Ubiquitylation of Fe65 adaptor protein by neuronal precursor cell expressed developmentally down regulated 4-2 (Nedd4-2) via the WW domain interaction with Fe65

Fe65 has been characterized as an adaptor protein, originally identified as an expressed sequence tag (EST) corresponding to an mRNA expressed at high levels in the rat brain. It contains one WW domain and two phosphotyrosine interaction/phosphotyrosine binding domains (PID1/PID2). As the neuronal precursor cell expressed developmentally down regulated 4-2 (Nedd4-2) has a putative WW domain binding motif (⁷²PPLP⁷⁵) in the N-terminal domain, we hypothesized that Fe65 associates with Nedd4-2 through a WW domain interaction, which has the characteristics of E3 ubiquitin-protein ligase. In this paper, we present evidence for the interaction between Fe65 WW domain and Nedd4-2 through its specific motif, using a pull down approach and co-immunoprecipitation. Additionally, the co-localization of Fe65 and Nedd4-2 were observed via confocal microscopy. Co-localization of Fe65 and Nedd4-2 was disrupted by either the mutation of Fe65 WW domain or its putative binding motif of Nedd4-2. When the ubiquitin assay was performed, the interaction of Nedd4-2 (wt) with Fe65 is required for the cell apoptosis and the ubiquitylation of Fe65. We also observed that the ubiquitylation of Fe65 (wt) was augmented depending on Nedd4-2 expression levels, whereas the Fe65 WW domain mutant (W243KP245K) or the Nedd4-2 AL mutant (⁷²PPLP⁷⁵ was changed to ⁷²APLA⁷⁵) was under-ubiquitinated significantly. Thus, our observations implicated that the protein-protein interaction between the WW domain of Fe65 and the putative binding motif of Nedd4-2 down-regulates Fe65 protein stability and subcellular localization through its ubiquitylation, to contribute cell apoptosis.     

Two-Person Second-Order Games,Part 1: Formulation and Transition Anatomy

It is well known that human psychology determines his/her action and behavior. This fact has not been fully incorporated in game theory. This paper intends to incorporate human psychology in formulating games as people play them. In Part 1 of the paper, we formulate a two-person game by the habitual domain theory and the Markov chain theory. Using the habitual domains theory, we present a new model describing the evolution of the states of mind of players over time, the two-person second-order game. We introduce the concept of the focal mind profile as well as the solution concept of the win-win mind profile. In addition, we provide also a method to predict the average number of steps needed for a game to reach a focal or win-win mind profile. Then, in Part 2 of the paper, under some reasonable assumptions, we derive the possibility theorem stating that it is always possible to reach a win-win mind profile when suitable conditions are satisfied. This research was partially supported by the National Science Council, Taiwan, NSC96-2416-H009-013.     

Multiply Connected Quadrature Domains and the Bergman Kernel Function

This paper derives general analytical formulae for the conformal maps from multiply connected circular preimage domains to multiply connected quadrature domains by considering the Bergman kernel functions of the preimage and target domains. The new formulae are expressed in terms of the Schottky–Klein prime function. They generalize, to the case of arbitrary connectivity, a formula relevant to doubly connected domains derived by Y. Avci in 1977. Submitted: September 17, 2007. Accepted: June 5, 2008.     

Quadrature Domains with Infinite Volume

We discuss quadrature domains for subharmonic functions and prove the existence of core quadrature domains for certain positive measures. The core quadrature domains are the smallest quadrature domains as measures and inherit good properties from quadrature domains with finite volume. We next discuss new balayage for the class of harmonic functions integrable in a neighborhood of ∞. We give several estimates of balayage measures. The new balayage is introduced to construct quadrature domains for harmonic functions. Submitted: June 26, 2008. Accepted: July 24, 2008.     

Symmetric Stable Processes on Unbounded Domains

Let be a symmetric -stable process in , , . We give necessary and sufficient condition under which the expectation of a very general function of the exit time from horns is finite. These domains include the symmetric domains given by increasing functions studied earlier by various authors. Our methods differ from those in earlier papers in that we obtain our results from estimates on the transition densities instead of harmonic measure. Some of this estimates are of independent interest.Supported in part by NSF grant #9700585-DMS and RTN Harmonic Analysis and Related Problems contract HPRN-CT-2001-00273-HARP.     

Hardy's inequality on exterior domains

Let be a smooth exterior domain in and . We prove that when , Hardy's inequality is valid on .

     

Some remarks on James-Schreier spaces

The James-Schreier spaces Vp, where 1?p<∞, were recently introduced by Bird and Laustsen (in press) [5] as an amalgamation of James' quasi-reflexive Banach space on the one hand and Schreier's Banach space giving a counterexample to the Banach-Saks property on the other. The purpose of this note is to answer some questions left open in Bird and Laustsen (in press) [5]. Specifically, we prove that (i) the standard Schauder basis for the first James-Schreier space V₁ is shrinking, and (ii) any two Schreier or James-Schreier spaces with distinct indices are non-isomorphic. The former of these results implies that V₁ does not have Pe?czyński's property (u) and hence does not embed in any Banach space with an unconditional Schauder basis.     

Extending the choice of starting points for Newton's method

In this paper, we propose a center Lipschitz condition for the second derivative together with the use of restricted domains in order to improve the starting points for Newton's method when compared with previous results. Moreover, we present some numerical examples validating the theoretical results.