A mathematical theory of gravitational collapse

We study the asymptotic behaviour, as the retarded timeu tends to infinity, of the solutions of Einstein's equations in the spherically symmetric case with a massless scalar field as the material model. We prove that when the final Bondi massM ₁ is different from zero, asu , a black hole forms of massM ₁ surrounded by vacuum. We find the rate of decay of the metric functions and the behaviour of the scalar field on the horizon.Research supported in part by National Science Foundation grants MCS-8201599 to the Courant Institute and PHY-8318350 to Syracuse University     

Mapping long-range interactions in alpha-synuclein using spin-label NMR and ensemble molecular dynamics simulations

The intrinsically disordered protein alpha-synuclein plays a key role in the pathogenesis of Parkinson's disease (PD). We show here that the native state of alpha-synuclein consists of a broad distribution of conformers with an ensemble-averaged hydrodynamic radius significantly smaller than that expected for a random coil structure. This partial condensation is driven by interactions between the highly charged C-terminus and a large hydrophobic central region of the protein sequence. We suggest that this structure could inhibit the formation of alpha-synuclein aggregates, which are thought to be the cytotoxic species responsible for neurodegeneration in PD.     

The problem of a self-gravitating scalar field

In this paper we begin the study of the global initial value problem for Einstein's equations in the spherically symmetric case with a massless scalar field as the material model. We reduce the problem to a single nonlinear evolution equation. Taking as initial hypersurface a future light cone with vertex at the center of symmetry, we prove, the local, in retarded time, existence and global uniqueness of classical solutions. We also prove that if the initial data is sufficiently small there exists a global classical solution which disperses in the infinite future.Research supported in part by National Science Foundation grants MCS-8201599 to the Courant Institute and PHY-8318350 to Syracuse University     

Transient tertiary structure formation within the ribosome exit port

The exit tunnel of the ribosome is commonly considered to be sufficiently narrow that co-translational folding can begin only when specific segments of nascent chains are fully extruded from the tunnel. Here we show, on the basis of molecular simulations and comparison with experiment, that the long-range contacts essential for initiating protein folding can form within a nascent chain when it reaches the last 20 ? of the exit tunnel. We further show that, in this "exit port", a significant proportion of native and non-native tertiary structure can form without steric overlap with the ribosome itself, and provide a library of structural elements that our simulations predict can form in the exit tunnel and is amenable to experimental testing. Our results show that these elements of folded tertiary structure form only transiently and are at their midpoints of stability at the boundary region between the inside and the outside of the tunnel. These findings provide a framework for interpreting a range of recent experimental studies of ribosome nascent chain complexes and for understanding key aspects of the nature of co-translational folding.     

Pesticide residues analysis in honey using ethyl acetate extraction method: validation and pilot survey in real samples

This paper presents a cost-effective and validated multi residue confirmatory method for the determination of 167 chemically different pesticides and a survey study on Cyprus honey samples. This method uses ethyl acetate for the extraction of pesticides from honey and the determination is performed with liquid chromatography (LC) coupled to mass spectrometry (MS) operating in tandem mode (MS/MS) and with GC–ECD (gas chromatography with electron capture detector) analysis. The LC-MS/MS analytical system is especially important in the analysis of polar and non-volatile pesticides. For the validation of the method, blank honey samples were spiked with 146 pesticides (organophosphorous, carbamates, triazoles, amides, neonicodinoids, strobilurines, phenylureas, bendimidazoles and others) for the LC-MS/MS analysis at three levels: 0.01, 0.05 and 0.1 mg kg^?1 and with 21 pesticides for the GC-ECD analysis at two levels: 0.01 and 0.05 mg kg^?1for organochlorines and 0.05 and 0.2 mg kg^?1for the pyrethroids. As blank sample, a sample of honey which did not contain detectable levels of the analytes sought was used. The validation study was in accordance to the DG SANCO guidelines. The scope of validation included recovery, linearity, limits of quantification and precision. Linearity is demonstrated all along the range of concentration that was investigated with correlation coefficients ≥0.98. Recoveries of the majority of compounds were in the 70%–120% range and were characterised by precision lower or equal to 20%. The validated method was used for a survey of 36 samples of honey produced in different areas of Cyprus and this is the first work on Cypriot honey samples investigating a broad range of pesticides. Only coumaphos was detected at concentrations higher than 0.01 mg kg^?1 in the 58.6% of the honey samples analysed for Coumaphos. The results were evaluated in accordance to the provisions of the Commission Regulation (EU) No 37/2010 on pharmacologically active substances and their classification regarding maximum residue limits (MRLs) in foodstuffs of animal origin. The concentrations of coumaphos in all positive samples were at levels much lower than the MRL.