A system to enrich for primitive streak-derivatives, definitive endoderm and mesoderm, from pluripotent cells in culture

Two lineages of endoderm develop during mammalian embryogenesis, the primitive endoderm in the pre-implantation blastocyst and the definitive endoderm at gastrulation. This complexity of endoderm cell populations is mirrored during pluripotent cell differentiation in vitro and has hindered the identification and purification of the definitive endoderm for use as a substrate for further differentiation. The aggregation and differentiation of early primitive ectoderm-like (EPL) cells, resulting in the formation of EPL-cell derived embryoid bodies (EPLEBs), is a model of gastrulation that progresses through the sequential formation of primitive streak-like intermediates to nascent mesoderm and more differentiated mesoderm populations. EPL cell-derived EBs have been further analysed for the formation of definitive endoderm by detailed morphological studies, gene expression and a protein uptake assay. In comparison to embryoid bodies derived from ES cells, which form primitive and definitive endoderm, the endoderm compartment of embryoid bodies formed from EPL cells was comprised almost exclusively of definitive endoderm. Definitive endoderm was defined as a population of squamous cells that expressed Sox17, CXCR4 and Trh, which formed without the prior formation of primitive endoderm and was unable to endocytose horseradish peroxidase from the medium. Definitive endoderm formed in EPLEBs provides a substrate for further differentiation into specific endoderm lineages; these lineages can be used as research tools for understanding the mechanisms controlling lineage establishment and the nature of the transient intermediates formed. The similarity between mouse EPL cells and human ES cells suggests EPLEBs can be used as a model system for the development of technologies to enrich for the formation of human ES cell-derived definitive endoderm in the future.Sveltana Vassilieva, Hweee Ngee Goh, Kevin X. Lau, James N. Hughes, Mary Familari, Peter D. Rathjen and Joy Rathje

CAVE3: A general transient heat transfer computer code utilizing eigenvectors and eigenvalues

The method of solution is a hybrid analytical numerical technique which utilizes eigenvalues and eigenvectors. The method is inherently stable, permitting large time steps even with the best of conductors with the finest of mesh sizes which can provide a factor of five reduction in machine time compared to conventional explicit finite difference methods when structures with small time constants are analyzed over long time periods. This code will find utility in analyzing hypersonic missile and aircraft structures which fall naturally into this class. The code is a completely general one in that problems involving any geometry, boundary conditions and materials can be analyzed. This is made possible by requiring the user to establish the thermal network conductances between nodes. Dynamic storage allocation is used to minimize core storage requirements. This report is primarily a user's manual for CAVE3 code. Input and output formats are presented and explained. Sample problems are included which illustrate the usage of the code as well as establish the validity and accuracy of the method

Nodal network generator for CAVE3

A new extension of CAVE3 code was developed that automates the creation of a finite difference math model in digital form ready for input to the CAVE3 code. The new software, Nodal Network Generator, is broken into two segments. One segment generates the model geometry using a Tektronix Tablet Digitizer and the other generates the actual finite difference model and allows for graphic verification using Tektronix 4014 Graphic Scope. Use of the Nodal Network Generator is described

