Blind assessment of localisation microscope image resolution

Abstract Background This paper analyses the resolution achieved in localisation microscopy experiments. The resolution is an essential metric for the correct interpretation of super-resolution images, but it varies between specimens due to different localisation precisions and densities. Methods By analysing localisation microscopy as a statistical method of Density Estimation, we present a method that produces a blind estimate of the resolution in a super-resolved image. This estimate is derived directly from the raw image data without the need for comparisons with known calibration specimens. It is corroborated with simulated and experimental data. Results and discussion Localisation microscopy has a resolution limit equal to 2σ, where σ is the r.m.s. localisation precision, evaluated as an average Thompson precision, Cramer Rao bound, or otherwise. Further, for a limited-sampling case in which there is only one localisation per fluorophore, the expected resolution of an optimised super-resolution image is worsened to approximately 3σ, due to smoothing processes that are necessarily involved in visualising the specimen with limited data. This 2σ or 3σ resolution can be estimated for any localisation microscopy specimen, and this metric can corroborate or replace empirical estimates of resolution. Other quantifiable resolution losses arise from sparse labelling, fluorescent label size, and motion blur.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

Developing a prioritisation framework in an English Primary Care Trust.

BACKGROUND: In the English NHS, Primary Care Trusts (PCTs) are required to commission health services, to maximise the well-being of the population, subject to the available budget. There are numerous techniques employed to make decisions, some more rational and transparent than others. A weighted benefit score can be used to rank options but this does not take into account value for money from investments. METHODS: We developed a weighted benefit score framework for use in an English PCT which ranked options in order of 'cost-value' or 'cost per point of benefit'. Our method differs from existing techniques by explicitly combining cost and a composite weighted benefit score into the cost-value ratio. RESULTS: The technique proved readily workable, and was able to accommodate a wide variety of data and competing criteria. Participants felt able to assign scores to proposed services, and generate a ranked list, which provides a solid starting point for the PCT Board to discuss and make funding decisions. Limitations included potential for criteria to be neither exhaustive nor mutually exclusive and the lack of an interval property in the benefit score limiting the usefulness of a cost-value ratio. CONCLUSION: A technical approach to decision making is insufficient for making prioritisation decisions, however our technique provides a very valuable, structured and informed starting point for PCT decision making

The Formation of the First Low-Mass Stars From Gas With Low Carbon and Oxygen Abundances

The first stars in the Universe are predicted to have been much more massive than the Sun. Gravitational condensation accompanied by cooling of the primordial gas due to molecular hydrogen, yields a minimum fragmentation scale of a few hundred solar masses. Numerical simulations indicate that once a gas clump acquires this mass, it undergoes a slow, quasi-hydrostatic contraction without further fragmentation. Here we show that as soon as the primordial gas - left over from the Big Bang - is enriched by supernovae to a carbon or oxygen abundance as small as ~0.01-0.1% of that found in the Sun, cooling by singly-ionized carbon or neutral oxygen can lead to the formation of low-mass stars. This mechanism naturally accommodates the discovery of solar mass stars with unusually low (10^{-5.3} of the solar value) iron abundance but with a high (10^{-1.3} solar) carbon abundance. The minimum stellar mass at early epochs is partially regulated by the temperature of the cosmic microwave background. The derived critical abundances can be used to identify those metal-poor stars in our Milky Way galaxy with elemental patterns imprinted by the first supernovae.Comment: 14 pages, 2 figures (appeared today in Nature

A direct image of the obscuring disk surrounding an active galactic nucleus

Active galactic nuclei (AGN) are generally accepted to be powered by the release of gravitational energy in a compact accretion disk surrounding a massive black hole. Such disks are also necessary to collimate powerful radio jets seen in some AGN. The unifying classification schemes for AGN further propose that differences in their appearance can be attributed to the opacity of the accreting material, which may obstruct our view of the central region of some systems. The popular model for the obscuring medium is a parsec-scale disk of dense molecular gas, although evidence for such disks has been mostly indirect, as their angular size is much smaller than the resolution of conventional telescopes. Here we report the first direct images of a pc-scale disk of ionised gas within the nucleus of NGC 1068, the archetype of obscured AGN. The disk is viewed nearly edge-on, and individual clouds within the ionised disk are opaque to high-energy radiation, consistent with the unifying classification scheme. In projection, the disk and AGN axes align, from which we infer that the ionised gas disk traces the outer regions of the long-sought inner accretion disk.Comment: 14 pages, LaTeX, PSfig, to appear in Nature. also available at http://hethp.mpe-garching.mpg.de/Preprint

