–15 (2010)
Asano, M., Ohya, M., Tanaka, Y., Basieva, I., Khrennikov, A.: Dynamics of entropy in quantum-like model of decision making. J. Theor. Biol. 281, 56–64 (2011)
Ogryzko, V.V.: A quantum-theoretical approach to the phenomenon of directed mutations in bacteria (hypothesis). Biosystems 43, 83–95 (1997)
Ogryzko, V.V.: On two quantum approaches to adaptive mutations in bacteria. http://arxiv.org/ftp/arxiv/papers/0805/0805.4316.pdf
McFadden, J.J., Al-Khalili, J.V.: A quantum mechanical model of adaptive mutation. Biosystems 50, 203–211 (1999)
McFadden, J.: Quantum Evolution. Harper (2000)
Donald, M.J.: A Review of Quantum Evolution. (2001) http://arxiv.org/abs/quant-ph/0101019
Fuchs, C. A.: Quantum mechanics as quantum information (and only a little more). In: Khrennikov, A. (ed.), Quantum Theory: Reconsideration of Foundations, Ser. Math. Modeling 2, Växjö University Press, Växjö, pp. 463–543 (2002)
Caves, C.M., Fuchs, C.A., Schack, R.: Quantum probabilities as Bayesian probabilities. Phys. Rev. A. 65, 022–305 (2002)
Fuchs, ChA, Schack, R.: A quantum-Bayesian route to quantum-state space. Found. Phys. 41, 345–356 (2011)
Zeilinger, A.: Dance of the Photons: From Einstein to Quantum Teleportation. Farrar, Straus and Giroux, New York (2010)
Balazs, A.: Some introductory formalizations on the affine Hilbert spaces model of the origin of life. I. On quantum mechanical measurement and the origin of the genetic code: a general physical framework theory. Biosystems 85, 114–125 (2006)
Karafyllidis, I.: Quantum mechanical model for information transfer from DNA to protein. Biosystems 93, 191–198 (2008)
Ingarden, R.S., Kossakowski, A., Ohya, M.: Information Dynamics and Open Systems: Classical and Quantum Approach. Kluwer, Dordrecht (1997)
Ohya. M., Volovich I.V.: Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems, Springer (2011)
Rooney, P., Bloch, A., Rangan, C.H.: Decoherence control and purification of two-dimensional quantum density matrices under Lindblad dissipation. (2012) http://arxiv.org/abs/1201.0399
Fisher, R.A.: The Genetical Theory of Natural Selection. Clarendon Press, Oxford (1930)
Khrennikov, A.: On quantum-like probabilistic structure of mental information. Open. Syst. Inf. Dyn. 11, 267–275 (2004)
Khrennikov, A.: Quantum-like brain: Interference of minds. Biosystems 84, 225–241 (2006)
Acacio de Barros, J., Suppes, P.: Quantum mechanics, interference, and the brain. Math. Psychology 53, 306–313 (2009)
Khrennikov, A.: Detection model based on representation of quantum particles by classical random fields: Born’s rule and beyond. Found. Phys. 39, 997–1022 (2009)
Khrennikov, A., Ohya, M., Watanabe, N.: Classical signal model for quantum channels. J. Russ. Laser Res. 31, 462–468 (2010)
Khrennikov, A.: Prequantum classical statistical field theory: Schrödinger dynamics of entangled systems as a classical stochastic process. Found. Phys. 41, 317–329 (2011)
Khrennikov, A.: Description of composite quantum systems by means of classical random fields. Found. Phys. 40, 1051–1064 (2010)
Khrennikov, A., Ohya, M., Watanabe, N.: Quantum probability from classical signal theory. Int. J. Quantum Inf. 9, 281–292 (2011)
Khrennikov, A.: On the physical basis of theory of “mental waves”. Neuroquantology 8, S71–S80 (2010)
Khrennikov, A.: Quantum-like model of processing of information in the brain based on classical electromagnetic field. Biosystems 105(3), 250–262 (2011)
Haven, E., Khrennikov, A.: Quantum Soc. Sci. Cambridge Press, Cambridge (2012)
Sollars, V., Lu, X., Xiao, L., Wang, X., Garfinkel, M.D., Ruden, D.M.: Evidence for an epigenetic mechanism by which HSP90 acts as a capacitor for morphological evolution. Nat. Genet. 33, 70–74 (2003)
Waddington, C.H.: Canalization of development and the inheritance of acquired characters. Nature 150, 563–565 (1942)
Waddington, C.H.: Genetic assimilation of an acquired character. Evolution 7, 118–126 (1953)
Bender, J.: Plant epigenetics. Curr. Biol. 12, R412–R414 (2002)
Koonin, E. V., Wolf, Yu. I.: Evolution of microbes and viruses: A paradigm shift in evolutionary biology? Frontiers in Cellular and Infection Microbiology. 1192 (2012)
Kohler, C., Grossniklaus, U.: Epigenetics: the flowers that come in from the cold. Curr. Biol. 12(4), R129–R131 (2002)
Gould, S.J., Eldredge, N.: Punctuated equilibrium comes of age. Nature 366, 223–227 (1993)
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Asano, M., Khrennikov, A., Ohya, M., Tanaka, Y., Yamato, I. (2015). Epigenetic Evolution and Theory of Open Quantum Systems: Unifying Lamarckism and Darwinism. In: Quantum Adaptivity in Biology: From Genetics to Cognition. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9819-8_8
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