A coarse-grained model for the formation of alpha helix with a noninteger period on simple cubic lattices

Periodicity is an important parameter in the characterization of a helix in proteins. In this work, a coarse-grained model for a homopolypeptide in simple cubic lattices has been extended to build an alpha helix with a noninteger period. The lattice model is based on the bond fluctuation algorithm in which bond lengths and orientations are altered in a quasicontinuous way, and the simulation is performed via dynamic Monte Carlo simulation. Hydrogen bonds are assumed to be formed between a virtual-carbonyl group in a residue and a downstream virtual-imino group in another residue. Consequently, the period of the formed alpha helix is a noninteger. An improved spatial correlation function has been suggested to quantitatively describe the periodicity of the helical conformation, by which helical period and helical persistent length can be calculated by statistics. The resultant periods are very close to 3.6 residues; the persistent length based upon the improved definition can be larger or smaller than the chain length and reflect the inherent regularity of a chain including one or multiple helical blocks. The simulation outputs agree with the calculation of the Zimm-Bragg theory based upon the associated nucleation parameter and propagation parameter as well.     

Model study for large deformation of physical polymeric gels

A model for large deformation of polymer gels with physical cross-linking is developed and shown to be in good agreement with experimental stress-strain curves which show strain hardening in intermediate strains followed by strain softening in large deformations near the yield strain. The model takes into account the coil-helix transition equilibrium and allows for the distribution of the end-to-end distance. The gel is considered to be formed by long flexible chains and crystalline zones acting as junctions of the chains. The number of segments contained in a flexible chain is variable due to the equilibrium between the two regions. As the end-to-end distance increases due to the deformation, more and more segments are reeled out from the junction zone. Finally, one end of the chain is librated from the junction and the chain becomes dangling. The appearance of dangling chains causes the strain softening because they cease to contribute to the elasticity. From the parameter dependence of the stress-strain relations, it was found that the yield behavior depends strongly on the distribution of end-to-end distance. The yield strain is approximately given by the ratio of the upper limit of the number of segments and the average end-to-end distance. The standard deviation of the end-to-end distance affects significantly the width of the peak in the stress-strain curve, thus determining the degree of strain softening.     

Shear-induced conformational ordering, relaxation, and crystallization of isotactic polypropylene

The shear-induced coil-helix transition of isotactic polypropylene (iPP) has been studied with time-resolved Fourier transform infrared spectroscopy at various temperatures. The effects of temperature, shear rate, and strain on the coil-helix transition were studied systematically. The induced conformational order increases with the shear rate and strain. A threshold of shear strain is required to induce conformational ordering. High temperature reduces the effect of shear on the conformational order, though a simple correlation was not found. Following the shear-induced conformational ordering, relaxation of helices occurs, which follows the first-order exponential decay at temperatures well above the normal melting point of iPP. The relaxation time versus temperature is fitted with an Arrhenius law, which generates an activation energy of 135 kJ/mol for the helix-coil transition of iPP. At temperatures around the normal melting point, two exponential decays are needed to fit well on the relaxation kinetic of helices. This suggests that two different states of helices are induced by shear: (i) isolated single helices far away from each other without interactions, which have a fast relaxation kinetic; (ii) aggregations of helices or helical bundles with strong interactions among each other, which have a much slower relaxation process. The helical bundles are assumed to be the precursors of nuclei for crystallization. The different helix concentrations and distributions are the origin of the three different processes of crystallization after shear. The correlation between the shear-induced conformational order and crystallization is discussed.     

On the inner structure and topology of clusters in two-component lipid bilayers. Comparison of monomer and dimer Ising models

It has been shown on model and biological systems that membrane clusters can affect in-plane membrane reactions and can control biochemical reaction cascades. Clusters of two-component phospholipid bilayers have been simulated by two Ising-type lattice models: the monomer and the dimer model. In each model the plane of one layer of the bilayer is represented by a triangular lattice, each site of which is occupied by an acyl chain of either a component 1 or a component 2 lipid molecule. The dimer model assumes that pairs of acyl chains (lipid molecules) are permanently connected, forming dimers on the lattice, while in the case of the monomer model this covalent connection between acyl chains is ignored. Phase diagrams of two-component phospholipid bilayers were successfully calculated by both models. In this work, we use Monte Carlo techniques to calculate thermodynamic averages of global and local characteristics of the largest component 2 cluster (such as outer/inner perimeter, percolation, minimal linear size, and local density) and compare the results obtained by the two models. A new method is developed to characterize the inner structure of the clusters. Each point of a cluster is classified based on its shortest distance (or depth) from the cluster's outer perimeter. Then local cluster properties, such as density, are calculated as a function of the depth. The depth analysis reveals that toward the cluster interior the average density usually decreases in midsize clusters and remains constant in very large clusters. On the basis of the simulations the following typical cluster topologies are identified at different cluster sizes and cooperativity parameter values: (i) branch-like, (ii) circular, (iii) band-like, and (iv) planar.We did not find qualitative differences between the cluster structures in the dimer and monomer model. However, at the same cluster size and cooperativity parameter value the cluster of the dimer model is more compact. The cluster properties of the dimer model are different from that of the monomer model because of the lower mixing entropy and higher formation energy of an elementary inner island.     

