Classical Heisenberg model of magnetic molecular ring clusters: Accurate approximants for correlation functions and susceptibility

The article of record as published may be found at https://doi.org/10.1063/1.476144We show that the measured magnetic susceptibility of molecular ring clusters can be accurately reproduced, for all but low temperatures T, by a classical Heisenberg model of N identical spins S on a ring that interact with isotropic nearest-neighbor interactions. While exact expressions for the two-spin correlation function, C{sub N}(n,T), and the zero-field magnetic susceptibility, {chi}{sub N}(T), are known for the classical Heisenberg ring, their evaluation involves summing infinite series of modified spherical Bessel functions. By contrast, the formula C{sub N}(n,T)=(u{sup n}+u{sup N{minus}n})/(1+u{sup N}), where u(K)=cothK{minus}K{sup {minus}1} is the Langevin function and K=JS(S+1)/(k{sub B}T) is the nearest-neighbor dimensionless coupling constant, provides an excellent approximation if N{ge}6 for the regime {vert_bar}K{vert_bar}{lt}3. This choice of approximant combines the expected exponential decay of correlations for increasing yet small values of n, with the cyclic boundary condition for a finite ring, C{sub N}(n,T)=C{sub N}(N{minus}n,T). By way of illustration, we show that, for T{gt}50K, the associated approximant for the susceptibility derived from the approximate correlation function is virtually indistinguishable from both the exact theoretical susceptibility and the experimental data for the {open_quotes}ferric wheel{close_quotes} molecular cluster ([Fe(OCH{sub 3}){sub 2}(O{sub 2}CCH{sub 2}Cl)]{sub 10}), which contains N=10 interacting Fe{sup 3+} ions, each of spin S=5/2, that are symmetrically positioned in a nearly planar ring. {copyright} {ital 1998 American Institute of Physics.

Supersymmetric version of a Gaussian irrotational compressible fluid flow

The Lie point symmetries and corresponding invariant solutions are obtained for a Gaussian, irrotational, compressible fluid flow. A supersymmetric extension of this model is then formulated through the use of a superspace and superfield formalism. The Lie superalgebra of this extended model is determined and a classification of its subalgebras is performed. The method of symmetry reduction is systematically applied in order to derive special classes of invariant solutions of the supersymmetric model. Several new types of algebraic, hyperbolic, multi-solitonic and doubly periodic solutions are obtained in explicit form.Comment: Expanded introduction and added new section on classical Gaussian fluid flow. Included several additional reference

BCS-BEC crossover at finite temperature in the broken-symmetry phase

The BCS-BEC crossover is studied in a systematic way in the broken-symmetry phase between zero temperature and the critical temperature. This study bridges two regimes where quantum and thermal fluctuations are, respectively, important. The theory is implemented on physical grounds, by adopting a fermionic self-energy in the broken-symmetry phase that represents fermions coupled to superconducting fluctuations in weak coupling and to bosons described by the Bogoliubov theory in strong coupling. This extension of the theory beyond mean field proves important at finite temperature, to connect with the results in the normal phase. The order parameter, the chemical potential, and the single-particle spectral function are calculated numerically for a wide range of coupling and temperature. This enables us to assess the quantitative importance of superconducting fluctuations in the broken-symmetry phase over the whole BCS-BEC crossover. Our results are relevant to the possible realizations of this crossover with high-temperature cuprate superconductors and with ultracold fermionic atoms in a trap.Comment: 21 pages, 15 figure

Generalization of the Darboux transformation and generalized harmonic oscillators

The Darbroux transformation is generalized for time-dependent Hamiltonian systems which include a term linear in momentum and a time-dependent mass. The formalism for the $N$-fold application of the transformation is also established, and these formalisms are applied for a general quadratic system (a generalized harmonic oscillator) and a quadratic system with an inverse-square interaction up to N=2. Among the new features found, it is shown, for the general quadratic system, that the shape of potential difference between the original system and the transformed system could oscillate according to a classical solution, which is related to the existence of coherent states in the system

