Subgradient of distance functions with applications to Lipschitzian stability

The paper is devoted to studying generalized differential properties of distance functions that play a remarkable role in variational analysis, optimization, and their applications. The main object under consideration is the distance function of two variables in Banach spaces that signifies the distance from a point to a moving set. We derive various relationships between Fréchet-type subgradients and limiting (basic and singular) subgradients of this distance function and corresponding generalized normals to sets and coderivatives of set-valued mappings. These relationships are essentially different depending on whether or not the reference point belongs to the graph of the involved set-valued mapping. Our major results are new even for subdifferentiation of the standard distance function signifying the distance between a point and a fixed set in finite-dimensional spaces. The subdifferential results obtained are applied to deriving efficient dual-space conditions for the local Lipschitz continuity of distance functions generated by set-valued mappings, in particular, by those arising in parametric constrained optimization. Dedicated to Terry Rockafellar in honor of his 70th birthday. This research was partially supported by the National Science Foundation under grant DMS-0304989 and by the Australian Research Council under grant DP-0451158.     

Differentiation of AB‐FUBINACA positional isomers by the abundance of product ions using electron ionization–triple quadrupole mass spectrometry

Mass spectrometric differentiation of structural isomers is important for the analysis of forensic samples. Presently, there is no mass spectrometric method for differentiating halogen positional isomers of cannabimimetic compounds. We describe here a novel and practical method for differentiating one of these compounds, N‐(1‐amino‐3‐methyl‐1‐oxobutan‐2‐yl)‐1‐(4‐fluorobenzyl)‐1H‐indazole‐3‐carboxamide (AB‐FUBINACA (para)), and its fluoro positional (ortho and meta) isomers in the phenyl ring by electron ionization–triple quadrupole mass spectrometry. It was found that the three isomers differed in the relative abundance of the ion at m/z 109 and 253 in the product ion spectra, while the detected product ions were identical. The logarithmic values of the abundance ratio of the ions at m/z 109 to 253 (ln(A₁₀₉/A₂₅₃)) were in the order meta < ortho < para and increased linearly with collision energy. The differences in abundances were attributed to differences in the dissociation reactivity between the indazole moiety and the fluorobenzyl group because of the halogen‐positional effect on the phenyl ring. Our methodology, which is based on the abundance of the product ions in mass spectra, should be applicable to determination of the structures of other newly encountered designer drugs. Copyright © 2016 John Wiley & Sons, Ltd.     

Structural Elucidation of β‐Lactam Diastereoisomers through Ion Mobility Mass Spectrometry Studies and Theoretical Calculations

The ion mobility combined with mass spectrometry and theoretical calculations were used to characterize and separate six diastereoisomeric β‐lactams. The influence of traveling wave height and wave velocity, size of the alkali metal ion (Li⁺, Na⁺ and K⁺) and drift gases with varying masses and polarizabilities (N₂ and CO₂) on separation efficacy was additionally examined. The best separation of diastereoisomers of β‐lactams was observed for adducts with Na⁺ and Li⁺ ions, whereas other parameters had little impact on separation process. The isomeric β‐lactams were characterized by both experimental and theoretical collision cross sections. The theoretically calculated values of collision cross sections obtained from extensive molecular dynamics and density functional theory calculations for model structures agreed well with those established experimentally. The relationship between separation efficacy and the configuration at the carbon atoms C5 and C6 of β‐lactam ring was defined. Copyright © 2016 John Wiley & Sons, Ltd.     

