Pattern formation in generalized Turing systems

Turing's model of pattern formation has been extensively studied analytically and numerically, and there is recent experimental evidence that it may apply in certain chemical systems. The model is based on the assumption that all reacting species obey the same type of boundary condition pointwise on the boundary. We call these scalar boundary conditions. Here we study mixed or nonscalar boundary conditions, under which different species satisfy different boundary conditions at any point on the boundary, and show that qualitatively new phenomena arise in this case. For example, we show that there may be multiple solutions at arbitrarily small lengths under mixed boundary conditions, whereas the solution is unique under homogeneous scalar boundary conditions. Moreover, even when the same solution exists under scalar and mixed boundary conditions, its stability may be different in the two cases. We also show that mixed boundary conditions can reduce the sensitivity of patterns to domain changes.Supported in part by NIH Grant # GM29123     

A molecular dynamics boundary condition for heat exchange between walls and a fluid

In molecular dynamics simulations of heat transfer in micro channels, a lot of computation time is used when the wall molecules are explicitly simulated. To save computation time, implicit boundary conditions, such as the Maxwell conditions, can be used. With these boundary conditions, heat transfer is still a problem. In this work, we derive a new boundary condition based on a vibrating potential wall. The heat-transfer properties of the new boundary condition are shown to be comparable with those of the explicit wall. The computation time needed for the implicit boundary condition is very small compared with that needed for the explicit simulation.     

A stage-specific factor confers Fab-7 boundary activity during early embryogenesis in Drosophila

The Fab-7 boundary is required to ensure that the iab-6 and iab-7 cis-regulatory domains in the Drosophila Bithorax complex can function autonomously. Though Fab-7 functions as a boundary from early embryogenesis through to the adult stage, this constitutive boundary activity depends on subelements whose activity is developmentally restricted. In the studies reported here, we have identified a factor, called early boundary activity (Elba), that confers Fab-7 boundary activity during early embryogenesis. The Elba factor binds to a recognition sequence within a Fab-7 subelement that has enhancer-blocking activity during early embryogenesis, but not during mid-embryogenesis or in the adult. We found that the Elba factor is present in early embryos but largely disappears during mid-embryogenesis. We show that mutations in the Elba recognition sequence that eliminate Elba binding in nuclear extracts disrupt the early boundary activity of the Fab-7 subelement. Conversely, we find that early boundary activity can be reconstituted by multimerizing the Elba recognition site.     

刚性与弹性相结合的城市开发边界划定——以浙江省义乌市为例

在快速城市化背景下,以协调城市快速扩张与资源环境保护的突出矛盾为出发点,引入城市开发边界概念,在明确城市开发边界内涵的基础上,选择浙江省义乌市作为典型案例,运用生态红线判别法、生态敏感性评价划定生态本底边界,作为生态基本约束区;运用MCE-CA模型对2020年城市扩展进行模拟研究,并与生态敏感区进行互动调整,界定出城市开发边界和弹性控制区.结果表明: 研究区生态本底边界外生态约束区总面积为385.2 km²,是城市发展建设的生态安全警戒线;城市发展边界总面积为163.3 km²,是现时可进行建设的空间界限,同时又能满足未来发展建设的区域;在生态本底边界与城市发展边界之间的区域是弹性控制区,允许城市开发活动在此区域进行,但建设规模不得超过城市发展边界总面积的8.5%.从边界的刚性与弹性结合角度划定城市开发边界,有利于引导城市空间有序发展,为我国城市开发边界的合理管控提供参考和借鉴.     

The enhancer-blocking activity of the Fab-7 boundary from the Drosophila bithorax complex requires GAGA-factor-binding sites

In the work reported here we have analyzed the role of the GAGA factor [encoded by the Trithorax-like (Trl) gene] in the enhancer-blocking activity of Frontabdominal-7 (Fab-7), a domain boundary element from the Drosophila melanogaster bithorax complex (BX-C). One of the three nuclease hypersensitive sites in the Fab-7 boundary, HS1, contains multiple consensus-binding sequences for the GAGA factor, a protein known to be involved in the formation and/or maintenance of nucleosome-free regions of chromatin. GAGA protein has been shown to localize to the Fab-7 boundary in vivo, and we show that it recognizes sequences from HS1 in vitro. Using two different transgene assays we demonstrate that GAGA-factor-binding sites are necessary but not sufficient for full Fab-7 enhancer-blocking activity. We show that distinct GAGA sites are required for different enhancer-blocking activities at different stages of development. We also show that the enhancer-blocking activity of the endogenous Fab-7 boundary is sensitive to mutations in the gene encoding the GAGA factor Trithorax-like.     

