Quantitative and sensitive detection of rare mutations using droplet-based microfluidics

Somatic mutations within tumoral DNA can be used as highly specific biomarkers to distinguish cancer cells from their normal counterparts. These DNA biomarkers are potentially useful for the diagnosis, prognosis, treatment and follow-up of patients. In order to have the required sensitivity and specificity to detect rare tumoral DNA in stool, blood, lymph and other patient samples, a simple, sensitive and quantitative procedure to measure the ratio of mutant to wild-type genes is required. However, techniques such as dual probe TaqMan(?) assays and pyrosequencing, while quantitative, cannot detect less than ～1% mutant genes in a background of non-mutated DNA from normal cells. Here we describe a procedure allowing the highly sensitive detection of mutated DNA in a quantitative manner within complex mixtures of DNA. The method is based on using a droplet-based microfluidic system to perform digital PCR in millions of picolitre droplets. Genomic DNA (gDNA) is compartmentalized in droplets at a concentration of less than one genome equivalent per droplet together with two TaqMan(?) probes, one specific for the mutant and the other for the wild-type DNA, which generate green and red fluorescent signals, respectively. After thermocycling, the ratio of mutant to wild-type genes is determined by counting the ratio of green to red droplets. We demonstrate the accurate and sensitive quantification of mutated KRAS oncogene in gDNA. The technique enabled the determination of mutant allelic specific imbalance (MASI) in several cancer cell-lines and the precise quantification of a mutated KRAS gene in the presence of a 200,000-fold excess of unmutated KRAS genes. The sensitivity is only limited by the number of droplets analyzed. Furthermore, by one-to-one fusion of drops containing gDNA with any one of seven different types of droplets, each containing a TaqMan(?) probe specific for a different KRAS mutation, or wild-type KRAS, and an optical code, it was possible to screen the six common mutations in KRAS codon 12 in parallel in a single experiment.     

Mixing enhancement in a multi-stream injection nozzle

We present quantitative analysis of image sequences of multi-stream injection nozzle flows with several different injection geometries in an experiment simulating mixing in a chemical oxygen-iodine laser. To visualize mixing, image sequences were acquired with planar laser-induced fluorescence (PLIF) in iodine that was injected into the main flow. The injection nozzle consisted of a slot, ejector, and injector block, with rows of ejector and injector holes along the slot length. The ejector flow exits in an underexpanded state so that upon expanding it forces the slot and injector flows together to enhance mixing. For this study, the diameter and geometry of ejector holes were varied to assess their effect on mixing. Two configurations of ejector holes were used, each with two different diameters for a total of four cases with data collected at downstream stations. We carry out a quantitative mixing analysis for these configurations, using two methods to quantify the mixing. The first method considers the statistics of the PLIF image intensity histograms, which are bimodal for poorly-mixed flows and have a single peak in well-mixed flows. The second method quantifies the properties of the mixing interface. Our analysis shows that two injection schemes significantly enhance mixing by stretching the mixing interface.     

The first Steklov eigenvalue, conformal geometry, and minimal surfaces

We consider the relationship of the geometry of compact Riemannian manifolds with boundary to the first nonzero eigenvalue σ₁ of the Dirichlet-to-Neumann map (Steklov eigenvalue). For surfaces Σ with genus γ and k boundary components we obtain the upper bound σ₁L(∂Σ)?2(γ+k)π. For γ=0 and k=1 this result was obtained by Weinstock in 1954, and is sharp. We attempt to find the best constant in this inequality for annular surfaces (γ=0 and k=2). For rotationally symmetric metrics we show that the best constant is achieved by the induced metric on the portion of the catenoid centered at the origin which meets a sphere orthogonally and hence is a solution of the free boundary problem for the area functional in the ball. For a general class of (not necessarily rotationally symmetric) metrics on the annulus, which we call supercritical, we prove that σ₁(Σ)L(∂Σ) is dominated by that of the critical catenoid with equality if and only if the annulus is conformally equivalent to the critical catenoid by a conformal transformation which is an isometry on the boundary. Motivated by the annulus case, we show that a proper submanifold of the ball is immersed by Steklov eigenfunctions if and only if it is a free boundary solution. We then prove general upper bounds for conformal metrics on manifolds of any dimension which can be properly conformally immersed into the unit ball in terms of certain conformal volume quantities. We show that these bounds are only achieved when the manifold is minimally immersed by first Steklov eigenfunctions. We also use these ideas to show that any free boundary solution in two dimensions has area at least π, and we observe that this implies the sharp isoperimetric inequality for free boundary solutions in the two-dimensional case.     

Photochemistry in ordered physisorbed monolayers of dinitrogen tetroxide

The effects of physisorption and two-dimensional ordering on the photochemistry of N₂O₄ were investigated. Ordered monolayers were prepared by adsorption of NO₂ at 100 K on a water-ice surface. Irradiation with a continuous light source in the wavelength region 300–400 nm or with pulsed laser radiation at 355 nm resulted in exclusive desorption of NO₂. This desorption was induced by electronic absorption directly in the adsorbate via a transition corresponding to the ( )¹B_2u←( )¹A_g transition in N₂O₄, as in the gas phase. However, the subsequent dynamics in the excited state were markedly different from the gas-phase counterpart. Time-of-flight mass spectrometry of NO₂ photodesorbed at 355 nm revealed a most probable fragment translational energy of ca. 17 meV; and the angular distribution of the nascent NO₂ was peaked sharply in a direction around 10° from the normal. It is apparent that, despite the weak interaction with the substrate, significant energy transfer occurs in the ordered physisorbed monolayer to yield nascent NO₂ with very low translational energy and a constrained angle of escape which is consistent with a high degree of adsorbate order and alignment.     

Electrochemical reduction of pyrethroid insecticides based on esters of α-cyano-3-phenoxybenzyl alcohol at glassy carbon and mercury electrodes in acetonitrile

The electrochemical reduction of eight commercially important pyrethroid insecticides which are esters of either α-cyano-3-phenoxybenzyl alcohol (cycloprothrin, cyphenothrin, cyhalothrin, deltamethrin, esfenvalerate and cypermethrin) or 4-fluro-α-cyano-3-phenoxybenzyl alcohol (cyfluthrin and flumethrin) has been studied under conditions of voltammetry and bulk electrolysis at both glassy carbon and mercury electrodes in acetonitrile. In general, the peak potential of the initial reduction process observed at very negative potentials at both electrode surfaces shifts to a more positive value under conditions of consecutive potential cycling. At the hanging mercury drop electrode the reduction occurs at even more negative potentials than at a glassy carbon electrode because a blocking mechanism appears to be operative. Despite this major difference in the primary reduction step, common voltammetric features are observed at less negative potentials on second and subsequent cycles of the electrode potential at either electrode surface. For example, the initial reduction process always results in the formation of a species which is reversibly reduced at less negative applied potentials. Furthermore, despite the definition of the voltammetric response being highly sensitive to the individual pyrethroid structure, long time-scale bulk electrolysis experiments at glassy carbon or mercury pool electrodes led to the formation of analogous final products. The fact that pyrethroids with a widely varying range of acid moieties exhibit similar voltammetric behaviour suggests that the acid moiety is not directly involved in the initial electron transfer process. Controlled potential electrolysis studies at both electrode surfaces coupled with HPLC and mass spectral identification of products obtained after ethylation with ethyl iodide showed that the reduction mechanism on the longer time-scale involves cleavage of the ester with liberation of free cyanide ion. The major reduction product identified was the anion of either 3-phenoxybenzoic acid or 4-fluoro-3-phenoxybenzoic acid in yields ranging from 31 to 66%.