Acyl chains linked to phospholipids of the yeast, Saccharomyces cerevisiae, are mainly C16:1 and C18:1 accompanied by minor amounts of C14:0, C16:0 and C18:0. In view of this rather simple fatty acid composition, the question arose whether in yeast, as in higher eukaryotes, fatty acyl groups were characteristically distributed among the sn-1 and sn-2 positions of distinct phospholipid classes. Analysis of fatty acids linked to the sn-1 and sn-2 positions of the major phospholipids showed that indeed saturated fatty acyl groups predominated in the sn-1 positions. While the percentage of saturated fatty acids was low (10%) in phosphatidylcholine (PtdCho) and phosphatidylethanolamine (PtdEtn) from cells grown on rich medium, it was higher in phosphatidylserine (PtdSer) (25%) and highest in phosphatidylinositol (PtdIns) (41%). Oleate was mainly linked to position sn-2, while palmitoleate predominated in position sn-1. Striking differences in the fatty acid distribution of phospholipids that are metabolically closely related (e.g. PtdSer and PtdEtn, PtdEtn and PtdCho, and PtdIns and PtdSer) suggest that pathways must exist for the generation of distinct phospholipid molecular species within the different phospholipid classes. The highly selective incorporation of exogenous [14C]palmitic acid (90%) and [3H]oleic acid (99%) into the sn-2 position of PtdCho, and the preferential incorporation of these fatty acids into the sn-2 position of PtdEtn (70 and 90%, respectively, for palmitic and oleic acid) are compatible with the postulate that phospholipase A2-mediated deacylation followed by reacylation of the lysophospholipids is involved in the generation of phospholipid species in yeast.
The Hosoya index and the Merrifield-Simmons index are typical examples of graph invariants used in mathematical chemistry for quantifying relevant details of molecular structure. In recent years, quite a lot of work has been done on the extremal problem for these two indices, i.e., the problem of determining the graphs within certain prescribed classes that maximize or minimize the index value. This survey collects and classifies these results, and also provides some useful auxiliary results, tools and techniques that are frequently used in the study of this type of problem.Keywords Hosoya index · Merrifield-Simmons index · Extremal problem · Molecular graphs Mathematics Subject Classification (2000) 92E10 · 05C35 · 05C70
History and Chemical BackgroundIn 1971 the Japanese chemist Haruo Hosoya introduced a molecular-graph based structure descriptor [35], which he named topological index and denoted by Z. He showed that certain physico-chemical properties of alkanes (= saturated hydrocarbons)-in particular, their boiling points-are well correlated with Z. He defined the quantity Z in the following manner.Let G be a (molecular) graph. Denote by m(G, k) the number of ways in which k mutually independent edges can be selected in G. By definition, m(G, 0) = 1 for all graphs, and
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