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.     

Remarks on the structure of the fixed-point sets of uniformly lipschitzian mappings in uniformly convex Banach spaces

It is shown, by asymptotic center techniques, that the set of fixed points of any uniformly k-lipschitzian mapping in a uniformly convex Banach space is a retract of the domain when k is less than a constant bigger than the constant from the paper [K. Goebel, W.A. Kirk, A fixed point theorem for transformations whose iterates have uniform Lipschitz constant, Studia Math. 47 (1973) 135-140]. Our result improves a recently result presented in [E. S?d?ak, A. Wi?nicki, On the structure of fixed-point sets of uniformly lipschitzian mappings, Topol. Methods Nonlinear Anal. 30 (2007) 345-350].     

Strong convergence theorems for a countable family of quasi-Lipschitzian mappings and its applications

We use the hybrid method in mathematical programming to obtain strong convergence to common fixed points of a countable family of quasi-Lipschitzian mappings. As a consequence, several convergence theorems for quasi-nonexpansive mappings and asymptotically κ-strict pseudo-contractions are deduced. We also establish strong convergence of iterative sequences for finding a common element of the set of fixed point, the set of solutions of an equilibrium problem, and the set of solutions of a variational inequality. With an appropriate setting, we obtain the corresponding results due to Tada-Takahashi and Nakajo-Shimoji-Takahashi.     

A renorming of some nonseparable Banach spaces with the Fixed Point Property

We prove that for every Banach space which can be embedded in c₀(Γ) (for instance, reflexive spaces or more generally spaces with M-basis) there exists an equivalent renorming which enjoys the (weak) Fixed Point Property for non-expansive mappings. As a consequence, we solve a longtime open question in Metric Fixed Point Theory: Every reflexive Banach can be renormed to satisfy the Fixed Point Property. Furthermore, this norm can be chosen arbitrarily closed to the original norm.     

Solvability and iterative algorithms for a higher order nonlinear neutral delay differential equation

The paper is concerned with the higher order nonlinear neutral delay differential equation

     

Asymptotics of the Best Polynomial Approximation of?|x|p and?of?the Best Laurent Polynomial Approximation of sgn(x) on Two Symmetric Intervals

We present a new method that allows us to get a direct proof of the classical Bernstein asymptotics for the error of the best uniform polynomial approximation of |x| ^p on two symmetric intervals. Note that, in addition, we get asymptotics for the polynomials themselves under a certain renormalization. Also, we solve a problem on asymptotics of the best approximation of sgn(x) on [−1,−a]∪[a,1] by Laurent polynomials.      

On conformal biharmonic immersions

This paper studies conformal biharmonic immersions. We first study the transformations of Jacobi operator and the bitension field under conformal change of metrics. We then obtain an invariant equation for a conformal biharmonic immersion of a surface into Euclidean 3-space. As applications, we construct a two-parameter family of non-minimal conformal biharmonic immersions of cylinder into and some examples of conformal biharmonic immersions of four-dimensional Euclidean space into sphere and hyperbolic space, thus providing many simple examples of proper biharmonic maps with rich geometric meanings. These suggest that there are abundant proper biharmonic maps in the family of conformal immersions. We also explore the relationship between biharmonicity and holomorphicity of conformal immersions of surfaces.      

An iterative algorithm based on -proximal mappings for a system of generalized implicit variational inclusions in Banach spaces

In this paper, we give the notion of M-proximal mapping, an extension of P-proximal mapping given in [X.P. Ding, F.Q. Xia, A new class of completely generalized quasi-variational inclusions in Banach spaces, J. Comput. Appl. Math. 147 (2002) 369–383], for a nonconvex, proper, lower semicontinuous and subdifferentiable functional on Banach space and prove its existence and Lipschitz continuity. Further, we consider a system of generalized implicit variational inclusions in Banach spaces and show its equivalence with a system of implicit Wiener–Hopf equations using the concept of M-proximal mappings. Using this equivalence, we propose a new iterative algorithm for the system of generalized implicit variational inclusions. Furthermore, we prove the existence of solution of the system of generalized implicit variational inclusions and discuss the convergence and stability analysis of the iterative algorithm.     

Roper-Suffridge算子上的偏差定理下界估计的简单证明

Liczberski-Starkov first found a lower bound for ||D(f)|| near the origin, where is the Roper-Suffridge operator on the unit ball Bn in Cn and F is a normalized convex function on the unit disk. Later, Liczberski-Starkov and Hamada-Kohr proved the lower bound holds on the whole unit ball using a complex computation. Here we provide a rather short and easy proof for the lower bound. Similarly, when F is a normalized starlike function on the unit disk, a lower bound of ||D(f)|| is obtained again.