Towards the stable chelation of radium for biomedical applications with an 18-membered macrocyclic ligand

Targeted alpha therapy is an emerging strategy for the treatment of disseminated cancer. [²²³Ra]RaCl₂ is the only clinically approved alpha particle-emitting drug, and it is used to treat castrate-resistant prostate cancer bone metastases, to which [²²³Ra]Ra²⁺ localizes. To specifically direct [²²³Ra]Ra²⁺ to non-osseous disease sites, chelation and conjugation to a cancer-targeting moiety is necessary. Although previous efforts to stably chelate [²²³Ra]Ra²⁺ for this purpose have had limited success, here we report a biologically stable radiocomplex with the 18-membered macrocyclic chelator macropa. Quantitative labeling of macropa with [²²³Ra]Ra²⁺ was accomplished within 5 min at room temperature with a radiolabeling efficiency of >95%, representing a significant advancement over conventional chelators such as DOTA and EDTA, which were unable to completely complex [²²³Ra]Ra²⁺ under these conditions. [²²³Ra][Ra(macropa)] was highly stable in human serum and exhibited dramatically reduced bone and spleen uptake in mice in comparison to bone-targeted [²²³Ra]RaCl₂, signifying that [²²³Ra][Ra(macropa)] remains intact in vivo. Upon conjugation of macropa to a single amino acid β-alanine as well as to the prostate-specific membrane antigen-targeting peptide DUPA, both constructs retained high affinity for ²²³Ra, complexing >95% of Ra²⁺ in solution. Furthermore, [²²³Ra][Ra(macropa-β-alanine)] was rapidly cleared from mice and showed low ²²³Ra bone absorption, indicating that this conjugate is stable under biological conditions. Unexpectedly, this stability was lost upon conjugation of macropa to DUPA, which suggests a role of targeting vectors in complex stability in vivo for this system. Nonetheless, our successful demonstration of efficient radiolabeling of the β-alanine conjugate with ²²³Ra and its subsequent stability in vivo establishes for the first time the possibility of delivering [²²³Ra]Ra²⁺ to metastases outside of the bone using functionalized chelators, marking a significant expansion of the therapeutic utility of this radiometal in the clinic.

The therapeutic alpha-emitter ²²³Ra can be stably complexed in vivo, creating opportunities for the development of targeted radiopharmaceutical agents with this radionuclide.     

Topological sweep of the complete graph

We present a novel, simple and easily implementable algorithm to report all intersections in an embedding of a complete graph. For graphs with N vertices and complexity K measured as the number of segments of the embedding, the running time of the algorithm is Θ(K+NM), where M is the maximum number of edges cut by any vertical line. Our algorithm handles degeneracies, such as vertical edges or multiply intersecting edges, without requiring numerical perturbations to achieve general position.The algorithm is based on the sweep line technique, one of the most fundamental techniques in computational geometry, where an imaginary line passes through a given set of geometric objects, usually from left to right. The algorithm sweeps the graph using a topological line, borrowing the concept of horizon trees from the topological sweep method [H. Edelsbrunner, L.J. Guibas, Topologically sweeping an arrangement, J. Comput. Syst. Sci. 38 (1989) 165-194; J. Comput. Syst. Sci. 42 (1991) 249-251 (corrigendum)].The novelty in our approach is to control the topological line through the use of the moving wall that separates at any time the graph into two regions: the region of known structure, in front of the moving wall, and the region that may contain intersections generated by edges-that have not yet been registered in the sweep process-behind the wall.Our method has applications to graph drawing and for depth-based statistical analysis, for computing the simplicial depth median for a set of N data points [G. Aloupis, S. Langerman, M. Soss, G. Toussaint, Algorithms for bivariate medians and a Fermat-Torricelli problem for lines, Comp. Geom. Theory Appl. 26 (1) (2003) 69-79].We present the algorithm, its analysis, experimental results and extension of the method to general graphs.     

