How does the coupling of secondary and tertiary interactions control the folding of helical macromolecules?

The authors study how the simultaneous presence of short-range secondary and long-range tertiary interactions controls the folding and collapse behavior of a helical macromolecule. The secondary interactions stabilize the helical conformation of the chain, while the tertiary interactions govern its overall three-dimensional shape. The authors have carried out Monte Carlo simulations to study the effect of chain length on the folding and collapse behavior of the chain. They have calculated state diagrams for four chain lengths and found that the physics is very rich with a plethora of stable conformational states. In addition to the helix-coil and coil-globule transitions, their model describes the coupling between them which takes place at low temperatures. Under these conditions, their model predicts a cascade of continuous, conformational transitions between states with an increase in the strength of the tertiary interactions. During each transition the chain shrinks, i.e., collapses, in a rapid and specific manner. In addition, the number of the transitions increases with increasing chain length. They have also found that the low-temperature regions of the state diagram between the transition lines cannot be associated with specific structures of the chain, but rather, with ensembles of various configurations of the chain with similar characteristics. Based on these results the authors propose a mechanism for the folding and collapse of helical macromolecules which is further supported by the analysis of configurational, configurational, and thermodynamic properties of the chain.     

Development of knotting during the collapse transition of polymers

A dynamic Monte Carlo simulation of the collapse transition of polymer chains is presented. The chains are represented as self-avoiding walks on the simple cubic lattice with a nearest-neighbor contact potential to model the effect of solvent quality. The knot state of the chains is determined using the knot group procedure presented in the accompanying paper. The equilibrium knot spectrum and the equilibrium rms radius of gyration as functions of the chain length and the contact potential are reported. The collapse transition was studied following quenches from good-to poor-solvent conditions. Our results confirm the prediction that the newly formed globule is not yet at equilibrium, since it has not yet achieved its equilibrium knot spectrum. For our model system, the relaxation of the knot spectrum is about an order of magnitude slower than that of the radius of gyration. The collapse transition is also studied for a model in which both ends of the chain remain in good-solvent conditions. Over the time scale of these simulations, knot formation is frustrated in this inhomogeneous model, verifying that the mechanism of knotting is the tunneling of chain ends in and out of the globule.     

Theory of ordering in three-dimensional polymer systems with local orientational-deformational interactions

The spontaneous ordering of a three-dimensional polymer system composed of flexible segments with a fixed mean-square length in the presence of local intra- and interchain orientational-deformational interactions was considered. The fixation of the segment chain length on average is possible only during relatively weak interchain interactions or at high temperatures, i.e., in the isotropic state. The three-dimensional model, unlike its two-dimensional version, suggests the existence of the critical point at which a second-order phase transition from the isotropic state to an ordered state takes place. The critical behavior of the multichain model is described by the spherical approximation for an anisotropic Heisenberg ferromagnetic. The dependence of the critical point and the parameters of short- and long-range dipole and quadrupole orientational orders on the chain rigidity and magnitude of interchain interactions was determined. In the isotropic state, orientation correlations of segments decline according to the Ornstein-Zernike law, as in the 3D model of Gaussian subchains without fixation of their mean-square length. In the ordered state, the correlation functions tend to a finite limiting value corresponding to the presence of long-range order, as in the case of the multichain model of rigidchain segments in the strong-order approximation. A comparison of the short-range and long-range orders in the model of chains composed of segments with a fixed mean-square length and undeformable (rodlike) elements in the mean-field approximation, on the one hand, and multichain models, on the other hand, showed their equivalence, especially at high degrees of ordering.     

Collapse of a two-state sticky hard sphere chain

The collapse of a homopolymer gaussian chain into a globule is represented as a transition between two states, viz., extended and collapsed. Appropriately, this model has been labeled as the all-or-none view of chain collapse. In the collapsed state, the single polymer partition function is expressed by a single Mayer diagram with the maximum number of f-bonds arising from nonbonded square well interactions. Our target is the dependence of the transition temperature on chain length and the interaction range of the square well, as indicated through the behavior of the radius of gyration and the constant volume heat capacity. Properties of the collapse transition are calculated exactly for chains with three to six backbone atoms and heuristically for long chains using arguments derived from the small chains and from conditions of integrability. Comparison with simulation studies is made.     

