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

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.