Showing papers in "Macromolecules in 1976"

A new derivation of average molecular weights of nonlinear polymers.

Abstract: A new method for calculating average molecular weights is presented for nonlinear polymers. In contrast to the previous methods of Flory and Stockmayer which first calculate the distribution of all species and then use the distributions to calculate average properties, the new method calculates these properties directly. In contrast to the method of Gordon, probability generating functions are not required. Starting with elementary probability and utilizing the recursive nature of network polymers property relations can be developed more simply. We illustrate the method for calculations of Mw Mz, and the gel point for a wide variety of polyfunctional polymerizations.

Medium- and long-range interaction parameters between amino acids for predicting three-dimensional structures of proteins.

Abstract: In a previous paper, a hypothesis for protein folding was proposed in which the native structure is formed by a three-step mechanism: (A) formation of ordered backbone structures by short-range interactions, (B) formation of small contact regions by medium-range interactions, and (C) association of the small contact regions into the native structure by long-range interactions. In this paper the empirical interaction parameters, used as a measure of the medium- and long-range interactions (the standard free energy, deltaGdegrees k,l, of formation of a contact between amino acids of species k and l) that include the role of the solvent (water) and determine the conformation of a protein in steps B and C, are evaluated from the frequency of contacts in the x-ray structures of native proteins. The numerical values of deltaG degrees k,l for all possible pairs of the 20 naturally occurring amino acids are presented. Contacts between highly nonpolar side chains of amino acids such as Ile, Phe, Trp, and Leu are shown quantitatively to be stable. On the contrary, contacts involving polar side chains of amino acids such as Ser, Asp, Lys, and Glu are significantly less stable. While this implies, in a quantitative manner, that it is generally more favorable for nonpolar groups to lie in the interior of the protein molecule and for the polar side chains to be exposed to the solvent (water) rather than to form contacts with other amino acids, many exceptions to this generalization are observed.

Determination of the structure of cellulose II.

Abstract: The structure of regenerated cellulose is shown by x-ray diffraction to be comprised of an array of antiparallel chain molecules. The determination was based on the intensity data from rayon fibers and utilized rigid-body least-squares refinement techniques. The unit cell is monoclinic with space group P2(1) and dimensions a = 8.01 A, b = 9.04 A, c = 10.36 A (fiber axis), and gamma = 117.1 degrees. Models containing chains with the same sense (parallel) or alternating sense (antiparallel) were refined against the intensity data. The only acceptable model contains antiparallel chains. The -CH2OH groups of the corner chain are oriented near to the gt position while those of the center chain are near to the tg position. Both chains possess an O3-H-O5' intramolecular hydrogen bond, and the center chain also has an O2'-H-O6 intramolecular bond. Intermolecular hydrogen bonding occurs along the 020 planes (o6-h-o2 bonds for the corner chains and O6-H-O3 bonds for the center chains) and also along the 110 planes with a hydrogen bond between the O2-H of the corner chain and the O2' of the center chain. This center-corner chain hydrogen bonding is a major difference between the native and regenerated structures and may account for the stability of the latter form.

On the Use of Classical Statistical Mechanics in the Treatment of Polymer Chain Conformation

Abstract: Two different treatments of the degrees of freedom of bond stretching and bond angle bending in chain polymers by classical statistical mechanics lead to different and nonequivalent expressions of the partition functions. If we fix the bond lengths and bond angles at the outset and treat them as constraints (the classical rigid model), the partition function is given by an integral of (det G)-'12 exp(-@F(Q)) over the space of the dihedral angles Q in a poly- mer chain, where the elements of the matrix G are the coefficients in the quadratic expression (in terms of general- ized momenta conjugate to Q) for the kinetic energy of the polymer chain, and F(Q) is the conformational energy of the polymer chain. If we conceptually allow bond lengths and bond angles to vary under an infinitely strong potential (the classical flexible model) and perform the integration of the Boltzmann factor over the momenta conjugate to the Cartesian coordinates, we obtain the partition function in the form of an integral of exp(-@F(Q)) over the space of the dihedral angles Q. The origin of the difference in these two expressions lies in the different treatments of the vi- brational motions involving bond lengths and bond angles. In order to decide which of the two expressions is to be used as the basis of a statistical mechanical study of the polymer chain in equilibrium, an expression for the partition function that is quantum mechanically correct for these vibrational motions is derived, and the approximations in- volved to obtain each of the two non-equivalent classical expressions from the quantum mechanical expression are examined. The classical rigid model can be derived from the quantum mechanical one (a) by applying the ground state approximation for all vibrations associated with bond stretching and bond angle bending (i.e., by neglecting contributions to the partition function from excited vibrational states), and (b) by neglecting the conformational de- pendence of the zero-point energy of these vibrations. The classical flexible model can be derived by treating all these vibrations classically, which would appear to be unwarranted because many of these vibrations are of sufficiently high frequency to require a quantum mechanical treatment. However, a quantitative analysis of the approximations involved in each of the two models reveals that, of the two nonequivalent classical treatments, the classical flexible model is better than the classical rigid model.

