Direct quantitation of peptide-mediated protein transport across a droplet-interface bilayer

We introduce a new method for monitoring and quantitating the transport of materials across a model cell membrane. As a proof-of-concept, the cell-penetrating peptide, Pep-1, was used to carry horseradish peroxidase (HRP) across droplet-interface bilayers (DIBs). Two submicroliter, lipid-encased aqueous droplets form a membrane at the contacting interface, through which enzyme-peptide complexes pass during transport. Following transport, the droplets are separated and the captured enzymes are assayed by a fluorogenic reaction. The DIB method recapitulates the findings of earlier studies involving Pep-1, including the dependence of protein transport on voltage and membrane charge, while also contributing new insights. Specifically, we found that leaflet charge symmetry may play a role in Pep-1-mediated protein translocation. We anticipate that the DIB method may be useful for a variety of transport-based studies.     

\ell -Adic properties of partition functions

Folsom, Kent, and Ono used the theory of modular forms modulo $\ell $ to establish remarkable “self-similarity” properties of the partition function and give an overarching explanation of many partition congruences. We generalize their work to analyze powers $p_r$ of the partition function as well as Andrews’s $spt$ -function. By showing that certain generating functions reside in a small space made up of reductions of modular forms, we set up a general framework for congruences for $p_r$ and $spt$ on arithmetic progressions of the form $\ell ^mn+\delta $ modulo powers of $\ell $ . Our work gives a conceptual explanation of the exceptional congruences of $p_r$ observed by Boylan, as well as striking congruences of $spt$ modulo 5, 7, and 13 recently discovered by Andrews and Garvan.     

Ring-opening of cyclic ethers with carbon–carbon bond formation by Grignard reagents

The ring-opening of cyclic ethers with concomitant C–C bond formation was studied with a number of Grignard reagents. The transformation was performed in a sealed vial by heating to ∼160 °C in an aluminum block or at 180 °C in a microwave oven. Good yields of the product alcohols were obtained with allyl- and benzylmagnesium halides when the ether was tetrahydrofuran or 3,3-dimethyloxetane. Lower yields were obtained with substituted tetrahydrofurans while no ring-opening was observed with tetrahydropyran. Only highly reactive allyl and benzyl Grignard reagents participated in the transformation while no reaction occurred with other alkylmagnesium halides.     

Atomic force microscopy studies of DNA-wrapped carbon nanotube structure and binding to quantum dots

Single-stranded DNA is an effective noncovalent dispersant for individual single-walled carbon nanotubes (CNTs) in aqueous solution, forming a CNT-DNA hybrid material that has advantages for CNT separations and applications. Atomic force microscopy (AFM) reveals a regular pattern on the surface of CNT-DNA. We found this pattern to be independent of the length and sequence of the wrapping DNA, yet different from the structures observed for CNTs dispersed with sodium dodecyl sulfate in the absence of DNA. We wrapped CNTs with thiol-modified DNA to form stable conjugates of CNT-DNA and core/shell CdSe/ZnS quantum dots; AFM imaging of these conjugates identified for the first time the location of DNA on the CNT-DNA nanomaterial. Our results suggest that the AFM pattern of CNT-DNA is formed by helical turns (approximately 14-nm pitch) of wrapped DNA strands that are closely arranged end-to-end in a single layer along the CNT. This work demonstrates the useful functionalization of CNTs with quantum dots in a manner that avoids direct, destructive modification of the CNT surface and suggests nearly complete surface coverage of the nanotubes with DNA.     

Mod 4 Galois representations and elliptic curves

Galois representations with cyclotomic determinant all arise from the -torsion of elliptic curves for . For , we show the existence of more than a million such representations which are surjective and do not arise from any elliptic curve.

     

Resistive-pulse detection of multilamellar liposomes

The resistive-pulse method was used to monitor the pressure-driven translocation of multilamellar liposomes with radii between 190 and 450 nm through a single conical nanopore embedded in a glass membrane. Liposomes (0% and 5% 1,2-dioleoyl-sn-glycero-3-phospho-l-serine (sodium salt) in 1,2-dilauroyl-sn-glycero-3-phosphocholine or 0%, 5%, and 9% 1,2-dipalmitoyl-sn-glycero-3-phospho(1'-rac-glycerol) (sodium salt) in 1,2-dipalmitoyl-sn-glycero-3-phosphocholine) were prepared by extrusion through a polycarbonate membrane. Liposome translocation through a glass nanopore was studied as a function of nanopore size and the temperature relative to the lipid bilayer transition temperature, T(c). All translocation events through pores larger than the liposome, regardless of temperature, show translocation times between 30 and 300 μs and current pulse heights between 0.2% and 15% from the open pore baseline. However, liposomes at temperatures below the T(c) were captured at the pore orifice when translocation was attempted through pores of smaller dimensions, but squeezed through the same pores when the temperature was raised above T(c). The results provide insights into the deformation and translocation of individual liposomes through a porous material.     

Some heuristics and results for small cycles of the discrete logarithm

Brizolis asked the question: does every prime have a pair such that is a fixed point for the discrete logarithm with base ? The first author previously extended this question to ask about not only fixed points but also two-cycles, and gave heuristics (building on work of Zhang, Cobeli, Zaharescu, Campbell, and Pomerance) for estimating the number of such pairs given certain conditions on and . In this paper we extend these heuristics and prove results for some of them, building again on the aforementioned work. We also make some new conjectures and prove some average versions of the results.

     

Governance implications of nanomaterials companies’ inconsistent risk perceptions and safety practices

Current research on the nanotechnology industry indicates its downstream expansion at a rapid pace, while toxicological research and best practices for environmental health and safety are still being developed. Companies that use and/or produce engineered nanomaterials (ENMs) have enormous potential to influence safe-handling practices for ENMs across the product life cycle. Knowledge of both industry practices and leaders’ perceptions of risk is vital for understanding how companies will act to control potential environmental and health risks. This article reports results from a new international survey of nanomaterials companies in 14 countries. In this survey, company participants reported relatively high levels of uncertainty and/or perceived risk with regard to ENMs. However, these perspectives were not accompanied by expected risk-avoidant practices or preferences for regulatory oversight. A majority of companies indicated “lack of information” as a significant impediment to implementing nano-specific safety practices, but they also reported practices that were inconsistent with widely available guidance. Additionally, in the absence of safe-handling regulations, companies reported nano-specific health and safety programs that were narrow in scope. Taken together, these findings indicate that health and safety guidance is not reaching industry. While industry leaders’ reluctance toward regulation might be expected, their own reported unsafe practices and recognition of possible risks suggest a more top-down approach from regulators is needed to protect workers and the environment.