Folding Behavior of Polypeptides. A Monte Carlo Study of Simplified Models

A simple model of polypeptide chains was designed and studied. The chains were constructed on a flexible [310] lattice and consisted of united atoms located at the position of alpha carbons. Each united atom represented amino acid residues of two kinds: hydrophilic and hydrophobic. The sequence of the residues was assumed to be characteristic for α- and β-type of proteins. The force field used consisted of the long-range contact potential between polymer segments, the short range repulsion, and the local potential preferring conformational states characteristic for α-helices and β-strands. The Monte Carlo simulations of this model were carried out using the replica exchange technique coupled with the histogram method. The influence of temperature and the local potential on the size and internal structure of collapsed low temperature chains were studied. Thermodynamics of these systems consisting mainly of α and β secondary structures were determined. The properties of the coil-to-globule transition were presented and compared with other theoretical predictions and simulation results.     

Monte Carlo Simulation of Coil-to-Globule Transition of Compact Polymer Chains: Role of Monomer Interacting

Coil-to-globule transitions are fundamental problems existing in polymer science for several decades; however, some features are still unclear, such as the effect of chain monomer interaction. Herein, we use Monte Carlo simulation to study the coil-to-globule transition of simple compact polymer chains. We first consider the finite-size effects for a given monomer interaction, where the short chain exhibits a one-step collapse while long chains demonstrate a two-step collapse, indicated by the specific heat. More interestingly, with the decrease of chain monomer interaction, the critical temperatures marked by the peaks of heat capacity shift to low values. A closer examination from the energy, mean-squared radius of gyration and shape factor also suggests the lower temperature of coil-to-globule transition.     

Monte Carlo Simulations of Self-Assembling Copolymer Brushes

We studied a simplified model of a polymer brush formed by linear chains, which were restricted to vertices of a simple cubic lattice. The macromolecules consisted of a sequence of two different kinds of united atoms arranged in a specific sequence. The chains were grafted to an impenetrable surface, i.e. they were terminally attached to the surface with one end. The model system was studied at different solvent quality from good to poor solvent. The properties of this model system were determined by means of Monte Carlo simulation using a Metropolis-like sampling algorithm based on local changes of chain's conformations. The size and the structure of the brush were determined.     

EPMA of Porous Media: A Monte Carlo Approach

 We examine the influence of the sample porosity on the X-ray emission from mesoporous alumina bombarded with kilovolt electrons. Experimental results show that there is a loss of X-rays (Al Kα and O Kα) from those samples when compared to a fully dense mono-crystalline alumina (sapphire), which depends on the X-ray line, the measurement time and the embedding medium. Both geometrical and charging effects may be responsibl e for this signal loss. Monte Carlo simulations of the X-ray intensity emitted from porous alumina, using different models to describe sample porosity, show that the geometrical effect of porosity itself cannot account for the X-ray loss. Charge trapping effect and/or its combination with porosity is therefore expected to be the major cause of the signal loss.     

Monte Carlo模拟研究抗体-抗原复合物生长的标度行为

通过Monte Carlo模拟方法对抗体-抗原复合物在等活性和非等活性条件下生长的标度行为进行了研究. 模拟所用算法的有效性通过在等活性条件下的模拟结果与解析结果之间的一致性得以证明. 在模拟中, 主要考察了抗体-抗原复合物的数量分布函数、重均聚合度以及特征关联长度在临界点附近的标度行为, 给出相应的标度指数, 并以其检验溶胶-凝胶相变的广义标度律. 研究结果表明, 非等活性对抗体-抗原复合物的生长具有显著影响, 可为临床免疫分析提供相应的理论线索.     

A Novel Exact Fixed-node Quantum Monte Carlo Algorithm

In this paper we proposed a novel exact fixed-node quantum Monte Carlo (EFNQMC)algorithm,which is a self-optimizing and self-improving procedure,In contrast to the previous EFNQMC method,the trial function is optimized synchronistically in the diffusion procedure,but not before the beginning of EFNQMC computation.In order to optimize the trial function,the improved steepest descent technique is used,in which the step size is automatically adjustable.The procedure is quasi-Newton and converges super linearly.We also use a novel trial function,which has correct electron-electron and electron-nucleus cusp conditions.The novel EFNQMC algorithm and the novel trial function are employed to calculate the energies of 1^1A1 state of CH2,^1Ag state of C8 and the ground-states of H2,LiH,Li2,H2O,respectively.The test results show that both the novel algorithm and the trial function proposed in the present paper are very excellent.     

