Hierarchical Lattice Models of Hydrogen Bond Networks in Water

We develop a graph-based model of the hydrogen bond network in water, with a view towards quantitatively modeling the molecular-level correlational structure of the network. The networks are formed are studied by the constructing the model on two infinite-dimensional lattices. Our models are built \emph{bottom up}, based on microscopic information coming from atomistic simulations, and we show that the predictions of the model are consistent with known results from ab-initio simulations of liquid water. We show that simple entropic models can predict the correlations and clustering of local-coordination defects around tetrahedral waters observed in the atomistic simulations. We also find that orientational correlations between bonds are longer ranged than density correlations, and determine the directional correlations within closed loops and show that the patterns of water wires within these structures are also consistent with previous atomistic simulations. Our models show the existence of density and compressibility anomalies, as seen in the real liquid, and the phase diagram of these models is consistent with the singularity-free scenario previously proposed by Sastry and co-workers (Sastry et al, PRE 53, 6144 (1996)).Comment: 17 pages, published versio

Size-dependent regulation of dorsal–ventral patterning in the early Drosophila embryo

How natural variation in embryo size affects patterning of the Drosophila embryo dorsal–ventral (DV) axis is not known. Here we examined quantitatively the relationship between nuclear distribution of the Dorsal transcription factor, boundary positions for several target genes, and DV axis length. Data were obtained from embryos of a wild-type background as well as from mutant lines inbred to size select embryos of smaller or larger sizes. Our data show that the width of the nuclear Dorsal gradient correlates with DV axis length. In turn, for some genes expressed along the DV axis, the boundary positions correlate closely with nuclear Dorsal levels and with DV axis length; while the expression pattern of others is relatively constant and independent of the width of the Dorsal gradient. In particular, the patterns of snail (sna) and ventral nervous system defective (vnd) correlate with nuclear Dorsal levels and exhibit scaling to DV length; while the pattern of intermediate neuroblasts defective (ind) remains relatively constant with respect to changes in Dorsal and DV length. However, in mutants that exhibit an abnormal expansion of the Dorsal gradient which fails to scale to DV length, only sna follows the Dorsal distribution and exhibits overexpansion; in contrast, vnd and ind do not overexpand suggesting some additional mechanism acts to refine the dorsal boundaries of these two genes. Thus, our results argue against the idea that the Dorsal gradient works as a global system of relative coordinates along the DV axis and suggest that individual targets respond to changes in embryo size in a gene-specific manner

A dynamic cell recruitment process drives growth of the Drosophila wing by overscaling the vestigial expression pattern

Organs mainly attain their size by cell growth and proliferation, but sometimes also grow through recruitment of undifferentiated cells. Here we investigate the participation of cell recruitment in establishing the pattern of Vestigial (Vg), the product of the wing selector gene in Drosophila. We find that the Vg pattern overscales along the dorsal-ventral (DV) axis of the wing imaginal disc, i.e., it expands faster than the DV length of the pouch. The overscaling of the Vg pattern cannot be explained by differential proliferation, apoptosis, or oriented-cell divisions, but can be recapitulated by a mathematical model that explicitly considers cell recruitment. When impairing cell recruitment genetically, we find that the Vg pattern almost perfectly scales and adult wings are approximately 20% smaller. Conversely, impairing cell proliferation results in very small wings, suggesting that cell recruitment and cell proliferation additively contribute to organ growth in this system. Furthermore, using fluorescent reporter tools, we provide direct evidence that cell recruitment is initiated between early and mid third-instar larval development. Altogether, our work quantitatively shows when, how, and by how much cell recruitment shapes the Vg pattern and drives growth of the Drosophila wing.Fil: Muñoz Nava, Luis Manuel. Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional; MéxicoFil: Alvarez, Hugo Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Flores Flores, Marycruz. Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional; MéxicoFil: Chara, Osvaldo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentina. Technische Universität Dresden; AlemaniaFil: Nahmad, Marcos. Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional; Méxic

