Measuring methotrexate polyglutamates in red blood cells: a new LC-MS/MS-based method

The folate antagonist methotrexate (MTX) is the anchor drug in the treatment of rheumatoid arthritis. The therapeutic effects of MTX are attributed to the intracellular levels of MTX, present in the cell as polyglutamates (MTXPGn). We developed a new liquid chromatography-electrospray ionization-tandem mass spectrometry (LC-ESI-MS/MS)-based assay to separately quantitate MTXPGn in red blood cells using stable-isotope-labelled internal standards. Samples were analyzed by LC-ESI-MS/MS using a Waters Acquity UPLC BEH C18 column with a 5–100% organic gradient of 10 mM ammonium bicarbonate (pH 10) and methanol. The analysis consisted of simple sample preparation and a 6-min run time. Detection was done using a Waters Acquity UPLC coupled to a Waters Quattro Premier XE with electrospray ionization operating in the positive ionization mode. Assay validation was performed following recent Food and Drug Administration guidelines. The method was linear from 1–1,000 nM for all MTXPGn (R ²?>?0.99). The coefficient of variation ranged from 1–4% for intraday precision and 6–15% for interday precision. Samples were stable for at least 1 month at ?80 °C. Recovery ranged from 98–100%, and the relative matrix-effect varied from 95–99%. The lower limit of quantitation was 1 nM for each MTXPGn. Fifty patient samples from the tREACH study were analyzed. The MTXPGn concentration and distribution of these samples were comparable with values reported in literature. The developed LC-ESI-MS/MS method for the quantitative measurement of MTXPGn in red blood cells is both sensitive and precise within the clinically relevant range. The method can be easily applied in clinical laboratories due to the combination of simple pre-treatment with robust LC-ESI-MS/MS.

The tetrahexahedric Calogero model

We consider the spherical reduction of the rational Calogero model (of type A _n-1, without the center of mass) as a maximally superintegrable quantum system. It describes a particle on the (n = 2)-sphere in a very special potential. A detailed analysis is provided of the simplest non-separable case, n = 4, whose potential blows up at the edges of a spherical tetrahexahedron, tesselating the two-sphere into 24 identical right isosceles spherical triangles in which the particle is trapped. We construct a complete set of independent conserved charges and of Hamiltonian intertwiners and elucidate their algebra. The key structure is the ring of polynomials in Dunkl-deformed angular momenta, in particular the subspaces invariant and antiinvariant under all Weyl reflections, respectively.     

Violation of the Bell inequality in quantum critical random spin-1/2 chains

We investigate the entanglement and nonlocality properties of two random XX spin-1/2 critical chains, in order to better understand the role of breaking translational invariance to achieve nonlocal states in critical systems. We show that breaking translational invariance is a necessary but not sufficient condition for nonlocality, as the random chains remain in a local ground state up to a small degree of randomness. Furthermore, we demonstrate that the random dimer model does not have the same nonlocality properties of the translationally invariant chain, even though they share the same universality class for a certain range of randomness.     

Point Spectrum and SULE for Time-Periodic Perturbations of Discrete 1D Schrödinger Operators with Electric Fields

We use the KAM technique to present a proof of pure point spectrum for the quasi-energy operator and a version of the SULE condition for suitable small time-periodic perturbations of discrete one-dimensional Schrödinger operators with uniform electric fields.     

Magic-Angle Spinning NMR and Molecular Mobility in Heterogeneous Systems

Magic-angle sample spinning (MAS) nuclear magnetic resonance (NMR) measurements are treated for heterogeneous systems with nanometer dimensions. An appreciable line narrowing in the MAS NMR spectra of the embedded molecules may be achieved also in the cases when the molecules still possess an appreciable local mobility. It appears that the MAS frequencies are of comparable order of magnitude as the frequencies which characterize the random molecular motional processes and which compete with MAS. It will be shown that this behavior may occur if inhomogeneous local magnetic fields due to susceptibility effects have a dominating influence on the widths and shapes of the resonance NMR lines. Properties of these local fields are described. Spectra simulations are carried for molecules embedded in these heterogeneous systems when the coherent averaging by MAS is superimposed by random local motions. This situation may occur for molecules contained in nanoporous solids and also for heterogeneous systems like membranes and biological tissues with flexible components like water, lipids, and small peptides. Several examples are treated which reveal advantages and limitations of these experiments and their theoretical interpretation.     

Weakly (and not so weakly) bound states of a relativistic particle in one dimension

We present the first exact calculation of the energy of the bound state of a one dimensional Dirac massive particle in weak short-range arbitrary potentials, using perturbation theory to fourth order (the analogous result for two dimensional systems with confinement along one direction and arbitrary mass is also calculated to second order). We show that the non-perturbative extension obtained using Padé approximants can provide remarkably good approximations even for deep wells, in certain range of physical parameters. As an example, we discuss the case of two gaussian wells, comparing numerical and analytical results, predicted by our formulas.     

Doubly Connected V-States for the Generalized Surface Quasi-Geostrophic Equations

In this paper, we prove the existence of doubly connected V-states for the generalized SQG equations with α ∈]0, 1[. They can be described by countable branches bifurcating from the annulus at some explicit “eigenvalues” related to Bessel functions of the first kind. Contrary to Euler equations Hmidi et al. (Doubly connected V-states for the planar Euler equations, arXiv:1409.7096, 2015), we find V-states rotating with positive and negative angular velocities. At the end of the paper we discuss some numerical experiments concerning the limiting V-states.     

The Angular Momentum Dilemma and Born–Jordan Quantization

The rigorous equivalence of the Schrödinger and Heisenberg pictures requires that one uses Born–Jordan quantization in place of Weyl quantization. We confirm this by showing that the much discussed “ angular momentum dilemma” disappears if one uses Born–Jordan quantization. We argue that the latter is the only physically correct quantization procedure. We also briefly discuss a possible redefinition of phase space quantum mechanics, where the usual Wigner distribution has to be replaced with a new quasi-distribution associated with Born–Jordan quantization, and which has proven to be successful in time-frequency analysis.     

Energy Propagation in Classical Harmonic Lattices with Diluted Disorder

We consider the problem of a harmonic lattice in which masses’ distribution is a superposition of a random and a periodic distribution. Classical equations for the mass displacement and velocities are solved using a second-order Euler formalism. Energy flow was investigated on two distinct experiments: (i) We injected an initial wave-packet with energy E ₀ and analyzed the dynamics of the resulting energy pulse; (ii) we pumped one of the sides of the lattice with a external signal and then we observed the propagation of the pulse until the other side of chain. Our calculations suggest that the diluted disordered mass distribution promotes energy dynamics at high frequency limit.