A polynomial primal-dual affine scaling algorithm for symmetric conic optimization

The primal-dual Dikin-type affine scaling method was originally proposed for linear optimization and then extended to semidefinite optimization. Here, the method is generalized to symmetric conic optimization using the notion of Euclidean Jordan algebras. The method starts with an interior feasible but not necessarily centered primal-dual solution, and it features both centering and reducing the duality gap simultaneously. The method’s iteration complexity bound is analogous to the semidefinite optimization case. Numerical experiments demonstrate that the method is viable and robust when compared to SeDuMi, MOSEK and SDPT3.     

Selective targeting of antibody conjugated multifunctional nanoclusters (nanoroses) to epidermal growth factor receptors in cancer cells

The ability of smaller than 100 nm antibody (Ab) nanoparticle conjugates to target and modulate the biology of specific cell types may enable major advancements in cellular imaging and therapy in cancer. A key challenge is to load a high degree of targeting, imaging, and therapeutic functionality into small, yet stable particles. A versatile method called thin autocatalytic growth on substrate (TAGs) has been developed in our previous study to form ultrathin and asymmetric gold coatings on iron oxide nanocluster cores producing exceptional near-infrared (NIR) absorbance. AlexaFluor 488 labeled Abs were used to correlate the number of Abs conjugated to iron oxide/gold nanoclusters (nanoroses) with the hydrodynamic size. A transition from submonolayer to multilayer aggregates of Abs on the nanorose surface was observed for 54 Abs and an overall particle diameter of ～60-65 nm. The hydrodynamic diameter indicated coverage of a monolayer of 54 Abs, in agreement with the prediction of a geometric model, by assuming a circular footprint of 16.9 nm diameter per Ab molecule. The targeting efficacy of nanoclusters conjugated with monoclonal Abs specific for epidermal growth factor receptor (EGFR) was evaluated in A431 cancer cells using dark field microscopy and atomic absorbance spectrometry (AAS) analysis. Intense NIR scattering was achieved from both high uptake of nanoclusters in cells and high intrinsic NIR absorbance of individual nanoclusters. Dual mode imaging with dark field reflectance microscopy and fluorescence microscopy indicates the Abs remained attached to the Au surfaces upon the uptake by the cancer cells. The ability to load intense multifunctionality, specifically strong NIR absorbance, conjugation of an Ab monolayer in addition to a strong r2 MRI contrast that was previously demonstrated in a total particle size of only 63 nm, is an important step forward in development of theranostic agents for combined molecular specific imaging and therapy.     

Liquid phase ion mobility spectrometry

A novel analytical method, called Liquid Phase Ion Mobility Spectrometry (LiPIMS) was demonstrated, where aqueous phase analytes were ionized and introduced into non-aqueous liquids, transported by an external electric field from the point of generation to a collection electrode. Ions were produced from a unique liquid phase ionization process, called Electrodispersion Ionization. Spectra of analyte ions illustrated the potential of LiPIMS as a new separation technique. Experimental data showed that electrodispersion ionization was effective in generating nanoampere level of ion current in hexane and benzene from aqueous samples. By controlling the ionization voltage in relation to the sample flow rate, it was possible to operate the electrodispersion ionization source in both continuous and pulsed ionization modes. Unique LiPIMS spectra of aqueous samples of tetramethylammonium bromide, tetrabutylammonium bromide and bradykinin were presented and their respected liquid phase ion mobility values were determined.     

Two-photon induced luminescence, singlet oxygen generation, cellular uptake and photocytotoxic properties of amphiphilic Ru(II) polypyridyl-porphyrin conjugates as potential bifunctional photodynamic therapeutic agents

