Abstract. Harary's & Randić's ideas of "forcing" & "freedom" involve subsets of double bonds of Kekule structure such as to be unique to that Kekule structure. Such forcing sets are argued to be greatly generalizable to deal with various other coverings, and thence forcing seems to be fundamental, and of notable potential utility. Various forcing invariants associated to (molecular) graphs ensue, with illustrative (chemical) examples and some mathematical consequences being provided. A complementary "uniqueness" idea is noted, and the general characteristic of "derivativity" of "forcing" is established (as is relevant for QSPR fittings). Different ways in which different sorts of forcings arise in chemistry are briefly indicated.(doi: 10.5562/cca2000)

Analysis of crystallized protein structures suggests that globular proteins are organized as consecutively connected units of 25-35 residues. These units are closed loops, that is returns of the polypeptide chain trajectory to a close contact with itself. This universal feature of apparently polymer-statistical nature is a basis for a principally novel view on the globular proteins as loop fold structures. The same unit size has been detected in protein sequences translated from complete prokaryotic genomes by positional autocorrelation analysis, which strongly indicates the evolutionary connection of the units. The units are further characterized by prototype sequences matching to their numerous derivatives in the translated genomes. The matches to five strongest prokaryotic prototypes and three prototypes of C. elegans are identified in the sequences of crystallized proteins, and their structures analyzed. Corresponding segments of the polypeptide chains in majority of cases form closed loops, though evolutionary fate of every prototype element is shown to be rather diverse. Then loop ends can be separated by a sequence-wise distant segments and stabilized by the spatial interactions in the context of the overall globular structure. The units belong to a presumably limited spectrum of the sequence prototypes, full repertoire of which would constitute a proteomic code.

No abstract

It has recently been discovered that globular proteins are universally built from standard loop-n-lock units of about 30 amino acid residues. The hypothesis has been put forward on the loop stage in the protein evolution when the units were autonomous. Later they joined together making longer chains. One would expect that the early individual loop-n-lock elements might still be detected in modern protein sequences as remnants of the hypothetical 30-residue sequence prototypes. Among several strong sequence motifs, extracted from protein sequences of 23 complete bacterial proteomes, one 32-residue prototype was studied here in detail. Numerous sequence segments related to the prototype are identified in the crystal structures of proteins of a PDB_SELECT database. Analysis of the respective chain trajectories for the cases with different degrees of sequence conservation confirms that the majority of the segments correspond to the closed loops. In the evolutionary diversification of the prototypes the secondary structure yields first, while the sequence is still moderately conserved. The last feature to go is the chain return property. Apparently, the opening of the loops would severely destabilize the protein fold, which explains their conservation.

Abstract. Known borane polyhedral cluster characteristics can be used for predicting new architectural constructs. We propose additional structures derived from B 18 H 22 : three positional isomers different from the well-known anti-B 18 H 22 and syn-B 18 H 22 boranes. We have also derived two new cyclic structures based on the condensation of borane pentagonal pyramids and bipyramids. The concatenation of polyhedral borane molecules is also considered from a mathematical point of view.