Current Organic Chemistry - Volume 19, Issue 3, 2015

In the present study, valence-topological charge-transfer indices are used to calculate the isoelectric point (pI). Dipoles are computed by vector semisums µvec and valence vector semisums µvec V comparing with isoelectronic series (cyclopentadiene, benzene, styrene). The valence vector semisum results intermediate between the vector semisum and experimental dipole. The steric effect stays constant and the dominating effect is electronic. The indices are applied to the dipole of homologous series of percutaneous enhancers and amino-acid pI. No collapse of Gi-Ji indices is observed in the fit of pI decreasing co-llinearity risk. A heteroatom in the π-electron systems is beneficial. Acidic and basic groups improve models of pI. Fragment fitting allows computing lysozyme pI. Globular protein models (lysozyme, myoglobin, albumin) cover a wide pI range. The purpose of the work is to extend the study to anionic lipid bilayers. The role of electrostatics is examined in cationic protein adsorption to zwitterionic phosphatidylcholine (PC) and anionic mixed PC/phosphatidylglycerol (PG) small unilamellar vesicles, via spectrofluorimetry and liquid chromatography. Parameters (partition, co-operativity) are calculated. At pI, binding reaches maximum. In Gouy-Chapman formalism, the activity coefficient rises with square charge; deviations from this model indicate asymmetric location of anionic phospholipid in the inner leaflet, in mixed vesicles for lysozyme- and myoglobin-PC/PG systems in agreement with experiments and molecular dynamics. Vesicles bind myoglobin anti-co-operatively while they attach lysozyme/albumin, co-operatively. A model is proposed for lysozyme/albumin composing two protein sub-layers with different structures and properties. The Hill coefficient reflects the subunit co-operativity of bi and tridomain proteins.

The edge-Wiener index We (G) of a simple connected graph G is defined as the sum of distances between all pairs of edges of G. The main goal of this survey is to collect all the hitherto obtained results on the edge-Wiener index.

The Timisoara-eccentricity (TM-EC) index of a molecular graph is defined as the sum of δiεiζi over all atoms i in Γ, where ζi, εi and ζi are the degree, eccentricity and the number of atoms at distance εi from atom i. The topological efficiency index of ζ is defined as ρ = 2W / Nw , where W denotes the Wiener index, w is the minimal vertex contribution and N is the number of carbon atoms. This paper is devoted to the study of nanocones and fullerenes by these new graph invariants. It is proved that the TM-EC index of a fullerene ζ can be bounded by a polynomial of degree 2, for twelve infinite series of fullerenes. It is also shown that in one pentagonal carbon nanocone with exactly 5n2 + 10n + 5 carbon atoms, we have ρ ≈ 1.24 and TM - EC = 280n3 + 385n2 + 195n + 40. Finally, we examine the dual of this nanocone and prove that we have ρ ≈ 1.24 and TM - EC = 70n3 + 20n2 - 5n.

This work presents chemical applications of topological methods in various sectors, from small molecule to biological systems, in studying for example enzyme-catalyzed reaction, protein folding kinetics, DNA sequence characterization. Topological descriptors participate to QSAR/QSPR models and, furthermore, are able to individuate the regions which are stabilized (or, vice versa, made reactive) by certain topological interactions. The Wiener indexes, and other distance-based invariants, constrained by the minimum-principle, oppose any unfavorable topological variation in the molecular structure (e.g. chemical transformations). Topological models characterize therefore chemical structures with astonishing details with computational simplicity predicting novel chemical mechanisms to be confirmed by subsequent ab-initio studies. Reported topological methods for simulating complex chemical mechanism and interesting chemical structures preserve the “usual” computational simplicity and still carry a large amount of chemical information stored in topology, an evident alliance between chemistry and mathematics in explaining how the nano-world works.

We consider generalization of the terminal matrix of Zaretsky, in which only distances are listed between terminal vertices of acyclic graphs, to a condensed matrix for cyclic and polycyclic systems. Some 50 years ago Zaretsky has proved that the distance matrix between terminal vertices of acyclic graphs allows full reconstruction of the graph. We consider the question: Is there a subset of vertices in cyclic and polycyclic graphs which would allow from information on their distances a full reconstruction of the graph? As we report in this publication a distance matrix confined to a distance between the set of ring closure vertices may offer a positive answer to the considered problem.

Herein, poly(ethylene glycol) and azobenzene are used as thermo- and photo-sensitive unit, respectively; and azobenzene, heptamethylene, and adamantyl are utilized as photo-responsive recognition group, second recognition group, and stopper for α-cyclodextrin to construct a novel dually thermo- and photo-responsive supramolecular system whose phase transition can be regulated by the photo-controlled selective molecular recognition of α-cyclodextrin.