Surface Fluorescence Studies of Tissue Mitochondrial Redox State in Isolated Perfused Rat Lungs

We designed a fiber-optic-based optoelectronic fluorometer to measure emitted fluorescence from the auto-fluorescent electron carriers NADH and FAD of the mitochondrial electron transport chain (ETC). The ratio of NADH to FAD is called the redox ratio (RR = NADH/FAD) and is an indicator of the oxidoreductive state of tissue. We evaluated the fluorometer by measuring the fluorescence intensities of NADH and FAD at the surface of isolated, perfused rat lungs. Alterations of lung mitochondrial metabolic state were achieved by the addition of rotenone (complex I inhibitor), potassium cyanide (KCN, complex IV inhibitor) and/or pentachlorophenol (PCP, uncoupler) into the perfusate recirculating through the lung. Rotenone- or KCN-containing perfusate increased RR by 21 and 30%, respectively. In contrast, PCP-containing perfusate decreased RR by 27%. These changes are consistent with the established effects of rotenone, KCN, and PCP on the redox status of the ETC. Addition of blood to perfusate quenched NADH and FAD signal, but had no effect on RR. This study demonstrates the capacity of fluorometry to detect a change in mitochondrial redox state in isolated perfused lungs, and suggests the potential of fluorometry for use in in vivo experiments to extract a sensitive measure of lung tissue health in real-time

Long properly colored cycles in edge colored complete graphs

Let $K_{n}^{c}$ denote a complete graph on $n$ vertices whose edges are colored in an arbitrary way. Let $\Delta^{\mathrm{mon}} (K_{n}^{c})$ denote the maximum number of edges of the same color incident with a vertex of $K_{n}^{c}$. A properly colored cycle (path) in $K_{n}^{c}$ is a cycle (path) in which adjacent edges have distinct colors. B. Bollob\'{a}s and P. Erd\"{o}s (1976) proposed the following conjecture: if $\Delta^{\mathrm{mon}} (K_{n}^{c})<\lfloor \frac{n}{2} \rfloor$, then $K_{n}^{c}$ contains a properly colored Hamiltonian cycle. Li, Wang and Zhou proved that if $\Delta^{\mathrm{mon}} (K_{n}^{c})< \lfloor \frac{n}{2} \rfloor$, then $K_{n}^{c}$ contains a properly colored cycle of length at least $\lceil \frac{n+2}{3}\rceil+1$. In this paper, we improve the bound to $\lceil \frac{n}{2}\rceil + 2$.Comment: 8 page

Trivariate polynomial approximation on Lissajous curves

We study Lissajous curves in the 3-cube, that generate algebraic cubature formulas on a special family of rank-1 Chebyshev lattices. These formulas are used to construct trivariate hyperinterpolation polynomials via a single 1-d Fast Chebyshev Transform (by the Chebfun package), and to compute discrete extremal sets of Fekete and Leja type for trivariate polynomial interpolation. Applications could arise in the framework of Lissajous sampling for MPI (Magnetic Particle Imaging)

The action of the plant growth hormone

Although the control of cell elongation in plant tissues by a special growth-promoting substance or substances has been well established for some time, the processes by which this substance is able to bring about growth have remained obscure. Since the general properties of the response to growth substance by plant tissues, in particular of the Arena coleoptiles which have been most extensively studied, have been recently summarized by Thimann and Bonner (1933), only the principal points of interest for the present discussion need be given. These are briefly as follows: (a) The growth-promoting substance of the Avena coleoptile is produced only in the coleoptile tip and passes from there downward (Went, 1928). After removal of the tip new growth substance is formed by the uppermost cells of the stump ("physiological regeneration," Dolk, 1926). (b) The growth of the Avena coleoptile is for some time proportional to the amount of growth substance supplied to it (Thimann and Bonner, 1933). (c) The growth substance which enters the plant and causes growth cannot be recovered; i.e., is used up (Went, 1928). (d) Growth substance is an unsaturated acid of empirical formula C18H32O5 (Kögl, Haagen-Smit and Erxleben, 1933) and readily loses its growth-promoting activity by oxidation. (e) The growth substance is a true hormone, i.e., it acts in minute amounts and bears no direct stoichiometrical relationship to the number of molecules of soluble substance transformed during growth into, for example, cell walls. Thus one molecule of growth substance causes an amount of growth of the Avena coleoptile at 27°C. which requires the changing of 3 X 10^5 molecules of hexose to cellulose in cell walls (Thimann and Bonner, 1933). The changes in the physical properties of coleoptiles under the influence of growth substance have been studied to some extent. Heyn (1931), and independently, Söding (1931, 1932) have shown that the plasticity, and also to a considerable extent the elasticity, of the coleoptile is increased after action of growth substance, and that this increase is independent of whether growth has occurred or not; i.e., this action of growth substance is preliminary to active elongation. Heyn also found an increase in extensibility in coleoptiles which had been plasmolyzed after growth substance action, so that it is the physical properties of the cell wall, and not of the protoplasm, which are changed. The action of growth substance has now been further studied, and a few of the results will be described in the present paper. This study has been made easier by discovery of the fact that short sections of coleoptiles grow at a rapid rate if immersed in a growth substance solution of suitable concentration. This method of using coleoptiles is convenient because, under proper conditions, a large amount of growth takes place in a relatively short time, and the "physiological regeneration" mentioned in (a) occurs slightly or not at all. It has the added advantage that the effect of known concentrations of growth substance upon the growth of younger and older portions of the same coleoptile may be examined independently

The Hilbert series of N=1 SO(N_c) and Sp(N_c) SQCD, Painlev\'e VI and Integrable Systems

We present a novel approach for computing the Hilbert series of 4d N=1 supersymmetric QCD with SO(N_c) and Sp(N_c) gauge groups. It is shown that such Hilbert series can be recast in terms of determinants of Hankel matrices. With the aid of results from random matrix theory, such Hankel determinants can be evaluated both exactly and asymptotically. Several new results on Hilbert series for general numbers of colours and flavours are thus obtained in this paper. We show that the Hilbert series give rise to families of rational solutions, with palindromic numerators, to the Painlev\'e VI equations. Due to the presence of such Painlev\'e equations, there exist integrable Hamiltonian systems that describe the moduli spaces of SO(N_c) and Sp(N_c) SQCD. To each system, we explicitly state the corresponding Hamiltonian and family of elliptic curves. It turns out that such elliptic curves take the same form as the Seiberg-Witten curves for 4d N=2 SU(2) gauge theory with 4 flavours.Comment: 45 pages, 3 table