FRACTAL DIMENSION OF NUCLEIC ACID SEQUENCES AND ITS RELATION TO EVOLUTIONARY LEVEL

The fractal dimension(FD)in base space of nucleic acid sequences is introduced and calculated fog 14 categories of nucleic acids.It is discovered that there exists a possible statistical relation between FDs and evolutionary levels of these sequences.

SUPERRADIANCE FROM AN ARBITRARY DIMENSIONAL LATTICE

Superradiance of two level atoms from a lattice of arbitrary dimension is discussed which is resonant sharply with some definite momenta of photons.Both the photon superradiant and the photon trapping(squeezing)from the lattice are expected theoretically.

SQUEEZING EFFECT FROM PHOTON SCATTERING

It is proved that the photon-scattering term in Hamiltonian of Dicke problem would cause the additional squeezing effect.

Quantum theory on protein folding

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 shown 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 was calculated and a general formulas for protein folding rate was deduced.The analytical form of the formula was utilized to study the temperature dependence of protein folding rate and the curious non-Arrhenius temperature relation was interpreted.By using temperature dependence data the multi-torsion correlation was studied.The decoherence time of quantum torsion state is estimated.The proposed folding rate formula gives a unifying approach for the study of a large class problems of biological conformational change.

The dynamical contact order:Protein folding rate parameters based on quantum conformational transitions

Protein folding is regarded as a quantum transition between the torsion states of a polypeptide chain.According to the quantum theory of conformational dynamics,we propose the dynamical contact order(DCO) defined as a characteristic of the contact described by the moment of inertia and the torsion potential energy of the polypeptide chain between contact residues.Conse-quently,the protein folding rate can be quantitatively studied from the point of view of dynamics.By comparing theoretical calculations and experimental data on the folding rate of 80 proteins,we successfully validate the view that protein folding is a quantum conformational transition.We conclude that(i) a correlation between the protein folding rate and the contact inertial moment exists;(ii) multi-state protein folding can be regarded as a quantum conformational transition similar to that of two-state proteins but with an intermediate delay.We have estimated the order of magnitude of the time delay;(iii) folding can be classified into two types,exergonic and endergonic.Most of the two-state proteins with higher folding rate are exergonic and most of the multi-state proteins with low folding rate are endergonic.The folding speed limit is determined by exergonic folding.

Protein photo-folding and quantum folding theory

The rates of protein folding with photon absorption or emission and the cross section of photon-protein inelastic scattering are calculated from quantum folding theory by use of a field-theoretical method.All protein photo-folding processes are compared with common protein folding without the interaction of photons(non-radiative folding).It is demonstrated that there exists a common factor(thermo-averaged overlap integral of the vibration wave function,TAOI) for protein folding and protein photo-folding.Based on this finding it is predicted that(i) the stimulated photo-folding rates and the photon-protein resonance Raman scattering sections show the same temperature dependence as protein folding;(ii) the spectral line of the electronic transition is broadened to a band that includes an abundant vibration spectrum without and with conformational transitions,and the width of each vibration spectral line is largely reduced.The particular form of the folding rate-temperature relation and the abundant spectral structure imply the existence of quantum tunneling between protein conformations in folding and photo-folding that demonstrates the quantum nature of the motion of the conformational-electronic system.