Properties of simple models of polymer networks. A Monte Carlo simulation

A model polymer network was constructed from branched chains. Each chain was built on a simple cubic lattice forming a star-branched polymer consisting of f = 3 arms of equal lengths. The fragment of network under consideration consisted of 1, 2 and 3 star polymers with different topology of connections. The only potential used was excluded volume (athermal chains). The properties of the network were determined by the means of computer simulations using the classical Metropolis sampling algorithm (local micromodifications of chain conformation). The behaviour of linear chains of the same molecular weight was also studied as a state of reference. The influence of attaching the next star-branched chain to the network on its static and dynamic properties was studied. The short-time dynamic behaviour of chain fragments was determined and discussed.     

Fixed—node Quantum Monte Carlo：A Novel Approach

The fixed-node quantum Monte Carlo (FNQMC)1,2 method has made it possible to calculate the electronic structure of relatively large molecular systems. These large systems range from positron complexes [NH2, Ps] with ～10 electrons to C20 isomers with 120 electrons, silicon crystal structures of 250 atoms and 1000 valence electrons. In the practical calculation for FNQMC method, in general, a minimal basis set of Slater-type atomic orbital (STO) and Jastrow functions are taken to cons…     

Structure of Adsorbed Polymer Chains: A Monte Carlo Study

The structure of adsorbed polymer chains was studied using simplified lattice models. The model chains were adsorbed on an impenetrable surface with an attractive potential. The dynamic Monte Carlo simulations based in the Metropolis scheme were carried out using these models. The influence of the internal chain architecture (linear, star‐branched and ring chains) and the degree of adsorption on the chain's structure was studied. It was shown that for weakly adsorbed chain regime the ring polymers which exhibit an almost twice as high degree of adsorption compared to linear and star chains have a higher number of adsorbed parts of chain (trains). But the length of such train remains almost the same for all types of a polymer chain. Star‐branched chains exhibit a slightly different change in number and the mean length of trains, loops and tails with the temperature and the chain total length compared to two other types of chain.     

聚硅烷链形状的Monte Carlo研究

用ＭｏｎｔｅＣａｒｌｏ方法对θ溶液中考虑二级相互作用的聚硅烷链的形状进行了研究。结果表明聚硅烷链的形状明显偏离球形，它与链长有关，长链极限的比值＜Ｌ２１＞∶＜Ｌ２２＞∶＜Ｌ２３＞约为１∶２．７∶１２．１。还发现聚硅烷链转动惯量的最长主轴与末端距矢量之间夹角的统计平均值＜θ＞的极限值约为２７°。     

Monte Carlo simulation for the micellar behavior of amphiphilic comb-like copolymers

Micellar behaviors in 2D and 3D lattice models for amphiphilic comb-like copolymers in water phase and in water/oil mixtures were simulated. A dynamical algorithm together with chain reptation movements was used in the simulation. Three-dimension displaying program was pro-grammed and free energy was estimated by Monte Carlo technigue. The results demonstrate that reduced interaction energy influences morphological structures of micelle and emulsion stems greatly; 3D simulation showing can display more direct images of morphological structures; the amphiphilic comb-like polymers with a hydrophobic main chain and hydrophilic side chains have lower energy in water than in oil.     