Epigallocatechin-3-Gallate Promotes Osteo-/Odontogenic Differentiation of Stem Cells from the Apical Papilla through Activating the BMP–Smad Signaling Pathway

Stem cells from apical papilla (SCAPs) are desirable sources of dentin regeneration. Epigallocatechin-3-gallate (EGCG), a natural component of green tea, shows potential in promoting the osteogenic differentiation of bone mesenchymal stem cells. However, whether EGCG regulates the odontogenic differentiation of SCAPs and how this occurs remain unknown. SCAPs from immature human third molars (16–20 years, n = 5) were treated with a medium containing different concentrations of EGCG or bone morphogenic protein 2 (BMP2), with or without LDN193189 (an inhibitor of the canonical BMP pathway). Cell proliferation and migration were analyzed using a CCK-8 assay and wound-healing assay, respectively. Osteo-/odontogenic differentiation was evaluated via alkaline phosphatase staining, alizarin red S staining, and the expression of osteo-/odontogenic markers using qPCR and Western blotting. We found that EGCG (1 or 10 μM) promoted the proliferation of SCAPs, increased alkaline phosphatase activity and mineral deposition, and upregulated the expression of osteo-/odontogenic markers including dentin sialophosphoprotein (Dspp), dentin matrix protein-1 (Dmp-1), bone sialoprotein (Bsp), and Type I collagen (Col1), along with the elevated expression of BMP2 and phosphorylation level of Smad1/5/9 (p < 0.01). EGCG at concentrations below 10 μM had no significant influence on cell migration. Moreover, EGCG-induced osteo-/odontogenic differentiation was significantly attenuated via LDN193189 treatment (p < 0.01). Furthermore, EGCG showed the ability to promote mineralization comparable with that of recombinant BMP2. Our study demonstrated that EGCG promotes the osteo-/odontogenic differentiation of SCAPs through the BMP–Smad signaling pathway.     

Poly(1,3‐propylene sebacate) and Poly(sebacoyl diglyceride): A Pair of Potential Polymers for the Proliferation and Differentiation of Retinal Progenitor Cells

Using suitable polymers as a carrier for growing and delivering retinal progenitor cells (RPCs) is a promising therapeutic strategy in retinal cell‐replacement therapy. Herein recently developed polymer, poly(sebacoyl diglyceride) (PSeD), is selected and its nonhydroxylized counterpart poly(1,3‐propylene sebacate) (PPS) is designed to evaluate their potentials for RPC growth and future RPC application. The structures and mechanical properties of the polymers are characterized. The cytocompatibility and effects of these polymers on RPC proliferation, differentiation, and migration are systematically investigated in vitro. Our data show that PPS and PSeD display excellent cytocompatibility with low expression of inflammation and apoptosis factors, which benefit RPC growth. In proliferation assays reveal that RPCs expands well on the polymers, but PPS performs the best for RPC expansion, indicating that PPS can remarkably promote RPC proliferation. In differentiation conditions, RPCs grown on PSeD are more likely to differentiate toward retinal neurons, including photoreceptors, the most interesting type of cells for retinal cell‐replacement therapy. Additionally, our results demonstrate that RPCs grown on PSeD display an outstanding ability to migrate. In conclusion, PPS can markedly promote RPC proliferation, whereas PSeD can enhance RPC differentiation toward retinal neurons, suggesting that PSeD and PPS have potential applications in future retinal cell‐replacement therapies.

     

In Vivo Osteogenic Differentiation of Human Dental Pulp Stem Cells Embedded in an Injectable In Vivo‐Forming Hydrogel

In this study, human dental pulp stem cells (hDPSCs) are examined as a cellular source for bone tissue engineering using an in vivo‐forming hydrogel. The hDPSCs are easily harvested in large quantities from extracted teeth. The stemness of harvested hDPSCs indicates their relative tolerance to ex vivo manipulation in culture. The in vitro osteogenic differentiation of hDPSCs is characterized using Alizarin Red S (ARS), von Kossa (VK), and alkaline phosphatase (ALP) staining. The solution of hDPSCs and a methoxy polyethylene glycol‐polycaprolactone block copolymer (PC) is easily prepared by simple mixing at room temperature and in no more than 10 s it forms in vivo hydrogels after subcutaneous injection into rats. In vivo osteogenic differentiation of hDPSCs in the in vivo‐forming hydrogel is confirmed by micro‐computed tomography (CT), histological staining, and gene expression. Micro‐CT analysis shows evidence of significant tissue‐engineered bone formation in hDPSCs‐loaded hydrogel in the presence of osteogenic factors. Differentiated osteoblasts in in vivo‐forming hydrogel are identified by ARS and VK staining and are found to exhibit characteristic expression of genes like osteonectin, osteopontin, and osteocalcin. In conclusion, hDPSCs embedded in an in vivo‐forming hydrogel may provide benefits as a noninvasive formulation for bone tissue engineering applications.