Polyelectrolytes in solutions with multivalent salt. Effects of flexibility and contour length

It has been experimentally observed that trivalent ions are capable of promoting compaction of semi-flexible polyelectrolyte chains. In this work we perform Monte Carlo simulations on single chain model systems with varying chain size and stiffness and evaluate the action of multivalent salt on the chain conformation. It is observed that longer chains tend to achieve relatively more compact conformations than shorter ones, and the dimensions of the collapsed structures do not significantly vary with contour length. The influence of contour length and intrinsic stiffness in the process of ion condensation is studied by analysis of the ion-ion nearest-neighbor distribution. The general trend is an increase of the degree of ion condensation as the chain length increases, in accordance with experimental evidence. A decreased importance of end-effects and, especially, larger volume charge densities are responsible for such behavior. The influence of chain stiffness is nontrivial, and depends on salt concentration. The results emphasize the complex nature of ion-correlation phenomena in flexible or semi-flexible chains and call for the development of more sophisticated analytical theories.     

The phase diagram of a single polymer chain: New insights from a new simulation method

We present simulation results for the phase behavior of a single chain for a flexible lattice polymer model using the Wang-Landau sampling idea. Applying this new algorithm to the problem of the homopolymer collapse allows us to investigate not only the high temperature coil–globule transition but also an ensuing crystallization at lower temperature. Performing a finite size scaling analysis on the two transitions, we show that they coincide for our model in the thermodynamic limit corresponding to a direct collapse of the random coil into the crystal without intermediate coil–globule transition. As a consequence, also the many chain phase diagram of this model can be predicted to consist only of gas and crystal phase in the limit of infinite chain length. This behavior is in agreement with findings on the phase behavior of hard-sphere systems with a relatively short-ranged attractive square well. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2542–2555, 2006     

端基附壁高分子模型链的塌缩转变

借MonteCarlo和模拟退火方法研究了端基附壁高分子尾形链在不同温度下的形态变化 ,链的模型采用有最近邻相互吸引作用的自避行走 .计算机实验结果表明 ,对于端基附壁的高分子尾形链 ,与自由链一样 ,当温度逐渐降低时高分子链会发生从松散的无规线团到紧密球体的塌缩转变 .计算机模拟得到了端基附壁链的均方末端距及其分量 ,均方回转半径及分布随温度的变化 .由于刚性壁的影响 ,使得有限链长的高分子尾形链与自由链相比 ,其表示链尺寸 温度关系的曲线要稍低 .模拟还发现 ,在高温时壁对链形状的影响比较大 ,壁垂直方向上尺寸明显大于平行方向的尺寸 ,后者接近于自由链的尺寸分量 .然而 ,低于θ温度时 ,尤其是完全塌缩之后 ,壁对链形状的影响已经很小 .     

Effects of hydrophobic and dipole-dipole interactions on the conformational transitions of a model polypeptide

We studied the effects of hydrophobicity and dipole-dipole interactions between the nearest-neighbor amide planes on the secondary structures of a model polypeptide by calculating the free energy differences between different peptide structures. The free energy calculations were performed with low computational costs using the accelerated Monte Carlo simulation (umbrella sampling) method, with a bias-potential method used earlier in our accelerated molecular dynamics simulations. It was found that the hydrophobic interaction enhances the stability of alpha helices at both low and high temperatures but stabilizes beta structures only at high temperatures at which alpha helices are not stable. The nearest-neighbor dipole-dipole interaction stabilizes beta structures under all conditions, especially in the low temperature region where alpha helices are the stable structures. Our results indicate clearly that the dipole-dipole interaction between the nearest neighboring amide planes plays an important role in determining the peptide structures. Current research provides a more unified and quantitative picture for understanding the effects of different forms of interactions on polypeptide structures. In addition, the present model can be extended to describe DNA/RNA, polymer, copolymer, and other chain systems.     

