The polybase properties of polyvinylamine hydrobromide were studied by pH‐metric titration at concentrations ranging from 10−4 to 10−1 M, in the presence, as well as in the absence, of neutral monomonovalent salt at high concentrations. The dependence of pH on degree of ionization, in all the range of concentrations studied, diverges from the known behavior of polyacids and polybases. The titration curve could not be characterized by a single dissociation constant, even when the electrostatic potential, determined electrophoretically, was taken into account, or when this potential was suppressed by high concentrations of neutral salt. An attempt is made to explain the unusual behavior of polyvinylamine by taking into account the nearest neighbor interaction. A statistical treatment, based on the unidimensional Ising model, leads to potentiometric equations involving two constants‐the intrinsic dissociation constant pK, and a nearest neighbor interaction constant ΔpK. The experimental titration curve could be satisfactorily described by these theoretical potentiometric equations. The titration constants for polyvinylamine derived by this procedure are pK = 9.4 and ΔpK = 1.20. These values compare favorably with the constants obtained from the microscopic dissociation constants of diethylenetriamine and of triethylenetetramine.

By using conformational free energy calculations, we have studied the sequence dependence of flexibility and its anisotropy along various conformational variables of DNA base pairs. The results show the AT base step to be very flexible along the twist coordinate. On the other hand, homonucleotide steps, GG(CC) and AA(TT), are among the most rigid sequences. For the roll motion that would correspond to a bend, the TA step is most flexible, while the GG(CC) step is least flexible. The flexibility of roll is quite anisotropic; the ratio of fluctuations toward the major and minor grooves is the largest for the GC step and the smallest for the AA(TT) and CG steps. Propeller twisting of base pairs is quite flexible, especially of A.T base pairs; propeller twist can reach 19 degrees by thermal fluctuation. We discuss the effect of electrostatic parameters, comparison with available experimental results, and biological relevance of these results.

Abstract(1) The electrostatic free energy of randomly kinked, ionized, macromolecules was calculated for polyelectrolyte solutions of finite ionic strenght. A detailed analysis of the charging process and the reference state of the free energy is given. The mutual electrostatic repulsion of the fixed charges on the macromolecule is the main part of the electrostatic free energy. Its calculation is based on two main assumptions: the validity of Kuhn's statistics and of Debye's approximation. (2) The electrostatic contribution per macromolecule to the free energy of the solution is found to be Fe = (v2ϵ2/Dh)ln {1 + (6h/κh)}, where v is the number of charged groups per polymolecule, ϵ the unit of charge, D the dielectric constant, κ Debye's inverse radius, based on the number of free ions in solution, h the end‐to‐end distance of the charged molecule, and h0 the corresponding end‐to‐end distance in and uncharged reference state. (3) Activity coefficients of free ions in polyelectrolyte solutions have been derived from the theory. The calculated values compare favorably with the activity coefficients from measurements on Donnan distribution of salt.

Detailed studies of structures of biological macromolecules, even in simplified models, involve many costly and time-consuming calculations. Any thorough methods require sampling of an extremely large conformation and momentum space. Calculations of electrostatic interactions, which depend on many physical factors, such as the details of solvent, solvent accessibility in macromolecules, and molecular polarizability, are always developed in a compromise between more rigorous, detailed models and the need for immediate application to complicated biological systems. In this paper, a middle ground is taken between the more exact theoretical models and the simplest constant values for the dielectric constant. The effects of solvent, counterions, and molecular polarizability are incorporated through a set of adjustable parameters that should be determined from experimental conditions. Several previous forms for the dielectric function are compared with the new ones. The present methods use Langevin functions to span the region of dielectric constant between bulk solvent and cavity values. Application of such dielectric models to double-helical DNA is important because base-stacking preferences were previously demonstrated [A. Sarai, J. Mazur, R. Nussinov, and R. L. Jernigan (1988) Biochemistry, vol. 27, pp. 8498-8502] to be sensitive to the electrostatic formulation. Here we find that poly(dG).poly(dC) can be A form for high screening and B form for low screening. By contrast, poly(dA).poly(dT) can only take the B form. Base stacking is more sensitive to the form of the dielectric function than are the sugar-phosphate backbone conformations. Also in B form, the backbone conformations are not so affected by the base types as in A form.

Conformational analysis of DNA shows that the origin of the B-form double helix can be attributed in large part to the atomic charge pattern in the base pairs. The charge patterns favor specific helical stacking of the base pairs. Base pairs alone--without backbones--have a strong tendency to form helix, indicating that the backbones play a rather passive role in determining the basic helical structure of DNA. It is mainly the electrostatic interactions determined by the charge pattern on base pairs that stabilize a particular helical conformation. The charge pattern in the base pairs appears to be responsible for much of the sequence dependence of DNA conformation, rather than steric clashes.

Random walks that are not allowed to intersect themselves were generated on the simple cubic and face-centered cubic lattices and used as a model of a linear polymer chain in dilute solution with excluded volume and attractive energies between the chain elements. The mean-square end-to-end distances and meansquared radii of gyration and their moments were computed for chain lengths up to 2000 segments and for a wide range of attractive energies. The partition functions of the chains were also computed. The attractive energy required for a given property of the chain to be the same as the given property of a random coil, the point, was investigated. The required attractive energy depended slightly on the particular property chosen for comparison, so rather than a unique point, a narrow range of points was found.

Defect energy was calculated as a function of dihedral angles of the bonds in a point dislocation for sequences of conformations that resulted in motion of the dislocation along the polyethylene chain. Paths that presented low barriers to diffusive motion of the defect were found by incrementing, in a particular sequence, selected dihedral angles around two separated bonds near the opposite ends of the defect as the computer searched for the lowest energy conformation of all the other parts of the defect. Thus, the diffusion of a point dislocation provides a plausible mechanism for diffusion of the chain along its axis.

The principal moments of the squared radius of gyration of polymer chains with excluded volume were computed for chains on the simple cubic and face-centered cubic lattices. The moments were ordered for each configuration by their magnitude, then averaged over a large number of chain configurations and divided by the squared radius of gyration to yield shape factors of the chain. These shape factors were found to be independent of chain length for long chains. The shape factors showed that the instantaneous shape of a polymer chain is very asymmetrical. With increasing interaction energy between the segments of the chains, the chains became less asymmetrical; at the point the shape factors became equal to those of the random coil as previously calculated by Sole and Stockmayer. The relative variations of the principal moments were also calculated. The largest principal moments were found to have the largest relative variations.Kuhn1 in the early thirties was able to show that for the freely jointed model of a polymer in solution, the instantaneous shape of the molecule is not spherical. However, he provided no picture of its instantaneous shape.Recently, Sole and Stockmayer2 and Sole3 have presented both analytical and Monte Carlo calculations on the random-coil polymer model which gave quantitative estimates on the deviations from sphericity. However, the random-coil model of a polymer in solution does not take into account the effects of either excluded volume or attractive energies between segments of the polymer. In this paper, we investigate the effects of excluded volume and attractive energy between nearest-neighbor segments on the deviations from sphericity of chains on a lattice generated by the Monte Carlo method.