‎In this paper‎, ‎we define and study the notion of zero elements in topoframes; a topoframe is a pair‎ ‎$(L‎, ‎tau)$‎, ‎abbreviated $L_{ tau}$‎, ‎consisting of a frame $L$ and a‎ ‎subframe $ tau $ all of whose elements are complemented elements in‎ ‎$L$‎. ‎We show that‎ ‎the $f$-ring $ mathcal{R}(L_tau)$‎, ‎the set of $tau$-real continuous functions on $L$‎, ‎is uniformly complete‎. ‎Also‎, ‎t...

We quantify spatial and temporal heterogeneity in supercooled glycerol at T=T(g)+14 K employing a widefield detection scheme and using rubrene as the probe molecule. We describe how microscopy configuration affects measured intensity, linear dichroism, and the resulting autocorrelation function. Rotational relaxation times tau(c) of 241 probe molecules are measured, and we find spatial heteroge...

In Alzheimer’s disease (AD) and Progressive Supranuclear Palsy (PSP), the cross-linking of phosphorylated tau into stable insoluble aggregates may lead to formation of paired helical filaments (PHFs) and neurofibrillary tangles (NFTs). NFT pathology is accompanied by oxidative stress in AD and PSP. Previous investigations have uncovered that phosphorylated tau is cross-linked by transglutaminas...

Tau is an intrinsically disordered protein (IDP) whose primary physiological role is to stabilize microtubules in neuronal axons at all stages of development. In Alzheimer's and other tauopathies, tau forms intracellular insoluble amyloid aggregates known as neurofibrillary tangles, a process that appears in many cases to be preceded by hyperphosphorylation of tau monomers. Understanding the sh...

We considered an irreversible biochemical intrachain reaction of supercoiled DNA as a random event that occurs, with certain probability, at the instant of collision between two reactive groups bound to distant DNA sites. Using the Brownian dynamics technique, we modeled this process for a supercoiled DNA molecule of 2.5 kb length in dilute aqueous solution at an NaCl concentration of 0.1 M. We...

The in vitro aggregation of tau constructs was monitored by a simple 90° angle light-scattering (LS) approach which was conducted directly on fluorescence instrument. At the optimum incident wavelength (550 nm, unpolarized), the sensitivity of LS was high enough to detect tau aggregation at micromolar range. The nucleation and elongation, different events in the aggregation process of 4RMBD con...

This paper presents a computational technique that called Tau-collocation method for the developed solution of non-linear integro-differential equations which involves a population model. To do this, the nonlinear integro-differential equations are transformed into a system of linear algebraic equations in matrix form without interpolation of non-poly-nomial terms of equations. Then, using coll...

PHF-tau proteins are the major components of the paired helical filament (PHF) from Alzheimer's disease (AD) neurofibrillary lesions. They differ both qualitatively and quantitatively in their degree of phosphorylation when compared with native tau proteins. However, little is known about the extent and heterogeneity of phosphorylated sites or the isoform composition and the isoelectric variant...