OMEGA: a software tool for the management, analysis, and dissemination of intracellular trafficking data that incorporates motion type classification and quality control [preprint]

MOTIVATION: Particle tracking coupled with time-lapse microscopy is critical for understanding the dynamics of intracellular processes of clinical importance. Spurred on by advances in the spatiotemporal resolution of microscopy and automated computational methods, this field is increasingly amenable to multi-dimensional high-throughput data collection schemes (Snijder et al, 2012). Typically, complex particle tracking datasets generated by individual laboratories are produced with incompatible methodologies that preclude comparison to each other. There is therefore an unmet need for data management systems that facilitate data standardization, meta-analysis, and structured data dissemination. The integration of analysis, visualization, and quality control capabilities into such systems would eliminate the need for manual transfer of data to diverse downstream analysis tools. At the same time, it would lay the foundation for shared trajectory data, particle tracking, and motion analysis standards. RESULTS: Here, we present Open Microscopy Environment inteGrated Analysis (OMEGA), a cross-platform data management, analysis, and visualization system, for particle tracking data, with particular emphasis on results from viral and vesicular trafficking experiments. OMEGA provides easy to use graphical interfaces to implement integrated particle tracking and motion analysis workflows while keeping track of error propagation and data provenance. Specifically, OMEGA: 1) imports image data and metadata from data management tools such as Open Microscopy Environment Remote Objects (OMERO; Allan et al., 2012); 2) tracks intracellular particles moving across time series of image planes; 3) facilitates parameter optimization and trajectory results inspection and validation; 4) performs downstream trajectory analysis and motion type classification; 5) estimates the uncertainty associated with motion analysis; and, 6) facilitates storage and dissemination of analysis results, and analysis definition metadata, on the basis of our newly proposed Minimum Information About Particle Tracking Experiments (MIAPTE; Rigano & Strambio-De-Castillia, 2016; 2017) guidelines in combination with the OME-XML data model (Goldberg et al, 2005)

Evolutionary Toggling of Vpx/Vpr Specificity Results in Divergent Recognition of the Restriction Factor SAMHD1

SAMHD1 is a host restriction factor that blocks the ability of lentiviruses such as HIV-1 to undergo reverse transcription in myeloid cells and resting T-cells. This restriction is alleviated by expression of the lentiviral accessory proteins Vpx and Vpr (Vpx/Vpr), which target SAMHD1 for proteasome-mediated degradation. However, the precise determinants within SAMHD1 for recognition by Vpx/Vpr remain unclear. Here we show that evolution of Vpx/Vpr in primate lentiviruses has caused the interface between SAMHD1 and Vpx/Vpr to alter during primate lentiviral evolution. Using multiple HIV-2 and SIV Vpx proteins, we show that Vpx from the HIV-2 and SIVmac lineage, but not Vpx from the SIVmnd2 and SIVrcm lineage, require the C-terminus of SAMHD1 for interaction, ubiquitylation, and degradation. On the other hand, the N-terminus of SAMHD1 governs interactions with Vpx from SIVmnd2 and SIVrcm, but has little effect on Vpx from HIV-2 and SIVmac. Furthermore, we show here that this difference in SAMHD1 recognition is evolutionarily dynamic, with the importance of the N- and C-terminus for interaction of SAMHD1 with Vpx and Vpr toggling during lentiviral evolution. We present a model to explain how the head-to-tail conformation of SAMHD1 proteins favors toggling of the interaction sites by Vpx/Vpr during this virus-host arms race. Such drastic functional divergence within a lentiviral protein highlights a novel plasticity in the evolutionary dynamics of viral antagonists for restriction factors during lentiviral adaptation to its hosts. © 2013 Fregoso et al

