ELASTIC BEHAVIOR OF PROTEIN-LIKE SINGLE CHAIN

The conformational properties and elastic behaviors of protein-like single chains in the process of tensile elongation were investigated by means of Monte Carlo method. The sequences of protein-like single chains contain two types of residues: hydrophobic (H) and hydrophilic (P). The average conformations and thermodynamics statistical properties of protein-like single chains with various elongation ratio λ were calculated. It was found that the mean-square end-to-end distance r increases with elongation ratio,λ. The tensor eigenvalues ratio of : decreases with elongation ratio λ for short (HP)x protein-like polymers, however, the ratio of : increases with elongation ratioλ,especially for long (H)x sequence. Average energy per bond increases with elongation ratioλ, especially for(H)x protein-like single chains. Helmholtz free energy per bond also increases with elongation ratioλ. Elastic force (f), energy contribution to force (fU) and entropy contribution to force (fs) for different protein-like single chains were also calculated.These investigations may provide some insights into elastic behaviors of proteins.     

DIMENSIONS OF ATACTIC POLY(α-METHYLSTYRENE) CHAINS WITH SIDE GROUPS

An improved configurational-confomational statistical method is developed and the mean-square radius of gyration for atactic poly(α-methylstyrene)(PαMS) chains is studied, in which the effect of large side groups is considered. The deduced formulas, based on the rotational isomer state theory, are used to investigate the configuration-dependent properties of the atactic polymer chain, and the statistical correlation of the unperturbed polymer chain dimension and structure parameters are calculated. For the fraction of meso dyads wm= 0.4, the dependence of the radius of gyration Rg and the intrinsic viscosity [η] on the molecule mass M are Rg = 2.63 × 10-2M0.50 nm and [η] = 7.36 × 10-2M0.497, respectively, which are in agreement with the previous experimental data for the PαMS samples. A small hump is detected in the curve of the characteristic ratio of the unperturbed mean-square radius of gyration versus the chain length for short PαMS chains. The Rg increases linearly with the temperature T, and the effects of the chain length and the tacticity on the temperature coefficient are remarkable. These are quite different from the results for PαMS chains not considering side groups or for the monosubstituted polystyrene chain.     

DIMENSIONS OF ATACTIC POLY（α-METHYLSTYRENE） CHAINS WITH SIDE GROUPS

An improved configurational-confomational statistical method is developed and the mean-square radius of gyration for atactic poly(α-methylstyrene)(PαMS)chains is studied,in which the effect of large side groups is considered. The deduced formulas,based on the rotational isomer state theory,are used to investigate the configuration-dependent properties of the atactic polymer chain,and the statistical correlation of the unperturbed polymer chain dimension and structure parameters are calculated.For the fraction of meso dyads w_m=0.4,the dependence of the radius of gyration R_g and the intrinsic viscosity[η]on the molecule mass M are R_g=2.63×10~(-2) M~(0.50) nm and[η]=7.36×10~(-2) M~(0.497),respectively, which are in agreement with the previous experimental data for the PαMS samples.A small hump is detected in the curve of the characteristic ratio of the unperturbed mean-square radius of gyration versus the chain length for short PαMS chains.The R_g increases linearly with the temperature T,and the effects of the chain length and the tacticity on the temperature coefficient are remarkable.These are quite different from the results for PαMS chains not considering side groups or for the monosubstituted polystyrene chain.     

RATE OF INTRA-MOLECULAR CONTACT FORMATION IN SHORT TWO-DIMENSIONAL COMPACT POLYMERS CHAINS

It is important to know the rate of intra-molecular contact formation in proteins in order to understand how proteins fold clearly. Here we investigate the rate of intra-molecular contact formation in short two-dimensional compact polymer chains by calculating the probability distribution p(r) of end-to-end distance r using the enumeration calculation method and HP model on two-dimensional square lattice. The probability distribution of end-to-end distance p(r) of short two-dimensional compact polymers chains may consist of two parts, i.e. p(r) = p1(r) p2(r), where p1(r) and p2(r) are different for small r. The rate of contact formation decreases monotonically with the number of bonds N, and the rate approximately conforms to the scaling relation of k(N) ∝ N-α. Here the value of α increases with the contact radius a and it also depends on the percentage of H (hydrophobic) residues in the sequences of compact chains and the energy parameters of εHH, εHP and εPP . Some comparisons of theoretical predictions with experimental results are also made. This investigation may help us to understand the protein folding.     

