Critical frontier of the Potts and percolation models in triangular-type and kagome-type lattices I: Closed-form expressions

We consider the Potts model and the related bond, site, and mixed site-bond percolation problems on triangular-type and kagome-type lattices, and derive closed-form expressions for the critical frontier. For triangular-type lattices the critical frontier is known, usually derived from a duality consideration in conjunction with the assumption of a unique transition. Our analysis, however, is rigorous and based on an established result without the need of a uniqueness assumption, thus firmly establishing all derived results. For kagome-type lattices the exact critical frontier is not known. We derive a closed-form expression for the Potts critical frontier by making use of a homogeneity assumption. The closed-form expression is new, and we apply it to a host of problems including site, bond, and mixed site-bond percolation on various lattices. It yields exact thresholds for site percolation on kagome, martini, and other lattices, and is highly accurate numerically in other applications when compared to numerical determination.Comment: 22 pages, 13 figure

Vertex Models and Random Labyrinths: Phase Diagrams for Ice-type Vertex Models

We propose a simple geometric recipe for constructing phase diagrams for a general class of vertex models obeying the ice rule. The disordered phase maps onto the intersecting loop model which is interesting in its own right and is related to several other statistical mechanical models. This mapping is also useful in understanding some ordered phases of these vertex models as they correspond to the polymer loop models with cross-links in their vulcanised phase.Comment: 8 pages, 6 figure

BCL-2 family protein expression and platinum drug resistance in ovarian carcinoma

The expression of the BCL-2 family proteins, BCL-2, BAX, BCLXLand BAK have been determined in a panel of 12 human ovarian carcinoma cell lines encompassing a wide range in sensitivity to cisplatin. Whereas BAX, BCLXLand BAK levels did not correlate with sensitivity, there was a statistically significant inverse correlation (r = –0.81;P = 0.002) between growth inhibition by cisplatin and BCL-2 levels. In sublines possessing acquired resistance to various platinum-based drugs or across a panel of human ovarian carcinoma xenografts, there was no consistent pattern of BCL-2 expression. Two relatively sensitive lines (A2780 and CH1) have been stably transfected with bcl-2 and bclXLrespectively and two relatively resistant lines (A2780cisR and SKOV-3) stably transfected with bax. Overexpression of BCL-2 in A2780 cells led to resistance to cisplatin compared to the vector control when assayed at 48 h post-drug incubation but a significant increase in sensitivity at 96 h. Relative rates of apoptosis at 48- and 96-h post-cisplatin exposure mirrored the growth inhibition. There was no significant difference in sensitivity of the pair of lines by clonogenic assay. No significant changes in chemosensitivity to a variety of DNA-damaging or tubulin-interactive agents were observed in the remaining transfected lines. Taken together, these results suggest that, in human ovarian carcinoma cells, high BCL-2 levels (either naturally occurring or through gene transfection) confers a trend towards sensitivity not resistance to platinum drugs. © 2000 Cancer Research Campaig

On the generalized continuity equation

A generalized continuity equation extending the ordinary continuity equation has been found using quanternions. It is shown to be compatible with Dirac, Schrodinger, Klein-Gordon and diffusion equations. This generalized equation is Lorentz invariant. The transport properties of electrons are found to be governed by Schrodinger-like equation and not by the diffusion equation.Comment: 9 Latex pages, no figure