Size-dependent regulation of dorsal–ventral patterning in the early Drosophila embryo

How natural variation in embryo size affects patterning of the Drosophila embryo dorsal–ventral (DV) axis is not known. Here we examined quantitatively the relationship between nuclear distribution of the Dorsal transcription factor, boundary positions for several target genes, and DV axis length. Data were obtained from embryos of a wild-type background as well as from mutant lines inbred to size select embryos of smaller or larger sizes. Our data show that the width of the nuclear Dorsal gradient correlates with DV axis length. In turn, for some genes expressed along the DV axis, the boundary positions correlate closely with nuclear Dorsal levels and with DV axis length; while the expression pattern of others is relatively constant and independent of the width of the Dorsal gradient. In particular, the patterns of snail (sna) and ventral nervous system defective (vnd) correlate with nuclear Dorsal levels and exhibit scaling to DV length; while the pattern of intermediate neuroblasts defective (ind) remains relatively constant with respect to changes in Dorsal and DV length. However, in mutants that exhibit an abnormal expansion of the Dorsal gradient which fails to scale to DV length, only sna follows the Dorsal distribution and exhibits overexpansion; in contrast, vnd and ind do not overexpand suggesting some additional mechanism acts to refine the dorsal boundaries of these two genes. Thus, our results argue against the idea that the Dorsal gradient works as a global system of relative coordinates along the DV axis and suggest that individual targets respond to changes in embryo size in a gene-specific manner

Isotropization of Bianchi type models and a new FRW solution in Brans-Dicke theory

Using scaled variables we are able to integrate an equation valid for isotropic and anisotropic Bianchi type I, V, IX models in Brans-Dicke (BD) theory. We analyze known and new solutions for these models in relation with the possibility that anisotropic models asymptotically isotropize, and/or possess inflationary properties. In particular, a new solution of curve ($k\neq0$) Friedmann-Robertson-Walker (FRW) cosmologies in Brans-Dicke theory is analyzed.Comment: 15 pages, 4 postscript figures, to appear in Gen. Rel. Grav., special issue dedicated in honour of Prof. H. Dehne

Dynamic Interpretation of Hedgehog Signaling in the Drosophila Wing Disc

Morphogens are classically defined as molecules that control patterning by acting at a distance to regulate gene expression in a concentration-dependent manner. In the Drosophila wing imaginal disc, secreted Hedgehog (Hh) forms an extracellular gradient that organizes patterning along the anterior–posterior axis and specifies at least three different domains of gene expression. Although the prevailing view is that Hh functions in the Drosophila wing disc as a classical morphogen, a direct correspondence between the borders of these patterns and Hh concentration thresholds has not been demonstrated. Here, we provide evidence that the interpretation of Hh signaling depends on the history of exposure to Hh and propose that a single concentration threshold is sufficient to support multiple outputs. Using mathematical modeling, we predict that at steady state, only two domains can be defined in response to Hh, suggesting that the boundaries of two or more gene expression patterns cannot be specified by a static Hh gradient. Computer simulations suggest that a spatial “overshoot” of the Hh gradient occurs, i.e., a transient state in which the Hh profile is expanded compared to the Hh steady-state gradient. Through a temporal examination of Hh target gene expression, we observe that the patterns initially expand anteriorly and then refine, providing in vivo evidence for the overshoot. The Hh gene network architecture suggests this overshoot results from the Hh-dependent up-regulation of the receptor, Patched (Ptc). In fact, when the network structure was altered such that the ptc gene is no longer up-regulated in response to Hh-signaling activation, we found that the patterns of gene expression, which have distinct borders in wild-type discs, now overlap. Our results support a model in which Hh gradient dynamics, resulting from Ptc up-regulation, play an instructional role in the establishment of patterns of gene expression