α-氨基酸在水-乙醇中羧基质子化热力学

Enthalpy changes for the protonation of carboxyl group of four α-amino acids(glycine,L-α-alanine,L-valine and L-serine) were measured in water-ethanol mixtures (10－ 70wt％) at 298.15K using LKB-2277 Bioactivity Monitor.The corresponding entropy and Gibbs energy changes were also calculated.The results show that both enthalpy changes and entropy changes are favorable to the protonation of carboxyl groups of the investigated amino acids in water-ethanol mixtures.However,the influence of the composition of ethanol in the mixed solvents on the enthalpy change and entropy changes is complicated.Both sδ and sδ ,the differences of enthalpy changes and entropy changes in mixed solvents and in pure water respectively,show a minimum approximately at xEtOH=0.1.The effects of side chains on the enthalpy change and entropy changes were also investigated using the proton transfer process between glycine and the other three amino acids.The results demonstrate that the proton transfer processes for alanine and valine are spontaneous but not for serine,which could be interpreted in terms of the electrostatic interaction between amino group and carboxyl group within the molecule and the interaction between carboxyl group and the solvent.     

Conformational statistics of polymer chain terminally attached to wall (I)——NRW model tail chain

The simplest form of a polymer chain adsorbed on a solid surface is that the polymer chain has only one end group attached to the surface, i.e. the polymer chain forms the "tail" conformation. In the present work, the problem was simplified as the random walk confined in the half-infinite space and studied systematically. The conformational distribution functions of the model tail chain in different dimensions were obtained. It has been found that the ratio of the conformational number of the model tail chains to that of the free chains varies as a power function N-12 when the chain length N→∞. It has also been proved that for the tail chain the component of the mean square end-to-end distance in the normal direction of the confined boundary is doubled and the other components are constant in comparison with the case of the free chain.     

THE SPATIAL DISTRIBUTION AND MOMENTS OF CIRCULAR FREELY JOINTED CHAIN

The spatial distribution function and second moments of circular freely jointed chain are derived based on an analytical method. The circular Gauss chain, which is simple for long chains, is compared with the circular freely jointed chain, which is exact for short chains. It is shown that the Gauss chain model predicts a more compact configurational distribution than the exact freely jointed chain. The two chain models, however, become closer to each other when the chain length increases. It is found that the difference of the mean square radius of gyration calculated with these two chain models is a constant, independent of the chain length.     

Highly Chemical and Regio－selective Catalytic Oxidation with a Novel Manganese Catalyst

The chemical selectivity of a novel active manganese compound [Mn2^IVμ-O)3(TMTACN)2] (PF6)2 (1) in catalytic oxidation reactions depended on the structure of substrates and 1 was able to catalyze the oxidation of toluene into benzaldehyde and/or benzoic acid under very mild conditions. The following results were obtained: (1) The selectivity of the oxidation depended on the electronic density of double bonds. Reactivity was absent when strong electron-witherawing groups were conjugated with double bonds. (2) Allylic oxidation reactions mostly take place when double bond is present inside a ring system, whilst epoxiclarion reactions occur when the alkene moiety is part of linear chain. (3) In ring systems, the methylene group was more likely to be oxidized than the methyl group on ailylic position. As expected, the C--H bonds at the bridgeheads were unreactive.The secondary hydroxyl groups are more easily to be oxidized than the primary hydroxyl groups.     

MONTE CARLO SIMULATION ON AQUEOUS SOLUTION OF BIOLOGICAL MOLECULES——ALANINE SOLUTION

The Monte Carlo simulation is performed for a cluster consisting of a neutral alanine molecule surrounded by 56 water molecules. The average water-water and alanine-water interaction energies are found. The space surrounding the alanine molecule is divided into three regions, where the central atoms are C' atom for the earboxyl group region, N atom for the amino group region and C~β atom for the methyl group region. The water-water and water-alanine interaction energies as functions of the distance between the oxygen atom in a water molecule and the central atom in each region are calculated. In each region the orientational correlation function for the dipole moments of water molecules, the radial distribution function for the oxygen and hydrogen atoms of water molecules are evaluated. In addition, the numbers of water molecules in the first solvation shells of each region and of entire alanine molecule are also counted.     

