Stationary patterns of coherence and incoherence in two-dimensional arrays of non-locally-coupled phase oscillators.

Recently, it has been shown that large arrays of identical oscillators with nonlocal coupling can have a remarkable type of solutions that display a stationary macroscopic pattern of coexisting regions with coherent and incoherent motions, often called chimera states. Here, we present a detailed numerical study of the appearance of such solutions in two-dimensional arrays of coupled phase oscillators. We discover a variety of stationary patterns, including circular spots, stripe patterns, and patterns of multiple spirals. Here, stationarity means that, for increasing system size, the locally averaged phase distributions tend to the stationary profile given by the corresponding thermodynamic limit equation.

To what extent can methyl derivatives be regarded as stabilized tautomers of xanthine?

Taking xanthine (Xan) as an example, validity of an approach to experimental investigations of nucleotide bases' tautomeric equilibrium, based on the use of methyl derivatives corresponding to their prototropic tautomers, was studied by (1)H NMR in dimethylsulfoxide (DMSO) and by quantum chemical calculations at the B3LYP/6-311++G(d,p) level of theory. From (1)H NMR spectra of m(7)Xan, m(9)Xan, Xan and m(3)Xan conclusion was made that the N7H tautomeric forms of the last two compounds dominate in solution, which was supported by quantum chemical data. Calculated relative energies of the N9H tautomers of Xan and m(3)Xan (8.74 and 9.57 kcal/mol, accordingly) are rather close to the m(9)Xan one (9.11 kcal/mol). Nonspecific influence of DMSO modelled by the COSMO algorithm therewith reduces these values by approximately 2-3 kcal/mol. The data obtained imply that methyl derivatives are rather good models of high-energy tautomers of nucleotide bases, if their relative energies are not less than a few kcal/mol.

[Effect of carboxylate and Na ions on the tautomeric status of 9-methylguanine]. / Vplyv karboksylat-iona ta iona Na na tautomernyi status 9-metylhuaninu.

Interactions of 9-methylguanine (m9Gua) with carboxylate ion of acetic acid (CH3COO-) and Na+ were studied by 1H NMR spectroscopy and ab initio quantum chemical calculations of the B3LYP/6-31++G(d,p) and B3LYP/6-311++G(d,p) levels of theory. Changes in the m9Gua 1H NMR spectrum in the presence of the equimolar amount of sodium acetate (NaAc), which in anhydrous DMSO dissociates to CH3COO- and Na+, were interpreted as a consequence of a complex formation of m9Gua in the amino-keto-N1H tautomeric form (m9GuaN1H) with carboxylate ions via two H-bonds involving amino and N1H-imino protons. Quantum chemical calculations of interactions of the m9GuaN1H ground-state tautomer and the m9GuaN3H high energy one with relative energy 20.01 kcal/mol show that the ground state tautomer forms the ground-state complex CH3COO-:mgGuaN1H, by 5.57 kcal/mol more stable than the CH3COO-:m9GuaN3H complex, and coordination of Na+ with the O6 and N7 atoms reduces this energy difference to 2.57 kcal/mol. Such a coordination of Na+ with tautomer m9GuaN3H therewith decreases its relative energy only to 13.31 kcal/mol. Non-additivity of the two ligands contributions to the 8-times reduction of the relative energy of the high energy tautomer in the CH3COO-:m9GuaN3H:Na+(O6,N7) triple complex was concluded, the role of CH3COO- being dominant. Besides, coordination with Na+ resulted in an iminoproton transfer from the base to CH3COO- in the triple complexes of both tautomers, according to calculations in vacuum. Biological significance of the results is noticed.