Closed trajectories of a particle model on null curves in anti-de Sitter 3-space

We study the existence of closed trajectories of a particle model on null curves in anti-de Sitter 3-space defined by a functional which is linear in the curvature of the particle path. Explicit expressions for the trajectories are found and the existence of infinitely many closed trajectories is proved.Comment: 12 pages, 1 figur

Hamiltonian flows on null curves

The local motion of a null curve in Minkowski 3-space induces an evolution equation for its Lorentz invariant curvature. Special motions are constructed whose induced evolution equations are the members of the KdV hierarchy. The null curves which move under the KdV flow without changing shape are proven to be the trajectories of a certain particle model on null curves described by a Lagrangian linear in the curvature. In addition, it is shown that the curvature of a null curve which evolves by similarities can be computed in terms of the solutions of the second Painlev\'e equation.Comment: 14 pages, v2: final version; minor changes in the expositio

Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves

We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms the $\tau$ function are presented. B\"acklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete motion of discrete plane curves described by the discrete potential modified KdV equation to motion of smooth plane curves characterized by the potential modified KdV equation

Epistasis Among Adaptive Mutations in Deer Mouse Hemoglobin

Epistatic interactions between mutant sites in the same protein can exert a strong influence on pathways of molecular evolution. We performed protein engineering experiments that revealed pervasive epistasis among segregating amino acid variants that contribute to adaptive functional variation in deer mouse hemoglobin (Hb). Amino acid mutations increased or decreased Hb-O2 affinity depending on the allelic state of other sites. Structural analysis revealed that epistasis for Hb-O2 affinity and allosteric regulatory control is attributable to indirect interactions between structurally remote sites. The prevalence of sign epistasis for fitness-related biochemical phenotypes has important implications for the evolutionary dynamics of protein polymorphism in natural populations

Observational signatures of forming young massive clusters: continuum emission from dense HII regions

Young massive clusters (YMCs) are the most massive star clusters forming in nearby galaxies and are thought to be a young analogue to the globular clusters. Understanding the formation process of YMCs leads to looking into very efficient star formation in high-redshift galaxies suggested by recent JWST observations. We investigate possible observational signatures of their formation stage, particularly when the mass of a cluster is increasing via accretion from a natal molecular cloud. To this end, we study the broad-band continuum emission from ionized gas and dust enshrouding YMCs, whose formation is followed by recent radiation-hydrodynamics simulations. We perform post-process radiative transfer calculations using simulation snapshots and find characteristic spectral features at radio and far-infrared frequencies. We show that a striking feature is long-lasting, strong free-free emission from a $\sim$ 10pc-scale HII region with a large emission measure of $\gtrsim 10^7 \mathrm{cm}^{-6} \ \mathrm{pc}$, corresponding to the mean electron density of $\gtrsim 10^3~\mathrm{cm}^{-3}$. There is a turnover feature below $\sim$ 10 GHz, a signature of the optically-thick free-free emission, often found in Galactic ultra-compact HII regions. These features come from the peculiar YMC formation process, where the cluster's gravity effectively traps photoionized gas for a long duration and enables continuous star formation within the cluster. Such large and dense HII regions show distinct distribution on the density-size diagram, apart from the standard sequence of Galactic HII regions. This is consistent with the observational trend inferred for extragalactic HII regions associated with YMCs.Comment: 12 pages, 10 figures, accepted for publication in MNRA

Deer mouse hemoglobin exhibits a lowered oxygen affinity owing to mobility of the E helix. Corrigendum

In the article by Inoguchi et al. (2013) the affiliation for two of the authors, Angela Fago and Roy E. Weber, was given incorrectly. The correct affiliation is Zoophysiology, Department of Bioscience, Aarhus University, Aarhus, Denmark

Deer mouse hemoglobin exhibits a lowered oxygen affinity owing to mobility of the E helix

The deer mouse, Peromyscus maniculatus, exhibits altitude-associated variation in hemoglobin oxygen affinity. To examine the structural basis of this functional variation, the structure of the hemoglobin was solved. Recombinant hemoglobin was expressed in Escherichia coli and was purified by ion-exchange chromatography. Recombinant hemoglobin was crystallized by the hangingdrop vapor-diffusion method using polyethylene glycol as a precipitant. The obtained orthorhombic crystal contained two subunits in the asymmetric unit. The refined structure was interpreted as the aquo-met form. Structural comparisons were performed among hemoglobins from deer mouse, house mouse and human. In contrast to human hemoglobin, deer mouse hemoglobin lacks the hydrogen bond between α1Trp14 in the A helix and α1Thr67 in the E helix owing to the Thr67Ala substitution. In addition, deer mouse hemoglobin has a unique hydrogen bond at the α1β1 interface between residues α1Cys34 and β1Ser128

Lagrangian Curves in a 4-dimensional affine symplectic space

Lagrangian curves in R4 entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic frame for Lagrangian curves. It allows us to classify La- grangrian curves with constant symplectic curvatures, to construct a class of Lagrangian tori in R4 and determine Lagrangian geodesic

Deer mouse hemoglobin exhibits a lowered oxygen affinity owing to mobility of the E helix

The deer mouse, Peromyscus maniculatus, exhibits altitude-associated variation in hemoglobin oxygen affinity. To examine the structural basis of this functional variation, the structure of the hemoglobin was solved. Recombinant hemoglobin was expressed in Escherichia coli and was purified by ion-exchange chromatography. Recombinant hemoglobin was crystallized by the hangingdrop vapor-diffusion method using polyethylene glycol as a precipitant. The obtained orthorhombic crystal contained two subunits in the asymmetric unit. The refined structure was interpreted as the aquo-met form. Structural comparisons were performed among hemoglobins from deer mouse, house mouse and human. In contrast to human hemoglobin, deer mouse hemoglobin lacks the hydrogen bond between α1Trp14 in the A helix and α1Thr67 in the E helix owing to the Thr67Ala substitution. In addition, deer mouse hemoglobin has a unique hydrogen bond at the α1β1 interface between residues α1Cys34 and β1Ser128