Morpholino artifacts provide pitfalls and reveal a novel role for pro-apoptotic genes in hindbrain boundary development

Morpholino antisense oligonucleotides (MOs) are widely used as a tool to achieve loss of gene function, but many have off-target effects mediated by activation of Tp53 and associated apoptosis. Here, we re-examine our previous MO-based loss-of-function studies that had suggested that Wnt1 expressed at hindbrain boundaries in zebrafish promotes neurogenesis and inhibits boundary marker gene expression in the adjacent para-boundary regions. We find that Tp53 is highly activated and apoptosis is frequently induced by the MOs used in these studies. Co-knockdown of Tp53 rescues the decrease in proneural and neuronal marker expression, which is thus an off-target effect of MOs. While loss of gene expression can be attributed to cell loss through apoptotic cell death, surprisingly we find that the ectopic expression of hindbrain boundary markers is also dependent on Tp53 activity and its downstream apoptotic effectors. We examine whether this non-specific activation of hindbrain boundary gene expression provides insight into the endogenous mechanisms underlying boundary cell specification. We find that the pro-apoptotic Bcl genes puma and bax-a are required for hindbrain boundary marker expression, and that gain of function of the Bcl-caspase pathway leads to ectopic boundary marker expression. These data reveal a non-apoptotic role for pro-apoptotic genes in the regulation of gene expression at hindbrain boundaries. In light of these findings, we discuss the precautions needed in performing morpholino knockdowns and in interpreting the data derived from their use.     

Categorical perception of human female physical attractiveness and health

Using realistic three-dimensional female body models, we found evidence for a categorical perception of female physical attractiveness and health in male and female Caucasian observers. In a rating task, we showed that these bodies were rated for attractiveness or health in the same way as real bodies. In a two-alternative forced-choice task, we showed that these bodies were categorized into attractive vs. unattractive or healthy vs. unhealthy nonlinearly, which allowed us to estimate the position of a categorical boundary between attractive and unattractive or healthy and unhealthy bodies. In a delayed match-to-sample task, we measured the sensitivity of discrimination between pairs of bodies. We found significantly better discrimination for pairs that crossed the attractive/unattractive or healthy/unhealthy boundary than pairs that did not, even though the physical changes in both conditions were identical. Thus, categorical perception enhances the perception of physical changes that cross the boundary between discrete perceptual categories of important judgments such as attractiveness or health, which can be a cue for mate selection.     

Membrane potential regulates Hedgehog signalling in the Drosophila wing imaginal disc

While the membrane potential of cells has been shown to be patterned in some tissues, specific roles for membrane potential in regulating signalling pathways that function during development are still being established. In the Drosophila wing imaginal disc, Hedgehog (Hh) from posterior cells activates a signalling pathway in anterior cells near the boundary which is necessary for boundary maintenance. Here, we show that membrane potential is patterned in the wing disc. Anterior cells near the boundary, where Hh signalling is most active, are more depolarized than posterior cells across the boundary. Elevated expression of the ENaC channel Ripped Pocket (Rpk), observed in these anterior cells, requires Hh. Antagonizing Rpk reduces depolarization and Hh signal transduction. Using genetic and optogenetic manipulations, in both the wing disc and the salivary gland, we show that membrane depolarization promotes membrane localization of Smoothened and augments Hh signalling, independently of Patched. Thus, membrane depolarization and Hh‐dependent signalling mutually reinforce each other in cells immediately anterior to the compartment boundary.     

Pattern formation in a generalized chemotactic model

Many models have been proposed for spatial pattern formation in embryology and analyzed for the standard case of zero-flux boundary conditions. However, relatively little attention has been paid to the role of boundary conditions on the form of the final pattern. Here we investigate, numerically, the effect of nonstandard boundary conditions on a model pattern generator, which we choose to be of a cell-chemotactic type. We specifically focus on the role of boundary conditions and the effects of scale and aspect ratio, and study the spatiotemporal dynamics of pattern formation. We illustrate the properties of the model by application to the spatiotemporal sequence of skeletal development.     