'Education, education, education' : legal, moral and clinical

This article brings together Professor Donald Nicolson's intellectual interest in professional legal ethics and his long-standing involvement with law clinics both as an advisor at the University of Cape Town and Director of the University of Bristol Law Clinic and the University of Strathclyde Law Clinic. In this article he looks at how legal education may help start this process of character development, arguing that the best means is through student involvement in voluntary law clinics. And here he builds upon his recent article which argues for voluntary, community service oriented law clinics over those which emphasise the education of students

Rhesus TRIM5α disrupts the HIV-1 capsid at the inter-hexamer interfaces

TRIM proteins play important roles in the innate immune defense against retroviral infection, including human immunodeficiency virus type-1 (HIV-1). Rhesus macaque TRIM5α (TRIM5αrh) targets the HIV-1 capsid and blocks infection at an early post-entry stage, prior to reverse transcription. Studies have shown that binding of TRIM5α to the assembled capsid is essential for restriction and requires the coiled-coil and B30.2/SPRY domains, but the molecular mechanism of restriction is not fully understood. In this study, we investigated, by cryoEM combined with mutagenesis and chemical cross-linking, the direct interactions between HIV-1 capsid protein (CA) assemblies and purified TRIM5αrh containing coiled-coil and SPRY domains (CC-SPRYrh). Concentration-dependent binding of CC-SPRYrh to CA assemblies was observed, while under equivalent conditions the human protein did not bind. Importantly, CC-SPRYrh, but not its human counterpart, disrupted CA tubes in a non-random fashion, releasing fragments of protofilaments consisting of CA hexamers without dissociation into monomers. Furthermore, such structural destruction was prevented by inter-hexamer crosslinking using P207C/T216C mutant CA with disulfide bonds at the CTD-CTD trimer interface of capsid assemblies, but not by intra-hexamer crosslinking via A14C/E45C at the NTD-NTD interface. The same disruption effect by TRIM5αrh on the inter-hexamer interfaces also occurred with purified intact HIV-1 cores. These results provide insights concerning how TRIM5α disrupts the virion core and demonstrate that structural damage of the viral capsid by TRIM5α is likely one of the important components of the mechanism of TRIM5α-mediated HIV-1 restriction. © 2011 Zhao et al

Conserving Gapless Mean-Field Theory for Weakly Interacting Bose Gases

This paper presents a conserving gapless mean-field theory for weakly interacting Bose gases. We first construct a mean-field Luttinger-Ward thermodynamic functional in terms of the condensate wave function $\Psi$ and the Nambu Green's function $\hat{G}$ for the quasiparticle field. Imposing its stationarity respect to $\Psi$ and $\hat{G}$ yields a set of equations to determine the equilibrium for general non-uniform systems. They have a plausible property of satisfying the Hugenholtz-Pines theorem to provide a gapless excitation spectrum. Also, the corresponding dynamical equations of motion obey various conservation laws. Thus, the present mean-field theory shares two important properties with the exact theory: ``conserving'' and ``gapless.'' The theory is then applied to a homogeneous weakly interacting Bose gas with s-wave scattering length $a$ and particle mass $m$ to clarify its basic thermodynamic properties under two complementary conditions of constant density $n$ and constant pressure $p$. The superfluid transition is predicted to be first-order because of the non-analytic nature of the order-parameter expansion near $T_{c}$ inherent in Bose systems, i.e., the Landau-Ginzburg expansion is not possible here. The transition temperature $T_{c}$ shows quite a different interaction dependence between the $n$-fixed and $p$-fixed cases. In the former case $T_{c}$ increases from the ideal gas value $T_{0}$ as $T_{c}/T_{0}= 1+ 2.33 an^{1/3}$, whereas it decreases in the latter as $T_{c}/T_{0}= 1- 3.84a(mp/2\pi\hbar^{2})^{1/5}$. Temperature dependences of basic thermodynamic quantities are clarified explicitly.Comment: 19 pages, 8 figure