Universal temperature dependence of the magnetization of gapped spin chains

Temperature dependence of the magnetization of the Haldane spin chain at finite magnetic field is analyzed systematically. Quantum Monte Carlo data indicates a clear minimum of magnetization as a function of temperature in the gapless regime. On the basis of the Tomonaga-Luttinger liquid theory, we argue that this minimum is rather universal and can be observed for general axially symmetric quasi-one-dimensional spin systems. Our argument is confirmed by the magnetic-field dependence of the spin-wave velocity obtained numerically. One can estimate a magnitude of the gap of any such systems by fitting the experimental data with the magnetization minimum.Comment: 9 pages, 7 figure

Probing for Binding Regions of the FtsZ Protein Surface through Site-Directed Insertions: Discovery of Fully Functional FtsZ-Fluorescent Proteins

FtsZ, a bacterial tubulin homologue, is a cytoskeletal protein that assembles into protofilaments that are one subunit thick. These protofilaments assemble further to form a “Z ring” at the center of prokaryotic cells. The Z ring generates a constriction force on the inner membrane and also serves as a scaffold to recruit cell wall remodeling proteins for complete cell division in vivo. One model of the Z ring proposes that protofilaments associate via lateral bonds to form ribbons; however, lateral bonds are still only hypothetical. To explore potential lateral bonding sites, we probed the surface of Escherichia coli FtsZ by inserting either small peptides or whole fluorescent proteins (FPs). Among the four lateral surfaces on FtsZ protofilaments, we obtained inserts on the front and back surfaces that were functional for cell division. We concluded that these faces are not sites of essential interactions. Inserts at two sites, G124 and R174, located on the left and right surfaces, completely blocked function, and these sites were identified as possible sites for essential lateral interactions. However, the insert at R174 did not interfere with association of protofilaments into sheets and bundles in vitro. Another goal was to find a location within FtsZ that supported insertion of FP reporter proteins while allowing the FtsZ-FPs to function as the sole source of FtsZ. We discovered one internal site, G55-Q56, where several different FPs could be inserted without impairing function. These FtsZ-FPs may provide advances for imaging Z-ring structure by superresolution techniques. IMPORTANCE One model for the Z-ring structure proposes that protofilaments are assembled into ribbons by lateral bonds between FtsZ subunits. Our study excluded the involvement of the front and back faces of the protofilament in essential interactions in vivo but pointed to two potential lateral bond sites, on the right and left sides. We also identified an FtsZ loop where various fluorescent proteins could be inserted without blocking function; these FtsZ-FPs functioned as the sole source of FtsZ. This advance provides improved tools for all fluorescence imaging of the Z ring and may be especially important for superresolution imaging

Reaction-diffusion kinetics on lattice at the microscopic scale

Lattice-based stochastic simulators are commonly used to study biological reaction-diffusion processes. Some of these schemes that are based on the reaction-diffusion master equation (RDME), can simulate for extended spatial and temporal scales but cannot directly account for the microscopic effects in the cell such as volume exclusion and diffusion-influenced reactions. Nonetheless, schemes based on the high-resolution microscopic lattice method (MLM) can directly simulate these effects by representing each finite-sized molecule explicitly as a random walker on fine lattice voxels. The theory and consistency of MLM in simulating diffusion-influenced reactions have not been clarified in detail. Here, we examine MLM in solving diffusion-influenced reactions in 3D space by employing the Spatiocyte simulation scheme. Applying the random walk theory, we construct the general theoretical framework underlying the method and obtain analytical expressions for the total rebinding probability and the effective reaction rate. By matching Collins-Kimball and lattice-based rate constants, we obtained the exact expressions to determine the reaction acceptance probability and voxel size. We found that the size of voxel should be about 2% larger than the molecule. MLM is validated by numerical simulations, showing good agreement with the off-lattice particle-based method, eGFRD. MLM run time is more than an order of magnitude faster than eGFRD when diffusing macromolecules with typical concentrations in the cell. MLM also showed good agreements with eGFRD and mean-field models in case studies of two basic motifs of intracellular signaling, the protein production-degradation process and the dual phosphorylation cycle. Moreover, when a reaction compartment is populated with volume-excluding obstacles, MLM captures the non-classical reaction kinetics caused by anomalous diffusion of reacting molecules

What Does mu-tau Symmetry Imply about Neutrino Mixings?

