Basic Quantum Field Model of the Self-Organization of Microtubules in Eukaryotic Cells

Abstract

The background of this contribution is the ongoing extended debate over quantum effects in the biology since decades. Typical examples of the quantum biology are photosynthesis, enzymatic activities, bird navigation and especially the coherent movement of microtubules. The reason for all these effects is dominantly the quantum coherence of waves. The objective of this contribution is the quantum description of the instability dynamics of microtubules at their assembly and disassembly phases during the interphase. The corresponding theoretical investigations of this article confirm the existence of quantum coherence of microtubules. Experimental results assert such vibrations of microtubules by the observation of γ-waves in the human brain generated by bundles of microtubules. Tubulin subunits and the accessory proteins are of nano size; therefore, they are modeled as field quanta in the framework of non-relativistic quantum field theory. This approach describes the dynamics of these quantum particles and their interactions, by accentuation of their different performances as coherent or incoherent waves. The achieved results strongly depend from the preconditions: whether the fluctuating forces are turned on or turned off. With the inset of fluctuations, the quantum coherence is destroyed, and only incoherent particle solutions are obeyed. Without the impact of fluctuations wave solutions dominate. Another type of wave solution are coherent wave packets which are counter-running, where their superposition can extinct or enhance them. This kind of interfering coherent solutions is applied on the polymerization of protofilaments. The calculations of this contribution demonstrate that the quantum coherence can be only observed when fluctuations are excluded. The conclusion is that that dedicated biological processes must be able to suppress the destroying influences of the local environment. In contrary to technical-based experiments, where coherence is only obtained when the fluctuations are deliberately excluded (e.g. quantum computer). Therefore, the answer why the processes of quantum biology can generate quantum coherence at least in case of microtubules is actually not answered. Kinesins in combination with microtubules are fundamental for cellular functions and morphogenesis. Recent genetic experiments uncovered their role for tumor suppression and developmental patterning. However, these findings which open exciting new areas of kinesin research are not included in this contribution, because the description of the kinesin-microtubule system is to comprehensive for one article.