A microfluidic processor for gene expression profiling of single human embryonic stem cells

The gene expression of human embryonic stem cells (hESC) is a critical aspect for understanding the normal and pathological development of human cells and tissues. Current bulk gene expression assays rely on RNA extracted from cell and tissue samples with various degree of cellular heterogeneity. These 'cell population averaging' data are difficult to interpret, especially for the purpose of understanding the regulatory relationship of genes in the earliest phases of development and differentiation of individual cells. Here, we report a microfluidic approach that can extract total mRNA from individual single-cells and synthesize cDNA on the same device with high mRNA-to-cDNA efficiency. This feature makes large-scale single-cell gene expression profiling possible. Using this microfluidic device, we measured the absolute numbers of mRNA molecules of three genes (B2M, Nodal and Fzd4) in a single hESC. Our results indicate that gene expression data measured from cDNA of a cell population is not a good representation of the expression levels in individual single cells. Within the G0/G1 phase pluripotent hESC population, some individual cells did not express all of the 3 interrogated genes in detectable levels. Consequently, the relative expression levels, which are broadly used in gene expression studies, are very different between measurements from population cDNA and single-cell cDNA. The results underscore the importance of discrete single-cell analysis, and the advantages of a microfluidic approach in stem cell gene expression studies.     

Direct measurement of fine structure changing collisional losses in cold trapped 85Rb

Using a technique that consists in ionizing atoms out of the 5P _1/2 fragments originated in the cold collision process, we have measured the contribution of the fine structure changing collision (FS) to the total trap loss rate of cold ⁸⁵Rb. Our results show that FS contribution is responsible for about 4% of the total trap loss. This result should stimulate new theoretical discussions involving exoergic cold collisions. Received 26 October 1998 and Received in final form 2 February 1999     

Numerical experiments with parallel two‐step W‐methods for DAEs

We study the numerical behavior of parallel two‐step W‐methods (PTSW methods) applied to index 2 and index 3 DAE test‐problems. In this experiments we do not observe an order reduction in the differential components of the solution and we obtain the same orders as in the ODE and index 1 case. Our methods perform comparably with RADAU for the test‐problems in sequential computations and superior in parallel mode. We conclude that PTSW methods are an interesting choice for solving DAEs, at least up to index 2.     

Equilibrium attractivity of Krylov-W-methods for nonlinear stiff ODEs

Since implicit integration schemes for differential equations which use Krylov methods for the approximate solution of linear systems depend nonlinearly on the actual solution a classical stability analysis is difficult to perform. A different, weaker property of autonomous dissipative systemsy′=f(y) is that the norm ‖f(y(t))‖ decreases for any solutiony(t). This property can also be analysed for W-methods using a Krylov-Arnoldi approximation. We discuss different additional assumptions onf and conditions on the Arnoldi process that imply this kind of attractivity to equilibrium points for the numerical solution. One assumption is general enough to cover quasilinear parabolic problems. This work was supported by Deutsche Forschungsgemeinschaft.     

Conformal Covariance and Positivity of Energy in Charged Sectors

It has been recently noted that diffeomorphism covariance of a Chiral Conformal QFT in the vacuum sector automatically ensures Möbius covariance in all charged sectors. In this article it is shown that diffeomorphism covariance and positivity of the energy in the vacuum sector even ensure the positivity of energy in the charged sectors.The main observation of this paper is that the positivity of energy — at least in case of a Chiral Conformal QFT — is a local concept: it is related to the fact that the energy density, when smeared with some local nonnegative test functions, remains bounded from below (with the bound depending on the test function).The presented proof relies in an essential way on recently developed methods concerning the smearing of the stress-energy tensor with nonsmooth functions.     

Partitioned adaptive Runge-Kutta methods for the solution of nonstiff and stiff systems

Summary For the numerical solution of initial value problems of ordinary differential equations partitioned adaptive Runge-Kutta methods are studied. These methods consist of an adaptive Runge-Kutta methods for the treatment of a stiff system and a corresponding explicit Runge-Kutta method for a nonstiff system. First we modify the theory of Butcher series for partitioned adaptive Runge-Kutta methods. We show that for any explicit Runge-Kutta method there exists a translation invariant partitoned adaptive Runge-Kutta method of the same order. Secondly we derive a special translaton invariant partitioned adaptive Runge-Kutta method of order 3. An automatic stiffness detection and a stepsize control basing on Richardson-extrapolation are performed. Extensive tests and comparisons with the partitioned RKF4RW-algorithm from Rentrop [16] and the partitioned algorithm LSODA from Hindmarsh [9] and Petzold [15] show that the partitoned adaptive Runge-Kutta algorithm works reliable and gives good numericals results. Furthermore these tests show that the automatic stiffness detection in this algorithm is effective.