Tau Function Research Articles

Dual Modification of Tau by Pseudophosphorylation and Glycation Does Not Enhance Amorphous Aggregation

Background/Aims: The neurofibrillary tangles consisting of Tau protein are an important pathology in Alzheimer’s disease. The paired helical filaments of Tau form most of the NFTs. These PHFs of Tau are found to carry numerous post-translational modifications, which stabilize them and aid in aggregation. The mechanistic function of Tau is to bind and stabilize the axonal microtubules. Hyperphosphorylation of Tau causes it to compromise its physiological function and accumulate in the neurons in the form of aggregates. Such residue-specific phosphorylation has been studied by employing Tau pseudophosphorylation mutants. But in addition to phosphorylation, several other modifications also aid in stabilizing the Tau PHF. Glycation is one such non-enzymatic PTM caused by sugars and their reactive intermediates. In this study, we employed the pseudophosphorylated Tau double mutants (262/404D, 262/396D, and 231/262) for studying their modification by methyl glyoxal, a reactive intermediate of glucose metabolism. Methods: We studied various biophysical properties like aggregation propensity, Advanced glycation end-product formation, and global conformation of the Tau with dual modifications. Our study includes the use of in vitro techniques e.g., ThS fluorescence assay, electron microscopy, CD spectroscopy, SDS-PAGE. Results: The overall result of the study suggest that the MG-induced Tau aggregation is influenced by the residue-specific Tau phosphorylation. Conclusion: In conclusion, the combinatorial effect of discreet PTMs on Tau function could lead to a better understanding of Tauopathy.

On the dispersionless Davey-Stewartson hierarchy: the tau function, the Riemann-Hilbert problem and the Hamilton-Jacobi theory

The dDS (dispersionless Davey-Stewartson) hierarchy is constructed by two eigenfunctions of a special Hamiltonian vector field. This hierarchy consists of the infinite symmetries of the dDS system. Further, this paper explores the tau function, the Riemann-Hilbert problem and Hamilton-Jacobi theory related to dDS hierarchy.

Toda and Laguerre–Freud equations and tau functions for hypergeometric discrete multiple orthogonal polynomials

In this paper, the authors investigate the case of discrete multiple orthogonal polynomials with two weights on the step line, which satisfy Pearson equations. The discrete multiple orthogonal polynomials in question are expressed in terms of τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document}-functions, which are double Wronskians of generalized hypergeometric series. The shifts in the spectral parameter for type II and type I multiple orthogonal polynomials are described using banded matrices. It is demonstrated that these polynomials offer solutions to multicomponent integrable extensions of the nonlinear Toda equations. Additionally, the paper characterizes extensions of the Nijhoff–Capel totally discrete Toda equations. The hypergeometric τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document}-functions are shown to provide solutions to these integrable nonlinear equations. Furthermore, the authors explore Laguerre–Freud equations, nonlinear equations for the recursion coefficients, with a particular focus on the multiple Charlier, generalized multiple Charlier, multiple Meixner II, and generalized multiple Meixner II cases.

Tau functions of the discrete modified KP hierarchy

In this paper, we prove the existence of tau functions of the discrete modified Kadomtsev-Petviashvili (KP) hierarchy. Meanwhile, the Fay identity with its difference form, the squared eigenfunction potentials, and the symmetry flows acting on tau functions are obtained.

EB1 Increases the Dynamics of Tau Droplets and Inhibits Tau Aggregation: Implications in Tauopathies.