A vibronic approach to the band-filling and temperature-dependent metal-insulator transition

A model of vibronic origin is used to investigate the important issue of metal-insulator transition in low-dimensional materials. For zero temperature, the stability of the single-band model chain is controlled by the competition between the internal electron-phonon coupling and the nearest-neighbor hopping integral. Assuming one particular deformation mode, one can analytically derive an instability criterion in which the band filling is explicitly included. The carrier doping directly controls the stability of a one-dimensional chain. For a half-filled band, the Peierls instability is recovered. For finite temperatures, a similar criterion is derived and can be used to investigate the metal-insulator transition temperatures.     

A lattice-gas model for halide adsorption on single-crystal electrodes

A lattice-gas model is described for the adsorption of halides on single-crystal electrodes. The lateral interactions between the adsorbed halides include a short-range nearest-neighbor interaction and a long-range electrostatic interaction. By Monte Carlo simulations the model is used to fit the experimental isotherm of bromide adsorption on Ag(100), giving information about the relative importance of the long-range and short-range interactions. The model reproduces the order–disorder transition observed experimentally, and the way in which the long-ranged interactions influence the properties of this phase transition is discussed. The Monte Carlo simulations are also compared to analytical mean-field and quasi-chemical approximations to the isotherm. Finally, the kinetics of the disorder–order transition are studied by dynamic Monte Carlo simulations, and some results on isotherms and ordered phases on (110) and (111) surfaces are described.     

The single chain limit of structural relaxation in a polyolefin blend

The influence of composition on component dynamics and relevant static properties in a miscible polymer blend is investigated using molecular dynamics simulation. Emphasis is placed on dynamics in the single chain dilution limit, as this limit isolates the role of inherent component mobility in the polymer's dynamic behavior when placed in a blend. For our systems, a biased local concentration affecting dynamics must arise primarily from chain connectivity, which is quantified by the self-concentration, because concentration fluctuations are minimized due to restraints on chain lengths arising from simulation considerations. The polyolefins simulated [poly(ethylene-propylene) (PEP) and poly(ethylene-butene) (PEB)] have similar structures and glass transition temperatures, and all interactions are dispersive in nature. We find that the dependence of dynamics upon composition differs between the two materials. Specifically, PEB (slower component) is more influenced by the environment than PEP. This is linked to a smaller self-concentration for PEB than PEP. We examine the accuracy of the Lodge-McLeish model (which is based on chain connectivity acting over the Kuhn segment length) in predicting simulation results for effective concentration. The model predicts the simulation results with high accuracy when the model's single parameter, the self-concentration, is calculated from simulation data. However, when utilizing the theoretical prediction of the self-concentration the model is not quantitatively accurate. The ability of the model to link the simulated self-concentration with biased local compositions at the Kuhn segment length provides strong support for the claim that chain connectivity is the leading cause of distinct mobility in polymer blends. Additionally, the direct link between the willingness of a polymer to be influenced by the environment and the value of the self-concentration emphasizes the importance of the chain connectivity. Furthermore, these findings are evidence that the Kuhn segment length is the relevant length scale controlling segmental dynamics.     

Theory of the cooperative transition between two ordered conformations of poly(L-proline). I. Phenomenological theory.

The states of three residues are correlated in a nearest-neighbor Ising model matrix treatment of a one-dimensional phase transition, in which nucleation is assumed to differ at each end of a regular sequence (asymmetric nucleation). The correlation of the states of three residues requires a 4 X 4 matrix, which cannot be reduced in size because of the asymmetric nature of the nucleation. Also, because of the asymmetry, at least four independent parameters for a homopolymer (rather than the two usually encountered in the helix-coil transition), ant at least five for a specific-sequence copolymer, are required to describe the transition behavior. The most important current interest in such a treatment (for a homopolymer) is its applicability to the poly(L-proline) form I in equilibrium form II interconversion.The earlier treatment of Schwarz, using the nearest-neighbor Ising model (with correlation of only two residues), is identical with the above treatment, and requires only a 2 X 2 matrix which greatly simplifies numerical computations, which are presented in the next two papers of this series. However, the 4 X 4 matrix treatment is required in order to make the asymmetric nature of the nucleation explicit and physically understandable, for a homopolymer; for a specific-sequence copolymer, such as a protein, it is essential in order to show how the asymmetric nature of helix nucleation differs from one amino acid to another.     

