We develop here a highly efficient variant of the Monte Carlo method for direct evaluation of the partition function, free energy, and other configurational dependent physical properties for long polymer chains. This method (CC–BB) combines continuous configurational biased sampling with Boltzmann factor biased enrichment. To illustrate the efficiency and to validate the bias correction for weighting the torsion and chain enrichments, we applied this model to isolated single chains using a united atom force field. For a 50 monomer polymer chain CC–BB with 400 chains leads to an accuracy of 0.1% in the free energy whereas simple sampling direct Monte Carlo requires about 109 chains for this accuracy. This leads to cost savings by a factor of about 350 000. CC–BB is easily extended to multichain systems, to the condensed state, to more realistic force fields, and to evaluating the mixing free energy for polymer blends.

We present the generate-and-select hierarchy for tertiary protein structure prediction. The foundation of this hierarchy is the Restrained Generic Protein (RGP) Direct Monte Carlo method. The RGP method is a highly efficient off-lattice residue buildup procedure that can quickly generate the complete set of topologies that satisfy a very small number of interresidue distance restraints. For three restraints uniformly distributed in a 72-residue protein, we demonstrate that the size of this set is ∼104. The RGP method can generate this set of structures in less than 1 h using a Silicon Graphics R10000 single processor workstation. Following structure generation, a simple criterion that measures the burial of hydrophobic and hydrophilic residues can reliably select a reduced set of ∼102 structures that contains the native topology. A minimization of the structures in the reduced set typically ranks the native topology in the five lowest energy folds. Thus, using this hierarchical approach, we suggest that de novo prediction of moderate resolution globular protein structure can be achieved in just a few hours on a single processor workstation.

Small-angle X-ray scattering, light scattering, and viscosity measurements were made on 18 sharp fractions of poly(isophthaloyl-frans-2,5-dimethylpiperazine) (PIDP), a flexible polyamide, ranging in weight-average molecular weight Afw from 2.6 X 103 to 2.4 X 106, with IV-methyl-2-pyrrolidone (NMP) at 25 °C as the solvent. Both gyration radius and intrinsic viscosity data showed PIDP in NMP to be essentially unperturbed below Afw ~104 and perturbed above it by volume effect. When modeled by Kratky and Porod's wormlike chain, the unperturbed PIDP chain was characterized by a persistence length of 1.2 nm and a molar mass per unit contour length of 310 nm-1. It was found that the combination of the Yamakawa-Stockmayer perturbation theory for the radius expansion factor of a wormlike chain and the Domb-Barrett equation for a flexible chain accurately describes the dimensional behavior of PIDP in NMP over the entire range of Mw studied.

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