EB1, a microtubule plus end-tracking protein (+TIP), regulates microtubule dynamics. Recent evidence indicates cross-talk between EB proteins and tau, a microtubule-associated neuronal protein that is important for the growth and stability of microtubules. We investigated the interaction between tau and EB1 and the effect of binding of EB1 on tau function and aggregation. EB1 colocalized with tau in SH-SY5Y cells and coimmunoprecipitated with tau. Further, purified EB1 impaired the ability of adult tau to induce tubulin polymerization in vitro. EB1 bound to tau with a dissociation constant of 2.5 ± 0.7 μM. EB1 reduced heparin-induced tau aggregation with a half-maximal inhibitory concentration of 4.3 ± 0.2 μM, and increased the dynamics of tau in phase-separated droplets. The fluorescence recovery rate in tau droplets increased from 0.02 ± 0.01 to 0.07 ± 0.03 s-1, while the half-time of recovery decreased from 44.5 ± 14 to 13.5 ± 6 s in the presence of 8 μM EB1, suggesting a delay in the transition of tau from the soluble to aggregated form in tau liquid-liquid phase separation. EB1 decreased the rate of aggregation and increased the critical concentration of tau aggregation. Dynamic light scattering, atomic force microscopy, dot blot assays, and SDS-PAGE analysis showed that EB1 inhibited the formation of oligomers and higher-order aggregates of tau. The data suggest a novel role for EB1 as a regulator of tau function and aggregation, and the findings indicated the role of the EB family proteins in neuronal function and neurodegeneration.

Ramanujan’s Tau-Function and Convolution Sums

We study certain type of convolution sums involving an arbitrary arithmetic function f, which it is applied to Ramanujan’s tau function when f coincides with the sum of divisors function.

Temporal and region-specific tau hyperphosphorylation in the medulla and forebrain coincides with development of functional changes in male obese Zucker rats.

Metabolic syndrome (MetS) is associated with development of tauopathies that contribute to cognitive decline. Without functional leptin receptors, male obese Zucker rats (OZRs) develop MetS, and they have increased phosphorylated tau (ptau) with impaired cognitive function. In addition to regulating energy balance, leptin enhances activation of the hippocampus, which is essential for spatial learning and memory. Whether spatial learning and memory are always impaired in OZRs or develop with MetS is unknown. We hypothesized that male OZRs develop MetS traits that promote regional increases in ptau and functional deficits associated with those brain regions. In the medulla and cortex, tau-pSer199,202 and tau-pSer396 were comparable in juvenile (7-8 wk old) lean Zucker rats (LZRs) and OZRs but increased in 18- to 19-wk-old OZRs. Elevated tau-pSer396 was concentrated in the dorsal vagal complex of the medulla, and by this age OZRs had hypertension with increased arterial pressure variability. In the hippocampus, tau-pSer199,202 and tau-pSer396 were still comparable in 18- to 19-wk-old OZRs and LZRs but elevated in 28- to 29-wk-old OZRs, with emergence of deficits in Morris water maze performance. Comparable escape latencies observed during acquisition in 18- to 19-wk-old OZRs and LZRs were increased in 28- to 29-wk-old OZRs, with greater use of nonspatial search strategies. Increased ptau developed with changes in the insulin/phosphatidylinositol 3-kinase (PI3K)/Akt signaling pathway in the hippocampus and cortex but not medulla, suggesting different underlying mechanisms. These data demonstrate that leptin is not required for spatial learning and memory in male OZRs. Furthermore, early development of MetS-associated autonomic dysfunction by the medulla may be predictive of later hippocampal dysfunction and cognitive impairment.NEW & NOTEWORTHY Male obese Zucker rats (OZRs) lack functional leptin receptors and develop metabolic syndrome (MetS). At 16-19 wk, OZRs are insulin resistant, with increased ptau in dorsal medulla and impaired autonomic regulation of AP. At 28-29 wk OZRs develop increased ptau in hippocampus with deficits in spatial learning and memory. Juvenile OZRs lack elevated ptau and these deficits, demonstrating that leptin is not essential for normal function. Elevated ptau and deficits emerge before the onset of diabetes in insulin-resistant OZRs.

Scalar quasi-normal modes of accelerating Kerr-Newman-AdS black holes

We study linear scalar perturbations of slowly accelerating Kerr-Newman-anti-de Sitter black holes using the method of isomonodromic deformations. The conformally coupled Klein-Gordon equation separates into two second-order ordinary differential equations with five singularities. Nevertheless, the angular equation can be transformed into a Heun equation, for which we provide an asymptotic expansion for the angular eigenvalues in the small acceleration and rotation limit. In the radial case, we recast the boundary value problem in terms of a set of initial conditions for the isomonodromic tau function of Fuchsian systems with five regular singular points. For the sake of illustration, we compute the quasi-normal modes frequencies.

