Approximate Profile Maximum Likelihood

We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML has appealing theoretical properties, but is difficult to compute exactly. Inspired by observations gleaned from exactly solvable cases, we look for an approximate PML solution, which, intuitively, clumps comparably frequent symbols into one symbol. This amounts to lower-bounding a certain matrix permanent by summing over a subgroup of the symmetric group rather than the whole group during the computation. We extensively experiment with the approximate solution, and find the empirical performance of our approach is competitive and sometimes significantly better than state-of-the-art performance for various estimation problems

Chiral (SO)–N–(SO) Sulfoxide Pincer Complexes of Mg, Rh, and Ir: N–H Activation and Selective Sulfoxide Reduction upon Ligand Coordination

Multigram quantities of the optically pure amino–bis-sulfoxide ligand (<i>S,S</i>)-bis­(4-<i>tert</i>-butyl-2-(<i>p</i>-tolylsulfinyl)­phenyl)­amine ((<i>S,S</i>)-<b>3</b>) are accessible by in situ lithiation of bis­(2-bromo-4-<i>tert</i>-butylphenyl)­amine (<b>1</b>) followed by a nucleophilic displacement reaction with Andersen’s sulfinate <b>2</b>. Deprotonation of (<i>S,S</i>)-<b>3</b> with MgPh₂ yields the magnesium amido–bis-sulfoxide salt (<i>S,S</i>)-<b>4</b> quantitatively. Metathetical exchange of (<i>S,S</i>)-<b>4</b> with [RhCl­(COE)₂]₂ affords the optically pure pseudo-<i>C</i>₂-symmetric Rh­(I)–amido bis-sulfoxide pincer complex <i>mer-</i>(<i>R,R</i>)-[Rh­(bis­(4-(<i>tert</i>-butyl)-2-(<i>p</i>-tolylsulfinyl)­phenyl)­amide)­(COE)] (<i>mer-</i>(<i>R,R</i>)-<b>5</b>). This complex reacts with 3 equiv of HCl to give the facial Rh­(III) complex <i>fac-</i>(<i>S,R,R</i>)-[Rh­(bis­(4-(<i>tert</i>-butyl)-2-(<i>p</i>-tolylsulfinyl)­phenyl)­amine)­Cl₃] (<i>fac-</i>(<i>S,R,R</i>)-<b>6</b>), in which one of the sulfoxide functions has been reduced to the sulfide and in which the resulting sulfoxide–sulfide–amine ligand is facially coordinated. The same complexes <b>5</b> and <b>6</b> form in a 1:2 ratio in a disproportionation reaction when [RhCl­(COE)₂]₂ is treated with 2 equiv of neutral ligand <b>3</b>. N–H activation is directly observed in the reaction of [IrCl­(COE)₂]₂ with <b>3</b>, affording the amido–hydrido–Ir­(III) complex [Ir­(bis­(4-(<i>tert</i>-butyl)-2-(<i>p</i>-tolylsulfinyl)­phenyl)­amide)­(Cl)­(H)­(COE)] (<b>8</b>)

s‑Block Metal Dibenzoazepinate Complexes: Evidence for Mg–Alkene Encapsulation

The dibenzo­[<i>b</i>,<i>f</i>]­azepinate (DBAP) complexes (DBAP)­Li·(THF)₃, (DBAP)₂Mg·(THF)₂, and (DBAP)₂Ca·(THF)₃ could be isolated as highly air-sensitive compounds in yields of 93%, 72%, and 48%, respectively. Crystal structures of these THF adducts reveal monomeric complexes in which the degree of ring puckering depends on the nature of the metal. The most extreme deviation from planarity is found for the most covalent bound metal, Mg, but in all cases no interaction between the metal and the azepine CC bond is observed. The THF-free complex [(DBAP)₂Mg]₂, which could be obtained in 77% yield, crystallizes as an unusual dimer with three bridging and one terminal DBAP ligand. The bridging DBAP ligands are highly bent and span a cavity in which a Mg²⁺ ion is bound through three alkene–Mg interactions with an average Mg···C distance of 2.794(3) Å. Theoretical calculations support these contacts. A combination of AIM and NPA analyses shows polarization of the alkene π-electron density toward the metal (vertical polarization) but also demonstrates a polarization of electron density toward the C atom closest to Mg (horizontal polarization). Such metal–alkene interactions and implicit CC bond polarization are key features in main group metal catalyzed alkene conversions

Developing P‑Stereogenic, Planar–Chiral P‑Alkene Ligands: Monodentate, Bidentate, and Double Agostic Coordination Modes on Ru(II)

