The Dominant Eigenvalue of an Essentially Nonnegative Tensor

It is well known that the dominant eigenvalue of a real essentially nonnegative matrix is a convex function of its diagonal entries. This convexity is of practical importance in population biology, graph theory, demography, analytic hierarchy process and so on. In this paper, the concept of essentially nonnegativity is extended from matrices to higher order tensors, and the convexity and log convexity of dominant eigenvalues for such a class of tensors are established. Particularly, for any nonnegative tensor, the spectral radius turns out to be the dominant eigenvalue and hence possesses these convexities. Finally, an algorithm is given to calculate the dominant eigenvalue, and numerical results are reported to show the effectiveness of the proposed algorithm

DNA and Peptide Functionalized Gold Nanoparticles for Biological Imaging and Transfection

This dissertation focuses on the development of DNA and peptide functionalized gold nanoparticles. Three nanoparticle systems have been developed:: 1) nucleic acid-directed self-assembly of a gold nanoparticle PET imaging agent;: 2) cationic peptide functionalized gold nanoparticles;: 3) gold nanoparticle templated peptide nanoshells. The first functionalized gold nanoparticles were constructed by assembling ODN: oligodeoxynucleotide)-derivatized gold nanoparticles with functionalized complementary PNAs: peptide nucleic acids). The PNAs were conjugated with DOTA for chelating chelating 64Cu for PET imaging, PEG for conferring stealth properties, and Cy5 for fluorescent imaging. The resulting functionalized nanoparticles showed good stability both in vitro and in vivo and had biodistribution properties expected for a PEGylated gold nanoparticle rather than that for the functionalized PNAs used in the construction. The second nanoparticle system was arginine-rich peptide and lysine-rich peptide functionalized cationic gold nanoparticles as transfection agents. A series of cysteine containing oligoarginine was synthesized by automated solid phase Fmoc synthesis. chloroauric acid was reduced in the presence of the peptides. The resulting gold nanoparticles were around 13 nm in diameter with zeta potential around 29 mV. Compare to other reported cationic gold nanoparticles, the arginine-rich gold nanoparticles were highly stable in up to 0.6 M NaCl solutions and up to pH 8.5 in non-phosphate containing buffers. In phosphate buffers, however, the nanoparticles started to aggregate at above pH 6, though aggregation was reversible by lowering the pH. The strong affinity between arginine and phosphate groups also resulted in the nanoparticle\u27s strong ODN binding ability. Despite of the reported cytotoxicity of oligoarginines, the arginine-rich gold nanoparticles showed no cytotoxicity even at a very high concentration. An improved assembly approach was also investigated. Cationic peptides were exchanged with cetyltrimethylammonium bromide: CTAB) on gold nanoparticles fabricated by seeded growth method. This approach allowed quick assembly of a library of different peptide on the gold surface. The approach was validated by synthesizing three cationic gold nanoparticles, R13C-AuNP, K10Y2C-AuNP and R13C/K10Y2C-AuNP. All of the nanoparticles retained the monodispersity of the original CTAB·AuNP colloid. Their stability and ODN binding ability showed distinct difference due to their different surface composition. All of the colloids were proved to be non-toxic at high concentration but further optimization is needed in the transfection efficiency. The third nanoparticle system was developed based on the ligand exchange approach. A cysteine containing lysine-rich peptide was deposited on CTAB·AuNP. Then the lysines were crosslinked by a biodegradable crosslinker, Sulfo-EGS: Ethylene glycol bis[sulfosuccinimidylsuccinate]), at various peptide/crosslinker ratio. The gold core was then removed by potassium cyanide. The resulting peptide nanoshells were about 40 nm in diameter, compare to the 15 nm diameter before the gold core was removed. Crosslinking also resulted in dramatic decrease of the ODN binding ability of the nanoparticle and the nanoshells. This approach showed great potential of making a combinatorial library of biodegradable nanostructures quickly for a broad range of applications

The Dual Role of Hypoxia-Inducible Factor-1 in Ischemic Stroke: Neuroprotection and Blood-Brain Barrier Disruption