Density Functional Calculations on a Double Hydrogen-bonded Dimer

Density functional theory (DFT) calculations on a double hydrogen-bonded dimer of o-hydroxybenzoic acid were carried out at the B3LYP/6-31G^* level. The optimized geometry of the dimer closely resembles that of the crystal. The calculated results show that the total energy of the dimer is much lower than the sum energies of the two monomers, and the average strength of the double hydrogen bonds is about 38.37 kJ/mol. In order to probe the origin of the interactions in the dimer, natural bond orbital analyses were performed. The thermodynamic properties of the title compound at different temperatures have also been calculated on the basis of vibrational analyses and ΔGT, the change of Gibbs free energy for the aggregation from monomer to the dimmer, is 26.47 kJ/mol at 298.15 K and 0.1MPa, implying the spontaneous process of forming the dimer. The correlation graphics of Sm^0 Hm^0 and temperatures is depicted.     

Contacts between segments in the random-flight model of polymer chains

The probabilities of single and double contacts, and correlations among contacts were calculated for the random-flight model of a polymer chain. The problem was studied earlier by various authors using the Gaussian statistics of the random-flight chain, which is applicable only for long chains, and for contacts which are formed by pair of residues (i,j) which are far from each other (i.e. |i−j|≫1). We used the exact (non-Gaussian) solution of the random flight model, so that our results are applicable also for residues which are relatively close to each other. We applied the results to close contacts of the β-sheet type and α-helix type in proteins, and compared the exact solutions of the problem with Gaussian approximations.     

Importance of chirality and reduced flexibility of protein side chains: a study with square and tetrahedral lattice models

Side chains of amino acid residues are the determining factor that distinguishes proteins from other unstable chain polymers. In simple models they are often represented implicitly (e.g., by spin states) or simplified as one atom. Here we study side chain effects using two-dimensional square lattice and three-dimensional tetrahedral lattice models, with explicitly constructed side chains formed by two atoms of different chirality and flexibility. We distinguish effects due to chirality and effects due to side chain flexibilities, since residues in proteins are L residues, and their side chains adopt different rotameric states. For short chains, we enumerate exhaustively all possible conformations. For long chains, we sample effectively rare events such as compact conformations and obtain complete pictures of ensemble properties of conformations of these models at all compactness region. This is made possible by using sequential Monte Carlo techniques based on chain growth method. Our results show that both chirality and reduced side chain flexibility lower the folding entropy significantly for globally compact conformations, suggesting that they are important properties of residues to ensure fast folding and stable native structure. This corresponds well with our finding that natural amino acid residues have reduced effective flexibility, as evidenced by statistical analysis of rotamer libraries and side chain rotatable bonds. We further develop a method calculating the exact side chain entropy for a given backbone structure. We show that simple rotamer counting underestimates side chain entropy significantly for both extended and near maximally compact conformations. We find that side chain entropy does not always correlate well with main chain packing. With explicit side chains, extended backbones do not have the largest side chain entropy. Among compact backbones with maximum side chain entropy, helical structures emerge as the dominating configurations. Our results suggest that side chain entropy may be an important factor contributing to the formation of alpha helices for compact conformations.     

Soft effective interactions between weakly charged polyelectrolyte chains

We apply extensive molecular dynamics simulations and analytical considerations in order to study the conformations and the effective interactions between weakly charged, flexible polyelectrolyte chains in salt-free conditions. We focus on charging fractions lying below 20%, for which case there is no Manning condensation of counterions and the latter can be thus partitioned in two states: those that are trapped within the region of the flexible chain and the ones that are free in the solution. We examine the partition of counterions in these two states, the chain sizes and the monomer distributions for various chain lengths, finding that the monomer density follows a Gaussian shape. We calculate the effective interaction between the centers of mass of two interacting chains, under the assumption that the chains can be modeled as two overlapping Gaussian charge profiles. The analytical calculations are compared with measurements from molecular dynamics simulations. Good quantitative agreement is found for charging fractions below 10%, where the chains assume coil-like configurations, whereas deviations develop for charge fraction of 20%, in which case a conformational transition of the chain towards a rodlike configuration starts to take place.     

