Toposes for semigroups: an invitation

This is an expository paper in which we explain the basic ideas of topos theory in connection with semigroup theory. We focus mainly on the classifying topos of an inverse semigroup or pseudogroup, and to some extent on creating a dictionary between the language of semigroups and topos theory. We begin with the algebraic theory having to do with inverse semigroups, and then turn to an analysis of pseudogroups using sheaf theory. Our work includes some new material on wide semigroup homomorphisms and their geometric morphisms.

     

Bottom-up design and synthesis of limit size lipid nanoparticle systems with aqueous and triglyceride cores using millisecond microfluidic mixing

Limit size systems are defined as the smallest achievable aggregates compatible with the packing of the molecular constituents in a defined and energetically stable structure. Here we report the use of rapid microfluidic mixing for the controlled synthesis of two types of limit size lipid nanoparticle (LNP) systems, having either polar or nonpolar cores. Specifically, limit size LNP consisting of 1-palmitoyl, 2-oleoyl phosphatidylcholine (POPC), cholesterol and the triglyceride triolein were synthesized by mixing a stream of ethanol containing dissolved lipid with an aqueous stream, employing a staggered herringbone micromixer. Millisecond mixing of aqueous and ethanol streams at high flow rate ratios (FRR) was used to rapidly increase the polarity of the medium, driving bottom-up synthesis of limit size LNP systems by spontaneous assembly. For POPC/triolein systems the limit size structures consisted of a hydrophobic core of triolein surrounded by a monolayer of POPC where the diameter could be rationally engineered over the range 20-80 nm by varying the POPC/triolein ratio. In the case of POPC and POPC/cholesterol (55/45; mol/mol) the limit size systems achieved were bilayer vesicles of approximately 20 and 40 nm diameter, respectively. We further show that doxorubicin, a representative weak base drug, can be efficiently loaded and retained in limit size POPC LNP, establishing potential utility as drug delivery systems. To our knowledge this is the first report of stable triglyceride emulsions in the 20-50 nm size range, and the first time vesicular systems in the 20-50 nm size range have been generated by a scalable manufacturing method. These results establish microfluidic mixing as a powerful and general approach to access novel LNP systems, with both polar or nonpolar core structures, in the sub-100 nm size range.     

Copper-catalyzed asymmetric ring opening of oxabicyclic alkenes with organolithium reagents

A highly efficient method is reported for the asymmetric ring opening of oxabicyclic alkenes with organolithium reagents. Using a copper/chiral phosphoramidite complex together with a Lewis acid (BF(3)·OEt(2)), full selectivity for the anti isomer and excellent enantioselectivities were obtained for the ring opened products.     

Effect of surface roughness and softness on water capillary adhesion in apolar media

The roughness and softness of interacting surfaces are both important parameters affecting the capillary condensation of water in apolar media, yet are poorly understood at present. We studied the water capillary adhesion between a cellulose surface and a silica colloidal probe in hexane by AFM force measurements. Nanomechanical measurements show that the Young's modulus of the cellulose layer in water is significantly less (~7 MPa) than in hexane (~7 GPa). In addition, the cellulose surface in both water and hexane is rather rough (6-10 nm) and the silica probe has a comparable roughness. The adhesion force between cellulose and silica in water-saturated hexane shows a time-dependent increase up to a waiting time of 200 s and is much (2 orders of magnitude) lower than that expected for a capillary bridge spanning the whole silica probe surface. This suggests the formation of one or more smaller bridges between asperities on both surfaces, which is confirmed by a theoretical analysis. The overall growth rate of the condensate cannot be explained from diffusion mediated capillary condensation alone; thin film flow due to the presence of a wetting layer of water at both the surfaces seems to be the dominant contribution. The logarithmic time dependence of the force can also be explained from the model of the formation of multiple capillary bridges with a distribution of activation times. Finally, the force-distance curves upon retraction show oscillations. Capillary condensation between an atomically smooth mica surface and the silica particle show less significant oscillations and the adhesion force is independent of waiting time. The oscillations in the force-distance curves between cellulose and silica may stem from multiple bridge formation between the asperities present on both surfaces. The softness of the cellulose surface can bring in additional complexities during retraction of the silica particle, also resulting in oscillations in the force-distance curves.     

