Numerical Study of the Cahn-Hilliard Equation in One, Two and Three Dimensions

The Cahn-Hilliard equation is related with a number of interesting physical phenomena like the spinodal decomposition, phase separation and phase ordering dynamics. On the other hand this equation is very stiff an the difficulty to solve it numerically increases with the dimensionality and therefore, there are several published numerical studies in one dimension (1D), dealing with different approaches, and much fewer in two dimensions (2D). In three dimensions (3D) there are very few publications, usually concentrate in some specific result without the details of the used numerical scheme. We present here a stable and fast conservative finite difference scheme to solve the Cahn-Hilliard with two improvements: a splitting potential into a implicit and explicit in time part and a the use of free boundary conditions. We show that gradient stability is achieved in one, two and three dimensions with large time marching steps than normal methods.Comment: 20 pages with 12 figs. Accepted in the Physica

Macrophage Activation and Differentiation Signals Regulate Schlafen-4 Gene Expression: Evidence for Schlafen-4 as a Modulator of Myelopoiesis

Background: The ten mouse and six human members of the Schlafen (Slfn) gene family all contain an AAA domain. Little is known of their function, but previous studies suggest roles in immune cell development. In this report, we assessed Slfn regulation and function in macrophages, which are key cellular regulators of innate immunity

Excitons in quasi-one dimensional organics: Strong correlation approximation

An exciton theory for quasi-one dimensional organic materials is developed in the framework of the Su-Schrieffer-Heeger Hamiltonian augmented by short range extended Hubbard interactions. Within a strong electron-electron correlation approximation, the exciton properties are extensively studied. Using scattering theory, we analytically obtain the exciton energy and wavefunction and derive a criterion for the existence of a $B_u$ exciton. We also systematically investigate the effect of impurities on the coherent motion of an exciton. The coherence is measured by a suitably defined electron-hole correlation function. It is shown that, for impurities with an on-site potential, a crossover behavior will occur if the impurity strength is comparable to the bandwidth of the exciton, corresponding to exciton localization. For a charged impurity with a spatially extended potential, in addition to localization the exciton will dissociate into an uncorrelated electron-hole pair when the impurity is sufficiently strong to overcome the Coulomb interaction which binds the electron-hole pair. Interchain coupling effects are also discussed by considering two polymer chains coupled through nearest-neighbor interchain hopping $t_{\perp}$ and interchain Coulomb interaction $V_{\perp}$. Within the $t$ matrix scattering formalism, for every center-of-mass momentum, we find two poles determined only by $V_{\perp}$, which correspond to the interchain excitons. Finally, the exciton state is used to study the charge transfer from a polymer chain to an adjacent dopant molecule.Comment: 24 pages, 23 eps figures, pdf file of the paper availabl

Micron-scale mapping of megagauss magnetic fields using optical polarimetry to probe hot electron transport in petawatt-class laser-solid interactions

The transport of hot, relativistic electrons produced by the interaction of an intense petawatt laser pulse with a solid has garnered interest due to its potential application in the development of innovative x-ray sources and ion-acceleration schemes. We report on spatially and temporally resolved measurements of megagauss magnetic fields at the rear of a 50-μm thick plastic target, irradiated by a multi-picosecond petawatt laser pulse at an incident intensity of ~1020 W/cm2. The pump-probe polarimetric measurements with micron-scale spatial resolution reveal the dynamics of the magnetic fields generated by the hot electron distribution at the target rear. An annular magnetic field profile was observed ~5 ps after the interaction, indicating a relatively smooth hot electron distribution at the rear-side of the plastic target. This is contrary to previous time-integrated measurements, which infer that such targets will produce highly structured hot electron transport. We measured large-scale filamentation of the hot electron distribution at the target rear only at later time-scales of ~10 ps, resulting in a commensurate large-scale filamentation of the magnetic field profile. Three-dimensional hybrid simulations corroborate our experimental observations and demonstrate a beam-like hot electron transport at initial time-scales that may be attributed to the local resistivity profile at the target rear