Reactivity of bis(2,2,5,5-tetramethyl-2,5-disila-1-azacyclopent-1-yl)tin with CO(2), OCS, and CS(2) and comparison to that of bis[bis(trimethylsilyl)amido]tin

The heterocumulenes carbon dioxide (CO(2)), carbonyl sulfide (OCS), and carbon disulfide (CS(2)) were treated with bis(2,2,5,5-tetramethyl-2,5-disila-1-azacyclopent-1-yl)tin {[(CH(2))Me(2)Si](2)N}(2)Sn, an analogue of the well-studied bis[bis(trimethylsilyl)amido]tin species [(Me(3)Si)(2)N](2)Sn, to yield an unexpectedly diverse product slate. Reaction of {[(CH(2))Me(2)Si](2)N}(2)Sn with CO(2) resulted in the formation of 2,2,5,5-tetramethyl-2,5-disila-1-oxacyclopentane, along with Sn(4)(μ(4)-O){μ(2)-O(2)CN[SiMe(2)(CH(2))(2)]}(4)(μ(2)-N═C═O)(2) as the primary organometallic Sn-containing product. The reaction of {[(CH(2))Me(2)Si](2)N}(2)Sn with CS(2) led to formal reduction of CS(2) to [CS(2)](2-), yielding [{[(CH(2))Me(2)Si](2)N}(2)Sn](2)CS(2){[(CH(2))Me(2)Si](2)N}(2)Sn, in which the [CS(2)](2-) is coordinated through C and S to two tin centers. The product [{[(CH(2))Me(2)Si](2)N}(2)Sn](2)CS(2){[(CH(2))Me(2)Si](2)N}(2)Sn also contains a novel 4-membered Sn-Sn-C-S ring, and exhibits a further bonding interaction through sulfur to a third Sn atom. Reaction of OCS with {[(CH(2))Me(2)Si](2)N}(2)Sn resulted in an insoluble polymeric material. In a comparison reaction, [(Me(3)Si)(2)N](2)Sn was treated with OCS to yield Sn(4)(μ(4)-O)(μ(2)-OSiMe(3))(5)(η(1)-N═C═S). A combination of NMR and IR spectroscopy, mass spectrometry, and single crystal X-ray diffraction were used to characterize the products of each reaction. The oxygen atoms in the final products come from the facile cleavage of either CO(2) or OCS, depending on the reacting carbon dichalogenide.     

Synthesis of azepino[3,4b]indoles via the Plancher rearrangement

The reaction of benzyl 3-formylpiperidine-1-carboxylate and aryl hydrazines under standard Fisher Indole conditions followed by reductive work-up affords azepino[3,4b]indoles in moderate to good yields. The products are proposed to be derived via a Plancher rearrangement [(a) Plancher, G. Gazz. Chim. Ital. 1898, 28, II, 374; (b) Plancher, G. Atti. Accad.Lincei1900, 9, 5, 115; (c) Boyd-Barrett, H. S. J. Chem. Soc.1932, 321].     

Co-ordinating Two Searchers for an Object Hidden on an Interval

Two unit-speed searchers starting at 0 seek a stationary target hidden according to a known bounded symmetric distribution. The objective is to minimize the expected time for the searchers to return to 0 after one of them has found the target. We find a general optimality condition and use it to solve the problem when the target has a uniform, triangular, or truncated, exponential distribution. The problem has applications to parallel processing and to the optimal choice of drilling depths in the search for an underground mineral.     

Home to School: Numeracy Practices and Mathematical Identities

Drawing on a perspective of mathematics as situated social practice, we focus on 4 children in an urban preschool classroom and follow those children between home and school sites to shed light on urban children's persistent underachievement in mathematics. In this article, we describe the ways in which numeracy practices travel with children between home and school and, within those contexts, shape complex and sometimes limited social identities for children. We found that school imperatives, such as assessments and socialization curricula, often obscure teachers' views of children's mathematical practices. Deficit assumptions about family and community support for children, and limited interaction between caregivers and teachers, further contribute to the tendency of school personnel to overlook the mathematical practices that children bring with them to school. We further suggest that vignettes drawn from ethnographic-type research such as this have potential for professional development for classroom teachers.