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The aim of this paper is to investigate and give a new family of multi-variable Apostol-type polynomials. This family is related to Apostol-Euler, Apostol-Bernoulli, Apostol-Genocchi and Apostol-laguerre polynomials. Moreover, we derive some implicit summation formulae and general symmetry identities. The new family of polynomials introduced here, gives many interesting special cases.

Tauopathy is a pathological hallmark of many neurodegenerative diseases. It is characterized by abnormal aggregates of pathological phosphotau and somatodendritic redistribution. One suggested strategy for treating tauopathy is to stimulate autophagy, hence, getting rid of these pathological protein aggregates. One key controller of autophagy is mTOR. Since stimulation of mTOR leads to inhibition of autophagy, inhibitors of mTOR will cause stimulation of autophagy process. In this report, tauopathy was induced in mice using annonacin. Blocking of mTOR was achieved through stereotaxic injection of siRNA against mTOR. The behavioral and immunohistochemical evaluation revealed the development of tauopathy model as proven by deterioration of behavioral performance in open field test and significant tau aggregates in annonacin-treated mice. Blocking of mTOR revealed significant clearance of tau aggregates in the injected side; however, tau expression was not affected by mTOR blockage.

Rotenone is widely used insecticide and pesticide. It is an environmental neurotoxin that induces accumulation of α-synuclein and deterioration of dopaminergic neurons in substantia nigra pars compacta (SNpc). Autophagymediated self-digestion of cytoplasmic inclusions may be defensive against neurodegeneration caused by rotenone toxicity. This study designed to assess the autophagy role in rotenone-induced neurotoxic effects. Sixteen C57 black 6 male mice were divided into rotenone & control groups, each group contains 8 mice: the rotenone group; mice were administrated rotenone (3 mg/kg/day intraperitoneally). In the control group carboxymethyl cellulose 0.5% (a vehicle for rotenone) was given as 3mL/Kg/day intraperitoneal. Neuro-behavioural locomotor tests, histopathological and immuno-histochemical analysis of the brain dopaminergic neuronal cells and counting of microtubule Associated Protein Light Chain 3 (LC3) positive cells expression were investigated. Results showed that rotenone administration increases the total distance travelled, numbers of line crossing, average speed, maximum speed and rotations of the animal's body. However, it significantly decreases the efficient path and the total mobile and immobile episodes and induced severe degenerative changes in histo-pathological examination. Also, it decreased significantly the quantity of LC3 positive cells in the brain sections of exposed mice i.e. neurodegeneration and inhibition of autophagy in dopaminergic system. From this study it can be concluded that rotenone can induce neurotoxicity through inhibition of autophagy.

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