Cucurbit[n]uril binding of platinum anticancer complexes

The encapsulation of cisplatin by cucurbit[7]uril (Q[7]) and multinuclear platinum complexes linked via a 4,4′-dipyrazolylmethane (dpzm) ligand by Q[7] and cucurbit[8]uril (Q[8]) has been studied by NMR spectroscopy and molecular modelling. The NMR studies suggest that some cisplatin binds in the cucurbituril cavity, while cis-[PtCl(NH3)2(H2O)]+ only binds at the portals. Alternatively, the dpzm-linked multinuclear platinum complexes are quantitatively encapsulated within the cavities of both Q[7] and Q[8]. Upon encapsulation, the non-exchangeable proton resonances of the multinuclear platinum complexes show significant upfield shifts in 1H NMR spectra. The H3/H3* resonances shift upfield by 0.08 to 0.55 ppm, the H5/H5* shift by 0.9 to 1.6 ppm, while the methylene resonances shift by 0.74 to 0.88 ppm. The size of the resonance shift is dependent on the cavity size of the encapsulating cucurbituril, with Q[7] encapsulation producing larger shifts than Q[8]. The upfield shifts of the dpzm resonances observed upon cucurbituril encapsulation indicate that the Q[7] or Q[8] is positioned directly over the dpzm linking ligand. The terminal platinum groups of trans-[{PtCl(NH3)2}2μ-dpzm]2+ (di-Pt) and trans-[trans-{PtCl(NH3)2}2-trans-{Pt(dpzm)2(NH3)2}]4+ (tri-Pt) provide a barrier to the on and off movement of cucurbituril, resulting in binding kinetics that are slow on the NMR timescale for the metal complex. Although the dpzm ligand has relatively few rotamers, encapsulation by the larger Q[8] resulted in a more compact di-Pt conformation with each platinum centre retracted further into each Q[8] portal. Encapsulation of the hydrolysed forms of di-Pt and tri-Pt is considerably slower than for the corresponding Cl forms, presumably due to the high-energy cost of passing the +2 platinum centres through the cucurbituril portals. The results of this study suggest that cucurbiturils could be suitable hosts for the pharmacological delivery of multinuclear platinum complexe

DNA cleavage and antitumour activity of platinum(II) and copper(II) compounds derived from 4-methyl-2-N-(2-pyridylmethyl)aminophenol: spectroscopic, electrochemical and biological investigation

The reaction of the redox-active ligand, Hpyramol (4-methyl-2-N-(2-pyridylmethyl)aminophenol) with K2PtCl4 yields monofunctional square-planar [Pt(pyrimol)Cl], PtL-Cl, which was structurally characterised by single-crystal X-ray diffraction and NMR spectroscopy. This compound unexpectedly cleaves supercoiled double-stranded DNA stoichiometrically and oxidatively, in a non-specific manner without any external reductant added, under physiological conditions. Spectro-electrochemical investigations of PtL-Cl were carried out in comparison with the analogue CuL-Cl as a reference compound. The results support a phenolate oxidation, generating a phenoxyl radical responsible for the ligand-based DNA cleavage property of the title compounds. Time-dependent in vitro cytotoxicity assays were performed with both PtL-Cl and CuL-Cl in various cancer cell lines. The compound CuL-Cl overcomes cisplatin-resistance in ovarian carcinoma and mouse leukaemia cell lines, with additional activity in some other cells. The platinum analogue, PtL-Cl also inhibits cell-proliferation selectively. Additionally, cellular-uptake studies performed for both compounds in ovarian carcinoma cell lines showed that significant amounts of Pt and Cu were accumulated in the A2780 and A2780R cancer cells. The conformational and structural changes induced by PtL-Cl and CuL-Cl on calf thymus DNA and phi X174 supercoiled phage DNA at ambient conditions were followed by electrophoretic mobility assay and circular dichroism spectroscopy. The compounds induce extensive DNA degradation and unwinding, along with formation of a monoadduct at the DNA minor groove. Thus, hybrid effects of metal-centre variation, multiple DNA-binding modes and ligand-based redox activity towards cancer cell-growth inhibition have been demonstrated. Finally, reactions of PtL-Cl with DNA model bases (9-Ethylguanine and 5'-GMP) followed by NMR and MS showed slow binding at Guanine-N7 and for the double stranded self complimentary oligonucleotide d(GTCGAC)(2) in the minor groove

