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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 5511-5524 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a new application of the chain growth algorithm to lattice generation of protein structure and thermodynamics. Given the difficulty of ab initio protein structure prediction, this approach provides an alternative to current folding algorithms. The chain growth algorithm, unlike Metropolis folding algorithms, generates independent protein structures to achieve rapid and efficient exploration of configurational space. It is a modified version of the Rosenbluth algorithm where the chain growth transition probability is a normalized Boltzmann factor; it was previously applied only to simple polymers and protein models with two residue types. The independent protein configurations, generated segment-by-segment on a refined cubic lattice, are based on a single interaction site for each amino acid and a statistical interaction energy derived by Miyazawa and Jernigan. We examine for several proteins the algorithm's ability to produce nativelike folds and its effectiveness for calculating protein thermodynamics. Thermal transition profiles associated with the internal energy, entropy, and radius of gyration show characteristic folding/unfolding transitions and provide evidence for unfolding via partially unfolded (molten-globule) states. From the configurational ensembles, the protein structures with the lowest distance root-mean-square deviations (dRMSD) vary between 2.2 to 3.8 Å, a range comparable to results of an exhaustive enumeration search. Though the ensemble-averaged dRMSD values are about 1.5 to 2 Å larger, the lowest dRMSD structures have similar overall folds to the native proteins. These results demonstrate that the chain growth algorithm is a viable alternative to protein simulations using the whole chain. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 585-604 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Two sets of integral equations are presented in this paper for dynamic pair correlation functions for polymeric liquids subjected to shearing. One set of the integral equations is a dynamic and polymeric extension of the Percus–Yevick integral equation for the equilibrium pair correlation function of a simple fluid, whereas the other is that of the hypernetted chain equation. These integral equations are coupled, in the case of uniform temperature, to the momentum balance equation and the constitutive equations for the stress tensor and the diffusion fluxes in the system. When this coupled system of evolution equations (generalized hydrodynamic equations) is solved subject to appropriate initial and boundary conditions, the dynamic structure factors and correlation functions can be computed for the polymeric liquid of interest. The first-order iterative solution of the integral equations for correlation functions is computed for the case of equilibrium polymers. It yields a qualitatively correct chain-length dependence of the maximum position of the end-to-end distance distribution function and thus the mean square end-to-end distance of the polymer. The shear-induced effect on the end-to-end distance distribution function is numerically computed based on the first-order perturbation solution, which indicates that the distribution becomes anisotropic, having two twofold symmetry axes, when the polymer is sheared. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 2261-2276 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Conformational properties of isolated linear copolymers are studied by means of the integral equation theory of polymers. We examine two-letter copolymers that have repeated-block symmetry; the potential between like monomers is repulsive and that between unlike ones is a Lennard-Jones potential. This class of copolymer sequences satisfies an approximate translational invariance symmetry for the correlation functions. Conformational behavior of any given copolymer is analyzed by computing its configurational and thermodynamic properties from the information of its sequence and potentials of interaction. All properties calculated show that they are independent of sequence heterogeneity at high temperatures. The influence of sequence heterogeneity becomes significant below the theta point. Sequences that are compact and have low excess entropy generally exhibit two key features: (a) their monomer composition is symmetric and (b) the unlike monomer species tend to alternate in the sequence. These conditions are consistent with the minimization of unfavorable interactions. In addition, the thermodynamics functions of copolymers are discussed in the context of the Flory-type theory. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 100 (1994), S. 5922-5935 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this paper, we continue investigations on the solution methods for the generalized Percus–Yevick equations for the pair correlation functions of polymers, which were formulated in the previous papers of this series [J. Chem. Phys. 99, 4084, 4103 (1993)]. Previously, they were reduced to recursive integral equations and solved numerically. In this paper, a translational invariance approximation is used to reduce the number of integral equations to solve. In this approximation, only N integral equations out of N2 integral equations are required for a polymer consisting of N beads (monomers). The behavior of an isolated polymer is studied with three different potential models, a soft sphere, a hard sphere, and a Lennard-Jones potential. The main motivation for considering these three potential models is in testing the idea of universality commonly believed to hold for some properties of polymers. We find that the universality holds for the power law exponent for the expansion factor of polymers at high temperatures. The end-to-end distance distribution functions, intermediate distribution functions, chemical potentials, the density distributions, and various expansion factors of the polymer chain are computed from the solutions of the integral equations in the case of coiled, ideal, and collapsed states of the polymer. The expansion factors in the collapsed regime are found to obey power laws with respect to the length of the polymer and [B(T)−B(θ¯)], where B(T) is the second virial coefficient and θ¯ is a modified θ temperature. The values of these exponents approach those from the known theories of polymer collapse as the chain length becomes long and the ratio of bond length to bead radius becomes large.