On the composition of convex envelopes for quadrilinear terms

International audienceWithin the framework of the spatial Branch-and-Bound algorithm for solving Mixed-Integer Nonlinear Programs, different convex relaxations can be obtained for multilinear terms by applying associativity in different ways. The two groupings ((x1x2)x3)x4 and (x1x2x3)x4 of a quadrilinear term, for example, give rise to two different convex relaxations. In [6] we prove that having fewer groupings of longer terms yields tighter convex relaxations. In this paper we give an alternative proof of the same fact and perform a computational study to assess the impact of the tightened convex relaxation in a spatial Branch-and-Bound setting

XMeis3 Is Necessary for Mesodermal Hox Gene Expression and Function

Hox transcription factors provide positional information during patterning of the anteroposterior axis. Hox transcription factors can co-operatively bind with PBC-class co-factors, enhancing specificity and affinity for their appropriate binding sites. The nuclear localisation of these co-factors is regulated by the Meis-class of homeodomain proteins. During development of the zebrafish hindbrain, Meis3 has previously been shown to synergise with Hoxb1 in the autoregulation of Hoxb1. In Xenopus XMeis3 posteriorises the embryo upon ectopic expression. Recently, an early temporally collinear expression sequence of Hox genes was detected in Xenopus gastrula mesoderm (see intro. P3). There is evidence that this sequence sets up the embryo's later axial Hox expression pattern by time-space translation. We investigated whether XMeis3 is involved in regulation of this early mesodermal Hox gene expression. Here, we present evidence that XMeis3 is necessary for expression of Hoxd1, Hoxb4 and Hoxc6 in mesoderm during gastrulation. In addition, we show that XMeis3 function is necessary for the progression of gastrulation. Finally, we present evidence for synergy between XMeis3 and Hoxd1 in Hoxd1 autoregulation in mesoderm during gastrulation

Dynamic Computational Model Suggests That Cellular Citizenship Is Fundamental for Selective Tumor Apoptosis

Computational models in the field of cancer research have focused primarily on estimates of biological events based on laboratory generated data. We introduce a novel in-silico technology that takes us to the next level of prediction models and facilitates innovative solutions through the mathematical system. The model's building blocks are cells defined phenotypically as normal or tumor, with biological processes translated into equations describing the life protocols of the cells in a quantitative and stochastic manner. The essentials of communication in a society composed of normal and tumor cells are explored to reveal “protocols” for selective tumor eradication. Results consistently identify “citizenship properties” among cells that are essential for the induction of healing processes in a healthy system invaded by cancer. These properties act via inter-cellular communication protocols that can be optimized to induce tumor eradication along with system recovery. Within the computational systems, the protocols universally succeed in removing a wide variety of tumors defined by proliferation rates, initial volumes, and apoptosis resistant phenotypes; they show high adaptability for biological details and allow incorporation of population heterogeneity. These protocols work as long as at least 32% of cells obey extra-cellular commands and at least 28% of cancer cells report their deaths. This low percentage implies that the protocols are resilient to the suboptimal situations often seen in biological systems. We conclude that our in-silico model is a powerful tool to investigate, to propose, and to exercise logical anti-cancer solutions. Functional results should be confirmed in a biological system and molecular findings should be loaded into the computational model for the next level of directed experiments

Characterization of the Regulatory Region of the Zebrafish Prep1.1 Gene: Analogies to the Promoter of the Human PREP1

Prep1 is a developmentally essential TALE class homeodomain transcription factor. In zebrafish and mouse, Prep1 is already ubiquitously expressed at the earliest stages of development, with important tissue-specific peculiarities. The Prep1 gene in mouse is developmentally essential and has haploinsufficient tumor suppressor activity [1]. We have determined the human Prep1 transcription start site (TSS) by primer extension analysis and identified, within 20 bp, the transcription start region (TSR) of the zebrafish Prep1.1 promoter. The functions of the zebrafish 5′ upstream sequences were analyzed both by transient transfections in Hela Cells and by injection in zebrafish embryos. This analysis revealed a complex promoter with regulatory sequences extending up to −1.8, possibly −5.0 Kb, responsible for tissue specific expression. Moreover, the first intron contains a conserved tissue-specific enhancer both in zebrafish and in human cells. Finally, a two nucleotides mutation of an EGR-1 site, conserved in all species including human and zebrafish and located at a short distance from the TSS, destroyed the promoter activity of the −5.0 Kb promoter. A transgenic fish expressing GFP under the −1.8 Kb zebrafish promoter/enhancer co-expressed GFP and endogenous Prep1.1 during embryonic development. In the adult fish, GFP was expressed in hematopoietic regions like the kidney, in agreement with the essential function of Prep1 in mouse hematopoiesis. Sequence comparison showed conservation from man to fish of the sequences around the TSS, within the first intron enhancer. Moreover, about 40% of the sequences spread throughout the 5 Kbof the zebrafish promoter are concentrated in the −3 to −5 Kb of the human upstream region