Theory of d-density wave viewed from a vertex model and its implications

The thermal disordering of the $d$-density wave, proposed to be the origin of the pseudogap state of high temperature superconductors, is suggested to be the same as that of the statistical mechanical model known as the 6-vertex model. The low temperature phase consists of a staggered order parameter of circulating currents, while the disordered high temperature phase is a power-law phase with no order. A special feature of this transition is the complete lack of an observable specific heat anomaly at the transition. There is also a transition at a even higher temperature at which the magnitude of the order parameter collapses. These results are due to classical thermal fluctuations and are entirely unrelated to a quantum critical point in the ground state. The quantum mechanical ground state can be explored by incorporating processes that causes transitions between the vertices, allowing us to discuss quantum phase transition in the ground state as well as the effect of quantum criticality at a finite temperature as distinct from the power-law fluctuations in the classical regime. A generalization of the model on a triangular lattice that leads to a 20-vertex model may shed light on the Wigner glass picture of the metal-insulator transition in two-dimensional electron gas. The power-law ordered high temperature phase may be generic to a class of constrained systems and its relation to recent advances in the quantum dimer models is noted.Comment: RevTex4, 10 pages, 11 figure

Variational method and duality in the 2D square Potts model

The ferromagnetic q-state Potts model on a square lattice is analyzed, for q>4, through an elaborate version of the operatorial variational method. In the variational approach proposed in the paper, the duality relations are exactly satisfied, involving at a more fundamental level, a duality relationship between variational parameters. Besides some exact predictions, the approach is very effective in the numerical estimates over the whole range of temperature and can be systematically improved.Comment: 20 pages, 5 EPS figure

Gene-specific repair of Pt/DNA lesions and induction of apoptosis by the oral platinum drug JM216 in three human ovarian carcinoma cell lines sensitive and resistant to cisplatin

JM216, an oral platinum drug entering into phase III clinical trial, exhibited comparable cytotoxicity to cisplatin in three human ovarian carcinoma cell lines: the sensitive (CH1), acquired resistant (CH1cisR) and intrinsically resistant (SKOV-3). Platinum accumulation and binding to DNA were similar in each of the three cell lines at equimolar doses, indicating that the resistant cell lines could tolerate higher intracellular platinum levels and platinum bound to DNA at IC50 concentrations of drug. Comparison with cisplatin demonstrated that intracellular platinum levels were marginally higher with JM216, but that platinum binding to DNA was similar for the two drugs in each of the cell lines. Each of the cell lines exhibited an ability to repair JM216 induced platinum/DNA lesions in the N-ras gene (gene-specific repair) at equitoxic concentrations of drug. However, this occurred to a greater extent in the two resistant cell lines such that by 24 h the CH1cisR and SKOV-3 had removed 72% and 67% respectively compared with approximately 32% for the CH1. Reduced gene-specific repair capacity in CH1 cells was also seen following incubation with 25 μM (or 5 μM – 2 × IC50) cisplatin, whereas the CH1cisR and SKOV-3 cell lines were repair proficient. JM216 induced apoptosis in the three cell lines following a 2h incubation with 2 × the IC50 of drug. Fluorescent microscopy of cells stained with propidium iodide showed that the detached cell population displayed typical apoptotic nuclei. Furthermore, field inversion gel electrophoresis demonstrated the presence of DNA fragments approximately 23–50 kb in size, indicative of apoptosis, in the detached cells. JM216 induced an S phase slow down in each of the three cell lines accompanied by a G2 block in the CH1 pair. Incubation with this concentration of JM216 also resulted in the induction of p53 in the CH1 and CH1cisR. These studies suggest that the relative sensitivity of the CH1 cell line to cisplatin and JM216 is at least partly attributable to a deficiency in gene-specific repair. The oral platinum drug, JM216, exerts its cytotoxic effects through the induction of apoptosis following a slow-down in S phase in both the sensitive and resistant lines. © 1999 Cancer Research Campaig