Genome Digging: Insight into the Mitochondrial Genome of Homo

A fraction of the Neanderthal mitochondrial genome sequence has a similarity with a 5,839-bp nuclear DNA sequence of mitochondrial origin (numt) on the human chromosome 1. This fact has never been interpreted. Although this phenomenon may be attributed to contamination and mosaic assembly of Neanderthal mtDNA from short sequencing reads, we explain the mysterious similarity by integration of this numt (mtAncestor-1) into the nuclear genome of the common ancestor of Neanderthals and modern humans not long before their reproductive split.Exploiting bioinformatics, we uncovered an additional numt (mtAncestor-2) with a high similarity to the Neanderthal mtDNA and indicated that both numts represent almost identical replicas of the mtDNA sequences ancestral to the mitochondrial genomes of Neanderthals and modern humans. In the proteins, encoded by mtDNA, the majority of amino acids distinguishing chimpanzees from humans and Neanderthals were acquired by the ancestral hominins. The overall rate of nonsynonymous evolution in Neanderthal mitochondrial protein-coding genes is not higher than in other lineages. The model incorporating the ancestral hominin mtDNA sequences estimates the average divergence age of the mtDNAs of Neanderthals and modern humans to be 450,000-485,000 years. The mtAncestor-1 and mtAncestor-2 sequences were incorporated into the nuclear genome approximately 620,000 years and 2,885,000 years ago, respectively.This study provides the first insight into the evolution of the mitochondrial DNA in hominins ancestral to Neanderthals and humans. We hypothesize that mtAncestor-1 and mtAncestor-2 are likely to be molecular fossils of the mtDNAs of Homo heidelbergensis and a stem Homo lineage. The d(N)/d(S) dynamics suggests that the effective population size of extinct hominins was low. However, the hominin lineage ancestral to humans, Neanderthals and H. heidelbergensis, had a larger effective population size and possessed genetic diversity comparable with those of chimpanzee and gorilla

Osteo-Chondroprogenitor–Specific Deletion of the Selenocysteine tRNA Gene, Trsp, Leads to Chondronecrosis and Abnormal Skeletal Development: A Putative Model for Kashin-Beck Disease

Kashin-Beck disease, a syndrome characterized by short stature, skeletal deformities, and arthropathy of multiple joints, is highly prevalent in specific regions of Asia. The disease has been postulated to result from a combination of different environmental factors, including contamination of barley by mold mycotoxins, iodine deficiency, presence of humic substances in drinking water, and, importantly, deficiency of selenium. This multifunctional trace element, in the form of selenocysteine, is essential for normal selenoprotein function, including attenuation of excessive oxidative stress, and for the control of redox-sensitive molecules involved in cell growth and differentiation. To investigate the effects of skeletal selenoprotein deficiency, a Cre recombinase transgenic mouse line was used to trigger Trsp gene deletions in osteo-chondroprogenitors. Trsp encodes selenocysteine tRNA[Ser]Sec, required for the incorporation of selenocysteine residues into selenoproteins. The mutant mice exhibited growth retardation, epiphyseal growth plate abnormalities, and delayed skeletal ossification, as well as marked chondronecrosis of articular, auricular, and tracheal cartilages. Phenotypically, the mice thus replicated a number of the pathological features of Kashin-Beck disease, supporting the notion that selenium deficiency is important to the development of this syndrome

A Catalytic Mechanism for Cysteine N-Terminal Nucleophile Hydrolases, as Revealed by Free Energy Simulations

