Khrennikov Andrei, Yurova Ekaterina
International Center for Mathematical Modeling in Physics and Cognitive Sciences, Linnaeus University, Växjö, S-35195, Sweden.
Prog Biophys Mol Biol. 2017 Nov;130(Pt A):2-14. doi: 10.1016/j.pbiomolbio.2017.02.003. Epub 2017 Feb 15.
In this conceptual paper we propose to explore the analogy between ontic/epistemic description of quantum phenomena and interrelation between dynamics of conformational and functional states of proteins. Another new idea is to apply theory of automata to model the latter dynamics. In our model protein's behavior is modeled with the aid of two dynamical systems, ontic and epistemic, which describe evolution of conformational and functional states of proteins, respectively. The epistemic automaton is constructed from the ontic automaton on the basis of functional (observational) equivalence relation on the space of ontic states. This reminds a few approaches to emergent quantum mechanics in which a quantum (epistemic) state is treated as representing a class of prequantum (ontic) states. This approach does not match to the standard protein structure-function paradigm. However, it is perfect for modeling of behavior of intrinsically disordered proteins. Mathematically space of protein's ontic states (conformational states) is modeled with the aid of p-adic numbers or more general ultrametric spaces encoding the internal hierarchical structure of proteins. Connection with theory of p-adic dynamical systems is briefly discussed.
在这篇概念性论文中，我们提议探讨量子现象的本体/认知描述与蛋白质构象和功能状态动力学之间的类比关系。另一个新想法是应用自动机理论来模拟后者的动力学。在我们的模型中，蛋白质的行为借助两个动力学系统进行建模，即本体动力学系统和认知动力学系统，它们分别描述蛋白质构象和功能状态的演化。认知自动机是基于本体状态空间上的功能（观测）等价关系，从本体自动机构建而来的。这让人联想到一些关于涌现量子力学的方法，其中量子（认知）态被视为代表一类前量子（本体）态。这种方法与标准的蛋白质结构 - 功能范式不相符。然而，它非常适合对内在无序蛋白质的行为进行建模。在数学上，蛋白质本体状态（构象状态）的空间借助p进数或更一般的超度量空间进行建模，这些空间编码了蛋白质的内部层次结构。我们还简要讨论了与p进动力系统理论的联系。
