Organizing and Disorganizing Resonances of Microtubules, Stem Cells, and Proteins Calculated by a Quantum Equation of Coherence

Abstract

Conformational states of microtubules and proteins have typical spatial-spectral arrangements of atoms, called spatial coherence, that are characteristic for building, homeostasis, decay, and apoptosis. Microtubules show a principle of a self-organizing-synergetic structure called a Fr ö hlich-Bose-Einstein state. The spatial coherence of this state can be described by a toroidal quantum equation of coherence. In this space, microtubules and proteins have typical discrete frequency patterns. These frequencies comply with two proposed quantum wave equations of respective coherence (regulation) and decoherence (deregulation), that describe quantum entangled and disentangled states. The proposed equation of coherence shows the following typical scale invariant distribution of energy: E n = ħ ω ref 2 q 3 m . The proposed model supports quantum entanglement and is in line with the earlier published models of Fr ö hlich, Davydov, and Chern. A meta-analysis shows a semi-harmonic scale-invariant pattern for microtubules, stem cells, proteins, and EEG- and MEG-patterns. A fit has been found for about 50 different organizing frequencies and 5 disorganizing frequencies of measured microtubule frequencies that fit with the calculated values of the proposed quantum equations, which are positioned in a nested toroidal geometry. All measured and analysed frequencies of microtubules comply with the same energy distribution found for Bose-Einstein condensates. The overall results show a presence of an informational quantum code, a direct relation with the eigenfrequencies of microtubules, stem cells, DNA, and proteins, that supplies information to realize biological order in life cells and substantiates a collective Fr ö hlich-Bose-Einstein type of behaviour and further support the models of Tuszynski, Hameroff, Bandyopadhyay, Del Giudice and Vitiello, Katona, Pettini, and Pokorny.