# A model of epigenetic evolution based on theory of open quantum systems

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## Abstract

We present a very general model of epigenetic evolution unifying (neo-)Darwinian and (neo-)Lamarckian viewpoints. The evolution is represented in the form of adaptive dynamics given by the quantum(-like) master equation. This equation describes development of the information state of epigenome under the pressure of an environment. We use the formalism of quantum mechanics in the purely operational framework. (Hence, our model has no direct relation to quantum physical processes inside a cell.) Thus our model is about probabilities for observations which can be done on epigenomes and it does not provide a detailed description of cellular processes. Usage of the operational approach provides a possibility to describe by one model all known types of cellular epigenetic inheritance.

## Keywords

Epigenetic markers Quantum-like operational model Cellular epigenetic evolution Neo-Darwinism Neo-Lamarckism Open quantum systems## Notes

### Acknowledgments

This paper was written under the support of the grant Quantum Bio-Informatics of Tokyo University of Science and the grant Mathematical Modeling of Complex Information Systems of Linnaeus University. Intensive discussions related to the last version of the paper took place during the visit of one of coauthors (A. Kh.) to Tokyo University of Science, February–March 2013. He would like to thank N. Watanabe for hospitality.

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