A Tale of Two Set Theories

We describe the relationship between two versions of Tarski-Grothendieck set theory: the first-order set theory of Mizar and the higher-order set theory of Egal. We show how certain higher-order terms and propositions in Egal have equivalent first-order presentations. We then prove Tarski's Axiom A (an axiom in Mizar) in Egal and construct a Grothendieck Universe operator (a primitive with axioms in Egal) in Mizar

A practical device for pinpoint delivery of molecules into multiple neurons in culture

We have developed a device for pinpoint delivery of chemicals, proteins, and nucleic acids into cultured cells. The principle underlying the technique is the flow of molecules from the culture medium into cells through a rupture in the plasma membrane made by a needle puncture. DNA transfection is achieved by stabbing the needle tip into the nucleus. The CellBee device can be attached to any inverted microscope, and molecular delivery can be coupled with conventional live cell imaging. Because the position of the needle relative to the targeted cultured cells is computer-controlled, efficient delivery of molecules such as rhodamine into as many as 100 HeLa cells can be completed in 10 min. Moreover, specific target cells within a single dish can be transfected with multiple DNA constructs by simple changes of culture medium containing different plasmids. In addition, the nano-sized needle tip enables gentle molecular delivery, minimizing cell damage. This method permits DNA transfection into specific hippocampal neurons without disturbing neuronal circuitry established in culture

Aquaglyceroporin-null trypanosomes display glycerol transport defects and respiratory-inhibitor sensitivity

Aquaglyceroporins (AQPs) transport water and glycerol and play important roles in drug-uptake in pathogenic trypanosomatids. For example, AQP2 in the human-infectious African trypanosome, Trypanosoma brucei gambiense, is responsible for melarsoprol and pentamidine-uptake, and melarsoprol treatment-failure has been found to be due to AQP2-defects in these parasites. To further probe the roles of these transporters, we assembled a T. b. brucei strain lacking all three AQP-genes. Triple-null aqp1-2-3 T. b. brucei displayed only a very moderate growth defect in vitro, established infections in mice and recovered effectively from hypotonic-shock. The aqp1-2-3 trypanosomes did, however, display glycerol uptake and efflux defects. They failed to accumulate glycerol or to utilise glycerol as a carbon-source and displayed increased sensitivity to salicylhydroxamic acid (SHAM), octyl gallate or propyl gallate; these inhibitors of trypanosome alternative oxidase (TAO) can increase intracellular glycerol to toxic levels. Notably, disruption of AQP2 alone generated cells with glycerol transport defects. Consistent with these findings, AQP2-defective, melarsoprol-resistant clinical isolates were sensitive to the TAO inhibitors, SHAM, propyl gallate and ascofuranone, relative to melarsoprol-sensitive reference strains. We conclude that African trypanosome AQPs are dispensable for viability and osmoregulation but they make important contributions to drug-uptake, glycerol-transport and respiratory-inhibitor sensitivity. We also discuss how the AQP-dependent inverse sensitivity to melarsoprol and respiratory inhibitors described here might be exploited

Detecting intratumoral heterogeneity of EGFR activity by liposome-based in vivo transfection of a fluorescent biosensor

Despite decades of research in the epidermal growth factor receptor (EGFR) signalling field, and many targeted anti-cancer drugs that have been tested clinically, the success rate for these agents in the clinic is low, particularly in terms of the improvement of overall survival. Intratumoral heterogeneity is proposed as a major mechanism underlying treatment failure of these molecule-targeted agents. Here we highlight the application of fluorescence lifetime microscopy (FLIM)-based biosensing to demonstrate intratumoral heterogeneity of EGFR activity. For sensing EGFR activity in cells, we used a genetically encoded CrkII-based biosensor which undergoes conformational changes upon tyrosine-221 phosphorylation by EGFR. We transfected this biosensor into EGFR-positive tumour cells using targeted lipopolyplexes bearing EGFR-binding peptides at their surfaces. In a murine model of basal-like breast cancer, we demonstrated a significant degree of intratumoral heterogeneity in EGFR activity, as well as the pharmacodynamic effect of a radionuclide-labeled EGFR inhibitor in situ. Furthermore, a significant correlation between high EGFR activity in tumour cells and macrophage-tumour cell proximity was found to in part account for the intratumoral heterogeneity in EGFR activity observed. The same effect of macrophage infiltrate on EGFR activation was also seen in a colorectal cancer xenograft. In contrast, a non-small cell lung cancer xenograft expressing a constitutively active EGFR conformational mutant exhibited macrophage proximity-independent EGFR activity. Our study validates the use of this methodology to monitor therapeutic response in terms of EGFR activity. In addition, we found iNOS gene induction in macrophages that are cultured in tumour cell-conditioned media as well as an iNOS activity-dependent increase in EGFR activity in tumour cells. These findings point towards an immune microenvironment-mediated regulation that gives rise to the observed intratumoral heterogeneity of EGFR signalling activity in tumour cells in vivo

