环状高分子对胶体稳定性影响的理论研究

将改进的基本度量理论与热力学微扰理论相结合,提出了胶体/高分子系统排空相互作用的IRDFT理论。该理论解释了在实际胶体系统中起重要作用的排斥体积效应和高分子链内相关性的竞争机制。应用该IRDFT,分别以线性链状和环状结构的高分子及其单体为排空元,计算了不同排空元条件下的胶体间排空相互作用。研究表明:对于絮凝破坏,自由环状高分子具有更大的优势。     

On the Temperature–Pressure Free‐Energy Landscape of Proteins

We studied the thermodynamic stability of a small monomeric protein, staphylococcal nuclease (Snase), as a function of both temperature and pressure, and expressed it as a 3D free‐energy surface on the p,T‐plane using a second‐order Taylor expansion of the Gibbs free‐energy change ΔG upon unfolding. We took advantage of a series of different techniques (small‐angle Xray scattering, Fourier‐transform infrared spectroscopy, differential thermal analysis, pressure perturbation calorimetry and densitometry) in the evaluation of the conformation of the protein and in evaluating the changes in the thermodynamic parameters upon unfolding, such as the heat capacity, enthalpy, entropy, volume, isothermal compressibility and expansivity. The calculated results of the free‐energy landscape of the protein are in good agreement with experimental data of the p,T‐stability diagram of the protein over a temperature range from 200 to 400 K and at pressures from ambient pressure to 4000 bar. The results demonstrate that combined temperature–pressure‐dependent studies can help delineate the free‐energy landscape of proteins and hence help elucidate which features and thermodynamic parameters are essential in determining the stability of the native conformational state of proteins. The approach presented may also be used for studying other systems with so‐called re‐entrant or Tamman loop‐shaped phase diagrams.     

Protein secondary structure and stability determined by combining exoproteolysis and matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

In the post-genomic era, several projects focused on the massive experimental resolution of the three-dimensional structures of all the proteins of different organisms have been initiated. Simultaneously, significant progress has been made in the ab initio prediction of protein three-dimensional structure. One of the keys to the success of such a prediction is the use of local information (i.e. secondary structure). Here we describe a new limited proteolysis methodology, based on the use of unspecific exoproteases coupled with matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS), to map quickly secondary structure elements of a protein from both ends, the N- and C-termini. We show that the proteolytic patterns (mass spectra series) obtained can be interpreted in the light of the conformation and local stability of the analyzed proteins, a direct correlation being observed between the predicted and the experimentally derived protein secondary structure. Further, this methodology can be easily applied to check rapidly the folding state of a protein and characterize mutational effects on protein conformation and stability. Moreover, given global stability information, this methodology allows one to locate the protein regions of increased or decreased conformational stability. All of this can be done with a small fraction of the amount of protein required by most of the other methods for conformational analysis. Thus limited exoproteolysis, together with MALDI-TOF MS, can be a useful tool to achieve quickly the elucidation of protein structure and stability.     

Gradient of the ZAPT2 energy

 An explicit expression for the analytical first derivative of the Z-averaged perturbation theory taken to second order energy, due to Lee and Jayatilaka, is presented for application to high-spin systems described by a restricted open-shell Hartree–Fock wavefunction. The use of frozen core orbitals is incorporated into the derivation. Received: 23 April 2001 / Accepted: 31 August 2001 / Published online: 9 January 2002     

Improved third-order Møller-Plesset perturbation theory

Based on a partitioning of the total correlation energy into contributions from parallel‐ and antiparallel‐spin pairs of electrons, a modified third‐order Møller–Plesset (MP) perturbation theory is developed. The method, termed SCS–MP3 (SCS for spin‐component‐scaled) continues previous work on an improved version of MP2 (S. Grimme, J Chem Phys 2003, 118, 9095). A benchmark set of 32 isogyric reaction energies, 11 atomization energies, and 11 stretched geometries is used to assess to performance of the model in comparison to the standard quantum chemical approaches MP2, MP3, and QCISD(T). It is found, that the new method performs significantly better than usual MP2/MP3 and even outperforms the more costly QCISD method. Opposite to the usual MP series, the SCS third‐order correction uniformly improves the results. Dramatic enhancements are especially observed for the more difficult atomization energies, some of the stretched geometries, and reaction and ionization energies involving transition metal compounds where the method seems to be competitive or even superior to the widely used density functional approaches. Further tests performed for other complex systems (biradicals, C₂₀ isomers, transition states) demonstrate that the SCS–MP3 model yields often results of QCISD(T) accuracy. The uniformity with which the new approach improves for very different correlation problems indicates significant robustness, and suggests it as a valuable quantum chemical method of general use. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 1529–1537, 2003     

一类带扰动的随机脉冲泛函微分方程解的渐近性北大核心CSCD

该文讨论了一类带扰动的随机脉冲泛函微分方程解的渐近性.通过比较扰动方程的解和原方程的解,得到了两者逼近的充分条件.首先,两者在有限的时间区间上相互逼近;其次,当扰动趋于零时,区间长度趋于无穷大,在这个区间上两个解仍然是相互逼近的.最后,举例说明了结果的有效性.     

Some problems of linear differential equations on abstract spaces and unbounded perturbations of linear operator semigroup

This paper is a survey for development of linear distributed parameter system. At first we point out some questions existing in current study of control theory for the L^p linear system with an unbounded control operator and an unbounded observation operator, such as stabilization problem and observer theory that are closely relevant to state feedback operator. After then we survey briefly some results on relevant problems that are related to solvability of linear differential equations in general Banach space and semigroup perturbations. As a principle, we propose a concept of admissible state feedback operator for system (A, B). Finally we give an existence result of admissible state feedback operators, including semigroup generation and the equivalent conditions of admissibility of state feedback operators, for an L^p well-posed system.     

Superexponential stability of KAM tori

We study the dynamics in the neighborhood of an invariant torus of a nearly integrable system. We provide an upper bound to the diffusion speed, which turns out to be of superexponentially small size exp[-exp(1/)], being the distance from the invariant torus. We also discuss the connection of this result with the existence of many invariant tori close to the considered one.     

Absence of absolutely continuous spectrum of Floquet operators

The spectrum of the Floquet operator associated with time-periodic perturbations of discrete Hamiltonians is considered. If the gap between successive eigenvalues _j of the unperturbed Hamiltonian grows as _j - _j-1 j and the multiplicity of _j grows asj with >0 asj tends to infinity, then the corresponding Floquet operator possesses no absolutely continuous spectrum provided the perturbation is smooth enough.     

Sensitivity analysis of the greatest eigenvalue of a symmetric matrix via the ɛ-subdifferential of the associated convex quadratic form

LetA(·) be ann × n symmetric affine matrix-valued function of a parameteruR ^m , and let (u) be the greatest eigenvalue ofA(u). Recently, there has been interest in calculating (u), the subdifferential of atu, which is useful for both the construction of efficient algorithms for the minimization of (u) and the sensitivity analysis of (u), namely, the perturbation theory of (u). In this paper, more generally, we investigate the Legendre-Fenchel conjugate function of (·) and the -subdifferential (u) of atu. Then, we discuss relations between the set (u) and some perturbation bounds for (u).The author is deeply indebted to Professor J. B. Hiriart-Urruty who suggested this study and provided helpful advice and constant encouragement. The author also thanks the referees and the editors for their substantial help in the improvement of this paper.