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Quantum-like modeling in biology with open quantum systems and instruments.

Irina Basieva1, Andrei Khrennikov1, Masanao Ozawa2

  • 1Linnaeus University, International Center for Mathematical Modeling in Physics and Cognitive Sciences Växjö, SE-351 95, Sweden.

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Summary

This study introduces a quantum-like mathematical modeling approach for biological information processes. It applies quantum measurement theory to model cognitive effects and gene regulation in bacteria.

Keywords:
Biological functionsCognitionEpigenetic mutationGene regulationMathematical formalism of quantum mechanicsOpen quantum systemsPsychological effectsQuantum Markov dynamicsQuantum instruments

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Area of Science:

  • Mathematical Biology
  • Quantum Information Theory
  • Systems Biology

Background:

  • Traditional mathematical models often struggle to capture the complexity of information processing in biological systems.
  • Quantum theory offers a powerful framework for understanding information and measurement, traditionally applied to physical phenomena.
  • Bridging quantum formalism with biological processes requires novel modeling strategies.

Purpose of the Study:

  • To introduce a novel quantum-like mathematical modeling approach for information processes in biosystems.
  • To adapt quantum measurement theory and the theory of open quantum systems for biological applications.
  • To demonstrate the utility of this approach in modeling complex biological functions.

Main Methods:

  • Utilizing the mathematical formalism and methodology of quantum theory, specifically quantum measurement theory (von Neumann formulation to quantum instruments).
  • Representing biosystem states using quantum information and modeling dynamics within the framework of open quantum systems.
  • Applying quantum Markov processes and quantum master equations to model biological functions.

Main Results:

  • Successfully modeled combinations of cognitive effects and gene regulation of glucose/lactose metabolism in Escherichia coli.
  • Formalized biological concepts like Helmholtz sensation-perception theory using quantum measurement schemes.
  • Modeled psychological functions and epigenetic mutations within the open quantum systems framework.

Conclusions:

  • The quantum-like approach provides a robust mathematical framework for modeling complex information processing in biosystems.
  • Quantum measurement theory and open quantum systems dynamics offer valuable tools for understanding biological functions.
  • This interdisciplinary approach has the potential to advance our understanding of cognition, gene regulation, and other biological phenomena.