The N-terminal nucleophile (Ntn) hydrolases are a superfamily of enzymes specialized in the hydrolytic cleavage of amide bonds. Even though several members of this family are emerging as innovative drug targets for cancer, inflammation, and pain, the processes through which they catalyze amide hydrolysis remains poorly understood. In particular, the catalytic reactions of cysteine Ntn-hydrolases have never been investigated from a mechanistic point of view. In the present study, we used free energy simulations in the quantum mechanics/molecular mechanics framework to determine the reaction mechanism of amide hydrolysis catalyzed by the prototypical cysteine Ntn-hydrolase, conjugated bile acid hydrolase (CBAH). The computational analyses, which were confirmed in water and using different CBAH mutants, revealed the existence of a chair-like transition state, which might be one of the specific features of the catalytic cycle of Ntn-hydrolases. Our results offer new insights on Ntn-mediated hydrolysis and suggest possible strategies for the creation of therapeutically useful inhibitors

Interaction of TGFβ and BMP Signaling Pathways during Chondrogenesis

TGFβ and BMP signaling pathways exhibit antagonistic activities during the development of many tissues. Although the crosstalk between BMP and TGFβ signaling pathways is well established in bone development, the relationship between these two pathways is less well defined during cartilage development and postnatal homeostasis. We generated hypomorphic mouse models of cartilage-specific loss of BMP and TGFβ signaling to assess the interaction of these pathways in postnatal growth plate homeostasis. We further used the chondrogenic ATDC5 cell line to test effects of BMP and TGFβ signaling on each other's downstream targets. We found that conditional deletion of Smad1 in chondrocytes resulted in a shortening of the growth plate. The addition of Smad5 haploinsufficiency led to a more severe phenotype with shorter prehypertrophic and hypertrophic zones and decreased chondrocyte proliferation. The opposite growth plate phenotype was observed in a transgenic mouse model of decreased chondrocytic TGFβ signaling that was generated by expressing a dominant negative form of the TGFβ receptor I (ΔTβRI) in cartilage. Histological analysis demonstrated elongated growth plates with enhanced Ihh expression, as well as an increased proliferation rate with altered production of extracellular matrix components. In contrast, in chondrogenic ATDC5 cells, TGFβ was able to enhance BMP signaling, while BMP2 significantly reduces levels of TGF signaling. In summary, our data demonstrate that during endochondral ossification, BMP and TGFβ signaling can have antagonistic effects on chondrocyte proliferation and differentiation in vivo. We also found evidence of direct interaction between the two signaling pathways in a cell model of chondrogenesis in vitro

Conditional Expression of Wnt4 during Chondrogenesis Leads to Dwarfism in Mice

Wnts are expressed in the forming long bones, suggesting roles in skeletogenesis. To examine the action of Wnts in skeleton formation, we developed a genetic system to conditionally express Wnt4 in chondrogenic tissues of the mouse. A mouse Wnt4 cDNA was introduced into the ubiquitously expressed Rosa26 (R26) locus by gene targeting in embryonic stem (ES) cells. The expression of Wnt4 from the R26 locus was blocked by a neomycin selection cassette flanked by loxP sites (floxneo) that was positioned between the Rosa26 promoter and the Wnt4 cDNA, creating the allele designated R26(floxneoWnt4). Wnt4 expression was activated during chondrogenesis using Col2a1-Cre transgenic mice that express Cre recombinase in differentiating chondrocytes. R26(floxneoWnt4); Col2a1-Cre double heterozygous mice exhibited a growth deficiency, beginning approximately 7 to 10 days after birth, that resulted in dwarfism. In addition, they also had craniofacial abnormalities, and delayed ossification of the lumbar vertebrae and pelvic bones. Histological analysis revealed a disruption in the organization of the growth plates and a delay in the onset of the primary and secondary ossification centers. Molecular studies showed that Wnt4 overexpression caused decreased proliferation and altered maturation of chondrocytes. In addition, R26(floxneoWnt4); Col2a1-Cre mice had decreased expression of vascular endothelial growth factor (VEGF). These studies demonstrate that Wnt4 overexpression leads to dwarfism in mice. The data indicate that Wnt4 levels must be regulated in chondrocytes for normal growth plate development and skeletogenesis. Decreased VEGF expression suggests that defects in vascularization may contribute to the dwarf phenotype