Sigma model instantons and singular tau function

The generating series for the instanton contribution to Green functions of the $2D$ sigma model was found in the works of Schwarz, Fateev and Frolov. We show that this series can be written as a formal tau function of the two-sided two-component KP hierarchy. We call it formal singular tau function because this tau function is a sum where each term is the infrared and ultraviolet divergent one exactly as the series found by the mentioned authors. However one can regularize this singluar tau function and to obtain regular observables. This is because observables contains ratious of mentioned divergent expressions. Thus, we enladge the families of tau functions to work with.

Tau's function and dysfunction in the brain: when small changes have big consequences.

Tau's function and dysfunction in the brain: when small changes have big consequences.

The O-GlcNAc Modification of Recombinant Tau Protein and Characterization of the O-GlcNAc Pattern for Functional Study.

The neuronal microtubule-associated tau protein is characterized in vivo by a large number of post-translational modifications along the entire primary sequence that modulates its function. The primary modification of tau is phosphorylation of serine/threonine or tyrosine residues that is involved in the regulation of microtubule binding and polymerization. In neurodegenerative disorders referred to as tauopathies including Alzheimer's disease, tau is abnormally hyperphosphorylated and forms fibrillar inclusions in neurons progressing throughout different brain area during the course of the disease. The O-β-linked N-acetylglucosamine (O-GlcNAc) is another reversible post-translational modification of serine/threonine residues that is installed and removed by the unique O-GlcNAc transferase (OGT) and O-GlcNAc hydrolase (OGA), respectively. This modification was described as a potential modulator of tau phosphorylation and functions in the physiopathology. Moreover, reducing protein O-GlcNAc levels in the brain upon treatment of tauopathy mouse models with an OGA inhibitor reveals a beneficial effect on tau pathology and neurodegeneration. However, whether the role of tau O-GlcNAcylation is responsible of the protective effect against tau toxicity remains to be determined. The production of O-GlcNAc modified recombinant tau protein is a valuable tool for the investigations of the impact of O-GlcNAcylation on tau functions, modulation of interactions with partners and crosstalk with other post-translational modifications, including but not restricted to phosphorylation. We describe here the in vitro O-GlcNAcylation of tau with recombinant OGT for which we provide an expression and purification protocol. The use of the O-GlcNAc tau protein in functional studies requires the analytical characterization of the O-GlcNAc pattern. Here, we describe a method for the O-GlcNAc modification of tau protein with recombinant OGT and the analytical characterization of the resulting O-GlcNAc pattern by a combination of methods for the overall characterization of tau O-GlcNAcylation by chemoenzymatic labeling and mass spectrometry, as well as the quantitative, site-specific pattern by NMR spectroscopy.

Quantification of Methylation and Phosphorylation Stoichiometry.

Tauopathies including Alzheimer's disease (AD) are neurodegenerative disorders accompanied by the conversion of functional forms of the microtubule associated protein Tau into non-functional aggregates. A variety of post-translational modifications (PTMs) on Tau precede or accompany the conversion, placing them in position to modulate Tau function as well as its propensity to aggregate. Although Tau PTMs can be characterized by their sites of modification, their total stoichiometry when summed over all sites also is an important metric of their potential impact on function. Here we provide a protocol for rapidly producing recombinant Tau with enzyme-specific PTMs at high stoichiometry in vitro and demonstrate its utility in the context of hyperphosphorylation. Additionally, protocols for estimating phosphorylation and methylation stoichiometry on Tau proteins isolated from any source are presented. Together these methods support experimentation on Tau PTM function over a wide range of experimental conditions.