The requirement of the mu-tau symmetry in the neutrino sector that yields the maximal atmospheric neutrino mixing is shown to yield either sin(\theta_{13})=0 (referred to as C1)) or sin(\theta_{12})=0 (referred to as C2)), where \theta_{12(13)} stands for the solar (reactor) neutrino mixing angle. We study general properties possessed by approximately mu-tau symmetric textures. It is argued that the tiny mu-tau symmetry breaking generally leads to cos(2\theta_{23}) \simsin(\theta_{13}) for C1) and cos(2\theta_{23}) \sim \Delta m^2_\odot/\Delta m^2_{atm}(\equiv R) for C2), which indicates that the smallness of cos(2\theta_{23}) is a good measure of the mu-tau symmetry breaking, where \Delta m^2_{atm} (\Delta m^2_\odot) stands for the square mass differences of atmospheric (solar) neutrinos. We further find that the relation R \sim sin^2(\theta_{13}) arises from contributions of O(sin^2(\theta_{13})) in the estimation of the neutrino masses (m_{1,2,3}) for C1), and that possible forms of textures are strongly restricted to realize sin^2(2\theta_{12})=O(1) for C2). To satisfy R \sim sin^2(\theta_{13}) for C1), neutrinos exhibit the inverted mass hierarchy, or the quasi degenerate mass pattern with | m_{1,2,3}| \sim O(\sqrt{\Delta m^2_{atm}}), and, to realize sin^2(2\theta_{12})=O(1) for C2), there should be an additional small parameter \eta whose size is comparable to that of the mu-tau symmetry breaking parameter \epsilon, giving tan(2\theta_{12}) \sim \epsilon/\eta with \eta \sim \epsilon to be compatible with the observed large mixing.Comment: 10 pages, title slightly modified, comments added in the introdction, typos corrected, references updated, version to appear in Physical Reviews

Diagram-based Problem Solving: Th e Case of an Impossible Problem

Diagram-based problem solving is an activity in which subjects solve problems that are specified in the form of diagrams. Since the diagram contains critical information necessary for problem solving, this is an activity that clearly requires reasoning with the diagram. Recent research on diagrammatic reasoning has uncovered many interesting aspects of this process. One such aspect that the authors have been exploring, by means of a set of verbal and gestural protocol analysis experiments, is the role of the diagram in guiding the reasoning process. The trajectory of reasoning is revealed both by the intermediate hypotheses gen?erated, and by the shifts of focus induced from problem solving protocols. In this paper w e focus on the protocols collected for a particularly interesting problem, one whose solution is ar?rived at through a pair of contradictory inferences. W e derived the reasoning trajectories of subjects by extracting the temporal order and spatial distribution of their intermediate hypotheses leading toward the final solution. These trajectories indicate that the spatio-temporal order of hypotheses depend on more than the device structure depicted in the diagram and inferred causation of events from the diagram. W e propose that subjects employ impUcit search strategies which together with their in?ternal goals to verify hypotheses and the need to replenish short term memory influence their reasoning trajectorie

A Study of Diagrammatic Reasoning from Verbal and Gestural Data

This paper reports on an exploratory study of diagrammatic reasoning. Concurrent think-aloud protocols and gestures of subjects solving a set of device behavior hypothesis problems presented as labeled diagrams were collected. In addition to analyzing verbal protocols, the gestures and marks made by the subjects were examined and used to annotate encoded verbal data. A model of diagrammatic reasoiung in this task is proposed and compared with results of analyzing the protocols. Besides lending support to results of previous experimental studies, this study also revealed some interesting aspects of diagrammatic reasoning that merit further investigation