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 3235-3240 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A systematic comparison of computer simulation data for linear hard-sphere and square-well chains with the results of single-chain integral equation is reported. The single-chain integral equation is derived from the polymer Kirkwood hierarchy for site–site or pair distribution functions. Quantities compared include radius of gyration, end-to-end distance, and internal energy. We examine chain lengths up to 1000 sites for hard-sphere chains. The radius of gyration and end-to-end distance from the theory are found to agree quantitatively with Monte Carlo simulation data. Results for square-well chains with the range λ=1.5 are compared with Monte Carlo and constant temperature molecular dynamics simulation data for chains having up to 64 sites. The radius of gyration and internal energy generally deviate from simulation data by about 10% for reduced temperatures greater than 1. The values of the radius of gyration at reduced temperatures below 1 are larger than those from simulations. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 2011-2022 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Effects of the solvent on the conformation of a polymeric chain molecule are examined by using a set of polymer–solvent integral equations for correlation functions for the polymer and the solvent. Solutions of the integral equations are used for computing the polymer–solvent distribution, chain conformations, and scaling properties associated with polymer swell and collapse in good and poor solvents. The variation of chain properties with the solvent density and the solvent quality is examined for chains having up to 100 bonds. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 1664-1675 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A method of constructing three-dimensional structures of model protein conformations is presented. The method consists of self-consistent field integral equations for pair correlation functions of constituent units in a heteropolymer chain and the use of the distance matrix and the embedding algorithm for constructing conformations. The pair correlation functions obey integral equations that are derived from the Kirkwood hierarchy by applying closure approximations; they appear as a generalized form of the liquid-state Percus–Yevick integral equation. Model protein sequences that exhibit the formation of secondary-like patterns and tertiary-like structures are examined. These structural features are formed at low temperatures and they are stabilized by strong hydrogen bonding forces. To obtain the structure in three dimensions, the method of distance geometry is used to refine the distance matrix of a folded structure which is then embedded in the three-dimensional space by an embedding algorithm. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 4323-4341 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Improved self-consistent intermolecular integral equations for a chain-molecular liquid are derived from the polymer Kirkwood hierarchy. The present work is a continuation of our recent work reported in a previous paper [J. Chem. Phys. 103, 2140 (1995)]. It is shown that the reference interaction site model (RISM) equation and extensions thereof can be obtained from the new intermolecular equations. The solutions of the new self-consistent set of intra- and intermolecular equations are compared with computer simulation data for chains with repulsive interaction potentials whose lengths N vary from 4 to 100 sites. The intermolecular correlation functions obtained from simulations are accurately reproduced. Comparisons with simulation data for the pressure equation of state and excess chemical potential show that the predictions of the self-consistent theory are accurate for packing fractions up to 0.4. These thermodynamic functions are found to scale as N for N(approximately-greater-than)16, implying that results obtained for short chains can be extrapolated to much longer chains. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 99 (1993), S. 4103-4111 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A recursive integral equation for the intramolecular correlation function of an isolated linear polymer of N bonds is derived from the integral equations presented in the preceding paper. The derivation basically involves limiting the density of the polymer to zero so that polymers do not interact with each other, and thus taking into account the intramolecular part only. The integral equation still has the form of a generalized Percus–Yevick integral equation. The intramolecular correlation function of a polymer of N bonds is recursively generated by means of it from those of polymers of 2, 3,..., (N−1) bonds. The end-to-end distance distribution functions are computed by using the integral equation for various chain lengths, temperatures, and bond lengths in the case of a repulsive soft-sphere potential. Numerical solutions of the recursive integral equation yield universal exponents for the mean square end-to-end distance in two and three dimensions with values which are close to the Flory results: 0.77 and 0.64 vs Flory's values 0.75 and 0.6 for two and three dimensions, respectively. The intramolecular correlation functions computed can be fitted with displaced Gaussian forms. The N dependence of the internal chemical potential is found to saturate after some value of N depending on the ratio of the bond length to the bead radius.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 558-564 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The consequences of the derivatives of the Ornstein–Zernike relation with respect to the density (ρ) and temperature (T) are examined. An approximate closure for the Ornstein–Zernike relation is used to evaluate the derivatives of the pair-correlation function to all orders without knowing explicitly the correlation functions higher in order than the pair-correlation function. The first- and second-order thermodynamic (ρ or T) derivatives of the pair-correlation function are calculated and compared with the experiments of Egelstaff et al. In addition, the thermodynamic functions involving these derivatives are evaluated to demonstrate the utility and accuracy of the method.
    Type of Medium: Electronic Resource
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