Structure of flexible and semiflexible polyelectrolyte chains in confined spaces of slit micro/nanochannels

Understanding the behavior of a polyelectrolyte in confined spaces has direct relevance in design and manipulation of microfluidic devices, as well as transport in living organisms. In this paper, a coarse-grained model of anionic semiflexible polyelectrolyte is applied, and its structure and dynamics are fully examined with Brownian dynamics (BD) simulations both in bulk solution and under confinement between two negatively charged parallel plates. The modeling is based on the nonlinear bead-spring discretization of a continuous chain with additional long-range electrostatic, Lennard-Jones, and hydrodynamic interactions between pairs of beads. The authors also consider the steric and electrostatic interactions between the bead and the confining wall. Relevant model parameters are determined from experimental rheology data on the anionic polysaccharide xanthan reported previously. For comparison, both flexible and semiflexible models are developed accompanying zero and finite intrinsic persistence lengths, respectively. The conformational changes of the polyelectrolyte chain induced by confinements and their dependence on the screening effect of the electrolyte solution are faithfully characterized with BD simulations. Depending on the intrinsic rigidity and the medium ionic strength, the polyelectrolyte can be classified as flexible, semiflexible, or rigid. Confined flexible and semiflexible chains exhibit a nonmonotonic variation in size, as measured by the radius of gyration and end-to-end distance, with changing slit width. For the semiflexible chain, this is coupled to the variations in long-range bond vector correlation. The rigid chain, realized at low ionic strength, does not have minima in size but exhibits a sigmoidal transition. The size of confined semiflexible and rigid polyelectrolytes can be well described by the wormlike chain model once the electrostatic effects are taken into account by the persistence length measured at long length scale.     

Modeling the amide I bands of small peptides

In this paper different floating oscillator models for describing the amide I band of peptides and proteins are compared with density functional theory (DFT) calculations. Models for the variation of the frequency shifts of the oscillators and the nearest-neighbor coupling between them with respect to conformation are constructed from DFT normal mode calculations on N-acetyl-glycine-N(')-methylamide. The calculated frequencies are compared with those obtained from existing electrostatic models. Furthermore, a new transition charge coupling model is presented. We suggest a model which combines the nearest-neighbor maps with long-range interactions accounted for using the new transition charge model and an existing electrostatic map for long-range interaction frequency shifts. This model and others, which account for the frequency shifts by electrostatic maps exclusively, are tested by comparing the predicted IR spectra with those from DFT calculations on the pentapeptide [Leu]-enkephalin. The new model described above gives the best agreement and, after a systematic blueshift is accounted for, reproduces the DFT frequencies to within 3.5 cm(-1). The correlation of the intensities for this model with intensities from DFT calculations is 0.94.     

基于化学缔合统计理论的链状流体状态方程

基于化学缔合统计理论的链状流体状态方程(EOS)能够反映实际分子的形状、链节成链、缔合等具体信息,在实际流体热力学性质计算中有着广泛应用.一般的链状流体EOS仅考虑相邻链节间的相关性,我们则借助统计力学和计算机模拟结果在模型中纳入了相间链节间的相关性,获得的硬球链流体(HSCF)模型能够更好地预测模型流体的压缩因子和第二维里系数.以HSCF为参考,引入方阱色散微扰项获得了实际方阱链流体(SWCF)EOS;结合根据黏滞球模型导得的缔合项,进一步构建了缔合流体EOS.最近,我们根据微扰理论和积分方程方法又开发了一新的变阱宽方阱链流体(SWCF-VR)模型.SWCF和SWCF-VREOSs可很好地用于计算小分子、聚合物、离子液体等纯流体及混合物的相行为、热焓、表面张力、黏度等热力学及传递性质,显示了模型良好的工程应用价值.本文就本课题组多年来在自由空间范畴内基于化学缔合统计理论开发链状流体EOS及其实际应用作系统的总结.     