Error bounds for monomial convexification in polynomial optimization

Convex hulls of monomials have been widely studied in the literature, and monomial convexifications are implemented in global optimization software for relaxing polynomials. However, there has been no study of the error in the global optimum from such approaches. We give bounds on the worst-case error for convexifying a monomial over subsets of $[0,1]^n$. This implies additive error bounds for relaxing a polynomial optimization problem by convexifying each monomial separately. Our main error bounds depend primarily on the degree of the monomial, making them easy to compute. Since monomial convexification studies depend on the bounds on the associated variables, in the second part, we conduct an error analysis for a multilinear monomial over two different types of box constraints. As part of this analysis, we also derive the convex hull of a multilinear monomial over $[-1,1]^n$.Comment: 33 pages, 2 figures, to appear in journa

HoxA-11 and FOXO1A Cooperate to Regulate Decidual Prolactin Expression: Towards Inferring the Core Transcriptional Regulators of Decidual Genes

During the menstrual cycle, the ovarian steroid hormones estrogen and progesterone control a dramatic transcriptional reprogramming of endometrial stromal cells (ESCs) leading to a receptive state for blastocyst implantation and the establishment of pregnancy. A key marker gene of this decidualization process is the prolactin gene. Several transcriptional regulators have been identified that are essential for decidualization of ESCs, including the Hox genes HoxA-10 and HoxA-11, and the forkhead box gene FOXO1A. While previous studies have identified downstream target genes for HoxA-10 and FOXO1A, the role of HoxA-11 in decidualization has not been investigated. Here, we show that HoxA-11 is required for prolactin expression in decidualized ESC. While HoxA-11 alone is a repressor on the decidual prolactin promoter, it turns into an activator when combined with FOXO1A. Conversely, HoxA-10, which has been previously shown to associate with FOXO1A to upregulate decidual IGFBP-1 expression, is unable to upregulate PRL expression when co-expressed with FOXO1A. By co-immunoprecipitation and chromatin immunoprecipitation, we demonstrate physical association of HoxA-11 and FOXO1A, and binding of both factors to an enhancer region (−395 to −148 relative to the PRL transcriptional start site) of the decidual prolactin promoter. Because FOXO1A is induced upon decidualization, it serves to assemble a decidual-specific transcriptional complex including HoxA-11. These data highlight cooperativity between numerous transcription factors to upregulate PRL in differentiating ESC, and suggest that this core set of transcription factors physically and functionally interact to drive the expression of a gene battery upregulated in differentiated ESC. In addition, the functional non-equivalence of HoxA-11 and HoxA-10 with respect to PRL regulation suggests that these transcription factors regulate distinct sets of target genes during decidualization

Mitochondrial fusion is regulated by Reaper to modulate Drosophila programmed cell death

In most multicellular organisms, the decision to undergo programmed cell death in response to cellular damage or developmental cues is typically transmitted through mitochondria. It has been suggested that an exception is the apoptotic pathway of Drosophila melanogaster, in which the role of mitochondria remains unclear. Although IAP antagonists in Drosophila such as Reaper, Hid and Grim may induce cell death without mitochondrial membrane permeabilization, it is surprising that all three localize to mitochondria. Moreover, induction of Reaper and Hid appears to result in mitochondrial fragmentation during Drosophila cell death. Most importantly, disruption of mitochondrial fission can inhibit Reaper and Hid-induced cell death, suggesting that alterations in mitochondrial dynamics can modulate cell death in fly cells. We report here that Drosophila Reaper can induce mitochondrial fragmentation by binding to and inhibiting the pro-fusion protein MFN2 and its Drosophila counterpart dMFN/Marf. Our in vitro and in vivo analyses reveal that dMFN overexpression can inhibit cell death induced by Reaper or γ-irradiation. In addition, knockdown of dMFN causes a striking loss of adult wing tissue and significant apoptosis in the developing wing discs. Our findings are consistent with a growing body of work describing a role for mitochondrial fission and fusion machinery in the decision of cells to die

A Gain-of-Function Germline Mutation in Drosophila ras1 Affects Apoptosis and Cell Fate during Development

The RAS/MAPK signal transduction pathway is an intracellular signaling cascade that transmits environmental signals from activated receptor tyrosine kinases (RTKs) on the cell surface and other endomembranes to transcription factors in the nucleus, thereby linking extracellular stimuli to changes in gene expression. Largely as a consequence of its role in oncogenesis, RAS signaling has been the subject of intense research efforts for many years. More recently, it has been shown that milder perturbations in Ras signaling during embryogenesis also contribute to the etiology of a group of human diseases. Here we report the identification and characterization of the first gain-of-function germline mutation in Drosophila ras1 (ras85D), the Drosophila homolog of human K-ras, N-ras and H-ras. A single amino acid substitution (R68Q) in the highly conserved switch II region of Ras causes a defective protein with reduced intrinsic GTPase activity, but with normal sensitivity to GAP stimulation. The ras1R68Q mutant is homozygous viable but causes various developmental defects associated with elevated Ras signaling, including cell fate changes and ectopic survival of cells in the nervous system. These biochemical and functional properties are reminiscent of germline Ras mutants found in patients afflicted with Noonan, Costello or cardio-facio-cutaneous syndromes. Finally, we used ras1R68Q to identify novel genes that interact with Ras and suppress cell death