Monte Carlo simulation for the adsorption of symmetric triblock copolymers II. Adsorption layer information

By using Monte Carlo simulation, adsorption of both end-adsorbed and middle-adsorbed symmetric triblock copolymers from a non-selective solvent on an impenetrable surface has been studied. Influences of the adsorption energy, the bulk concentration, the chain composition and the chain length on the adsorption behavior including the surface coverage, the adsorption amount and the layer thickness are presented. It is shown that the total surface coverage for both end-adsorbed and middle-adsorbed copolymers increases monotonically as the bulk concentration increases. The higher the adsorption energy and the more the attractive segments, the higher the total surface coverage is exhibited. Surface coverage θ decreases with increasing the length of the non-attractive segments, but the product of θ and the proportion of the non-attractive segments in a triblock copolymer chain is nearly independent of the chain length. The adsorption amount increases almost monotonically with the bulk concentration. The logarithm of the adsorption amount is a linear function of the reciprocal of the reduced temperature. When the adsorption energy is large, the adsorption amount exhibits a maximum as the composition of the attractive segment increases. The adsorption isotherms of copolymers with different length of the non-attractive segments can be mapped onto a single curve under certain energy indicating that copolymers with different chain length have the same adsorption amount. The adsorption layer thickness for the end-adsorbed copolymers decreases as the energy and the number of adsorbing segments increases. The longer non-attractive segments, the larger adsorbed layer thickness is found. The tails mainly governs the adsorption layer thickness.     

Monte Carlo simulations of polymer dynamics: Recent advances

A brief review is given of applications of Monte Carlo simulations to study the dynamical properties of coarse-grained models of polymer melts, emphasizing the crossover from the Rouse model toward reptation, and the glass transition. The extent to which Monte Carlo algorithms can mimic the actual chain dynamics is critically examined, and the need for the use of coarse-grained rather than fully atomistic models for such simulations is explained. It is shown that various lattice and continuum models yield qualitatively similar results, and the behavior agrees with the findings of corresponding molecular dynamics simulations and experiments, where available. It is argued that these simulations significantly enhance our understanding of the theoretical concepts on the dynamics of dense macromolecular systems. © 1997 John Wiley & Sons, Inc.     

Monte Carlo Simulation in Electron Probe Microanalysis. Comparison of Different Simulation Algorithms

Practical aspects of Monte Carlo simulation of EPMA experiments are considered. Simulations are performed using the general-purpose Monte Carlo code system Penelope, which is briefly described. This code includes geometry tools and variance reduction methods that allow the practical simulation of x-ray spectra from samples with complex geometries in moderate computing times. The reliability of simple interaction models and approximations, which have been frequently used in EPMA studies, is analyzed by studying their effects on the simulated x-ray spectra.     

The Structure and Thermodynamics of a Heteropolymer Chain in Confinement – Computer Simulation Studies

A coarse‐grained model of heteropolymer (polypeptide) chains in a slit was designed in order to study the folding process in confinement. The idealized chains represented heteropolymers consisted of hydrophobic and hydrophilic united atoms, which were restricted to vertices of a (310) lattice. The force field consisted of the excluded volume, the long‐distance potential between pairs of segments and the local helical potential. Monte Carlo simulations were performed using the algorithm with micromodifications of the chain's conformation and employing the Replica Exchange technique. The influence of the size of the slit, the temperature and the force field on the dimension and the structure of chains were studied. It was shown that a moderate confinement stabilizes folded chains while a strong confinement does not.

     

A Monte Carlo simulation of a knotted linear chain system as an elementary network fragment

We present the results of the Monte Carlo simulations of the dynamics of the linear chain system. The chains were constructed on a simple cubic lattice. The simulations were carried out by means of the classical Metropolis sampling method with the excluded volume effect present. No other interactions were introduced into the system (athermal polymer case). The linear chains in the system were constructed in such a way that there were knots at certain positions. Also, some chains were threaded through the knots forming the topological constraints in the system. The system under consideration underwent a series of micromodifications during the simulation run. Then the trajectory was analysed and the dynamics of the system was described by means of the autocorrelation functions. The short-time dynamics enabled us to investigate whether or not the knotted constraints affect the local dynamics of the chains. Also the long-time dynamics of the system can be useful in the characterizations of the dynamical properties of the fragments of the networks.     