Approximate theory of the viscoelasticity of chain-molecule solutions not infinitely dilute

The theories of viscoelasticity of chain-molecule solutions, based on the bead-spring model, have been modified to take into account approximately the effect of interactions among chain molecules. The motion of a given chain molecule has been analyzed in detail while all other chain molecules have been treated as a background of uniformly distributed beads in which the given chain molecule is suspended. The inclusion of intermolecular interactions leads to a hydrodynamic interaction tensor, which after averaging, differs from that of Kirkwood by a concentration-dependent correction term. The modified theory correctly predicts the transition from the non-draining to the free-draining behavior which has been observed in chain-molecule solutions as their concentrations are increased.     

Connecting the wetting and rheological behaviors of poly(dimethylsiloxane)-grafted silica spheres in poly(dimethylsiloxane) melts

Using dynamic light scattering, mechanical rheometry, and visual observation, the static wetting behavior of PDMS-grafted silica spheres (PDMS-g-silica) in PDMS melts is related to their rheology. A phase diagram is mapped out for a constant grafted chain length as a function of grafting density and free polymer chain length. The transition between stable and aggregated regions is determined optically and with dynamic light scattering. It is associated with a first-order wetting transition. In the stable region Newtonian behavior is observed for semidilute suspensions. The hydrodynamic brush thicknesses, deduced from viscosity measurements, correspond closely to values obtained from self-consistent field calculations for the various parameter values. At the transition, the brush collapses suddenly and shear-thinning and thixotropy appear. The rheology indicates a degree of aggregation that increases with increasing length of the free polymer, as suggested by the theory.     

良溶剂中接枝型聚两性电解质单链构象的布朗动力学模拟

采用布朗动力学研究了在良溶剂中荷电平衡的接枝聚两性电解质(GPA)的单链构象转变行为,讨论了主链链长、支链数及电荷密度对GPA分子链构象转变的影响.研究发现,随着静电相互作用的增强,GPA分子链构象转变过程由线团、主链与支链间的折叠、链段塌缩和电荷配对形成偶极子与四极子等4个阶段构成.与线型聚两性电解质不同,GPA存在的额外支链间空间排斥与静电排斥作用随着分子结构的变化而改变,并影响构象转变行为.在强静电相互作用下,良溶剂中的GPA链由于溶剂化作用会再伸展,以保证偶极子完全配对成四极子.减小主链长度或电荷密度或增加支链数目都会增大体系的排斥力和主链的刚性,阻滞分子链的塌缩,并使得分子链再伸展的幅度增大.     

不同边界条件下导电高分子电子结构的研究

用一维复式晶格作为反式聚乙炔的模型 ,在周期与非周期边界条件下 ,考虑链端效应并计及电子的非近邻跳跃 ,数值计算了格点数分别等于N =10、5 0、10 0和 2 0 0时聚乙炔的能谱和态密度 .讨论了不同格点数和结构参数对态密度及带宽的影响 ,并对两种边界条件下的计算结果进行了比较 .计算结果表明 ,当格点数N <5 0时 ,两者相差较大 ,这表明系统的边界将起很大作用 ;当格点数N≥ 5 0时 ,两者相差甚微 ,这时可利用周期性边界条件来研究有限系统问题 .     

Rheological properties of nanopowder alumina coated with adsorbed fatty acids

The rheological properties of a nanosized alumina powder coated with fatty acid steric stabilizers of varying chain length were investigated. The storage and loss moduli of the complex modulus were measured to characterize the behavior of the flocculated systems. As chain length increased, there was a transition from an elastic response to fluid behavior. However, the fluid system developed elastic characteristics at relatively low volume fractions of 22%. The length of the steric barrier required to produce the fluid dispersion was estimated to be approximately 2 nm and correlates with attractive interactions on the order of the system thermal energy. Moreover, in the flocculated systems, the storage modulus was found to be higher than reported previously in the literature. These higher values were related to the additional attractive forces due to van der Waals attractions between the hydrocarbon tails of the adsorbed fatty acid layers.