A topoframe, denoted by $L_{ tau}$,  is a pair $(L, tau)$ consisting of a frame $L$ and a subframe $ tau $ all of whose elements are complementary elements in $L$. In this paper, we define and study the notions of a $tau $-real-continuous function on a frame $L$ and the set of real continuous functions $mathcal{R}L_tau $ as an $f$-ring. We show that $mathcal{R}L_{ tau}$ is actually a generali...

Several human neurodegenerative diseases are associated with abnormal accumulations of aggregated tau proteins and glial degeneration in astrocytes, but the mechanism whereby tau proteins cause astrocytic degeneration is unclear. Here, we analyzed the biological consequences of overexpressing the longest human tau isoform in primary cultures of rat astrocytes using adenoviral-mediated gene tran...

Abnormal alternative splicing of tau exon 10 results in imbalance of 3R-tau and 4R-tau expression, which is sufficient to cause neurofibrillary degeneration. Splicing factor SC35, a member of the superfamily of the serine/arginine-rich (SR) proteins, promotes tau exon 10 inclusion. The molecular mechanism by which SC35 participates in tau exon 10 splicing remains elusive. In the present study, ...

Post-translational modifications of proteins are ubiquitous in living organisms, as they enable an accurate control the interactions these macromolecules. For mechanistic studies, it would be highly advantageous to able produce vitro post-translationally modified with site-specificity. Here, we demonstrate one facile way achieve this goal through use post-translational chemical mutagenesis. We ...

Non-centrosomal microtubule bundles play important roles in cellular organization and function. Although many diverse proteins are known that can bundle microtubules, biochemical mechanisms by which cells could locally control the nucleation and formation of microtubule bundles are understudied. Here, we demonstrate that the concentration of tubulin into a condensed, liquid-like compartment com...

Amyloid plaques and neurofibrillary tangles are the pathological hallmarks of Alzheimer's disease. However, there has been a long-standing discussion on the dynamic relations between Aβ and tau proteins, partially due to the lack of a tool to track protein dynamics in individual live neurons at the early stage of Aβ generation and tau phosphorylation. Here, we developed nanoplasmonic fiber tip ...

The major protein subunit of the paired helical filaments (PHF) of Alzheimer disease (AD) is the microtubule-associated protein tau. Tau is a family of phosphopolypeptides that are abnormally phosphorylated in PHF. In this study, a non-PHF pool of tau abnormally phosphorylated at Ser-199/202, and tau not phosphorylated at this site (AD P-tau and AD tau, respectively) were isolated from the 27,0...