Limit of Fractional Power Sobolev Inequalities

We derive the Moser-Trudinger-Onofri inequalities on the 2-sphere and the 4-sphere as the limiting cases of the fractional power Sobolev inequalities on the same spaces, and justify our approach as the dimensional continuation argument initiated by Thomas P. Branson.Comment: 17 page

Harmonic and quasi-harmonic spheres, part III. Rectifiablity of the parabolic defect measure and generalized varifold flows

We study weakly convergent sequences of suitable weak solutions of heat flows of harmonic maps or approximated harmonic maps. We prove a dimensional stratification for the space-time concentration measure and verify that the concentration measure, viewed as a generalized varifold, moves according to the generalized varifold flow rule which reduces to the Brakke’s flow of varifold provided that the limiting harmonic map flow is suitable. We also establish an energy quantization for the density of the limiting varifold

clues: An R Package for Nonparametric Clustering Based on Local Shrinking

Determining the optimal number of clusters appears to be a persistent and controversial issue in cluster analysis. Most existing R packages targeting clustering require the user to specify the number of clusters in advance. However, if this subjectively chosen number is far from optimal, clustering may produce seriously misleading results. In order to address this vexing problem, we develop the R package clues to automate and evaluate the selection of an optimal number of clusters, which is widely applicable in the field of clustering analysis. Package clues uses two main procedures, shrinking and partitioning, to estimate an optimal number of clusters by maximizing an index function, either the CH index or the Silhouette index, rather than relying on guessing a pre-specified number. Five agreement indices (Rand index, Hubert and ArabieâÂÂs adjusted Rand index, Morey and AgrestiâÂÂs adjusted Rand index, Fowlkes and Mallows index and Jaccard index), which measure the degree of agreement between any two partitions, are also provided in clues. In addition to numerical evidence, clues also supplies a deeper insight into the partitioning process with trajectory plots.

Copper-Free Click Chemistry Modification of Nanovectors For Integrin Targeted Cancer Therapy (Book Chapter)

Strain-promoted azide-alkyne cycloaddition (SPAAC) click chemistry is the chemical reaction between azide and cyclooctyne groups. This reaction can conjugate biological molecules, such as peptides, in a highly selective way under mild conditions without cross-reaction with the most widely existing reactive groups, such as amine, carboxylic acid, and hydroxide. Thus, the SPAAC reaction is very versatile for biomolecules conjugation. In this book chapter, we provide detailed protocols of conjugation of integrin targeting peptides to either amine or carboxylic acid terminated porous silicon nanovectors by SPAAC, which can be used to enhance the cellular uptake for intracellular cancer drug delivery and for in vivo cancer theranostics.Peer reviewe

Protective effect of rhamnopyranosyl vanilloyl isolated from Scrophularia ningpoensis Hemsl (Scrophulariaceae) root against acute liver injury in mice

Purpose: To investigate the protective effect of rhamnopyranosyl vanilloyl (RV) from Scrophularia ningpoensis root against tetrachloromethane (CCl4)-induced acute liver injury (ALI) in mice.Methods: RV was isolated from S. ningpoensis by column chromatography. ALI  model of mice was established by intraperitoneal injection of CCl4. Liver index, liver function indices, as well as serum alanine transaminase (ALT), aspartate  aminotransferase (AST) and total bilirubin (TBIL) were evaluated. Lipid peroxidation (LPO)-related indices, including malonaldehyde (MDA), glutathione (GSH), superoxide dismutase (SOD) and glutathione peroxidase (GSH-Px). Apoptotic proteins (Bcl-2, Bax and caspase-3) in liver tissue were determined by enzyme-linked immunosorbent assay (ELISA) and Western blot.Results: After treatment with RV (10, 20 or 40 mg/kg), liver index (5.65 - 5.21 vs. 6.68 %), ALT (90.18 - 79.68 vs. 112.47 U/L), AST (64.44 - 57.63 vs. 75.41 U/L) and TBIL (2.68 - 1.95 vs. 3.21 U/L) activities, as well as MDA (3.58 - 2.88 vs. 4.13 μmol/g), Bax and caspase-3 levels significantly (p < 0.05 or 0.01) decreased, compared with those in control group. After treatment with RV (10, 20 or 40 mg/kg), GSH (16.58 - 22.14 vs. 12.34 μmol/g), Bcl-2, SOD (86.45 - 107.61 vs. 68.43 U/mg) and GSH-Px (295.64 - 329.47 vs. 268.49 U/mg) levels or activities  significantly (p < 0.05 or 0.01) increased, compared with those in control group.Conclusion: RV has protective effect against CCl4-induced ALI in mice, and the mechanisms involve the inhibition of LPO and apoptosis in liver cells. Thus, RV is a potential drug for the treatment of liver injuryKeywords: Rhamnopyranosyl vanilloyl, Scrophularia ningpoensis, Liver injury,  Protective effect, Lipid peroxidation, Apoptosi