Therapeutic effects of long-term HBOT on Alzheimer's disease neuropathologies and cognitive impairment in APPswe/PS1dE9 mice

Alzheimer's disease (AD) is the most common neurodegenerative disorder with the pathological hallmarks of amyloid beta (Aβ) plaques and neurofibrillary tangles (NFTs) in the brain. Although there is a hope that anti-amyloid monoclonal antibodies may emerge as a new therapy for AD, the high cost and side effect is a big concern. Non-drug therapy is attracting more attention and may provide a better resolution for the treatment of AD. Given the fact that hypoxia contributes to the pathogenesis of AD, hyperbaric oxygen therapy (HBOT) may be an effective intervention that can alleviate hypoxia and improve AD. However, it remains unclear whether long-term HBOT intervention in the early stage of AD can slow AD progression and ultimately prevent cognitive impairment in this disease. In this study we applied consecutive 3-month HBOT interventions on 3-month-old APPswe/PS1dE9 AD mice which represent the early stage of AD. When the APPswe/PS1dE9 mice at 9-month-old which represent the disease stage we measured cognitive function, 24-h blood oxygen saturation, Aβ and tau pathologies, vascular structure and function, and neuroinflammation in APPswe/PS1dE9 mice. Our results showed that long-term HBOT can attenuate the impairments in cognitive function observed in 9-month-old APPswe/PS1dE9 mice. Most importantly, HBOT effectively reduced the progression of Aβ plaques deposition, hyperphosphorylated tau protein aggregation, and neuronal and synaptic degeneration in the AD mice. Further, long-term HBOT was able to enhance blood oxygen saturation level. Besides, long-term HBOT can improve vascular structure and function, and reduce neuroinflammation in AD mice. This study is the first to demonstrate that long-term HBOT intervention in the early stage of AD can attenuate cognitive impairment and AD-like pathologies. Overall, these findings highlight the potential of long-term HBOT as a disease-modifying approach for AD treatment.

Tau seeding without tauopathy

Neurodegenerative tauopathies such as Alzheimer’s disease (AD) are caused by brain accumulation of tau assemblies. Evidence suggests tau functions as a prion, and cells and animals efficiently propagate unique, transmissible tau pathology. This suggests a dedicated cellular replication machinery, potentially with a normal physiologic function for tau seeds. Consequently, we hypothesized that healthy control brains would have seeding activity. We have recently developed a novel monoclonal antibody (MD3.1) specific for tau seeds. We used this antibody to immunopurify tau from the parietal and cerebellar cortices of 19 healthy subjects without any neuropathology, ranging 19-65 years. We detected seeding in lysates from the parietal cortex, but not in the cerebellum. We also detected no seeding in brain homogenates from wild-type or human tau knockin mice, suggesting that cellular/genetic context dictates development of seed-competent tau. Seeding did not correlate with subject age or brain tau levels. We confirmed our essential findings using an orthogonal assay, RTQuIC, which amplifies tau seeds in vitro. Dot blot analyses revealed no AT8 immunoreactivity above background levels in parietal and cerebellar extracts and ∼1/100 of that present in AD. Based on binding to a panel of antibodies, the conformational characteristics of control seeds differed from AD, suggesting a unique underlying assembly, or structural ensemble. Tau’s ability to adopt self-replicating conformations under non-pathogenic conditions may reflect a normal function that goes awry in disease states.

Complex KdV rogue waves from gauge-Miura transformation

The gauge-Miura correspondence establishes a map between the entire KdV and mKdV hierarchies, including positive and also negative flows, from which new relations besides the standard Miura transformation arise. We use this correspondence to classify solutions of the KdV hierarchy in terms of elementary tau functions of the mKdV hierarchy under both zero and nonzero vacua. We illustrate how interesting nonlinear phenomena can be described analytically from this construction, such as “rogue waves” of a complex KdV system that corresponds to a limit of a vector nonlinear Schrödinger equation.

Shifted Witten classes and topological recursion

The Witten r r -spin class defines a non-semisimple cohomological field theory. Pandharipande, Pixton and Zvonkine studied two special shifts of the Witten class along two semisimple directions of the associated Dubrovin–Frobenius manifold using the Givental–Teleman reconstruction theorem. We show that the R R -matrix and the translation of these two specific shifts can be constructed from the solutions of two differential equations that generalise the classical Airy differential equation. Using this, we prove that the descendant intersection theory of the shifted Witten classes satisfies topological recursion on two 1 1 -parameter families of spectral curves. By taking the limit as the parameter goes to zero, we prove that the descendant intersection theory of the Witten r r -spin class can be computed by topological recursion on the r r -Airy spectral curve. We finally show that this proof suffices to deduce Witten’s r r -spin conjecture, already proved by Faber, Shadrin and Zvonkine, which claims that the generating series of r r -spin intersection numbers is the tau function of the r r -KdV hierarchy that satisfies the string equation.

