Linnaeus University, International Center for Mathematical Modeling in Physics and Cognitive Sciences Växjö, SE-351 95, Sweden.
Linnaeus University, International Center for Mathematical Modeling in Physics and Cognitive Sciences Växjö, SE-351 95, Sweden.
Biosystems. 2021 Mar;201:104328. doi: 10.1016/j.biosystems.2020.104328. Epub 2020 Dec 24.
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 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.
我们提出了一种新的生物系统信息过程数学建模方法。该方法探索了量子理论，特别是量子测量理论的数学形式和方法。这种方法被称为类量子方法，应与生物系统中真正的量子物理过程（量子生物物理学、量子认知）区分开来。它基于生物系统状态的量子信息表示，并在开放量子系统理论的框架内对其动力学进行建模。本文从量子测量理论的非物理学家友好表述开始，从原始的冯·诺依曼表述到现代量子仪器理论。然后，将其应用于模型组合认知效应和大肠杆菌葡萄糖/乳糖代谢的基因调控。最通用的量子仪器结构基于间接测量方案，在该方案中，测量仪器充当生物系统的环境。该方案的生物学本质通过亥姆霍兹感觉知觉理论的量子形式化来阐明。然后我们转向开放系统动力学，并考虑量子主方程，重点是量子马尔可夫过程。在这个框架中，我们对心理功能和表观遗传突变等生物功能的运作进行建模。