A Tale of Two Current Sheets

I outline a new model of particle acceleration in the current sheet separating the closed from the open field lines in the force-free model of pulsar magnetospheres, based on reconnection at the light cylinder and "auroral" acceleration occurring in the return current channel that connects the light cylinder to the neutron star surface. I discuss recent studies of Pulsar Wind Nebulae, which find that pair outflow rates in excess of those predicted by existing theories of pair creation occur, and use those results to point out that dissipation of the magnetic field in a pulsar's wind upstream of the termination shock is restored to life as a viable model for the solution of the "$\sigma$" problem as a consequence of the lower wind 4-velocity implied by the larger mass loading.Comment: 17 pages, 6 figures, Invited Review, Proceedings of the "ICREA Workshop on The High-Energy Emission from Pulsars and their Systems", Sant Cugat, Spain, April 12-16, 201

Quantitative Affinity Determination by Fluorescence Anisotropy Measurements of Individual Nanoliter Droplets

Fluorescence anisotropy measurements of reagents compartmentalized into individual nanoliter droplets are shown to yield high-resolution binding curves from which precise dissociation constants (K$_{d}$) for protein-peptide interactions can be inferred. With the current platform, four titrations can be obtained per minute (based on ∼100 data points each), with stoichiometries spanning more than 2 orders of magnitude and requiring only tens of microliters of reagents. In addition to affinity measurements with purified components, K$_{d}$ values for unpurified proteins in crude cell lysates can be obtained without prior knowledge of the concentration of the expressed protein, so that protein purification can be avoided. Finally, we show how a competition assay can be set up to perform focused library screens, so that compound labeling is not required anymore. These data demonstrate the utility of droplet compartments for the quantitative characterization of biomolecular interactions and establish fluorescence anisotropy imaging as a quantitative technique in a miniaturized droplet format, which is shown to be as reliable as its macroscopic test tube equivalent.This research was funded by the Engineering and Physical Sciences Research Council (EPSRC), the Wellcome Trust, the Medical Research Council (MRC), and Alzheimer Research U.K. M.B. was supported by a fellowship from the Schweizerischer Nationalfonds. F.H. is an ERC Investigator

Entangled-State Cycles of Atomic Collective-Spin States

We study quantum trajectories of collective atomic spin states of $N$ effective two-level atoms driven with laser and cavity fields. We show that interesting ``entangled-state cycles'' arise probabilistically when the (Raman) transition rates between the two atomic levels are set equal. For odd (even) $N$, there are $(N+1)/2$ ($N/2$) possible cycles. During each cycle the $N$-qubit state switches, with each cavity photon emission, between the states $(|N/2,m>\pm |N/2,-m>)/\sqrt{2}$, where $|N/2,m>$ is a Dicke state in a rotated collective basis. The quantum number $m$ ($>0$), which distinguishes the particular cycle, is determined by the photon counting record and varies randomly from one trajectory to the next. For even $N$ it is also possible, under the same conditions, to prepare probabilistically (but in steady state) the Dicke state $|N/2,0>$, i.e., an $N$-qubit state with $N/2$ excitations, which is of particular interest in the context of multipartite entanglement.Comment: 10 pages, 9 figure

Theory of disk accretion onto supermassive black holes

Accretion onto supermassive black holes produces both the dramatic phenomena associated with active galactic nuclei and the underwhelming displays seen in the Galactic Center and most other nearby galaxies. I review selected aspects of the current theoretical understanding of black hole accretion, emphasizing the role of magnetohydrodynamic turbulence and gravitational instabilities in driving the actual accretion and the importance of the efficacy of cooling in determining the structure and observational appearance of the accretion flow. Ongoing investigations into the dynamics of the plunging region, the origin of variability in the accretion process, and the evolution of warped, twisted, or eccentric disks are summarized.Comment: Mostly introductory review, to appear in "Supermassive black holes in the distant Universe", ed. A.J. Barger, Kluwer Academic Publishers, in pres

Improved RAD51 binders through motif shuffling based on the modularity of BRC repeats.