Comments on Exclusion of Polymer Chains from Small Pores and Its Relation to Gel Permeation Chromatography

Abstract: Some criticisms of our theoretical treatment of the partial exclusion of flexible-chain polymers in solution from cavities of macromolecular size and its application to gel permeation chromatography are examined. In other discussion, it is confirmed by simple reasoning that the identification, explicit or implicit in various studies, of the mean projection of a polymer molecule onto a line as a characteristic dimension governing the extent of permeation of simple pores does not depend on specific molecular models. Our previous calculation of permeation by certain random-flight branched-chain species is shown to lead, incidentally, to the mean projection for these structures. From relations between the mean projection and the hydrodynamic volume of a molecule, it appears that the product of intrinsic viscosity and molecular weight is not a common calibration factor for elution of all molecular species from a gel chromatographic column, but theory and experience do support the validity of this correlation among solutes with similar molecular architecture.

Functional polymeric microspheres based on 2-hydroxyethyl methacrylate for immunochemical studies

Abstract: Co gamma irradiation of 2-hydroxyethyl methacrylate in the presence or in the absence of other acrylic monomers was found to constitute an effective technique for the synthesis of hydrophilic functional microspheres in the size range of approximately 0.3 to 3 microns in diameter. The effect of monomer concentration, steric stabilization, and electrostatic interaction on the particle size was investigated. Experimental conditions were determined to obtain desired particle sizes of relatively narrow distribution. It was shown that particles may be formed without intermediate micelles, i.e., by homogeneous nucleation, and the rate of particle formation is affected primarily by the rate of particle coalescence in the initial stages of the reaction. When covalently bound to antibodies these microspheres were successfully used to label murine and human lymphocytes.

Stability of cis, trans, and nonplanar peptide groups.

Abstract: Conformational energy calculations using ECEPP (Empirical Conformational Energy Program for Peptides) were performed on the molecular fragment Calpha1C'ONHCalpha2, on N-methylacetamide, and on several peptide molecules including N-acetyl-N'-methylglycineamide (Gly single residue), N-acetyl-N',N'-dimethylglycine-amide, and N-acetyl-N'-methylamide dipeptides of Gly-Gly and Gly-Pro. Energy minimization was carried out with peptide groups taken in both the cis and trans conformations, and the librational entropy and conformational free energy were determined at each minimum. It was found that the instability of cis in Gly-Gly comes primarily from interactions of the Calpha1 and HCalpha1 atoms with the Calpha2 and HCalpha2 atoms, and also from avorable interactions present in the trans form which are disallowed in the cis form, and from conformational entropy. The instability of cis in Gly-Pro is much less than in Gly-Gly because unfavorable interactions of the type CalphaH-CalphaH present in the cis conformation of Gly-Gly are present in both the cis and trans forms of Gly-Pro. The instability of cis in Gly-Pro arises mainly from the change in electrostatic energy caused by the restricted rotation about the N-Calpha bond of Pro. Entropy accounts for about 0.5 kcal/mol of the instability of cis in Gly-Pro compared with about 1.5 kcal/mol in Gly-Gly. The calculated fraction (4%) of cis in Gly-pro is in good agreement with the experimental value (5%) for related peptides in nonpolar solvents. When the dihedral angle omega of the central peptide bond in these dipeptides is allowed to vary during energy minimization, the deviations from planarity are only 1-3 degrees in low-energy minima of Gly-Gly but as much as 10 degrees in Gly-Pro. A comparison of these results with calculations in which the peptide bond was held fixed in the planar trans conformation shows that conformation-dependent properties of blocked dipeptides can be represented adequately without allowing omega to vary.