10-Phenyl-5<i>H</i>-dibenz­[<i>b</i>,<i>f</i>]­azepine (<b>5</b>) is synthesized by Suzuki cross coupling of the protected bromo alkene <b>4</b> with PhB­(OH)₂. <b>5</b> reacts with PCl₃ to afford the dichlorophosphanyl-azepine <b>6</b> in >90% yield. Alkylation of <b>6</b> with 1 equiv of <i>t</i>-BuMgBr leads, after recrystallization in Et₂O, to the diastereomerically enriched (<i>dr</i> > 98:2) chloride <i>rac</i>-<b>7</b>, which the crystal structure reveals to be the (p<i>S</i>,<i>R</i>_P)/(p<i>R</i>,<i>S</i>_P) pair. The fact that <i>rac</i>-<b>7</b> crystallizes in the Sohncke space group <i>P</i>2₁2₁2₁ opens up the possibility of a mechanical separation of the enantiomers. Methylation of <i>rac</i>-<b>7</b> is perfectly stereoselective with inversion of configuration at the P atom to yield the new ligand <i>rac</i>-<b>8</b> as the (<i>R</i>,<i>R</i>)/(<i>S</i>,<i>S</i>) pair. The corresponding BH₃-protected diastereomer <i>rac</i>-<b>9</b> (i.e., the (<i>R</i>,<i>S</i>)/(<i>S</i>,<i>R</i>) pair), is isolated after flash column chromatography in 73% yield. Compounds <b>5</b>–<b>9</b> are accessible in multigram quantities. X-ray crystal structures of Ru­(II) complexes demonstrate the ambidentate nature of ligand <i>rac</i>-<b>8</b>: Complex <b>10</b> is exclusively P-coordinated, while in complex <b>11</b> two ligands bind Ru through their P donors and stabilize the 14-electron metal center with a double agostic interaction. In complex <b>12</b>, the ligand coordinates in a κ<i>P</i>,η²-alkene bidentate fashion

<i>C</i>₂‑Symmetric (SO)N(SO) Sulfoxide Pincer Complexes of Mg and Pd: Helicity Switch by Ambidentate <i>S</i>/<i>O</i>‑Coordination and Isolation of a Chiral Pd-Sulfenate

Quinine-based (<i>R</i>)-<i>tert</i>-butylsulfinate <b>3</b> reacts with tris-lithiated bis-arylamide <b>2</b> to afford gram-quantities of optically pure (S*O)­N­(S*O) sulfoxide pincer ligand (<i>R</i>,<i>R</i>)-<b>4</b>. Deprotonation of (<i>R</i>,<i>R</i>)-<b>4</b> and <i>p</i>-Tol-substituted analogue (<i>S</i>,<i>S</i>)-<b>5</b> with MgPh₂ and BnK yields respective Mg and K amido-bis-sulfoxides <b>6</b>–<b>9</b>. In Mg complexes <b>6</b> and <b>7</b>, the sulfoxide functions are <i>O</i>-coordinated, thereby imparting a pronounced helicity to the ligand backbone. Transmetalation of <b>6</b> and <b>7</b> with [PdCl₂(NCPh)₂] affords the <i>S</i>,<i>S</i>-coordinated <i>C</i>₂-symmetric and the <i>O</i>,<i>S</i>-coordinated <i>C</i>₁-symmetric chlorido complexes <b>10</b> and <b>11</b>, respectively, and reaction of potassium amides <b>8</b> and <b>9</b> with [PdCl­(CH₃)­(COD)] leads to methyl-palladium pincer complexes <b>12</b> and <b>13</b>, respectively. The crystal structures of <b>6</b>, <b>7</b>, <b>12</b>, and <b>13</b> reveal a chameleonic ligand system with predictable behavior: (<i>R</i>)-configured <b>4</b> induces pronounced λ backbone helicity in the <i>O</i>-coordinated Mg-complex and weaker δ helicity in <i>S</i>-coordinated Pd-complexes, while (<i>S</i>)-configured ligand <b>5</b> mirrors this stereochemistry. <i>S</i>-Coordination induces stronger, <i>C</i>₂-symmetric, steric crowding in the head-on quadrants compared to <i>O</i>-coordination. When (<i>R</i>,<i>R</i>)-<b>4</b> is reacted with 2 equiv of [Pd­(CH₃)₂(tmeda)], crystalline chiral Pd-sulfenate complex <b>16</b> forms by elimination of <i>iso</i>-butene and methane with inversion of configuration at the sulfenate S atom

Additional file 13 of Differential distribution and enrichment of non-coding RNAs in exosomes from normal and Cancer-associated fibroblasts in colorectal cancer

: Multiple alignment of the 42 sncRNAs over represented in CAF-EXO samples. (FASTA 8 kb

Additional file 2: of Differential distribution and enrichment of non-coding RNAs in exosomes from normal and Cancer-associated fibroblasts in colorectal cancer

Absolute and average relative counts of reads mapped to each ncRNAs biotype per sample and fraction. (XLSX 15 kb

Additional file 11: of Differential distribution and enrichment of non-coding RNAs in exosomes from normal and Cancer-associated fibroblasts in colorectal cancer

Table S1. sncRNAs distributed differently in CAF-EXO samples from in NF-EXO ones. Highly significant lncRNAs and sncRNAs (FDR < 1E-04) are highlighted in bold. (DOCX 79 kb

Additional file 3: of Differential distribution and enrichment of non-coding RNAs in exosomes from normal and Cancer-associated fibroblasts in colorectal cancer

Excel document with the two count files used as input to EdgeR for differential expression analysis; one with the counts of reads of all samples mapped on the lncRNA references and another with the read counts of reads mapped on scnRNAs. (XLSX 221 kb

Additional file 8: of Differential distribution and enrichment of non-coding RNAs in exosomes from normal and Cancer-associated fibroblasts in colorectal cancer

Mini web site presenting a dynamic venn diagram showing the relationships between the results cellular or exosomal over represented in the two analyses performed between NF- and CAF- exosomes. Clicking on any intersected number, the web site opens a dialog summarizing the ncRNAs species that correspond to the intersection. (HTML 47 kb