SynopsisExact algorithms for the calculation of melting curves of heterogeneous DNA with N base pairs apparently require computer time proportional to N2. However, it is shown that a decomposition of the loop entropy factor into a sum of I exponential functions (1) gives an extremely accurate approximation to the loop entropy factor for small values of I and (2) makes the computer time for the exact algorithms proportional to I-N. In effect, exact results for melting curves and lengths of helix or coil stretches are obtained with computer time comparable to that required for the Frank-Kamenetskii approximation. The remarkable accuracy of the latter for the fraction of helical content (errors of 0.01-0.05) is confirmed, but appreciably larger errors are found for the lengths of helix or coil stretches (typical errors of 30-100%).

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Second virial coefficients and radii of gyration for an off-lattice model of linear and star polymer chains in a good solvent (or excluded volume conditions) have been obtained by means of a Monte Carlo method. The results are discussed in terms of the dimensionless interpenetration factor, which combines these two quantities. Comparisons with theoretical prediction from the renormalization group theory and with existing simulation and experimental data are performed for the different types of chains.

Dimensions and intrinsic viscosities are calculated for different models of linear and star chains with a wide range of chain lengths. Viscosities are evaluated according to an efficient lower-bound method. The chain models mimic both the good-solvent and -solvent conditions. These calculations permit refinement of previous estimations from results calculated with an upper-bound method for considerably shorter chains. 25 4.16* 44.0 ± 0.2 2.13 ±0.01 49 8.16* 122 ±1 2.14 ±0.02 109 18.16* 412 ±2 2.18 ±0.01