The conformational change of biological macromolecule is investigated from the point of quantum transition. A quantum theory on protein folding is proposed based on the molecular torsion  as the slow variable of the system. Using the nonadiabaticity operator method we deduce the Hamiltonian describing conformational change. An analytical form of the formula on protein folding rate is obtained. The proposed quantum protein folding theory affords a unifying approach to the study of a large class problems of biological conformational change , for example, the quantum transition of tubulin dimer in microtubules, the ligand binding in G protein coupled receptors in membrane, the histone modification in nucleic acid through atomic group binding and the protein photo folding processes, etc. In all these applications the concise rate formula is suggested as a useful tool for investigators .
The conformational change of biological macromolecule is investigated from the point of quantum transition. A quantum theory on protein folding is proposed . Compared with other dynamical variables such as mobile electrons, chemical bonds and stretching-bending vibrations the molecular torsion has the lowest energy and can be looked as the slow variable of the system. Simultaneously, from the multi-minima property of torsion potential the local conformational states are well defined. Following the idea that the slow variables slave the fast ones and using the nonadiabaticity operator method we deduce the Hamiltonian describing conformational change. It is proved that the influence of fast variables on the macromolecule can fully be taken into account through a phase transformation of slow variable wave function. Starting from the conformation- transition Hamiltonian the nonradiative matrix element is calculated in two important cases: A, only electrons are fast variables and the electronic state does not change in the transition process; B, fast variables are not limited to electrons but the perturbation approximation can be used. Then, the general formulas for protein folding rate are deduced. The analytical form of the formula is utilized to study the temperature dependence of protein folding rate and the curious non-Arrhenius temperature relation is interpreted. The decoherence time of quantum torsion state is estimated and the quantum coherence degree of torsional angles in the protein folding is studied by using temperature dependence data. The proposed folding rate formula gives a unifying approach for the study of a large class problems of biological conformational change .
R
based on
. Compared with other dynamical variables such as mobile electrons, chemical bonds and stretching-bending vibrations
A
has the lowest energy and can be looked
R
Using the
Simultaneously, from the multi-minima property of torsion potential the local conformational states are well defined. Following the idea that the slow variables slave the fast ones and using the
R
An
It is proved that the influence of fast variables on the macromolecule can fully be taken into account through a phase transformation of slow variable wave function. Starting from the conformation- transition Hamiltonian the nonradiative matrix element is calculated in two important cases: A, only electrons are fast variables and the electronic state does not change in the transition process; B, fast variables are not limited to electrons but the perturbation approximation can be used. Then, the general formulas for protein folding rate are deduced. The
R
on
is utilized to study the temperature dependence of
R
is obtained. The proposed quantum protein folding theory affords
and the curious non-Arrhenius temperature relation is interpreted. The decoherence time of quantum torsion state is estimated and the quantum coherence degree of torsional angles in the protein folding is studied by using temperature dependence data. The proposed folding rate formula gives
R
to
for
D
, for example, the quantum transition of tubulin dimer in microtubules, the ligand binding in G protein coupled receptors in membrane, the histone modification in nucleic acid through atomic group binding and the protein photo folding processes, etc. In all these applications the concise rate formula is suggested as a useful tool for investigators