Explicit series solution for a glucose-induced electrical activity model of pancreatic beta-cells

In this work, we present the explicit series solution of a specific mathematical model from the literature, the Deng bursting model, that mimics the glucose-induced electrical activity of pancreatic beta-cells (Deng, 1993). To serve to this purpose, we use a technique developed to find analytic approximate solutions for strongly nonlinear problems. This analytical algorithm involves an auxiliary parameter which provides us with an efficient way to ensure the rapid and accurate convergence to the exact solution of the bursting model. By using the homotopy solution, we investigate the dynamical effect of a biologically meaningful bifurcation parameter rho, which increases with the glucose concentration. Our analytical results are found to be in excellent agreement with the numerical ones. This work provides an illustration of how our understanding of biophysically motivated models can be directly enhanced by the application of a newly analytic method.

Complexes of copper(II) with 3-(ortho-substituted phenylhydrazo)pentane-2,4-diones: syntheses,properties and catalytic activity for cyclohexane oxidation

Reactions of copper(II) with 3-phenylhydrazopentane-2,4-diones X-2-C6H4-NHN = C{C(= O)CH3}(2) bearing a substituent in the ortho-position [X = OH (H2L1) 1, AsO3H2 (H3L2) 2, Cl (HL3) 3, SO3H (H2L4) 4, COOCH3 (HL5) 5, COOH (H2L6) 6, NO2 (HL7) 7 or H (HL8) 8] lead to a variety of complexes including the monomeric [CuL4(H2O)(2)]center dot H2O 10, [CuL4(H2O)(2)] 11 and [Cu(HL4)(2)(H2O)(4)] 12, the dimeric [Cu-2(H2O)(2)(mu-HL2)(2)] 9 and the polymeric [Cu(mu-L-6)](n)] 13 ones, often bearing two fused six-membered metallacycles. Complexes 10-12 can interconvert, depending on pH and temperature, whereas the Cu(II) reactions with 4 in the presence of cyanoguanidine or imidazole (im) afford the monomeric compound [Cu(H2O)(4){NCNC(NH2)(2)}(2)](HL4)(2)center dot 6H(2)O 14 and the heteroligand polymer [Cu(mu-L-4)(im)](n) 15, respectively. The compounds were characterized by single crystal X-ray diffraction (complexes), electrochemical and thermogravimetric studies, as well as elemental analysis, IR, H-1 and C-13 NMR spectroscopies (diones) and ESI-MS. The effects of the substituents in 1-8 on the HOMO-LUMO gap and the relative stability of the model compounds [Cu(OH)(L-8)(H2O)]center dot H2O, [Cu(L-1)(H2O)(2)]center dot H2O and [Cu(L-4)(H2O)(2)]center dot H2O are discussed on the basis of DFT calculations that show the stabilization follows the order: two fused 6-membered > two fused 6-membered/5-membered > one 6-membered metallacycles. Complexes 9, 10, 12 and 13 act as catalyst precursors for the peroxidative oxidation (with H2O2) of cyclohexane to cyclohexanol and cyclohexanone, in MeCN/H2O (total yields of ca. 20% with TONs up to 566), under mild conditions.

Halogen-bonded tris (2,4-Bis(trichloromethyl)-1,3,5,triazapentadienato)-M(III) [M = Mn, Fe, Co] complexes and their catalytic activity in the peroxidative oxidation of 1-phenylethanol to acetophenone

One-pot template condensation of CCl3C=N with ammonia on a metal source [MnCl2 center dot 4H(2)O, FeCl3 center dot 6H(2)O or Co(CH3COO)(2)center dot 4H(2)O] in DMSO led to the formation of tris(2,4-bis(trichloromethyl)-1,3,5-triazapentadienato)-M(III) complexes, [M(NH=C(CCl3)NC(CCl3)=-NH}(3)]center dot n(CH3)(2)SO [M = Mn, n = 1 (1); M = Fe, n = 2 (2); M = Co, n = 2 (3)1, which were characterized using elemental analysis, and IR, ESI-MS and single-crystal X-ray analysis. The role of inter- and intramolecular non-covalent halogen and hydrogen bonds in the synthesis of 1-3 is discussed. It is shown that the crystal ionic radii of the metal ions [68.5 (Co) < 69 (Fe) < 72 (Mn), pm] are related to the corresponding Cl center dot center dot center dot Cl distances [3.178 (3) > 3.155 (2) > 3.133 (1) Al. Compounds 1-3 and the related di(triazapentadienato)-Cu(v) complex [Cu(NH=C(CCl3)NC(CCl3)=NH}2]center dot 2(CH3)(2)SO (4) act as catalyst precursors for the additive-free microwave (MW) assisted homogeneous oxidation of 1-phenylethanol with tert-butylhydroperoxide (TBHP), leading to the formation of acetophenone with yields up to 99% and TONs up to 5.0 x 10(3) after 1 h of low power (10 W) MW irradiation.