Intramolecularly ordered globules and the collapse of short chains

We investigate the poor-solvent collapse of short chains having different stiffness through self-consistent minimization of the intramolecular free energy under the constraint of fixed segment lengths between adjacent beads. At first the chains form the Random Gaussian Globule, where the beads are distributed at random at the same average distance from the centre of mass, while the segments show very little correlation. At a larger attractive potential, this collapsed globule undergoes a transition to one or more ordered compact states, depending on the chain stiffness. Under very strong contraction, all chains are described as a Compact Ordered Globule: the beads are again at a constant average distance from the centre of mass, while the segments jump back and forth at the globule's wall with a very large correlation. At intermediate contraction, the thinner and stiffer chains form the Oscillating Ordered Globule wherein the beads are alternatively distributed on two concentric on two concentric shells. In this case, we also find metastable states with nonsymmetrical conformations of the chain with respect to its ends. We also briefly discuss the thermodynamics of the coil-globule and globule-globule transitions, showing that in long polymer chains these ordered conformations cannot involve the whole chain. However, we suggest that they might still be found as local globules that form for kinetic reasons.     

Conformational and packing energy calculations on ethylene copolymers

A conformational analysis was performed on the isolated chains of ethylene-propene and ethylene-1-butene copolymers. The lowest energy conformations in accordance with the chain repeating distance of polyethylene were used in packing energy calculations. The results of our calculations suggest that both methyl and ethyl groups are tolerated in the crystalline conformation of a single polyethylene chain, but only the methyl group is acceptable in the crystalline state if the packing energies and the lattice deformations are taken into account.     

二维HP格点模型中的紧密高分子链构象及其热力学性质的研究

采用二维HP模型用精确计数法和MonteCarlo方法研究了链长为N(≤ 2 2 )的紧密高分子链的构象和热力学性质 .发现不同HP序列的紧密高分子链的平均自由能和平均配分函数与链长N存在关系 :〈F〉=aN+b ,　ln〈Z〉=a′N +b′ .同时发现对于可折叠成基态且简并度为 1的紧密高分子链 ,其平均自由能和平均配分函数与链长N也存在相似的关系 .在HP模型中对于链长为N的紧密高分子链 ,存在着 2 N + 1 个不同的HP序列 .我们发现可以折叠成基态且简并度为 1的蛋白质分子的HP序列数目NS 为NS =a× 2 N+ 1 　 (a =0 0 2 5 ) ,对应的HP序列中 ,疏水基团 (H)数目的含量为 4 0 %～ 6 0 %的序列出现的几率最大 .同时在这些紧密高分子链中有些具有相同的结构 ,发现结构的‘简并度’为 3 3～ 4 0 (10≤N≤ 16 ) .在紧密高分子链折叠过程中 ,折叠的初期能量下降比较快 ,折叠的中期能量下降比较缓慢 ,折叠的后期能量下降也是比较快     

Thermodynamic modelling of polymer solutions with a modified Staverman equation

A model describing the thermodynamic behaviour of polymer solutions is derived which explicitly accounts for the flexibility of the polymer chains. Based on computer simulations on various lattices it is shown that the flexibility of a polymer chain can be modelled by distinguishing different polymer conformations. Here each conformation is characterized by its corresponding number of external contact sites. The equilibrium between the different conformations is then solved for any polymer concentration and any combination of interaction energies utilizing a modified Staverman equation. The model predictions are in good agreement with the results of the computer simulations which were performed using the simple-sampling and the slithering-snake algorithm. Since the knowledge of the distribution of the conformations of a single polymer chain on an empty lattice is a prerequisite to perform the model calculations, Poisson distribution functions are fitted to the results of the corresponding computer simulations. The generalization of these distribution functions not only facilitates the use of the new model but also allows to model polymers of varying chain stiffness.     

Intrachain reaction of a pair of reactive groups attached to polymer ends. II. Monte carlo study on the intrachain reaction proceeding on trans/cis-polysarcosine chain.