Fully automated sequential solid phase approach towards viral RNA-nucleopeptides

The synthesis of two ribonucleoprotein fragments of unprecedented complexity is reported. These hybrid biomolecules are prepared combining the use of an automated solid phase peptide and oligonucleotide synthesizer on a single solid support.     

Dual template synthesis of a highly mesoporous SSZ-13 zeolite with improved stability in the methanol-to-olefins reaction

The dual template synthesis of zeolite SSZ-13 by use of trimethyl-adamantanammonium hydroxide and a diquaternary-ammonium mesoporogen induces considerable mesoporosity without impeding zeolite microporosity. The strongly improved accessibility of Br?nsted sites in mesoporous SSZ-13 increases its stability during application as an acid catalyst in the methanol-to-olefins reaction.     

From NMP to RAFT and Thiol‐Ene Chemistry by In Situ Functionalization of Nitroxide Chain Ends

A straightforward, novel strategy based on the in situ functionalization of polymers prepared by nitroxide‐mediated polymerization (NMP), for the use as an extension toward block copolymers and post‐polymerization modifications, has been investigated. The nitroxide end group is exchanged for a thiocarbonylthio end group by a rapid transfer reaction with bis(thiobenzoyl) disulfide to generate in situ reversible addition–fragmentation chain transfer (RAFT) macroinitiators. Moreover, not only have these macroinitiators been used in chain extension and block copolymerization experiments by the RAFT process but also a thiol‐terminated polymer is synthesized by aminolysis of the RAFT end group and subsequently reacted with dodecyl vinyl ether by thiol‐ene chemistry.     

Single‐Walled Carbon Nanotubes as Scaffolds to Concentrate DNA for the Study of DNA–Protein Interactions

Genomic DNA in bacteria exists in a condensed state, which exhibits different biochemical and biophysical properties from a dilute solution. DNA was concentrated on streptavidin‐covered single‐walled carbon nanotubes (Strep ? SWNTs) through biotin–streptavidin interactions. We reasoned that confining DNA within a defined space through mechanical constraints, rather than by manipulating buffer conditions, would more closely resemble physiological conditions. By ensuring a high streptavidin loading on SWNTs of about 1 streptavidin tetramer per 4 nm of SWNT, we were able to achieve dense DNA binding. DNA is bound to Strep ? SWNTs at a tunable density and up to as high as 0.5 mg mL^?1 in solution and 29 mg mL^?1 on a 2D surface. This platform allows us to observe the aggregation behavior of DNA at high concentrations and the counteracting effects of HU protein (a histone‐like protein from Escherichia coli strain U93) on the DNA aggregates. This provides an in vitro model for studying DNA–DNA and DNA–protein interactions at a high DNA concentration.     

(35/37)Cl and (16/18)O isotope resolved (195)Pt NMR: unique spectroscopic 'fingerprints' for unambiguous speciation of [PtCl(n)(H(2)O)(6-n)](4-n) (n = 2-5) complexes in an acidic aqueous solution

At high magnetic fields the 128.8 MHz (195)Pt NMR of all the species in the series [PtCl(n)(H(2)O)(6-n)](4-n) (n = 2-6) display unique (35/37)Cl isotope effects resulting in a unique 'fine-structure' of each individual resonance, which constitutes an unambiguous spectroscopic 'fingerprint' characteristic of the structure of the octahedral platinum(iv) complex, provided (195)Pt NMR are recorded at optimum magnetic field homogeneity and carefully controlled temperature (293 ± 0.1 K). The detailed (195)Pt resonance fine-structure observed experimentally can readily be accounted for by an isotopologue and isotopomer model for each complex, showing particularly noticeable differences between stereoisomer pairs such as the cis/trans- and fac/mer-complexes. Moreover partial isotopic (18)O enrichment of the coordinated water molecules in the series [Pt(35/37)Cl(n)(H(2)(16/18)O)(6-n)](n-2) (n = 2-6) confirms this model. This technique can thus be considered a novel, direct spectroscopic method of chemical speciation of appropriate platinum(iv) complexes in solution without reference to accurate chemical shifts of authentic members of such a series. These effects are interpreted qualitatively in terms of the high sensitivity of (195)Pt NMR shielding to very small and subtle Pt-(35/37)Cl and Pt-(16/18)OH(2) bond displacements. Preliminary work shows this also applied to the corresponding bromido-complexes.