Kinetics of helix-coil transition in all sizes of polypeptides.

The relaxation behavior of the helix-coil transition has been investigated for all sizes of polypeptides. Unlike previously reported results, regardless of the size of polypeptides, the first-order kinetics plays a principal role in the relaxation process when a helical state is relaxed to a half-coiled state [i.e. s(f) is congruent to 1, where s(f) is the helix stability parameter at the final state]. On the other hand, when a helical state is relaxed to a coiled state [i.e., s(f) is less than 1], the zeroth-order kinetics plays a major role. In addition, the range of the validity of a kinetic version of the zipper model has been investigated. We have found that when a helical state is relaxed to a state where s(f) is less than or equal to 1, the zipper model is valid for polypeptides with chain length N satisfying the relation N is less than 1/(sigmagammaC)1/2 where sigma is the cooperativity parameter and gammaC is the coil nucleation rate parameter.     

Rational design of a reversible pH-responsive switch for peptide self-assembly

Peptide TZ1H, based on the heptad sequence of a coiled-coil trimer, undergoes fully reversible, pH-dependent self-assembly into long-aspect-ratio helical fibers. Substitution of isoleucine residues with histidine at the core d-positions of alternate heptads introduces a mechanism by which self-assembly is coupled to the protonation state of the imidazole side chain. Circular dichroism spectroscopy, transmission electron microscopy, and microrheology techniques revealed that the self-assembly of TZ1H coincides with a distinct coil-helix conformational transition that occurs within a narrow pH range near the pKa of the imidazole side chains of the core histidine residues.     

高分子链形状与尺寸关联的Monte Carlo模拟

运用MonteCarlo方法对线型高分子链格点模型的构型进行了模拟,研究了构型的尺寸(采用平方末端距R²,平方回转半径S²来表征)和形状(由非球形因子A表征)之间的关联.对任何长度的高分子链,其关联系数CA,R²和CA,S²均为正值,表明高分子链的形状与尺寸之间存在正关联,即尺寸小的构型其非球形因子A一般也小,反之尺寸大的构型其非球形因子A一般也大.关联系数CA,R²和CA,S²均随链长的增大而减小,近似地与链长的倒数(n^-1)成正比.研究还表明,关联系数的极限值(链长n很大时)与格点的类型无关,与链样本产生的方式也无关,但与链是否考虑排斥体积有关,考虑了排斥体积后,关联系数增大.     

二维高聚物振动谱的研究

聚乙炔和聚苯胺通常由于链间耦合比较弱 ,具有一维特性 .但在增加压力的条件下可以使其链间距b减少 ,当达到与晶格常数a相近的程度时 ,这时应考虑其晶格链间耦合作用 ,它们就具有二维复式晶格结构 ,由此会带来新的物理效应 .本文考虑了由于增压作用可以使高聚物晶格链间耦合作用增强 ,并使链间距b减少 ,当b达到与晶格常数a相比拟时 ,它们可以被看作具有二维晶格结构 .基于这种情况建立了理想的二维复式晶格链模型 ,利用晶格动力学的方法 ,计算其晶格链间及原子次近邻间的相互作用 ,借助计算机计算分别在几种晶格链耦合作用下和不同质量比时的色散关系 ,模拟色散曲线 ,讨论第一布里渊区BrillouinZone(BZ)中格波高对称线上频谱的变化 ,分析了由此会带来的新的物理效应 .     

Orientational ordering of a polymer chain in a strong dipole field. Tetrahedral lattice model

Orientational and conformational properties have been investigated of a rotational isomeric model of a polar polymer chain on a tetrahedral lattice in a strong electric or mechanical field of dipole symmetry. Two types of dipole moment distribution along the chain are discussed: (A) constant signs of longitudinal components of the dipole moments, and (B) alternating signs of the longitudinal components of the dipole moments. The second case represents polymer chains such as $ \rlap{--} ({\rm CH}_{\rm 2} \hbox{---} {\rm CR}_{\rm 2} {\rm \rlap{--} )}_n $>/UEQN> when the dipole moments are oriented along the bisector of the CR₂-angle, i.e., normal to the extended trans-chain conformation. It is shown that only a discrete most probable orientation of the lattice relative to the field should be considered, namely that coinciding with one of the symmetry axes of the lattices. The average dipole order parameter and dichroic functions (quadrupole order parameter) are calculated in a strong external dipole field for unit vectors with different orientation relative to the chain backbone. The quadrupole order parameter for different unit vectors is obtained also as a function of chain elongation. The polarizability induced by an additional weak dipole field is calculated as a function of the magnitude of the strong external dipole field. For the model considered here the order parameters are more strongly influenced by the external field than those for the freely jointed chain (FJC) model having the same distribution of dipole moments along the chain. The orientational ordering of the chain in a dipole field is higher than in a quadrupole field of the same magnitude.     

