Simultaneous detection of 19 K‐ras mutations by free‐solution conjugate electrophoresis of ligase detection reaction products on glass microchips

We demonstrate here the power and flexibility of free‐solution conjugate electrophoresis (FSCE) as a method of separating DNA fragments by electrophoresis with no sieving polymer network. Previous work introduced the coupling of FSCE with ligase detection reaction (LDR) to detect point mutations, even at low abundance compared to the wild‐type DNA. Here, four large drag‐tags are used to achieve free‐solution electrophoretic separation of 19 LDR products ranging in size from 42 to 66 nt that correspond to mutations in the K‐ras oncogene. LDR‐FSCE enabled electrophoretic resolution of these 19 LDR‐FSCE products by CE in 13.5 min (E = 310 V/cm) and by microchip electrophoresis in 140 s (E = 350 V/cm). The power of FSCE is demonstrated in the unique characteristic of free‐solution separations where the separation resolution is constant no matter the electric field strength. By microchip electrophoresis, the electric field was increased to the maximum of the power supply (E = 700 V/cm), and the 19 LDR‐FSCE products were separated in less than 70 s with almost identical resolution to the separation at E = 350 V/cm. These results will aid the goal of screening K‐ras mutations on integrated “sample‐in/answer‐out” devices with amplification, LDR, and detection all on one platform.     

Homogenization in L

Homogenization of deterministic control problems with L^∞ running cost is studied by viscosity solutions techniques. It is proved that the value function of an L^∞ problem in a medium with a periodic micro-structure converges uniformly on the compact sets to the value function of the homogenized problem as the period shrinks to 0. Our main convergence result extends that of Ishii (Stochastic Analysis, control, optimization and applications, pp. 305-324, Birkhäuser Boston, Boston, MA, 1999.) to the case of a discontinuous Hamiltonian. The cell problem is solved, but, as non-uniqueness occurs, the effective Hamiltonian must be selected in a careful way. The paper also provides a representation formula for the effective Hamiltonian and gives illustrations to calculus of variations, averaging and one-dimensional problems.     

Poly-N-hydroxyethylacrylamide (polyDuramide): a novel,hydrophilic, self-coating polymer matrix for DNA sequencing by capillary electrophoresis

A replaceable polymer matrix, based on the novel monomer N-hydroxyethylacrylamide (HEA), has been synthesized for application in DNA separation by microchannel electrophoresis. The monomer was found by micellar electrokinetic chromatography analysis of monomer partitioning between water and 1-octanol to be more hydrophilic than acrylamide and N,N-dimethylacrylamide. Polymers were synthesized by free radical polymerization in aqueous solution. The weight-average molar mass of purified polymer was characterized by tandem gel permeation chromatography-multiangle laser light scattering. The steady-shear rheological behavior of the novel DNA sequencing matrix was also characterized, and it was found that the viscosity of the novel matrix decreases by more than 2 orders of magnitude as the shear rate is increased from 0.1 to 1000 s(-1). Moreover, in the shear-thinning region, the rate of change of matrix viscosity with shear rate increases with increasing polymer concentration. Poly-N-hydroxyethylacrylamide (PHEA) exhibits good capillary-coating ability, via adsorption from aqueous solution, efficiently suppressing electroosmotic flow (EOF) in a manner comparable to that of poly-N,N-dimethylacrylamide. Under DNA sequencing conditions, adsorptive PHEA coatings proved to be stable and to maintain negligible EOF for over 600 h of electrophoresis. Resolution of DNA sequencing fragments, particularly fragments > 500 bases, in PHEA matrices generally improves with increasing polymer concentration and decreasing electric field strength. When PHEA is used both as a separation matrix and as a dynamic coating in bare silica capillaries, the matrix can resolve over 620 bases of contiguous DNA sequence within 3 h. These results demonstrate the good potential of PHEA matrices for high-throughput DNA analysis by microchannel electrophoresis.     

Semicontinuous solutions for Hamilton-Jacobi equations and theL ∞control problem

We prove uniqueness for extended real-valued lower semicontinuous viscosity solutions of the Bellman equation forL -control problems. This result is then used to prove uniqueness for lsc solutions of Hamilton-Jacobi equations of the form –u _t +H(t, x, u, –Du)=0, whereH(t, x, r, p) is convex inp. The remaining assumptions onH in the variablesr andp extend the currently known results.Supported in part by Grant DMS-9300805 from the National Science Foundation.     

Capacity and entry issues in online exchanges

With the advent of open standards and Internet technologies, the number of sellers who can participate in online exchanges is greatly increased. We model the competition between identical sellers vying for the same business, and find that there exists a mixed-strategy equilibrium in prices. The results help us understand the dynamics between a seller’s capacity and his motivation to participate in an auction.     

A new approach to the solution of the Navier-Stokes equations

In the present paper a numerical algorithm is given for solving a standard problem in fluid dynamics, that of inviscid, irrotational, incompressible flow over an arbitrary symmetric profile. The purpose of the paper is to propose an alternative approach to solve certain fluid dynamic flows. This paper may be thought of as the first of a possible series of papers solving new and fundamental problems. In a sense, this new approach asks the question: what is the simplest and most efficient method of solving the problem considered by finite difference methods. It is believed that the following algorithm answers this question. Standard second-order finite difference techniques, such as SLOR and ADI, are used to solve numerically a mixed boundary value problem comprised of a pair of elliptic partial differential equations with constant coefficients.