Interpretation and Scaling of Positional Information During Development

Cells in a developing animal require information about their relative position in order to function and differentiate appropriately. In the classical view, cellular positional information is interpreted from the concentration of chemical signals known as morphogens. However, recent studies have questioned the ability of morphogens to establish gene expression patterns in a concentration-dependent manner. Here we combine theoretical tools and experimental work in Drosophila melanogaster to investigate the mechanisms by which positional information is interpreted from a morphogen gradient and the ability of patterns to scale with respect to the size of the system. First, we study how a concentration gradient of the signaling molecule Hedgehog establishes multiple patterns of gene expression along the anterior-posterior axis of the Drosophila wing disc. Using mathematical modeling as a hypotheses-generating tool, we predicted that positional information cannot be explained by different concentration thresholds from a static Hedgehog gradient. Instead, we propose that cells take into account their history of Hedgehog signaling exposure to determine patterns of gene expression. We provide experimental evidence that supports our model and conclude that gradient dynamics, resulting from the gene network architecture of the Hedgehog signaling pathway, determine pattern formation in the wing disc. Second, we introduce a theoretical formalism to study the role of morphogen gradient dynamics in developmental patterning. Given a mathematical model of pattern formation, we define and compute parameter perturbations that leave invariant the steady-state distribution of the relevant morphogen. We propose that this approach can be used as a tool to design genetic experiments that assay the function of morphogen dynamics. Lastly, we use dorsal-ventral patterning of the early Drosophila embryo as a model to study scaling of gene expression patterns with respect to natural variations in axis length, that is, the ability to establish positional information relative to the size of the system. We provide evidence that gene expression patterns that depend on the maternal factor Dorsal, scale along the dorsal-ventral axis. Our data suggest that scaling in this system is a gene-dependent rather than a position-dependent property. We propose that the mechanisms for scaling depend on feedback interactions downstream of Dorsal.</p

Steady-state invariant genetics: probing the role of morphogen gradient dynamics in developmental patterning

Morphogen-mediated patterning is the predominant mechanism by which positional information is established during animal development. In the classical view, the interpretation of positional signals depends on the equilibrium distribution of a morphogen, regardless of the dynamics of gradient formation. The problem of whether or not morphogen dynamics contribute to developmental patterning has not been explored in detail, partly because genetic experiments, which selectively affect signalling dynamics while maintaining unchanged the steady-state morphogen profile, are difficult to design and interpret. Here, I present a modelling-based approach to identify genetic mutations in developmental patterning that may affect the transient, but leave invariant the steady-state signalling gradient. As a case study, this approach is used to explore the dynamic properties of Hedgehog (Hh) signalling in the developing wing of the fruitfiy, Drosophila melanogaster. This analysis provides insights into how different properties of the Hh gradient dynamics, such as the duration of exposure to the signal or the maximum width of the transient gradient, can be genetically perturbed without affecting the steady-state distribution of the Hh concentration profile. I propose that this method can be used as an experimental design tool to investigate the role of transient morphogen gradients in developmental patterning and discuss the generality of these ideas in other problems

We also CanFly! The 2nd MexFly drosophila research conference

The 2nd Mexican Drosophila Research Conference (MexFly) took place on June 30th and July 1st, 2016 in Mexico City, at the Center for Research and Advanced Studies of the National Polytechnic Institute (Cinvestav). Principal investigators, postdocs, students, and technicians from Drosophila labs across Mexico attended. The guest speaker was Chris Rushlow from New York University, who presented work on Zelda, a key transcriptional activator of the early zygotic genome. Here we provide a brief report of the meeting, which sketches the present landscape of Drosophila research in Mexico. We also provide a brief historical note on one of the pioneers of the field in this country, Victor Salceda, personally trained by Theodosius Dobzhansky. Salceda presented at the meeting an update of his collaborative project with Dobzhansky on the distribution of Drosophila pseudoobscura chromosomal inversions, initiated over forty years ago