This is the final version. Available from the National Academy of Sciences via the DOI in this record. SI Appendix contains detailed descriptions of the cloning of bacterial expression constructs for the 64 shuffled BRC peptide variants, cloning of mammalian expression constructs, and notes on the soluble expression of the shuffled BRC peptide variants. Also included is a description of ITC used to cross-validate the microfluidic measurements, single concentration point measurements carried out with microfluidics, and exemplary titrations carried out by microfluidics. The fluorescence anisotropy data obtained for the 64 separate titrations as well as the Matlab script used in the analysis have been uploaded as separate files. The supplementary data also contain an analysis on the effect of shuffling of BRC peptides and in particular on the effect of the exact shuffle cutoff point placement. X-ray crystallography electron density map images, data collection, and refinement statistics are also to be found in SI Appendix. Additional cell images highlighting the pan-nuclear signal of RAD51 are also included in SI Appendix. The coordinates and corresponding structure factors for the monomeric RAD51:BRC8-2 complex have been deposited to the PDB under accession code 6HQU. As described previously (49), the transformation from intensity maps into anisotropy values from image data was carried out with a custom Matlab code available on GitHub (https://github.com/quantitativeimaging/icetropy). A custom Matlab script used to fit Kd values for the unlabeled competitive GB1-BRC peptides can be found in SI Appendix, Datasets S1–S4. All other study data are included in the article and/or supporting information.Exchanges of protein sequence modules support leaps in function unavailable through point mutations during evolution. Here we study the role of the two RAD51-interacting modules within the eight binding BRC repeats of BRCA2. We created 64 chimeric repeats by shuffling these modules and measured their binding to RAD51. We found that certain shuffled module combinations were stronger binders than any of the module combinations in the natural repeats. Surprisingly, the contribution from the two modules was poorly correlated with affinities of natural repeats, with a weak BRC8 repeat containing the most effective N-terminal module. The binding of the strongest chimera, BRC8-2, to RAD51 was improved by -2.4 kCal/mol compared to the strongest natural repeat, BRC4. A crystal structure of RAD51:BRC8-2 complex shows an improved interface fit and an extended β-hairpin in this repeat. BRC8-2 was shown to function in human cells, preventing the formation of nuclear RAD51 foci after ionizing radiation.Biotechnology and Biological Sciences Research CouncilEuropean Research CouncilMarie Curie Research GrantCancer Research UKEngineering and Physical Sciences Research CouncilEngineering and Physical Sciences Research CouncilWellcome TrustWellcome TrustMedical Research CouncilMedical Research CouncilSchweizerischer Nationalfond

Lepton Acceleration in Pulsar Wind Nebulae

Pulsar Wind Nebulae (PWNe) act as calorimeters for the relativistic pair winds emanating from within the pulsar light cylinder. Their radiative dissipation in various wavebands is significantly different from that of their pulsar central engines: the broadband spectra of PWNe possess characteristics distinct from those of pulsars, thereby demanding a site of lepton acceleration remote from the pulsar magnetosphere. A principal candidate for this locale is the pulsar wind termination shock, a putatively highly-oblique, ultra-relativistic MHD discontinuity. This paper summarizes key characteristics of relativistic shock acceleration germane to PWNe, using predominantly Monte Carlo simulation techniques that compare well with semi-analytic solutions of the diffusion-convection equation. The array of potential spectral indices for the pair distribution function is explored, defining how these depend critically on the parameters of the turbulent plasma in the shock environs. Injection efficiencies into the acceleration process are also addressed. Informative constraints on the frequency of particle scattering and the level of field turbulence are identified using the multiwavelength observations of selected PWNe. These suggest that the termination shock can be comfortably invoked as a principal injector of energetic leptons into PWNe without resorting to unrealistic properties for the shock layer turbulence or MHD structure.Comment: 19 pages, 5 figures, invited review to appear in Proc. of the inaugural ICREA Workshop on "The High-Energy Emission from Pulsars and their Systems" (2010), eds. N. Rea and D. Torres, (Springer Astrophysics and Space Science series