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

TL;DR

This paper introduces a quantum-like mathematical framework for modeling biological information processes using open quantum systems and instruments, applying quantum measurement theory to biological phenomena like gene regulation and perception.

Contribution

It develops a novel quantum-inspired modeling approach for biosystems, integrating quantum measurement theory and open quantum system dynamics, distinct from physical quantum processes.

Findings

Modeling of cognitive effects and gene regulation in E. coli using quantum instruments.

Application of quantum master equations to biological functions like perception and mutation.

Illustration of quantum formalization of Helmholtz sensation-perception theory.

Abstract

We present the novel approach to mathematical modeling of information processes in biosystems. It explores the mathematical formalism and methodology of quantum theory, especially quantum measurement theory. This approach is known as {\it quantum-like} and it should be distinguished from study of genuine quantum physical processes in biosystems (quantum biophysics, quantum cognition). It is based on quantum information representation of biosystem's state and modeling its dynamics in the framework of theory of open quantum systems. This paper starts with the non-physicist friendly presentation of quantum measurement theory, from the original von Neumann formulation to modern theory of quantum instruments. Then, latter is applied to model combinations of cognitive effects and gene regulation of glucose/lactose metabolism in Escherichia coli bacterium. The most general construction of quantum instruments is based on the scheme of indirect measurement, in that measurement apparatus plays the role of the environment for a biosystem. The biological essence of this scheme is illustrated by quantum formalization of Helmholtz sensation-perception theory. Then we move to open systems dynamics and consider quantum master equation, with concentrating on quantum Markov processes. In this framework, we model functioning of biological functions such as psychological functions and epigenetic mutation.