Stroke is a major cause of death and the leading cause of long-term disability in industrialized countries. Ischemic stroke-induced brain injury results from the interaction of complex pathophysiological processes, including energy failure, calcium overload, excitotoxicity, oxidative stress, disruption of blood-brain barrier (BBB) and inflammation. Despite the wealth of knowledge regarding the cellular and molecular mechanisms underlying neuronal death after stroke, research for several decades has failed to develop an effective and safe neuroprotective treatment. One complicating factor in the development of neuroprotective strategies is the dual nature of many of the processes that occur in the brain during stroke. Hypoxia-inducible factor 1 (HIF-1) is a master regulator of cellular and tissue adaption to hypoxia. It plays both protective and detrimental roles in ischemic stroke by inducing a wide array of target genes involved in angiogenesis, erythropoiesis, cell survival/death, and energy metabolism. The dual face of HIF-1 in the pathophysiology of cerebral ischemia is postulated to partially depend on thedifferent functions of its target proteins in specific type of brain cells. In the current studies, we hypothesize that neuronal HIF-1 accumulation is protective whereas endothelial HIF-1 induction is implicated in BBB disruption. We first evaluated HIF-1's role in the antioxidant N-acetylcysteine (NAC)-mediated neuroprotection in a transient cerebral ischemia animal model. The study demonstrated that pre-treatment of NAC increased the neuronal expression of HIF-1α, the regulatable subunit of HIF-1, and its target proteins erythropoietin (EPO) and glucose transporter (GLUT)-3 in the ischemic brain of rodents subjected to 90 min middle cerebral artery occlusion (MCAO) and 24 h reperfusion. Suppressing HIF-1 activity by pharmacological inhibitorsor by specific knock-out neuronal HIF-1α abolished NAC's neuroprotective effects. Furthermore, we observed that NAC increased HIF-1α stability through enhancingits interaction with heat-shock protein 90 (Hsp90) in ischemic brains. Increased BBB permeability and associated cerebral edema formation are potentially lethal complications of ischemic stroke. Accumulating evidence has shown that admission hyperglycemia in conjunction with ischemia/reperfusion causes exacerbated cerebrovascular endothelial cell dysfunction and increased BBB permeability, which leads to augmented brain edema and hemorrhagic transformation in ischemic stroke.The hypothesis of the second part of this dissertation is that endothelial HIF-1 is implicated in hyperglycemia-exacerbated BBB disruption after ischemia. Both in vitro and in vivo studies were undertaken to investigate the effect of hyperglycemia on (1) HIF-1α and its target genes expression; (2) ischemia-induced BBB permeability change; and (3) the effect of HIF-1α inhibition on BBB permeability after ischemia. The in vitrostudy showed that high glucose enhanced HIF-1αand its downstream factors expression in the endothelial cell culture after oxygen glucose deprivation (OGD)/reoxygenation. This was correlated withan increased paracellular permeability as well as diminished expression and disrupted continuity of tight junction (TJ) proteins. Suppressing HIF-1 activity by HIF-1α inhibitors ameliorated the alterations in paracellular permeability and expression and distribution pattern of TJ proteins induced by high glucose exposure. In in vivo studies, diabetic mice subjected to 90 min MCAOfollowed by reperfusiondemonstrated higher expression of HIF-1α and its target gene vascular endothelial growth factor (VEGF) in the ischemic brain microvessels than non-diabetic control mice. Diabetic mice also showed exacerbated BBB damage and TJ disruption, increased infarct volume, and worsened neurological deficits. SuppressingHIF-1 activity by specific knock-out endothelial HIF-1α ameliorated BBB leakage and brain infarction in diabetic animals. Taken together, these present studies provide new information concerning HIF-1's function in experimental models of acute ischemic stroke. Neuronal HIF-1α is an important mediator of antioxidant NAC's neuroprotective effect in ischemic stroke, whereas endothelial HIF-1α is involved in hyperglycemia-induced BBB breakdown after cerebral ischemia. The results suggest that developing therapeutic strategies by targeting HIF-1 needs to consider its multifunctional roles and differential effects on different cell types