Two Ru(II) polypyridyl-porphyrin and Zn(II) porphyrin conjugates (Ru-L and Ru-Zn-L) have been synthesized and their photophysical properties studied. The two conjugates, which contained a hydrophobic tetraphenylporphyrin L conjugated via an acetylide linker at its β-position with a hydrophilic Ru(II) polypyridyl complex, showed high singlet oxygen quantum yields (>70%) and substantial two-photon absorption cross-sections (~500 GM). Ru-L gave strong emissions at ~660 and ~733 nm through linear or two-photon excitation. Solvatochromism was observed in the fluorescence spectra of Ru-L and Ru-Zn-L, where in less polar solvents (i.e., toluene and dichloromethane) their fluorescence emissions became slightly blue-shifted with a 3-fold reduction in intensity relative to those observed in polar solvents (i.e., acetonitrile and methanol). Cell-based studies of these complex conjugates were conducted using human nasopharyngeal carcinoma HK-1 and cervical carcinoma HeLa cells on which Ru-L showed rapid cellular uptake, low dark-cytotoxicity, and high photo-cytotoxicity. Furthermore, Ru-L can be excited and emits in the "biological window"in vitro, making it a potential potent new generation photodynamic therapeutic agent capable of singlet oxygen generation and in vitro near-infrared emission.     

Tandem thiol switch synthesis of peptide thioesters via N-S acyl shift on thiazolidine

An efficient "thiol switch" approach for the synthesis of peptide thioesters via an acid-catalyzed N-S acyl shift and a thioester exchange reaction in tandem with concurrent removal of protecting groups is described. This method employs novel 2-(thiomethyl)thiazolidine (TMT)-anchored resins and is fully compatible with Fmoc chemistry.     

Acid-catalyzed tandem thiol switch for preparing peptide thioesters from mercaptoethyl esters

An efficient method compatible with Fmoc synthesis for preparing peptide thioesters via an acid-catalyzed tandem "thiol switch" of esters is described first by an intramolecular O-S acyl shift and then by an intermolecular S-S exchange, with concurrent deblocking of side chain protection groups.     

Interactions of halichondrin B and eribulin with tubulin

Compounds that modulate microtubule dynamics include highly effective anticancer drugs, leading to continuing efforts to identify new agents and improve the activity of established ones. Here, we demonstrate that [(3)H]-labeled halichondrin B (HB), a complex, sponge-derived natural product, is bound to and dissociated from tubulin rapidly at one binding site per αβ-heterodimer, with an apparent K(d) of 0.31 μM. We found no HB-induced aggregation of tubulin by high-performance liquid chromatography, even following column equilibration with HB. Binding of [(3)H]HB was competitively inhibited by a newly approved clinical agent, the truncated HB analogue eribulin (apparent K(i), 0.80 μM) and noncompetitively by dolastatin 10 and vincristine (apparent K(i)'s, 0.35 and 5.4 μM, respectively). Our earlier studies demonstrated that HB inhibits nucleotide exchange on β-tubulin, and this, together with the results presented here, indicated the HB site is located on β-tubulin. Using molecular dynamics simulations, we determined complementary conformations of HB and β-tubulin that delineated in atomic detail binding interactions of HB with only β-tubulin, with no involvement of the α-subunit in the binding interaction. Moreover, the HB model served as a template for an eribulin binding model that furthered our understanding of the properties of eribulin as a drug. Overall, these results established a mechanistic basis for the antimitotic activity of the halichondrin class of compounds.     

Faster least squares approximation

Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets n be the number of constraints and d be the number of variables, with n >> d{n \gg d}. Then, existing exact methods find a solution vector in O(nd ²) time. We present two randomized algorithms that provide accurate relative-error approximations to the optimal value and the solution vector of a least squares approximation problem more rapidly than existing exact algorithms. Both of our algorithms preprocess the data with the Randomized Hadamard transform. One then uniformly randomly samples constraints and solves the smaller problem on those constraints, and the other performs a sparse random projection and solves the smaller problem on those projected coordinates. In both cases, solving the smaller problem provides relative-error approximations, and, if n is sufficiently larger than d, the approximate solution can be computed in O(nd ln d) time.     

On q-analogues and stability theorems

In this survey recent results about q-analogues of some classical theorems in extremal set theory are collected. They are related to determining the chromatic number of the q-analogues of Kneser graphs. For the proof one needs results on the number of 0-secant subspaces of point sets, so in the second part of the paper recent results on the structure of point sets having few 0-secant subspaces are discussed. Our attention is focussed on the planar case, where various stability results are given.