Solvent-free simulations of fluid membrane bilayers

A molecular level model for lipid bilayers is presented. Lipids are represented by rigid, asymmetric, soft spherocylinders in implicit solvent. A simple three parameter potential between pairs of lipids gives rise to a rich assortment of phases including (but not limited to) micelles, fluid bilayers, and gel-like bilayers. Monte Carlo simulations have been carried out to verify self-assembly, characterize the phases corresponding to different potential parametrizations, and to quantify the physical properties associated with those parameter sets corresponding to fluid bilayer behavior. The studied fluid bilayers have compressibility moduli in agreement with experimental systems, but display bending moduli at least three times larger than typical biological membranes without cholesterol.     

Theoretical determination of helix-coil parameter sigma from a model of partly helical polypeptide chain.

The Zimm and Bragg parameter sigma is calculated numerically for poly(L-alanine), polyglycine, and the copolymers of L-alanine and glycine using the molecular theory of s and sigma as developed by Go, Go, and Scheraga in a modified formulation. In this formulation, sigma is obtained from the partition function of the whole chain in the helix-coil transition region and represents therefore the contributions from the ends of helical and coil sequences and from the interactions between atoms in a coil sequence with those in the neighboring helical sequence. When the parameter sigma is calculated numerically from a hard-sphere potential, it appears that steric intractions between atoms in the coil sequence with atoms in the neighboring helical sequence, which have been neglected in previous calculations, contribute significantly to the value of sigma. Owing to these interactions the entropy of the coil sequence as well as sigma decrease, but the decrease of sigma is larger in poly(L-alanine) than in polyglycine, because of the higher flexibility of the monomer in polyglycine. The numerical value of sigma for polyglycine compared with that of poly(L-alanine) might be overestimated however by the model presented here due to approximations inherent in the hard-sphere treatment and because only regular helical sequences are considered.     

Probing possible left- and right-handed poly(dinucleotide) helical conformations from (n–h) plots. models for polysequential nucleotides

Introducing the concept of the “dinucleotide” as the helical repeat, theoretical attempts have been made to determine possible single and double stranded helical structures by using helical parameter calculations and model building investigations. By virtue of its flexible framework, the dinucleotide repeat offers a much greater scope of finding new secondary structural forms for nucleic acids. Considering only those conformations which show tendency for at least partial base overlap as does the dinucleotide helical repeat, it has been possible to predict poly(dinucleotide) helical models in which successive phosphodiesters as well as nucleotide conformations alternate. More important, the recently found left-handed Z-type polynucleotide helix is characterized rather uniquely on the helical parameter plot. The results further suggest the possibility of other Z-type helices obtainable by alternative conformations for the exocyclic C4'–C5' bond and sugar pucker. Near neighbor long range conformational correlations between the dinucleotide repeat and the phosphodiester linking them have been established similar to poly(mononucleotide) helices. Need for considering higher repeats such as trinucleotide has been suggested to obtain models for looped out helical conformations.     

Helix formation in the polymer brush

This work considers the physics of a brush formed by polymers capable of undergoing a helix-coil transition. A self-consistent field approximation for strongly stretched polymer chains is used in combination with a lattice model of the interaction energy in helix-coil mixtures. Crowding-induced chain stretching stabilizes helix formation at moderate tethering densities while high tethering density causes sufficiently strong stretching to unravel segments of the helix, resulting in distinct layers of monomer density and helical content. Compared to a random-coil brush at low-to-moderate tethering density, a helicogenic brush is less resistant to compression in the direction perpendicular to stretching due to easy alignment of helices and fewer unfavorable interactions between helical segments. At higher tethering density, the abovementioned stretch-induced decrease in helical content resists further compression. The proposed model is useful for understanding an emerging class of biomaterials that utilize helix-forming polymer brushes to induce shape changes or to stabilize biofunctional helical peptide sequences.     

Control of hydrogen bonding in the design of new diol lattice inclusion compounds

Abstract

In order to be able to predict and then synthesize new lattice inclusion compounds with the helical tubuland diol host structure, the hydrogen bonding modes of a range of bicyclic and tricyclic diols have been studied using X-ray crystallography. Several distinct types of lattice structure have been recognized. Steric factors play a major role in determining which of these is produced in a given case. Establishment of a series of structural rules provides a window of opportunity for duplication of the helical tubuland host lattice by deliberate design and synthesis. New inclusion compounds resulting from this approach are presented.     

