从量子跃迁观点对蛋白质折叠速率的统计分析

理解蛋白质折叠速率是探明蛋白质结构和折叠机制物理基础的关键.蛋白质折叠速率的温度依赖关系是当前一个未解决的难题.假定蛋白质折叠是一个分子构象间的量子跃迁,导出了一个蛋白质折叠速率的解析公式.由此公式出发,计算了资料库中二态蛋白质的折叠速率和研究了它们的温度依赖性.从第一性原理出发,对实验给出的16个二态蛋白质折叠速率的非阿列尼乌斯(non-Arrhenius)温度关系给予成功解释,进而预测了这些蛋白质解折叠速率的温度依赖关系.依据量子折叠理论,给出了一个预测二态蛋白质折叠速率的统计公式,用于65个蛋白的资料库,理论和实验比较的相关系数为0.73.此外,理论还给出了与实验结果一致的最大和最小折叠速率估计.

理论生物物理学研究的回顾和展望

回顾了从基本粒子理论研究转向理论生物物理学的历程,以及在理论生物学和生物信息学方向上部分研究课题所获得的主要成果,特别强调了量子折叠理论信息生物学原理和细胞熵产生的研究,提出了进一步工作的展望和建议.

Electron Momentum Spectroscopy of Valence Orbitals of Cyclopentene:Nuclear Dynamics and Distorted Wave Effect

We report a measurement of electron momentum distributions of valence orbitals of cyclopentene employing symmetric noncoplanar(e,2e)kinematics at impact energies of 1200 and 1600 eV plus the binding energy.Experimental momentum profiles for individual ionization bands are obtained and compared with theoretical calculations considering nuclear dynamics by harmonic analytical quantum mechanical and thermal sampling molecular dynamics approaches.The results demonstrate that molecular vibrational motions including ring-puckering of this flexible cyclic molecule have obvious influences on the electron momentum profiles for the outer valence orbitals,especially in the low momentum region.Forπ^(*)-like molecular orbitals 3a′′,2a′′,and 3a′,the impact-energy dependence of the experimental momentum profiles indicates a distorted wave effect.

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.

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.

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.

A Gibbs free energy formula for protein folding derived from quantum statistics

The fundamental law for protein folding is the thermodynamic principle.The amino acid sequence of a protein determines its native structure and the native structure has the minimum Gibbs free energy.Lacking of a Gibbs free energy formula is the reason that all ab initio protein structure prediction only empirical and various empirical energy surfaces or landscapes are introduced to fill the gap.We make a quantum mechanics derivation of the Gibbs free energy formula G(X)using quantum statistics for a single conformation X.For simplicity,only monomeric self folding globular proteins are considered.

Statistical analyses of protein folding rates from the view of quantum transition

Understanding protein folding rate is the primary key to unlock the fundamental physics underlying protein structure and its folding mechanism.Especially,the temperature dependence of the folding rate remains unsolved in the literature.Starting from the assumption that protein folding is an event of quantum transition between molecular conformations,we calculated the folding rate for all two-state proteins in a database and studied their temperature dependencies.The non-Arrhenius temperature relation for 16 proteins,whose experimental data had previously been available,was successfully interpreted by comparing the Arrhenius plot with the first-principle calculation.A statistical formula for the prediction of two-state protein folding rate was proposed based on quantum folding theory.The statistical comparisons of the folding rates for 65 two-state proteins were carried out,and the theoretical vs.experimental correlation coefficient was 0.73.Moreover,the maximum and the minimum folding rates given by the theory were consistent with the experimental results.