Polynomial function intervals for floating-point software verification

The focus of our work is the verification of tight functional properties of numerical programs, such as showing that a floating-point implementation of Riemann integration computes a close approximation of the exact integral. Programmers and engineers writing such programs will benefit from verification tools that support an expressive specification language and that are highly automated. Our work provides a new method for verification of numerical software, supporting a substantially more expressive language for specifications than other publicly available automated tools. The additional expressivity in the specification language is provided by two constructs. First, the specification can feature inclusions between interval arithmetic expressions. Second, the integral operator from classical analysis can be used in the specifications, where the integration bounds can be arbitrary expressions over real variables. To support our claim of expressivity, we outline the verification of four example programs, including the integration example mentioned earlier. A key component of our method is an algorithm for proving numerical theorems. This algorithm is based on automatic polynomial approximation of non-linear real and real-interval functions defined by expressions. The PolyPaver tool is our implementation of the algorithm and its source code is publicly available. In this paper we report on experiments using PolyPaver that indicate that the additional expressivity does not come at a performance cost when comparing with other publicly available state-of-the-art provers. We also include a scalability study that explores the limits of PolyPaver in proving tight functional specifications of progressively larger randomly generated programs

Walking a Supramolecular Tightrope: A Self-Assembled Dodecamer from an 8-Aryl-2′-deoxyguanosine Derivative

Guanosine quadruplexes (GQs) have emerged in recent years as key players in the development of promising functional nanostruc-tures.1 GQs are formed by the self-assembly of guanosine subunits into planar tetramers (G-tetrads) that stack on each other, assisted by the complexation of a metal cation such as K+ or Na+. Alternatively, GQs can also form via the folding of G-rich oligonucleotides (e.g., DNA, RNA) leading to monomeric, dimeric, and tetrameric structures via the association of one, two, or four oligonucleotides, respectively.1d,2 In the latter, the number of G-tetrads is primarily controlled by the sequence (intrinsic param-eter) of the oligonucleotide, whereas, in the former, such control can be primarily achieved by adjusting extrinsic parameters (e.g., concentration, temperature, solvent,3 the cation template,4 and/or its counteranion5). Controlling the molecularity via intrinsic parameters (i.e., structural information in the supramolecula

Post-assembly modification of kinetically metastable Fe(II)2L3 triple helicates.

We report the covalent post-assembly modification of kinetically metastable amine-bearing Fe(II)2L3 triple helicates via acylation and azidation. Covalent modification of the metastable helicates prevented their reorganization to the thermodynamically favored Fe(II)4L4 tetrahedral cages, thus trapping the system at the non-equilibrium helicate structure. This functionalization strategy also conveniently provides access to a higher-order tris(porphyrinatoruthenium)-helicate complex that would be difficult to prepare by de novo ligand synthesis.This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC). D.A.R. acknowledges the Gates Cambridge Trust for Ph.D. (Gates Cambridge Scholarship) and conference funding.This is the final published version. It first appeared at http://pubs.acs.org/doi/abs/10.1021/ja5042397

Signal transduction in a covalent post-assembly modification cascade

Natural reaction cascades control the movement of biomolecules between cellular compartments. Inspired by these systems, we report a synthetic reaction cascade employing post-assembly modification reactions to direct the partitioning of supramolecular complexes between phases. The system is composed of a self-assembled tetrazine-edged FeII8L12 cube and a maleimide-functionalized FeII4L6 tetrahedron. Norbornadiene (NBD) functions as the stimulus that triggers the cascade, beginning with the inverse-electron-demand Diels–Alder reaction of NBD with the tetrazine moieties of the cube. This reaction generates cyclopentadiene as a transient by-product, acting as a relay signal that subsequently undergoes a Diels–Alder reaction with the maleimide-functionalized tetrahedron. Cyclooctyne can selectively inhibit the cascade by outcompeting NBD as the initial trigger. Initiating the cascade with 2-octadecyl NBD leads to selective alkylation of the tetrahedron upon cascade completion. The increased lipophilicity of the C18-tagged tetrahedron drives this complex into a non-polar phase, allowing its isolation from the initially inseparable mixture of complexes

DNA methylation at an enhancer of the three prime repair exonuclease 2 gene (TREX2) is linked to gene expression and survival in laryngeal cancer

Background: Genetic aberrations in DNA repair genes are linked to cancer, but less is reported about epigenetic regulation of DNA repair and functional consequences. We investigated the intragenic methylation loss at the three prime repair exonuclease 2 (TREX2) locus in laryngeal (n = 256) and colorectal cancer cases (n = 95) and in pan-cancer data from The Cancer Genome Atlas (TCGA). Results: Significant methylation loss at an intragenic site of TREX2 was a frequent trait in both patient cohorts (p = 0.016 and < 0.001, respectively) and in 15 out of 22 TCGA studies. Methylation loss correlated with immunohistochemically staining for TREX2 (p < 0.0001) in laryngeal tumors and improved overall survival of laryngeal cancer patients (p = 0.045). Chromatin immunoprecipitation, demethylation experiments, and reporter gene assays revealed that the region of methylation loss can function as a CCAAT/enhancer binding protein alpha (CEBPA)-responsive enhancer element regulating TREX2 expression. Conclusions: The data highlight a regulatory role of TREX2 DNA methylation for gene expression which might affect incidence and survival of laryngeal cancer. Altered TREX2 protein levels in tumors may affect drug-induced DNA damage repair and provide new tailored therapies

NEUROG3 Is a Critical Downstream Effector for STAT3-Regulated Differentiation of Mammalian Stem and Progenitor Spermatogonia

Spermatogenesis relies on coordinated differentiation of stem and progenitor spermatogonia, and the transcription factor STAT3 is essential for this process in mammals. Here we studied the THY1+ spermatogonial population in mouse testes, which contains spermatogonial stem cells (SSC) and non-stem cell progenitor spermatogonia, to further define the downstream mechanism regulating differentiation. Transcript abundance for the bHLH transcription factor Neurog3 was found to be significantly reduced upon transient inhibition of STAT3 signaling in these cells and exposure to GDNF, a key growth factor regulating self-renewal of SSCs, suppressed activation of STAT3 and in accordance Neurog3 gene expression. Moreover, STAT3 was found to bind the distal Neurog3 promoter/enhancer region in THY1+ spermatogonia and regulate transcription. Transient inhibition of Neurog3 expression in cultures of proliferating THY1+ spermatogonia increased stem cell content after several self-renewal cycles without effecting overall proliferation of the cells, indicating impaired differentiation of SSCs to produce progenitor spermatogonia. Furthermore, cultured THY1+ spermatogonia with induced deficiency of Neurog3 were found to be incapable of differentiation in vivo following transplantation into testes of recipient mice. Collectively, these results establish a mechanism by which activation of STAT3 regulates the expression of NEUROG3 to subsequently drive differentiation of SSC and progenitor spermatogonia in the mammalian germline