Tensile properties of microtubules: A study by nonlinear molecular structural mechanics modelling

A nonlinear molecular structural mechanics (MSM) model is proposed in this paper for studying the tensile properties of microtubules (MTs). In the nonlinear MSM models, the interactions between tubulin monomers in MTs are treated as nonlinear axial and torsional springs, whose stiffness coefficients are extracted from all-atom molecular dynamics simulations. The Young's modulus and fracture properties of MTs under tension extracted from the present nonlinear MSM models are found to agree well with the existing simulation and experiment results, which shows the efficiency and accuracy of the proposed nonlinear MSM models. In addition, the nonlinear MSM models are also extended to investigate the tensile properties including Young's modulus and fracture strain of MTs possessing lattice defects. The results obtained from nonlinear MSM models are utilized to develop a predictive equation for quickly predicting the tensile properties of MTs with different lattice defect levels.     

Escape from the quantum pigeon conundrum

It has recently been argued in Aharonov et al. (2016) that quantum mechanics violates the Pigeon Counting Principle (PCP) which states that if one distributes three pigeons among two boxes there must be at least two pigeons in one of the boxes. However, this conclusion cannot be justified by rigorous theoretical arguments. The issue is further complicated by experimental confirmation of the transition amplitudes predicted in this paper that nevertheless do not support the conclusion of PCP violation. Here we prove via a set of operator identities that the PCP is not violated within quantum mechanics, regardless of interpretation.     

Quantum fractionalism: The Born rule as a consequence of the complex Pythagorean theorem

Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in orthogonal projections from the complex line of a quantum state to eigenspaces of an observable. Unit total probability corresponds to a complex Pythagorean theorem: the measure of a subset of the complex line is the sum of the measures of its projections on all eigenspaces.Postulating the existence of a continuum infinity of identical quantum universes, all with the same quasi-classical worlds, we show that projection factors give relative amounts of worlds. These appear as relative frequencies of results in quantum experiments, and play the role of probabilities in decisions and inference. This solves the probability problem of Everett's theory, allowing its preferred basis problem to be solved as well, and may help settle questions about the nature of probability.     

Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics

The evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently is discussed. It is shown that the notion of a classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. The impossibility of evolving a separable state of a composite system made up of a classical and a quantum one into an entangled state by means of a unitary evolution is proven in accordance with Raggio’s theorem, which is extended to include a new family of separable states corresponding to the composition of a system with a totally disconnected space of outcomes and a quantum one.     

A new non-perturbative approach in quantum mechanics for time-independent Schr?dinger equations

A new non-perturbative approach is proposed to solve time-independent Schr?dinger equations in quantum mechanics.It is based on the homotopy analysis method(HAM)that was developed by the author in 1992 for highly nonlinear equations and has been widely applied in many fields.Unlike perturbative methods,this HAM-based approach has nothing to do with small/large physical parameters.Besides,convergent series solution can be obtained even if the disturbance is far from the known status.A nonlinear harmonic oscillator is used as an example to illustrate the validity of this approach for disturbances that might be one thousand times larger than the possible superior limit of the perturbative approach.This HAM-based approach could provide us rigorous theoretical results in quantum mechanics,which can be directly compared with experimental data.Obviously,this is of great benefit not only for improving the accuracy of experimental measurements but also for validating physical theories.     

Computer generation and theoretical study of alicyclic caged structures without small-size cycles

Computer design was concocted for a series of caged alicyclic structures without small cycles. With the help of molecular-mechanical calculations, the enthalpies of formation and the strain energies were determined for the corresponding compounds. The possibility of tile existence of highly strained frameworks without small cycles was analyzed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2430–2437, October, 1996.     

Mechanism of enhanced conversion of 1,2,3-trichloropropane by mutant haloalkane dehalogenase revealed by molecular modeling

1,2,3-Trichloropropane (TCP) is a highly toxic, recalcitrant byproduct of epichlorohydrin manufacture. Haloalkane dehalogenase (DhaA) from Rhodococcus sp. hydrolyses the carbon–halogen bond in various halogenated compounds including TCP, but with low efficiency (k _cat/K _m = 36 s^-1 M^-1). A Cys176Tyr-DhaA mutant with a threefold higher catalytic efficiency for TCP dehalogenation has been previously obtained by error-prone PCR. We have used molecular simulations and quantum mechanical calculations to elucidate the molecular mechanisms involved in the improved catalysis of the mutant, and enantioselectivity of DhaA toward TCP. The Cys176Tyr mutation modifies the protein access and export routes. Substitution of the Cys residue by the bulkier Tyr narrows the upper tunnel, making the second tunnel “slot” the preferred route. TCP can adopt two major orientations in the DhaA enzyme, in one of which the halide-stabilizing residue Asn41 forms a hydrogen bond with the terminal halogen atom of the TCP molecule, while in the other it bonds with the central halogen atom. The differences in these binding patterns explain the preferential formation of the (R)- over the (S)-enantiomer of 2,3-dichloropropane-1-ol in the reaction catalyzed by the enzyme.     

The changes in free energies and entropies from analytical radial distribution functions

The changes in Helmholtz free energies and entropies in dense fluids have been evaluated using three known analytical expressions for radial distribution functions (RDFs) of Lennard–Jones (L-J) fluid. This method provides a simpler and a more expeditious way for the calculation of free energy and entropy in L-J dense fluids through statistical mechanics. Previously, integral equations or perturbation theories were used for this purpose. Such approach not only tests the power of analytical distribution functions in predicting the changes in Helmholtz free energies and entropies, but also specifies better expressions in determining these properties. The results are compared with experimental data and an accurate analytic equation of state for the L-J fluid. It is shown if an expression properly presents RDFs as a function of interparticle distance, density and temperature, it is possible to calculate the changes in Helmholtz free energies and entropies from analytical distribution functions.     

煤显微组分分子结构模型的量子化学研究

采用分子力学和半经验量子化学方法，研究了神木煤显微组分的分子结构模型，比较了镜质组和惰质组分子模型的能量构成、不同类型键的键长和键裂解能。研究结果表明，扭转能和范德华能是分子中的主要作用力，取代基对体系能量有明显影响，烷基取代基使体系能量增加，而苯基取代基使体系能量降低；脂肪C—C键长比芳香C—C键长长，说明脂肪C—C在受热过程中比芳香C—C更容易断裂分解。对各键裂解能的计算结果表明，Car—Cal键的裂解能高于Cal—Cal，Car—O醚键的裂解能高于Cal—O醚键。而惰质组结构模型中除C—O醚键外，各键的裂解能均高于镜质组，说明惰质组结构模型比镜质组有较高的热稳定性。     

爆炸冲击波作用于墙体及对墙体绕射的实验研究

采用试验的方法,对爆炸冲击波作用于防爆墙及绕过墙体的规律进行了研究.采用压力传感器测压,获得了防爆墙前后不同距离的压力波形.试验结果表明:作用于前墙迎爆面反射超压一般要比墙后最大绕射超压大一个数量级,马赫反射一般发生在距离墙后1.5~2.0倍墙高处,药量与爆心距离对墙体反射超压及墙后绕射超压的变化规律有重要影响.通过综合分析和试验结果,得到了爆炸波绕射的内在机理,为防爆墙的设计与加固提供依据和参考.