ZX-Calculus: Cyclotomic Supplementarity and Incompleteness for Clifford+T quantum mechanics

The ZX-Calculus is a powerful graphical language for quantum mechanics and quantum information processing. The completeness of the language -- i.e. the ability to derive any true equation -- is a crucial question. In the quest of a complete ZX-calculus, supplementarity has been recently proved to be necessary for quantum diagram reasoning (MFCS 2016). Roughly speaking, supplementarity consists in merging two subdiagrams when they are parameterized by antipodal angles. We introduce a generalised supplementarity -- called cyclotomic supplementarity -- which consists in merging n subdiagrams at once, when the n angles divide the circle into equal parts. We show that when n is an odd prime number, the cyclotomic supplementarity cannot be derived, leading to a countable family of new axioms for diagrammatic quantum reasoning.We exhibit another new simple axiom that cannot be derived from the existing rules of the ZX-Calculus, implying in particular the incompleteness of the language for the so-called Clifford+T quantum mechanics. We end up with a new axiomatisation of an extended ZX-Calculus, including an axiom schema for the cyclotomic supplementarity.Comment: Mathematical Foundations of Computer Science, Aug 2017, Aalborg, Denmar

Evaluation of the Absorption of Methotrexate on Cells and Its Cytotoxicity Assay by Using an Integrated Microfluidic Device Coupled to a Mass Spectrometer

An integrated microfluidic device was developed for high-throughput drug screening with an online electrospray ionization quadrupole time-of-flight mass spectrometer (ESI-Q-TOF MS). The multiple gradient generator followed by an array of microscale cell culture chambers and on-chip solid-phase extraction (SPE) columns for sample pretreatment prior to mass analysis was integrated in the device which was fabricated in one single step. By using the combination system, the process for characterization of drug absorption and evaluation of cytotoxicity could be simultaneously realized. To validate the feasibility, the absorption of methotrexate and its effects on HepG2 and Caco-2 cells were investigated. With the increasing concentration of drugs, the percentage of apoptotic cells appeared in a dose-dependent fashion. By comparison with the results obtained from ESI-Q-TOF MS analysis and cytotoxicity assay, we found that higher intracellular drug concentration resulted in increased cell cytotoxicity. The technique presented herein provides an easy protocol to screen drugs rapidly with low drug consumption, high throughput, and high sensitivity

Study of Phospholipids in Single Cells Using an Integrated Microfluidic Device Combined with Matrix-Assisted Laser Desorption/Ionization Mass Spectrometry

Single-cell trapping and high-throughput mass spectrometry analysis remain challenging now. Current technologies for single-cell analysis have several limitations, such as throughput, space resolution, and multicomponent analysis. In this study, we demonstrate, for the first time, the combination of microfluidic chip and matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) for high-throughput and automatic single-cell phospholipids analysis. A microwell-array-based microfluidic chip was designed and fabricated for cell array formation on an indium tin oxide (ITO)-coated glass slide. Mass spectrometry imaging measurement with 25 μm pixel size was performed with a MALDI ion source. Eight phospholipids in a single A549 cell were detected, and their structures were further identified by MS/MS spectra. Selected ion images were generated with a bin width of Δ<i>m</i>/<i>z</i> ± 0.005. The selected ion images and optical images of the cell array showed excellent correlation, and mass spectrometry information on phospholipids from 1–3 cells was extracted automatically by selecting pixels with the same fixed interval between microwells on the chip. The measurement and data extraction could be processed in several minutes to achieve a high-throughput analysis. Through the optimization of different microwell sizes and different matrices, this method showed potential for the analysis of other metabolites or metabolic changes at the single-cell level

Supercritical Carbon Dioxide Dyeing for PET and Cotton Fabric with Synthesized Dyes by a Modified Apparatus

Supercritical carbon dioxide (SC-CO₂) dyeing for the polyethylene terephthalate (PET) and cotton fabric was implemented by a modified dynamic-recirculation apparatus that was successfully designed and constructed in our laboratory. This energy-efficient apparatus contains two horizontal dyeing vessels and equips the rotating warp beam. The circulating SC-CO₂ fluid and revolving fabrics facilitate the uniform adsorption and quick uptake of dye molecules to the fabrics. Moreover, three dyes were synthesized and applied for dyeing fabric samples performed in mild conditions of 353.2 K and 18.0 MPa for 60 min in SC-CO₂. Satisfactory and commercially acceptable products with reasonably good color uniformity, color strength and color fastness were obtained in dyeing experiments with this SC-CO₂ apparatus. Color characteristics of the dyed PET and cotton fabrics such as the absorption and reflectance spectra were determined, and their surface morphologies were investigated by scanning electron microscopy

Synthesis and Measurement of Solubilities of Reactive Disperse Dyes for Dyeing Cotton Fabrics in Supercritical Carbon Dioxide