Reversible programming of pluripotent cell differentiation

We have undertaken an in vitro differentiation analysis of two related, interconvertible, pluripotent cell populations, ES and early primitive ectoderm-like (EPL) cells, which are most similar in morphology, gene expression, cytokine responsiveness and differentiation potential in vivo to ICM and early primitive ectoderm, respectively. Pluripotent cells were differentiated in vitro as aggregates (embryoid bodies) and the appearance and abundance of cell lineages were assessed by morphology and gene expression. Differentiation in EPL cell embryoid bodies recapitulated normal developmental progression in vivo, but was advanced in comparison to ES cell embryoid bodies, with the rapid establishment of late primitive ectoderm specific gene expression, and subsequent loss of pluripotent cell markers. Nascent mesoderm was formed earlier and more extensively in EPL cell embryoid bodies, and resulted in the appearance of terminally differentiated mesodermal cell types prior to and at higher levels than in ES cell embryoid bodies. Nascent mesoderm in EPL cell embryoid bodies was not specified but could be programmed to alternative fates by the addition of exogenous factors. EPL cells remained competent to form primitive endoderm even though this is not the normal fate of primitive ectoderm in vivo. The establishment of primitive ectoderm-like gene expression and inability to participate in embryogenesis following blastocyst injection is therefore not directly associated with restriction in the ability to form extra-embryonic lineages. However, the EPL cell embryoid body environment did not support differentiation of primitive endoderm to visceral endoderm, indicating the lack of an inductive signal for visceral endoderm formation deduced to originate from the pluripotent cells. Similarly, the inability of EPL cells to form neurons when differentiated as embryoid bodies was attributable to perturbation of the differentiation environment and loss of inductive signals rather than a restricted differentiation potential. Reversion of EPL cells to ES cells was accompanied by restoration of ES cell-like differentiation potential. These results demonstrate the ability of pluripotent cells to adopt developmentally distinct, stable cell states with altered differentiation potentials.Julie-Anne Lake, Joy Rathjen, Jackie Remiszewski and Peter D. Rathje

Formation of a primitive ectoderm like cell population, EPL cells, from ES cells in response to biologically derived factors

The primitive ectoderm of the mouse embryo arises from the inner cell mass between 4.75 and 5.25 days post coitum, around the time of implantation. Positioned at a pivotal time in development, just prior to formation of the three germ layers of the embryo proper, the primitive ectoderm responds directly to the signals generated during gastrulation. We have identified a conditioned medium, MEDII, which caused the homogeneous conversion of ES cells to a morphologically distinct cell population, termed early primitive ectoderm-like (EPL) cells. EPL cells expressed the pluripotent cell markers Oct4, SSEA1 and alkaline phosphatase. However, the formation of EPL cells was accompanied by alterations in Fgf5, Gbx2 and Rex1 expression, a loss in chimaera forming ability, changes in factor responsiveness and modified differentiation capabilities, all consistent with the identification of EPL cells as equivalent to the primitive ectoderm population of the 5.5 to 6.0 days post coitum embryo. EPL cell formation could be reversed in the presence of LIF and withdrawal of MEDII, which suggested that EPL cell formation was not a terminal differentiation event but reflected the ability of pluripotent cells to adopt distinct cell states in response to specific factors. Partial purification of MEDII revealed the presence of two separable biological activities, both of which were required for the induction and maintenance of EPL cells. We show here the first demonstration of uniform differentiation of ES cells in response to biological factors. The formation of primitive ectoderm, both in vivo and in vitro, appears to be an obligatory step in the differentiation of the inner cell mass or ES cells into cell lineages of the embryonic germ layers. EPL cells potentially represent a model for the development of lineage specific differentiation protocols and analysis of gastrulation at a molecular level. An understanding of the active components of MEDII may provide a route for the identification of factors which induce primitive ectoderm formation in vivo.Joy Rathjen, Julie-Anne Lake, Michael D. Bettess, Jenny M. Washington, Gavin Chapman and Peter D. Rathje

Ordinal Analysis of Intuitionistic Power and Exponentiation Kripke Platek Set Theory

Until the 1970s, proof theoretic investigations were mainly concerned with theories of inductive definitions, subsystems of analysis and finite type systems. With the pioneering work of Gerhard Jäger in the late 1970 s and early 1980s, the focus switched to set theories, furnishing ordinal-theoretic proof theory with a uniform and elegant framework. More recently it was shown that these tools can even sometimes be adapted to the context of strong axioms such as the powerset axiom, where one does not attain complete cut elimination but can nevertheless extract witnessing information and characterize the strength of the theory in terms of provable heights of the cumulative hierarchy. Here this technology is applied to intuitionistic Kripke-Platek set theories IKP(P) and IKP(E), where the operation of powerset and exponentiation, respectively, is allowed as a primitive in the separation and collection schemata. In particular, IKP(P) proves the powerset axiom whereas IKP(E) proves the exponentiation axiom. The latter expresses that given any sets A and B, the collection of all functions from A to B is a set, too. While IKP(P) can be dealt with in a similar vein as its classical cousin, the treatment of IKP(E) posed considerable obstacles. One of them was that in the infinitary system the levels of terms become a moving target as they cannot be assigned a fixed level in the formal cumulative hierarchy solely based on their syntactic structure. As adumbrated in an earlier paper, the results of this paper are an important tool in showing that several intuitionistic set theories with the collection axiom possess the existence property, i.e., if they prove an existential theorem then a witness can be provably described in the theory, one example being intuitionistic Zermelo-Fraenkel set theory with bounded separation

