Enhanced Neural Progenitor/Stem Cells Self-Renewal via the Interaction of Stress-Inducible Protein 1 with the Prion Protein

Prion protein (PrPC), when associated with the secreted form of the stress-inducible protein 1 (STI1), plays an important role in neural survival, neuritogenesis, and memory formation. However, the role of the PrP(C)-STI1 complex in the physiology of neural progenitor/stem cells is unknown. In this article, we observed that neurospheres cultured from fetal forebrain of wild-type (Prnp(+/+)) and PrP(C)-null (Prnp(0/0)) mice were maintained for several passages without the loss of self-renewal or multipotentiality, as assessed by their continued capacity to generate neurons, astrocytes, and oligodendrocytes. The homogeneous expression and colocalization of STI1 and PrP(C) suggest that they may associate and function as a complex in neurosphere-derived stem cells. The formation of neurospheres from Prnp(0/0) mice was reduced significantly when compared with their wild-type counterparts. In addition, blockade of secreted STI1, and its cell surface ligand, PrP(C), with specific antibodies, impaired Prnp(+/+) neurosphere formation without further impairing the formation of Prnp(0/0) neurospheres. Alternatively, neurosphere formation was enhanced by recombinant STI1 application in cells expressing PrP(C) but not in cells from Prnp(0/0) mice. The STI1-PrP(C) interaction was able to stimulate cell proliferation in the neurosphere-forming assay, while no effect on cell survival or the expression of neural markers was observed. These data suggest that the STI1-PrP(C) complex may play a critical role in neural progenitor/stem cells self-renewal via the modulation of cell proliferation, leading to the control of the stemness capacity of these cells during nervous system development. STEM CELLS 2011;29:1126-1136

CONSTRUCTING QUANTUM OBSERVABLES AND SELF-ADJOINT EXTENSIONS OF SYMMETRIC OPERATORS. III. SELF-ADJOINT BOUNDARY CONDITIONS

This paper completes the review of the theory of self-adjoint extensions of symmetric operators for physicists as a basis for constructing quantum-mechanical observables. It contains a comparative presentation of the well-known methods and a newly proposed method for constructing ordinary self-adjoint differential operators associated with self-adjoint differential expressions in terms of self-adjoint boundary conditions. The new method has the advantage that it does not require explicitly evaluating deficient subspaces and deficiency indices (these latter are determined in passing) and that boundary conditions are of explicit character irrespective of the singularity of a differential expression. General assertions and constructions are illustrated by examples of well-known quantum-mechanical operators like momentum and Hamiltonian.

Self-adjoint extensions and spectral analysis in the Calogero problem

In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential alpha x(-2). Although the problem is quite old and well studied, we believe that our consideration based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in our previous works, adds some new points to its solution. To demonstrate that a consideration of the Calogero problem requires mathematical accuracy, we discuss some `paradoxes` inherent in the `naive` quantum-mechanical treatment. Using a self-adjoint extension method, we construct and study all possible self-adjoint operators (self-adjoint Hamiltonians) associated with a formal differential expression for the Calogero Hamiltonian. In particular, we discuss a spontaneous scale-symmetry breaking associated with self-adjoint extensions. A complete spectral analysis of all self-adjoint Hamiltonians is presented.