Solubilities of the reactive disperse dyes synthesized with the reactive group of 1,3,5-trichloro-2,4,6-triazine were investigated in supercritical carbon dioxide (SC-CO₂) at pressures of 10.0–25.0 MPa, temperatures of 333.2–393.2 K, and equilibrium contact time of 60 min. Meanwhile, dyeing experiments of cotton fabrics by using these dyes were performed at 373.2 K and 20.0 MPa for 60 min with a dye concentration of 0.5% owf in SC-CO₂. Solubilities of these dyes increased with increasing pressure and decreasing temperature. Additionally, the color strength and the color fastness of dyed cotton fabrics were measured, and reasonably good dyeing effects were obtained. Furthermore, the color characteristics of dyed cotton fabrics were studied in terms of the reflectance spectra, and their surface morphologies were investigated by SEM as well

Chemically Controlled Epigenome Editing through an Inducible dCas9 System

Although histone modifications are associated with gene activities, studies of their causal relationships have been difficult. For this purpose, we developed an inducible system integrating dCas9-based targeting and chemically induced proximity technologies to allow small molecule induced recruitment of P300 acetyltransferase and the acetylation of H3K27 at precise gene loci in cells. Employing the new technique, we elucidated the temporal order of histone acetylation and gene activation, as well as the stability of the installed histone modification

Effects of 8a on the level of MMP and expression of apoptosis-related proteins.

<p>(A) MMP affected by 8a in CCRF-CEM cells (n = 3). *<i>p</i><0.05 compared with vehicle control. (B) Western blot analysis of the effect of 8a on cytochrome C release in CCRF-CEM cells treated with indicated doses of 8a for 24 h. (C) Representative Western blots for the expression of cleaved caspase-3 in CCRF-CEM cells following exposure to different concentrations of 8a for 24 h. β-actin (∼42 kDa) was used as a loading control.</p

ROS and MDA levels in CCRF-CEM cells.

<p>(A) The level of ROS after treatment with compound 8a (0–2 µM) for 24 h. (B) MDA production after 8a (0–2 µM) treatment for 24 h. Data represent the mean±SD, n = 3, *<i>p</i><0.05 compared with vehicle control.</p

Acridone Derivative 8a Induces Oxidative Stress-Mediated Apoptosis in CCRF-CEM Leukemia Cells: Application of Metabolomics in Mechanistic Studies of Antitumor Agents

<div><p>A new acridone derivative, 2-aminoacetamido-10-(3, 5-dimethoxy)-benzyl-9(10H)-acridone hydrochloride (named 8a) synthesized in our lab shows potent antitumor activity, but the mechanism of action remains unclear. Herein, we report the use of an UPLC/Q-TOF MS metabolomic approach to study the effects of three compounds with structures optimized step-by-step, 9(10H)-acridone (A), 10-(3,5-dimethoxy)benzyl-9(10H)-acridone (I), and 8a, on CCRF-CEM leukemia cells and to shed new light on the probable antitumor mechanism of 8a. Acquired data were processed by principal component analysis (PCA) and orthogonal partial least squares discriminant analysis (OPLS-DA) to identify potential biomarkers. Comparing 8a-treated CCRF-CEM leukemia cells with vehicle control (DMSO), 23 distinct metabolites involved in five metabolic pathways were identified. Metabolites from glutathione (GSH) and glycerophospholipid metabolism were investigated in detail, and results showed that GSH level and the reduced/oxidized glutathione (GSH/GSSG) ratio were significantly decreased in 8a-treated cells, while L-cysteinyl-glycine (L-Cys-Gly) and glutamate were greatly increased. In glycerophospholipid metabolism, cell membrane components phosphatidylcholines (PCs) were decreased in 8a-treated cells, while the oxidative products lysophosphatidylcholines (LPCs) were significantly increased. We further found that in 8a-treated cells, the reactive oxygen species (ROS) and lipid peroxidation product malondialdehyde (MDA) were notably increased, accompanied with decrease of mitochondrial transmembrane potential, release of cytochrome C and activation of caspase-3. Taken together our results suggest that the acridone derivative 8a induces oxidative stress-mediated apoptosis in CCRF-CEM leukemia cells. The UPLC/Q-TOF MS based metabolomic approach provides novel insights into the mechanistic studies of antitumor drugs from a point distinct from traditional biological investigations.</p></div

Chemical structure and antiproliferative activity against CCRF-CEM cells of acridone derivative 2-aminoacetamido-10-(3, 5-dimethoxy)-benzyl-9(10H)-acridone hydrochloride (8a).

<p>(A) Chemical structure of 8a. (B) Viability of CCRF-CEM cells after 24 h of exposure to 8a. The viability of the control cells, which were exposed to DMSO only, was set as 100%. n = 6, *<i>p</i><0.05 compared with vehicle control. (C) Flow cytometric analysis of phosphatidylserine externalization (annexin V-binding) and cell membrane integrity (PI staining). CCRF-CEM cells were treated with 8a at 0.5 µM for 24 h.</p