Quantifying uncertainty in molecular dynamics simulations of grain boundary migration

Molecular dynamics simulations of simple bicrystal systems have been much used as a tool to explore how the migration of grain boundaries varies with their structure and with experimental conditions. In order to permit the exploration of a large parameter space, many studies are forced to rely on a small number of simulations (often a single simulation) for each configuration. The motion of a grain boundary is inherently statistical and any variability in the measured grain boundary velocity should be taken into account in subsequent analysis of trends in grain boundary mobility. Here we present the results of large numbers of simulations of equivalent boundaries, which show that this variability can be large, particularly when small systems are simulated. We show how a bootstrap resampling approach can be used to characterise the statistical uncertainty in boundary velocity using the information present in a single simulation. We show that the approach is robust across a variety of system sizes, temperatures and driving force strengths and types, and provides a good order-of-magnitude measure of the population standard deviation across multiple equivalent simulations.     

Identification of a multicopy chromatin boundary element at the borders of silenced chromosomal domains

The insulating properties required to delimit higher-order chromosomal domains have been shown to be shared by a variety of chromatin boundary elements (BEs). Boundary elements have been described in several species, from yeast to human, and we have previously reported the existence of a class of chromatin BEs in Drosophila melanogaster whose insulating activity requires the DNA-binding protein BEAF (boundary element-associated factor). Here we focus on the characterization of a moderately repeated 1.2 kb DNA sequence that encompasses boundary element 28 (BE28). We show that it directionally blocks enhancer/promoter communication in transgenic flies. This sequence contains a BEAF-binding sequence juxtaposed to an AT-rich sequence that harbors a strong nuclease-hypersensitive site. Using a combination of DNA-protein and protein blotting techniques, we found that this region is recognized by the A+T-binding D1 non-histone chromosomal protein of D. melanogaster, and we provide evidence that D1 and BEAF physically interact. In addition, the multicopy BE28 element maps to pericentric regions of the D. melanogaster 2L, 2R and X chromosome arms to which D1 has been shown to localize. In yeast, BEs that mark the periphery of silenced chromosomal domains have recently been shown to block the spreading of heterochromatin assembly. We propose that the BE28 repeat clusters could fulfill a similar function, acting as a local boundary between hetero- and euchromatin in a process involving interactions between the BEAF and D1 proteins.     

Survey of the differences between regenerative and non-regenerative animals

To investigate the boundaries between regenerative and non-regenerative animals, we first survey regenerative ability across animal phyla from sponges to chordates (including mammals). There are both regenerative and non-regenerative animals in each phylum. The cells participating in regeneration also vary among different species. Thus, it is hard to find clear rules concerning regeneration ability across the animal kingdom, suggesting that it is not useful to compare the difference of regenerative ability across phyla to seek the boundary between regenerative and non-regenerative animals. Instead, if we carefully compare the differences of regenerative ability between closely related species within each phylum and accumulate these differences at the cellular molecular levels, we may be able to clarify the boundary between regenerative and non-regenerative animals. Here we introduce our comparative analysis of cellular events after amputation of lower jaws between frogs and newts. Then we propose that such comparative analyses using closely related species within the same phylum should be accumulated to understand the boundary between regenerative and non-regenerative animals in order to apply this understanding for realizing regenerative medicine in the future.     

Testing a Primary and a Secondary Endpoint in a Group Sequential Design

Summary We consider a clinical trial with a primary and a secondary endpoint where the secondary endpoint is tested only if the primary endpoint is significant. The trial uses a group sequential procedure with two stages. The familywise error rate (FWER) of falsely concluding significance on either endpoint is to be controlled at a nominal level α. The type I error rate for the primary endpoint is controlled by choosing any α‐level stopping boundary, e.g., the standard O'Brien–Fleming or the Pocock boundary. Given any particular α‐level boundary for the primary endpoint, we study the problem of determining the boundary for the secondary endpoint to control the FWER. We study this FWER analytically and numerically and find that it is maximized when the correlation coefficient ρ between the two endpoints equals 1. For the four combinations consisting of O'Brien–Fleming and Pocock boundaries for the primary and secondary endpoints, the critical constants required to control the FWER are computed for different values of ρ. An ad hoc boundary is proposed for the secondary endpoint to address a practical concern that may be at issue in some applications. Numerical studies indicate that the O'Brien–Fleming boundary for the primary endpoint and the Pocock boundary for the secondary endpoint generally gives the best primary as well as secondary power performance. The Pocock boundary may be replaced by the ad hoc boundary for the secondary endpoint with a very little loss of secondary power if the practical concern is at issue. A clinical trial example is given to illustrate the methods.