A family of interesting exact solutions of the sine-Gordon equation

By using AKNS [Phys. Rev. Lett. 31 (1973) 125] system and introducing the wave function, a family of interesting exact solutions of the sine-Gordon equation are constructed. These solutions seem to be some soliton, kink, and anti-kink ones respectively for the different choice of the spectrum, whereas due to the interaction between two traveling-waves they have some properties different from usual soliton, kink, and anti-kink solutions.

双晶晶界在高温下的热稳定性的分子动力学研究

晶界结构在高温下的热稳定性问题是一个长期争论而又未能解决的问题，其争论的焦点是：在远低于熔点的温度下，晶界结构是否发生了可观察到的无序化，即是否存在一个远低于熔点的结构转化温度。为了能澄清这一争论，本文系统地研究了晶界结构的热稳定性。为了消除相互作用势的影响和系统误差，本文首先采用Morse势和经验多体势分别对铝、铜单晶的熔化过程进行了分子动力学模拟。在平衡态下，通过计算表征结构无序化的静态结构因子、径向分布函数和单晶原子位形图，获得了铝、铜单晶的熔点，结果表明：多体势计算的铝和铜的单晶熔点更接近实验值。因此，采用经验多体势应用分子动力学方法分别模拟了铝、铜Σ3、Σ5、Σ9、Σ11、Σ19、Σ33六种对称倾侧双晶晶界晶界结构由有序向无序转化的过程，计算了平衡态下的表征结构无序化的静态结构因子、径向分布函数和晶界原子位形图并将多体势获得的铝、铜单晶熔点作为晶界结构转化温度的约化熔点，获得了铝、铜Σ3、Σ5、Σ9、Σ11、Σ19、Σ33六种对称倾侧双晶晶界结构的转化温度和熔点，结果表明：1．Σ5、Σ9、Σ11、Σ19、Σ33五种对称倾侧双晶晶界均在远低于单晶熔点温度时，晶界结构发生了可观察到的无序化，而且双晶晶界结构的转变温度相差不大，双晶晶界熔点也低于单晶熔点。2．Σ3晶界在温度远低于熔点时，其晶界结构没有发生可观察到的无序化；Σ3晶界的转化温度与单晶熔点接近。所以，可以认为Σ3晶界不存在转化温度。这是由于Σ3晶界为共格孪晶，具有较低的能量。综上所述，除Σ3共格孪晶外，在远低于熔点温度下，晶界结构发生了可观察到的无序化，即：存在一个远低于熔点的转化温度，此时其静态结构因子约为0.5左右；晶界结构的熔点均低于单晶熔点，此时其静态结构因子约为0.15左右。从全文模拟结果可以看出，静态结构因子、径向分布函数、晶界原子位形图三种方法在确定晶界的结构转化温度和熔点时，静态结构因子是最有效、最准确的定量方法。

A scheme for multiple sequences alignment optimization-an improvement based on family representative mechanics features

As a basic tool of modern biology, sequence alignment can provide us useful information in fold, function, and active site of protein. For many cases, the increased quality of sequence alignment means a better performance. The motivation of present work is to increase ability of the existing scoring scheme/algorithm by considering residue–residue correlations better. Based on a coarse-grained approach, the hydrophobic force between each pair of residues is written out from protein sequence. It results in the construction of an intramolecular hydrophobic force network that describes the whole residue–residue interactions of each protein molecule, and characterizes protein's biological properties in the hydrophobic aspect. A former work has suggested that such network can characterize the top weighted feature regarding hydrophobicity. Moreover, for each homologous protein of a family, the corresponding network shares some common and representative family characters that eventually govern the conservation of biological properties during protein evolution. In present work, we score such family representative characters of a protein by the deviation of its intramolecular hydrophobic force network from that of background. Such score can assist the existing scoring schemes/algorithms, and boost up the ability of multiple sequences alignment, e.g. achieving a prominent increase (50%) in searching the structurally alike residue segments at a low identity level. As the theoretical basis is different, the present scheme can assist most existing algorithms, and improve their efficiency remarkably.

Generating artificial homologous proteins according to the representative family character in molecular mechanics properties - an attempt in validating an underlying rule of protein evolution

The molecular mechanics property is the foundation of many characters of proteins. Based on intramolecular hydrophobic force network, the representative family character underlying a protein’s mechanics property is described by a simple two-letter scheme. The tendency of a sequence to become a member of a protein family is scored according to this mathematical representation. Remote homologs of the WW-domain family could be easily designed using such a mechanistic signature of protein homology. Experimental validation showed that nearly all artificial homologs have the representative folding and bioactivity of their assigned family. Since the molecular mechanics property is the only consideration in this study, the results indicate its possible role in the generation of new members of a protein family during evolution.