     

Electroactive 3D Scaffolds Based on Silk Fibroin and Water‐Borne Polyaniline for Skeletal Muscle Tissue Engineering

Silk fibroin (SF) with good biocompatibility and degradability has great potential for tissue engineering. However, the SF based scaffolds lack the electroactivity to regulate the myogenic differentiation for the regeneration of muscle tissue, which is sensitive to electrical signal. Herein, a series of electroactive biodegradable scaffolds based on SF and water‐soluble conductive poly(aniline‐co‐N‐(4‐sulfophenyl) aniline) (PASA) via a green method for skeletal muscle tissue engineering are designed. SF/PASA scaffolds are prepared by vortex of aqueous solution of SF and PASA under physiological condition. Murine‐derived L929 fibroblast and C2C12 myoblast cells are used to evaluate cytotoxicity of SF/PASA scaffolds. Moreover, myogenic differentiation of C2C12 cells is investigated by analyzing the morphology of myotubes and related gene expression. These results suggest that electroactive SF/PASA scaffolds with a suitable microenvironment, which can enhance the myogenic differentiation of C2C12 cells, have a great potential for skeletal muscle regeneration.     

Comparative Study of Osteogenic Activity of Multilayers Made of Synthetic and Biogenic Polyelectrolytes

Polyelectrolyte multilayer (PEM) coatings on biomaterials are applied to tailor adhesion, growth, and function of cells on biomedical implants. Here, biogenic and synthetic polyelectrolytes (PEL) are used for layer‐by‐layer assembly to study the osteogenic activity of PEM with human osteosarcoma MG‐63 cells in a comparative manner. Formation of PEM is achieved with biogenic PEL fibrinogen (FBG) and poly‐l ‐lysine (PLL) as well as biotinylated chondroitin sulfate (BCS) and avidin (AVI), while poly(allylamine hydrochloride) (PAH) and polystyrene sulfonate (PSS) represent a fully synthetic PEM used as a reference system here. Surface plasmon resonance measurements show highest layer mass for FBG/PLL and similar for PSS/PAH and BCS/AVI systems, while water contact angle and zeta potential measurements indicate larger differences for PSS/PAH and FBG/PLL but not for BCS/AVI multilayers. All PEM systems support cell adhesion and growth and promote osteogenic differentiation as well. However, FBG/PLL layers are superior regarding MG‐63 cell adhesion during short‐term culture, while the BCS/AVI system increases alkaline phosphatase activity in long‐term culture. Particularly, a multilayer system based on affinity interaction like BCS/AVI may be useful for controlled presentation of biotinylated growth factors to promote growth and differentiation of cells for biomedical applications.

     

Enhanced Self‐Renewal and Accelerated Differentiation of Human Fetal Neural Stem Cells Using Graphene Oxide Nanoparticles

Graphene oxide (GO) has received increasing attention in bioengineering fields due to its unique biophysical and electrical properties, along with excellent biocompatibility. The application of GO nanoparticles (GO‐NPs) to engineer self‐renewal and differentiation of human fetal neural stem cells (hfNSCs) is reported. GO‐NPs added to hfNSC culture during neurosphere formation substantially promote cell‐to‐cell and cell‐to‐matrix interactions in neurospheres. Accordingly, GO‐NP‐treated hfNSCs show enhanced self‐renewal ability and accelerated differentiation compared to untreated cells, indicating the utility of GO in developing stem cell therapies for neurogenesis.