The multiple faces of self-assembled lipidic systems

Lipids, the building blocks of cells, common to every living organisms, have the propensity to self-assemble into well-defined structures over short and long-range spatial scales. The driving forces have their roots mainly in the hydrophobic effect and electrostatic interactions. Membranes in lamellar phase are ubiquitous in cellular compartments and can phase-separate upon mixing lipids in different liquid-crystalline states. Hexagonal phases and especially cubic phases can be synthesized and observed in vivo as well. Membrane often closes up into a vesicle whose shape is determined by the interplay of curvature, area difference elasticity and line tension energies, and can adopt the form of a sphere, a tube, a prolate, a starfish and many more. Complexes made of lipids and polyelectrolytes or inorganic materials exhibit a rich diversity of structural morphologies due to additional interactions which become increasingly hard to track without the aid of suitable computer models. From the plasma membrane of archaebacteria to gene delivery, self-assembled lipidic systems have left their mark in cell biology and nanobiotechnology; however, the underlying physics is yet to be fully unraveled

On Relating Theories: Proof-Theoretical Reduction

The notion of proof-theoretical or finitistic reduction of one theory to another has a long tradition. Feferman and Sieg (Buchholz et al., Iterated inductive definitions and subsystems of analysis. Springer, Berlin, 1981, Chap. 1) and Feferman in (J Symbol Logic 53:364–384, 1988) made first steps to delineate it in more formal terms. The first goal of this paper is to corroborate their view that this notion has the greatest explanatory reach and is superior to others, especially in the context of foundational theories, i.e., theories devised for the purpose of formalizing and presenting various chunks of mathematics. A second goal is to address a certain puzzlement that was expressed in Feferman’s title of his Clermont-Ferrand lectures at the Logic Colloquium 1994: “How is it that finitary proof theory became infinitary?” Hilbert’s aim was to use proof theory as a tool in his finitary consistency program to eliminate the actual infinite in mathematics from proofs of real statements. Beginning in the 1950s, however, proof theory began to employ infinitary methods. Infinitary rules and concepts, such as ordinals, entered the stage. In general, the more that such infinitary methods were employed, the farther did proof theory depart from its initial aims and methods, and the closer did it come instead to ongoing developments in recursion theory, particularly as generalized to admissible sets; in both one makes use of analogues of regular cardinals, as well as “large” cardinals (inaccessible, Mahlo, etc.). (Feferman 1994). The current paper aims to explain how these infinitary tools, despite appearances to the contrary, can be formalized in an intuitionistic theory that is finitistically reducible to (actually Π02 -conservative over) intuitionistic first order arithmetic, also known as Heyting arithmetic. Thus we have a beautiful example of Hilbert’s program at work, exemplifying the Hilbertian goal of moving from the ideal to the real by eliminating ideal elements

The Independence of the Prime Ideal Theorem from the Order-Extension Principle

It is shown that the boolean prime ideal theorem BPIT : every boolean algebra has a prime ideal, does not follow from the order-extension principle OE: every partial ordering can be extended to a linear ordering. The proof uses a Fraenkel--Mostowski model, where the family of atoms is indexed by a countable universal-homogeneous boolean algebra whose boolean partial ordering has a `generic' extension to a linear ordering. To illustrate the technique for proving that the order-extension principle holds in the model we also study Mostowski's ordered model, and give a direct verification of OE there. The key technical point needed to verify OE in each case is the existence of a support structure. 1 Introduction The order-extension principle OE states that any partial ordering can be extended to a linear (total) ordering. Here by an extension of a partial ordering (X; ) we just mean a linear ordering ¯ of X such that (8x; y 2 X)(x y ) x ¯ y). A straightforward application of Zorn's Le..