Long chain branch polymer chain dimensions: application of topology to the Zimm–Stockmayer model

From Molecular to Biological Structure and Back

A comparative analysis of the topological structure of molecules and molecular biology networks revealed both similarity and differences in the methods used, as well as in the essential features of the two types of systems. Molecular graphs are static and, due to the limitations in atomic valence, show neither power distribution of vertex degrees nor "small-world" properties, which are typical for dynamic evolutionary networks. Areas of mutual benefits from an exchange of methods and ideas are outlined for the two fields. More specifically, chemical graph theory might make use of some new descriptors of network structure. Of interest for quantitative structure-property relationship/quantitative structure-activity relationship and drug design might be the conclusion that descriptors based on distributions of vertex degrees, distances, and subgraphs seem to be more relevant to biological information than the single-number descriptors. The network concepts of centrality, clustering, and cliques provide a basis for similar studies in theoretical chemistry. The need of dynamic theory of molecular topology is advocated.

Mechanistic Information from Analysis of Molecular Weight Distributions of Starch

A methodology is developed for interpreting the molecular weight distributions of debranched amylopectin, based on techniques developed for quantitatively and qualitatively finding mechanistic information from the molecular weight distributions of synthetic polymers. If the only events occurring are random chain growth and stoppage (i.e., the rates are independent of degree of polymerization over the range in question), then the number of chains of degree of polymerization N, P(N), is linear in ln P(N) with a negative slope, where the slope gives the ratio of the stoppage and growth rates. This starting point suggests that mechanistic inferences can be made from a plot of lnP against N. Application to capillary electrophoresis data for the P(N) of debranched starch from across the major taxa, from bacteria (Escherichia coli), green algae (Chlamydomonas reinhardtii), mammals (Bos), and flowering plants (Oryza sativa, rice; Zea mays, maize; Triticum aestivum, wheat; Hordeum vulgare, barley; and Solanum tuberosum, potato), gives insights into the biosynthetic pathways, showing the differences and similarities of the alpha-1,4-glucans produced by the various species. Four characteristic regions for storage starch from the higher plants are revealed: (1) an initial increasing region corresponding to the formation of new branches, (2) a linear ln P region with negative slope, indicating random growth and stoppage, (3) a region corresponding to the formation of the crystalline lamellae and subsequent elongation of chains, and (4) a second linear ln P with negative slope region. Each region can be assigned to specific enzymatic processes in starch synthesis, including determining the ranges of degrees of polymerization which are subject to random and nonrandom processes.