Modular cis-regulatory organization of Endo16, a gut-specific gene of the sea urchin embryo

The Endo16 gene of Strongylocentrotus purpuratus is expressed at the blastula stage of embryogenesis throughout the vegetal plate, at the gastrula stage in the whole of the archenteron and in postgastrular stages only in the midgut. We showed earlier that a 2300 bp upstream sequence suffices to faithfully recreate this pattern of expression when fused to a CAT reporter gene. Here we define the functional organization of this cis-regulatory domain, which includes over thirty high specificity binding sites, serviced by at least thirteen different putative transcription factors, in addition to >20 sites for a factor commonly found in the regulatory sequences of other sea urchin genes as well (SpGCF1). The Endo16 cis-regulatory domain consists of several different functional elements, or modules, each containing one or two unique DNA-binding factor target sites, plus sites for factors binding in other modules as well. Modular regulatory function was defined in experiments in which regions of the cis-regulatory DNA containing specific clusters of sites were tested in isolation, combined with one another, or by selective deletion, and the effects on expression of the CAT reporter were determined by whole-mount in situ hybridization or CAT enzyme activity measurements. The most proximal module (A) is mainly responsible for early embryonic expression, and module A alone suffices to locate expression in the vegetal plate and archenteron. The adjacent module (B) is responsible for a steep postgastrular rise in expression, when the gene is transcribed only in the midgut and, prior to this module B alone also suffices to promote expression in the vegetal plate and archenteron. The most distal module, G, acts as a booster for either A or B modules. However, no combination of A, B and G modules generates vegetal plate or gut expression exclusively. Ectopic expression of A-, B- and G-CAT fusion constructs occurs in the adjacent (veg1-derived) ectoderm and in skeletogenic mesenchyme cells. For expression to be confined to endoderm requires negative regulatory functions mediated by modules E, F and DC. Modules E and F each repress ectopic expression specifically in veg1 ectoderm. Module DC represses ectopic expression specifically in skeletogenic mesenchyme. Expression of some Endo16 constructs is dramatically increased by treatment with LiCl, which expands the territory in which the endogenous Endo16 gene is expressed at the expense of veg1 ectoderm. The same modules that act to repress ectopic expression in untreated embryos are required for enhanced expression of constructs after LiC1 treatment. Furthermore, both the negative spatial control functions and response to LiC1 require the presence of module A. The total regulatory requirements of the Endo16 gene during embryogenesis can be expressed in terms of the positive and negative functions of the individual modules and the interactions between modules that are identified in this study

Pattern formation in finite size non-equilibrium systems and models of morphogenesis

Two canonical pattern forming systems, the Rayleigh-Benard convection and the Turing mechanism for biological pattern formation, are compared. The similarity and fundamental differences in the mathematical structure of the two systems are addressed, with special emphasis on how the linear onset of patterns is affected by the finite size and the boundary conditions. Our analysis is facilitated by continuously varying the boundary condition, from one that admits simple algebraic solution of the problem but is unrealistic to another which is physically realizable. Our investigation shows that the size dependence of the convection problem can be considered generic, in the sense that for the majority of boundary conditions the same trend is to be observed, while for the corresponding Turing mechanism one will rely crucially on the assumed boundary conditions to ensure that a particular sequence of patterns be picked up as the system grows in size. This suggests that, although different systems might exhibit similar pattern forming features, it is still possible to distinguish them by characteristics which are specific to the individual models

The Valuation and Redistribution Effect of the Korea National Pension

This paper evaluates the Korea National Pension (KNP) and investigates its redistribution effects. The educational level is used as a proxy for mortality and various socioeconomic factors are considered. The financial and utility-based analyses reveal strong progressive redistribution with income level. Also, the utility-based analysis indicates significant progressive redistribution with non-pension asset level but no significant redistribution with the educational level. Generally, the KNP is extremely valuable and its value seems higher with a pre-existing private annuity especially for the poor. Finally, when people are assumed to spend at least the minimum consumption level, it becomes more beneficial.Korea National Pension, Redistribution, Annuity Evaluation, Annuity Equivalent Wealth, Money's Worth Ratio, Bequest

Achievable Angles Between two Compressed Sparse Vectors Under Norm/Distance Constraints Imposed by the Restricted Isometry Property: A Plane Geometry Approach

The angle between two compressed sparse vectors subject to the norm/distance constraints imposed by the restricted isometry property (RIP) of the sensing matrix plays a crucial role in the studies of many compressive sensing (CS) problems. Assuming that (i) u and v are two sparse vectors separated by an angle thetha, and (ii) the sensing matrix Phi satisfies RIP, this paper is aimed at analytically characterizing the achievable angles between Phi*u and Phi*v. Motivated by geometric interpretations of RIP and with the aid of the well-known law of cosines, we propose a plane geometry based formulation for the study of the considered problem. It is shown that all the RIP-induced norm/distance constraints on Phi*u and Phi*v can be jointly depicted via a simple geometric diagram in the two-dimensional plane. This allows for a joint analysis of all the considered algebraic constraints from a geometric perspective. By conducting plane geometry analyses based on the constructed diagram, closed-form formulae for the maximal and minimal achievable angles are derived. Computer simulations confirm that the proposed solution is tighter than an existing algebraic-based estimate derived using the polarization identity. The obtained results are used to derive a tighter restricted isometry constant of structured sensing matrices of a certain kind, to wit, those in the form of a product of an orthogonal projection matrix and a random sensing matrix. Follow-up applications to three CS problems, namely, compressed-domain interference cancellation, RIP-based analysis of the orthogonal matching pursuit algorithm, and the study of democratic nature of random sensing matrices are investigated.Comment: submitted to IEEE Trans. Information Theor