表面单层组装多环芳烃荧光行为的Monte Carlo模拟

Recently,a series of sensing films based upon the supra-molecular behavior of aromatic compounds immobilized on substrate surfaces and its dependence to the composition of the medium have been successfully prepared. It is found that the properties and performances of the films depend upon various factors,including the nature of the sensing element,the way of immobilization,the nature of the substrate,and the density of the sensing element immobilized etc. To accelerate and deepen the studies,it was decided to carry out the theoretical simulation of the sensing films based upon the proposed principle. The fluorescence behavior of a functional plate,of which the surface is functionalized by single layer immobilization of aromatic compounds（sensing elements）,is simulated by Monte Carlo simulation method. The effects of the immobilization density of a sensing element,the excitation efficiency,and the association efficiency,P,which is a characteristic parameter of an aromatic compound,between the molecules of the sensing element on the ratio of the excimer emission to the monomer emission of the plate have been systematically examined. But the effects of the length and flexibility of a spacer are neglected,because in this simulation aromatic compounds are immobilized on a plate by the short stiff spacer. It is demonstrated that,for a functionalized plate of a short stiff spacer in a polar solvent（ in this case,the association tendency is strong,and P is close to 1）,aromatic compounds of middle excitation efficiency might be suitable as sensing elements. In addition,the immobilization density of the sensing element should be controlled. A recommended value is about 50%.     

Monte Carlo simulation for the adsorption of symmetric triblock copolymers I. Configuration distribution and density profiles of adsorbed chains

Monte Carlo simulations for the adsorption of symmetric triblock copolymers from a nonselective solvent at a solid-liquid interface have been performed on a lattice model. In simulations, triblock copolymer molecules are modeled as self-avoiding linear chains composed of m segments of A and n segments of B arranged as A_m/2B_nA_m/2. Either segment A or segment B is attractive, while the other is non-attractive to the surface. The microstructure of the adsorbed layers, including the segment-density profiles and the size distribution of loops, tails and trains are presented. The effect of the adsorption energy, the bulk concentration, the chain composition, as well as the chain length on various adsorption properties has been studied. The results have shown that the size distribution of various configurations is dependent of the adsorption energy, the chain composition and the chain length. The mean length of the loops, trains and tails is insensitive to the bulk concentration. The mean length of the trains increases and that of the tails decreases as the adsorption energy and the length of the attractive segments increase. The mean length of the loops for the end-adsorbed copolymers appears a maximum and that for middle-adsorbed copolymers appears a minimum as the length of attractive segments increases. The length of the non-attractive segments affects mostly the size distribution of the tails. The longer the chain is, the larger the tail appears. The mean length of the tails and loops increases linearly as the length of the non-attractive segments increases, but that of the trains approximately is unchanged.     

The Thermodynamics of Folding of a β Hairpin Peptide Probed Through Replica Exchange Molecular Dynamics Simulations

Peptides that possess a well defined native state are ideal model systems to study the folding of proteins. They possess many of the complexities of larger proteins, yet their small size renders their study computationally tractable. Recent advances in sampling techniques, including replica exchange molecular dynamics, now permit a full characterization of the thermodynamics of folding of small peptides. These simulations not only yield insight into the folding of larger proteins, but equally importantly, they allow, through comparison with experiment, an objective test of the accuracy of force fields, water models and of different numerical schemes for dealing with electrostatic interactions. In this account, we present a molecular dynamics simulation of a small β-hairpin peptide using the replica exchange algorithm and illustrate how this enhanced sampling scheme enables a thorough characterization of the native and unfolded states, and sheds new light into its folding mechanism.     

Monte Carlo Study of Heteroarm Star Copolymers in Good and Selective Solvents

Lattice Monte Carlo simulations of conformations of hereroarm star copolymers A_nB_n in selective solvents were performed using a special variant of the Siepman and Frenkel algorithm. The effects of solvent quality, the number and lengths of blocks on the collapse of the insoluble block A, segregation of the two types of blocks and the behavior of the soluble blocks B were studied mainly for “hairy” stars containing high numbers of long arms. The simulation shows that insoluble blocks collapse in strongly selective solvents and the gravity centers of soluble and insoluble blocks separate which suggests the possibility of the formation of non‐spherical structures.

Snapshots of star a in a very bad solvent (T = 3.00) for blocks A. There are two different views of the star with a total number of arms f = 16 and number of segments N = 300.