Transwells with Microstamped Membranes Produce Micropatterned Two-Dimensional and Three-Dimensional Co-Cultures

This article describes a simple and rapid cell patterning method to form co-culture microarrays in commercially available Transwells. A thin poly(dimethylsiloxane) (PDMS) layer is printed on the underside of a Transwell using a PDMS stamp. Arbitrary cellular patterns are generated according to the geometric features of the thin PDMS layer through hydrodynamic forces that guide cells onto the membrane only over the PDMS-uncoated regions. Micropatterns of surface-adhered cells (we refer to this as two-dimensional) or non-surface-adhered clusters of cells (we refer to this as three-dimensional) can be generated depending on the surface treatment of the filter membrane. Additionally, co-cultures can be established by introducing different types of cells on the membrane or in the bottom chamber of the Transwell. We show that this co-culture method can evaluate mouse embryonic stem (mES) cell differentiation based on heterogeneous cell-cell interactions. Co-culture of mES cells and HepG2 cells decreased SOX17 expression of mES cells, and direct cell-cell contact further decreased SOX17 expression, indicating that co-culture with HepG2 cells inhibits endoderm differentiation through soluble factors and cell-cell contact. This method is simple and user-friendly and should be broadly useful to study cell shapes and cell-cell interactions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90499/1/ten-2Etec-2E2010-2E0305.pd

A Novel Device for the Measurement of the Mechanical and Magnetic Axes of Superconducting Magnet Assemblies for Accelerators

In the context of the LHC superconducting magnet production, especially for dipoles and quadrupoles due to their complexity, it is foreseen to perform acceptance tests, at an early production stage, to detect possible significant deviations from the design values. The knowledge of the magnetic field geometry is very important, especially for the main magnets. In order to get this information a new device has been conceived that measures the magnets at room temperature during different stages of construction. This device incorporates a sensitive measuring probe and an efficient data acquisition system because the coils are only powered at about 10-5 of the nominal D.C. current. It is dedicated to Quadrupole and Dipole (by using Quadrupole-Configured Dipole (QCD) transformation) magnets, but is also easily adaptable to higher order magnets (n = 3, 4 and 5) by specific orientation of the search coils. It is equipped with magnetic sensors (4 fixed tangential coils and AC excitation current for the magnet) and position sensors (3D-laser tracker and light reflector) that allow the simultaneous detection of the magnetic field axis and the cold bore axis. It is equipped as well with a set of 4 LEDs and associated with a CCD camera that allows both the measurement of the cold bore diameter and its position with respect to the mole. This paper describes the system and reports the first results measured on the pre-series magnets recently assembled

A new foundational crisis in mathematics, is it really happening?

The article reconsiders the position of the foundations of mathematics after the discovery of HoTT. Discussion that this discovery has generated in the community of mathematicians, philosophers and computer scientists might indicate a new crisis in the foundation of mathematics. By examining the mathematical facts behind HoTT and their relation with the existing foundations, we conclude that the present crisis is not one. We reiterate a pluralist vision of the foundations of mathematics. The article contains a short survey of the mathematical and historical background needed to understand the main tenets of the foundational issues.Comment: Final versio

An order-theoretic characterization of the Howard-Bachmann-hierarchy

In this article we provide an intrinsic characterization of the famous Howard-Bachmann ordinal in terms of a natural well-partial-ordering by showing that this ordinal can be realized as a maximal order type of a class of generalized trees with respect to a homeomorphic embeddability relation. We use our calculations to draw some conclusions about some corresponding subsystems of second order arithmetic. All these subsystems deal with versions of light-face Π₁¹-comprehension