Chemical surface modification of porous silicon nanoparticles for cancer therapy

Anticancer drugs inhibit the cancer growth by killing the rapidly dividing cancer cells. However, anticancer drugs also kill the dividing healthy cells and cause severe damage to healthy tissues. More specific delivery of the cancer drugs to the cancer tissue can increase the drug delivery efficiency and reduce the drug s side effects. Nanocarriers can increase the solubility of poorly-water soluble anticancer drugs and be modified for targeted drug delivery and theranostic applications. For efficient drug delivery, the drug loading capacity has been one of the key issues for the development of nanoparticle (NP)-based drug delivery systems. The biocompatible and biodegradable porous silicon (PSi) nanomaterial presents high drug loading capacity and tunable surface chemistry which renders it an ideal candidate as a drug delivery carrier. Chemical surface modification, which is one of the approaches to improve the nanomaterials properties, can lead to a stable nanosystem for further drug delivery applications. The main aim of this dissertation was to employ chemical approaches and surface modified PSi nanoparticles (NPs) to improve the drug delivery efficiency for potential cancer therapy applications. Incorporating targeting moieties to the surfaces of the nanocarriers, such as targeting peptides, can increase the nanocarrier s accumulation into the cancer tissue after the intravenous administration. In this thesis, surface modification of amine-terminated PSi NPs was achieved with targeting peptides (RGDS and iRGD) via strain-promoted azide-alkyne cycloaddition click reaction. The functionalization of the PSi NPs with the targeting peptides did not comprise the drug loading capacity, but enhanced the cellular uptake and the drug delivery efficacy of the PSi NPs in vitro. In addition to the targeting NP surface modifications, a multifunctional nanosystem was prepared with simultaneous fluorescence- and radio-labeling, and iRGD surface modification of the carboxylic acid-terminated PSi NPs. Both labelings were accessible for the in vivo biodistribution evaluation in mice by single-photon emission computed tomography and X-ray computed tomography, and ex vivo by immunofluorescence staining, respectively. The iRGD modification enhanced the tumor uptake of the PSi NPs after the intravenous administration. In order to reduce the plasma protein adsorption onto the PSi NPs, five bioactive molecules (peptides and hydrophilic anti-fouling polymers) were used to modify the surface of alkyne-terminated PSi NPs using copper-catalized click chemistry. Dextran 40 kDa modified PSi NPs presented enhanced cellular uptake and the least protein adsorption of all the tested NPs. Furthermore, the chemical conjugation of drug molecules was studied. The targeting peptides were successfully conjugated to antisense interleukin-6 via copper-catalyzed [3+2] azide-alkyne cycloaddition for targeted angiogenic anti-inflammation in cancer. Finally, anticancer drug methotrexate (MTX) was chemically conjugated to the cationic PSi NPs and demonstrated to increase the cellular uptake of MTX with up to 96 h sustained drug release. A hydrophobic anti-angiogenic drug, sorafenib, was also loaded to the MTX-conjugated PSi NPs, and the dissolution rate of this drug was considerably increased. In conclusion, in this thesis different chemical approaches were used to biofunctionalize PSi NPs and to prepare drug-conjugates formulations for potential anti-cancer applications.Huokoisten Pii nanopartikkelien