A representation of a class of quasi-arithmetic means using a unary modifier operator

In this short communication, we will show that a quasi-arithmetic mean induced by an additive generator of a strict t-norm (strict t-conorm, respectively) can be represented by the composition of a unary operator (called the tau function) and the strict t-norm (strict t-conorm, respectively), both induced by the same generator function as the quasi arithmetic mean. Here, we will also state a connection between the idempotency of a transformed strict t-norm (strict t-conorm, respectively) and the tau function.

BIN1 in the Pursuit of Ousting the Alzheimer's Reign: Impact on Amyloid and Tau Neuropathology.

Alzheimer's disease contributes to 60-70% of all dementia cases in the general population. Belonging to the BIN1/amphiphysin/RVS167 (BAR) superfamily, the bridging integrator (BIN1) has been identified to impact two major pathological hallmarks in Alzheimer's disease (AD), i.e., amyloid beta (Aβ) and tau accumulation. Aβ accumulation is found to increase by BIN1 knockdown in cortical neurons in late-onset AD, due to BACE1 accumulation at enlarged early endosomes. Two BIN1 mutants, KR and PL, were identified to exhibit Aβ accumulation. Furthermore, BIN1 deficiency by BIN1-related polymorphisms impairs the interaction with tau, thus elevating tau phosphorylation, altering synapse structure and tau function. Even though the precise role of BIN1 in the neuronal tissue needs further investigation, the authors aim to throw light on the potential of BIN1 and unfold its implications on tau and Aβ pathology, to aid AD researchers across the globe to examine BIN1, as an appropriate target gene for disease management.

Tau protein modulates an epigenetic mechanism of cellular senescence in human SH-SY5Y neuroblastoma cells.

Introduction: Progressive Tau deposition in neurofibrillary tangles and neuropil threads is the hallmark of tauopathies, a disorder group that includes Alzheimer's disease. Since Tau is a microtubule-associated protein, a prevalent concept to explain the pathogenesis of tauopathies is that abnormal Tau modification contributes to dissociation from microtubules, assembly into multimeric β-sheets, proteotoxicity, neuronal dysfunction and cell loss. Tau also localizes in the cell nucleus and evidence supports an emerging function of Tau in DNA stability and epigenetic modulation. Methods: To better characterize the possible role of Tau in regulation of chromatin compaction and subsequent gene expression, we performed a bioinformatics analysis of transcriptome data obtained from Tau-depleted human neuroblastoma cells. Results: Among the transcripts deregulated in a Tau-dependent manner, we found an enrichment of target genes for the polycomb repressive complex 2. We further describe decreased cellular amounts of the core components of the polycomb repressive complex 2 and lower histone 3 trimethylation in Tau deficient cells. Among the de-repressed polycomb repressive complex 2 target gene products, IGFBP3 protein was found to be linked to increased senescence induction in Tau-deficient cells. Discussion: Our findings propose a mechanism for Tau-dependent epigenetic modulation of cell senescence, a key event in pathologic aging.

Darboux transformations of the modified BKP hierarchy by fermionic approach

The modified BKP (mBKP) hierarchy is an important integrable hierarchy related with BKP hierarchy. Darboux transformation is a powerful method to obtain various solutions of integrable systems. But for mBKP hierarchy, it is usually very difficult to construct the corresponding Darboux transformations, since it has a more complicated constraint on the Lax operator, compared with the BKP hierarchy. In this paper, we use the fermionic approach to obtain the explicit Darboux transformation operators of the mBKP hierarchy starting from the changes in tau functions. Also we investigate the relations among these new Darboux transformation operators. It is usually very difficult to convert the changes in tau functions to the ones in the Lax operator, while here we provide one successful example.