类蛋白质分子的二级结构对力学行为的影响

采用Kolinski等建立的类蛋白质分子的格点模型,研究了由典型的(HHPPHPP)x重复单元构成、含有α螺旋结构的类蛋白质分子链在拉伸过程中的构象性质和力学行为.发现不同强度的α螺旋相互作用会直接影响其拉伸过程.α螺旋相互作用强的类蛋白质分子链,具有更低的内能,更小的应力,在拉伸过程中更容易失去紧密接触对,同时也更容易被拉成“棒状”结构,但在整个拉伸过程中,α螺旋结构且能保持稳定;还发现类蛋白质分子的链长对拉伸也有影响,对较长的类蛋白质分子链,其内能更低,弹性力更小,自由能更大,紧密接触对的含量比例也更高,而“棒状化”程度较小.这些研究能够帮助我们加深对蛋白质分子的构象和弹性力学行为的理解.     

The equilibrium fraction of bridging chains and the swelling behavior of ABA triblock copolymer mesophases

The physical cross-linked network due to B blocks bridging different A domains of a microphase separated melt formed by an ABA copolymer in the strong-segregation limit is examined. The system is considered to consist of swollen elements of the same size, each containing an A domain and a B layer anchored to the A domain as loops or bridges. A lattice model and a generator-matrix method are employed to calculate the equilibrium fraction of the bridging B chains of the ABA mesophase and the equilibrium swelling concentration of the B layer in a selective solvent for the planar, cylindrical and spherical A domain structures. The effects of chain length and of two-dimensional surface density of the AB joints are discussed. The equilibrium fraction of the bridging chains as a function of chain stiffness and the equilibrium swelling concentration as a function of the fraction of bridging chains and of the interaction parameter are calculated. In addition, the segment density distributions of both loop and bridging chains for both the pure ABA and the swollen ABA mesophases are provided.     

Phase behaviors of nematic liquid crystal/linear polymer systems: Effect of specific interactions

A new model has been proposed that takes into account the specific interaction between nematic liquid crystal and polymer. A generalized lattice fluid model was employed to describe the specific interaction between liquid crystal and polymer. The proposed model postulates that a specific interaction between dissimilar components in a mixture has both an energetic and an entropic component. A degeneracy parameter and an interaction parameter are also discussed, followed by a comparison of the experimental data to the model. The results show that that a specific interaction plays an important role in the phase behaviors of the given systems. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 4128–4136, 2000     

SUY的晶胞参数和骨架振动频率与其硅铝比间的关系

用SiCl₄(气)高温处理HY制得一系列USY(T),以USY(T)的晶胞常数α₀对其单位晶胞中铝原子的数目作图,发现c₀在24.45～24.55有一断落区间。由实验结果推导出两个以晶胞常数计算USY骨架硅铝比的公式。用400～1500cm^-1范围的红外光谱研究了USY的骨架变化。一些骨架振动特征频率与晶胞常数,单位晶胞中铝原子分数的相关图,也都出现断落区间。当晶胞常数小于24.41时,460cm^-1及1145cm^-1的两个峰发生劈裂。随晶胞常数的减少光谱峰变窄。     

Stereoselective association of binuclear metallacycles in coordination polymers

A series of structurally related binuclear metallacycles [Cd(NO(3))(2)L](2), where L is an angular exo-bidentate ligand, have been synthesized. Each metallacycle contains two coordinatively unsaturated, chiral metal centers within a single molecule, and the assembly of these metallacycles into polymeric framework structures has been studied systematically for the first time. Stereoselective homochiral association of [Cd(NO(3))(2)L](2) leads to the formation of helical coordination polymers, whereas meso type association results in nonhelical chain structures. The type of stereoselective aggregation depends on the conditions of self-assembly as well as on ligand functionality. Both helical and nonhelical polymeric complexes have been isolated for the metallacycle [Cd(NO(3))(2)(2,4'-pyacph)](2) (2,4'-pyacph = 2,4'-(4-ethynylphenyl)bipyridyl). Homochiral association results in the formation of helical [Cd(NO(3))]( infinity ) chains which link the binuclear [Cd(NO(3))(2)(2,4'-pyacph)](2) metallacycles into racemic two-dimensional sheets which contain both P and M [Cd(NO(3))]( infinity ) helices. In contrast, meso-association leads to the formation of nonhelical one-dimensional chains. It is shown that the product of homochiral association is predominately formed at room temperature and that of meso-association is generated at elevated temperatures. Thus, it may be concluded that the homochiral association appears to be energetically less favorable than the meso-association, a conclusion that has been confirmed by theoretical calculations of the crystal lattice energy. Several high-yield syntheses of bipyridyl-type ligands used for metallacyclic assembly are also reported.