A model of quantum-von Neumann hybrid cellular automata: principles and simulation of quantum coherent superposition and decoherence in cytoskeletal microtubules

Abstract

Although experimental evidence suggests the influence of quantum effects in living organisms, one of the most critical problems in quantum biology is the explanation of how those effects that take place in a microscopic level can manifest in the macroscopic world of living beings. At present, quantum decoherence associated with the wave function collapse is one of the most accepted mechanisms explaining how the classical world of living beings emerges from the quantum world. Whatever the cause of wave function collapse, there exist biological systems where a biological function arises as a result of this collapse (e.g. birds navigation, plants photosynthesis, sense of smell, etc.), as well as the opposite examples (e.g. release of energy from ATP molecules at actomyosin muscle) where a biological function takes place in a quantum coherent environment. In this paper we report the modelling and simulation of quantum coherent superposition in cytoskeletal microtubules including decoherence, thus the effect of the collapse of the microtubule coherent state wave function. Our model is based on a new class of hybrid cellular automata (QvN), capable of performing as either a quantum cellular automata (QCA) or as a classical von Neumann automata (CA). These automata are able to simulate the transition or reduction from a quantum microscopic level with superposition of several quantum states, to a macroscopic level with a single stable state. Our results illustrate the significance of quantum biology explaining the emergence of some biological functions. We believe that in the future quantum biology will have a deep effect on the design of new devices, e.g. quantum hardware, in electrical engineering.