Abstract
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.
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Notes
- 1.
One may in principle speak about interaction with an environment. However, “interaction” is not the right term, since it assumes the presence of an interaction force. This is natural in classical physics, but not in quantum. In some sense a quantum system just “feels” the presence of the environment. There is no real force acting to a system from the side of the environment. In fact, in for cognitive phenomena we have the similar situation. By using “mental forces” one would make a model too mechanistic (of Newtonian type), see, however, [1, 2] for attempts to apply Bohmian mechanics to cognitive phenomena and, especially, finance.
- 2.
Everywhere below we shall use the term epimutation: a heritable change in gene expression that does not affect the actual base pair sequence of DNA, see, e.g., Jablonka and Raz [11] for an extended review of heritable epimutations, theory and experiment.
- 3.
Lamarck was one of the firsts who presented evolution in biology as a scientific theory. One of the basic ideas of J. B. Lamarck is that an organism can pass on characteristics that it acquired during its lifetime to its offspring. According to Lamarck evolution is fundamentally adaptive in its nature. Extension of Lamarckism to cellular evolution is known as neo-Lamarckism.
- 4.
These studies belong to the domain of quantum biology. Our QL model is not a part of quantum biology. We can play with terminology and call the domain of our research bio-quantumiology – to distinguish from research in quantum biology.
- 5.
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.
- 6.
Nowadays the term neo-Darwinism is used for theory of evolution, driven by natural selection acting on variation produced by genetic mutation and genetic recombination. Thus the Darwinian model of evolution liberated from ideas of Lamarckism was combined with genetics. Purely random genetic variations are subjected to natural selection under the environmental pressure. Neo-Darwinism is based on the main postulate of molecular biology: in a cell the information flow is possible only in one direction from DNA (RNA) to proteins, from genotype to phenotype; so, never backward: from phenotype to genotype.
- 7.
In our opinion, Kimura proposed that evolution or DNA changes occur neutral, but he did not propose that evolution occurs at non-functional areas. Even at functional areas DNA changes occur at any time, but when the phenotype of functional change appears (for example at heart muscle), we really have evolution making the birth of new species.
- 8.
For example, in quantum formalism one speaks about collapse of the wave function which happens instantly. However, by proceeding more carefully one talks about change of the quantum state as the result of measurement or more generally interaction with an environment. And such a process is not instantaneous.
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Acknowledgments
This paper was finished during the visit of A. Khrennikov to the Center of Quantum BioInformatics of Tokyo University of Science, February-March 2013.
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Asano, M., Basieva, I., Khrennikov, A., Ohya, M., Tanaka, Y., Yamato, I. (2014). Lamarckian Evolution of Epigenome from Open Quantum Systems and Entanglement. In: Atmanspacher, H., Haven, E., Kitto, K., Raine, D. (eds) Quantum Interaction. QI 2013. Lecture Notes in Computer Science(), vol 8369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54943-4_30
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