pinnan kemiallinen muokkaus syöpäterapiassa Syöpälääkkeet estävät syövän kasvua tappamalla nopeasti jakaantuvia syöpäsoluja. Lääkkeet kuitenkin tappavat myös terveitä nopeasti jakaantuvia soluja ja aiheuttavat vakavia vaurioita terveille kudoksille. Tarkempi syöpälääkkeen kuljetus syöpäkudokseen voi lisätä lääkkeen tehoa ja vähentää lääkkeen sivuvaikutuksia. Nanopartikkelit lääkkeen kuljettajina voivat parantaa huonosti veteen liukenevien syöpälääkkeiden liukoisuutta ja nanopartikkeleita voidaan muokata kohdentamaan lääkkeen kuljetusta syöpäkudokseen tai teranostisia tarkoituksia varten. Lääkeaineen kuljetuksessa nanopartikkelin kyky sitoa lääkeainetta on yksi oleellisista rajoittavista tekijöistä nanopartikkeleihin perustuvissa lääkeaineen kuljetus metodeissa. Huokoiset Pii nanopartikkelit (PSi) soveltuvat hyvin yhteen biologisten järjestelmien kanssa ja ovat biohajoavia. Myös niiden korkea lääkkeen sitomiskyky ja kemiallisesti muokattavat pinta ominaisuudet tekevät niistä ihanteellisia lääkkeen kuljetusta varten. Kemiallisten pinta ominaisuuksien muokkaus on yksi lähestymistapa jolla nanomateriaalien ominaisuuksia voidaan parantaa, kehitettäessä stabiilia lääkkeiden nanokuljetusjärjestelmää. Tämän väitöskirjan päätavoite on kehittää kemiallisesti muokkaamalla PSi nanopartikkeleiden pinta ominaisuuksia kuljettamaan lääkeaineita syöpäkudokseen. Liittämällä kohdentavia molekyylejä nanopartikkelien pintaan kuten ohjaus-peptideitä, voidaan lisätä nanopartikkelien kerääntymistä syöpäkudokseen. Tässä väitöskirjassa huokoisia amino-terminoituja Pii nanopartikkeleita modifioitiin RGD ja iRGD ohjauspeptideillä, tämä tehtiin käyttäen ketju promotoitua kupari katalysoitua azidi-alkyyni sykloadditioreaktiota. Peptideillä funktionalisointi ei haitannut nanopartikkelien lääkkeen sitomiskykyä, mutta lisäsi nanopartikkelien kulkeutumista soluihin ja paransi lääkkeen kuljetus kykyä in vitro olosuhteissa. Karboksyyli-terminoituja PSi nanopartikkeleita muokattiin monikäyttöisiksi lisäämällä niihin iRGD ohjauspeptidi, fluoresoiva- ja radioaktiivinenleima. Radioaktiivisen ja fluoresoivan leiman avulla voitiin määrittää partikkelien biodistribuutio in vivo joko röntgen emissio topografialla tai fotoni emissio topografialla. Radioaktiivisen ja fluoresoivan leiman avulla nanopartikkelit voitiin myös havaita ex-in vivo kudos ja soluleikkeistä. In vivo peptidi iRGD nosti nanopartikkelien kertymistä kasvaimeen. Alkyyni-terminoitujen PSi nanopartikkelien pinta ominaisuuksia muokattiin käyttäen kupari katalysoitua click reaktiota. Käytettiin viittä erilaista bioaktiivista molekyyliä jotta voitaisiin vaikuttaa plasman proteiinien adsorptioon ja partikkelien solun sisään ottoon. Voitiin havaita että Dextran 40 kDa modifioidut PSi nanopartikkelit adsorboivat vähiten proteiineja ja niiden sisään otto soluihin oli myös tehokkainta. Väitöskirjassa tutkittiin myös lääkeaineiden suoraa konjugoimista PSi nanopartikkeleihin ja ohjauspeptideihin. Antisense nukleotidia interleukiini 6 vastaan liitettiin onnistuneesti kupari katalysoidussa azidi-alkyyni sykloadditioreaktiossa useisiin ohjauspeptideihin. Syöpälääke Methotrexate (MTX) konjugoitiin kationisiin PSi nanopartikkeleihin. MTX lääkkeen soluun otto havaittiin tehokkaammaksi kun se on sidottu PSi nanopartikkeleihin ja lääkkeen myös havaittiin vapautuvan 96 tunnin ajan. Anti-angiogeenistä lääkettä Sorafenibia myös sidottiin PSi-MTX nanopartikkeleihin ja sen liukoisuus parani merkittävästi. Väitöskirjassa siis biofunktionalisoitiin PSi nanopartikkeleita ja liitettiin niihin lääkeaineita syöpäterapioita varten onnistuneesti