Monte Carlo calculation was performed to evaluate the ring-closure probability of short polysarcosine chains. Calculations were made for unperturbed trans- non-self-intersecting trans-, and non-self-intersecting trans- and non-self-intersecting trans/cis-polysarcosine chains. In the latter case, the main chain amide bond was allowed to take cis as well as trans conformations. The ring-closure probability for unperturbed trans-polysarcosine chains was found to be substantially greater than for non-self-intersecting trans chains. Virtually no difference was observed between the ring-closure probability was used to estimate the cyclization constant, i.e., the ratio of rate constant for the intramolecular reaction of the two groups attached to the polymer ends to that of the intermolecular one. The results were compared with the experimental data for the intrachain reaction proceeding on polysarcosine chain reported in the first paper of this series. The Monte Carlo results roughly reproduced the experimental data and the calculated chain length dependence was consistent with the observed one for longer chains.     

The effect of hydrogen bonding on oligoleucine structure in water: A molecular dynamics simulation study

Molecular dynamics simulations were conducted in order to improve our understanding of the forces that determine polyleucine chains conformations and govern polyleucine self-assembly in aqueous solutions. Simulations of 10 repeat unit oligoleucine in aqueous solution were performed using the optimized potential for liquid simulations (OPLS) - all atom force field using the canonical ensemble for a minimum of 1.3 ns. These simulations provided information on conformations, chain collapse and intermolecular aggregation. Simulations indicate that single isotactic oligoleucine chains in dilute solution assume tightly packed, regular hairpin conformations while atactic oligoleucine assumes a much less regular and less compact structure. The regular, compact collapsed isotactic chain exhibited a greater degree of intramolecular hydrogen bonding and an increased level of hydrophobic t-butyl functional group aggregation compared to the atactic chain. This occurs at the expense of reduced leucine-water hydrogen bonding.     

Miscibility behavior and single chain properties in polymer blends: a bond fluctuation model study

Computer simulation studies on the miscibility behavior and single chain properties in binary polymer blends are reviewed. We consider blends of various architectures in order to identify important architectural parameters on a coarse grained level and study their qualitative consequences for the miscibility behavior. The phase diagram, the relation between the exchange chemical potential and the composition, and the intermolecular pair correlation functions for symmetric blends of linear chains, blends of cyclic polymers, blends with an asymmetry in cohesive energies, blends with different chain lengths, blends with distinct monomer shapes, and blends with a stiffness disparity between the components are discussed. For strictly symmetric blends the Flory‐Huggins theory becomes quantitatively correct in the long chain length limit, when the χ parameter is identified via the intermolecular pair correlation function. For small chain lengths composition fluctuations are important. They manifest themselves in 3D Ising behavior at the critical point and an upward parabolic curvature of the χ parameter from small‐angle neutron scattering close to the critical point. The ratio between the mean field estimate and the true critical temperature decreases like √χ/(ρb³) for long chain lengths. The chain conformations in the minority phase of a symmetric blend shrink as to reduce the number of energeticaly unfavorable interactions. Scaling arguments, detailed self‐consistent field calculations and Monte Carlo simulations of chains with up to 512 effective segments agree that the conformational changes decrease around the critical point like 1/√N. Other mechanisms for a composition dependence of the single chain conformations in asymmetric blends are discussed. If the constituents of the blends have non‐additive monomer shapes, one has a large positive chain‐length‐independent entropic contribution to the χ parameter. In this case the blend phase separates upon heating at a lower critical solution temperature. Upon increasing the chain length the critical temperature approaches a finite value from above. For blends with a stiffness disparity an entropic contribution of the χ parameter of the order 10^–3 is measured with high accuracy. Also the enthalpic contribution increases, because a back folding of the stiffer component is suppressed and the stiffer chains possess more intermolecular contacts. Two aspects of the single chain dynamics in blends are discussed: (a) The dynamics of short non‐entangled chains in a binary blend are studied via dynamic Monte Carlo simulations. There is hardly any coupling between the chain dynamics and the thermodynamic state of the mixture. Above the critical temperatures both the translational diffusion and the relaxation of the chain conformations are independent of the temperature. (b) Irreversible reactions of a small fraction of reactive polymers at a strongly segregated interface in a symmetric binary polymer blend are investigated. End‐functionalized homopolymers of different species react at the interface instantaneously and irreversibly to form diblock copolymers. The initial reaction rate for small reactant concentrations is time dependent and larger than expected from theory. At later times there is a depletion of the reactive chains at the interface and the reaction is determined by the flux of the chains to the interface. Pertinent off‐lattice simulations and analytical theories are briefly discussed.