Mathematical Foundations of the Non-Hermitian Skin Effect.

We study the skin effect in a one-dimensional system of finitely many subwavelength resonators with a non-Hermitian imaginary gauge potential. Using Toeplitz matrix theory, we prove the condensation of bulk eigenmodes at one of the edges of the system. By introducing a generalised (complex) Brillouin zone, we can compute spectral bands of the associated infinitely periodic structure and prove that this is the limit of the spectra of the finite structures with arbitrarily large size. Finally, we contrast the non-Hermitian systems with imaginary gauge potentials considered here with systems where the non-Hermiticity arises due to complex material parameters, showing that the two systems are fundamentally distinct.

Stigmasterol isolated from Azadirachta indica flowers attenuated glutamate-induced neurotoxicity via downregulation of the Cdk5/p35/p25 signaling pathway in the HT-22 cells.

BACKGROUND: Glutamate, an excitatory neurotransmitter, was elevated in the brain of neurodegenerative disease (ND) patients. The excessive glutamate induces Ca2+ influx and reactive oxygen species (ROS) production which exacerbates mitochondrial function, leading to mitophagy aberration, and hyperactivates Cdk5/p35/p25 signaling leading to neurotoxicity in ND. Stigmasterol, a phytosterol, has been reported for its neuroprotective effects; however, the underlying mechanism of stigmasterol on restoring glutamate-induced neurotoxicity is not fully investigated. PURPOSE: We investigated the effect of stigmasterol, a compound isolated from Azadirachta indica (AI) flowers, on ameliorating glutamate-induced neuronal apoptosis in the HT-22 cells. STUDY DESIGN: To further understand the underlying molecular mechanisms of stigmasterol, we investigated the effect of stigmasterol on Cdk5 expression, which was aberrantly expressed in glutamate-treated cells. Cell viability, Western blot analysis, and immunofluorescence are employed. RESULTS: Stigmasterol significantly inhibited glutamate-induced neuronal cell death via attenuating ROS production, recovering mitochondrial membrane depolarization, and ameliorating mitophagy aberration by decreasing mitochondria/lysosome fusion and the ratio of LC3-II/LC3-I. In addition, stigmasterol treatment downregulated glutamate-induced Cdk5, p35, and p25 expression via enhancement of Cdk5 degradation and Akt phosphorylation. Although stigmasterol demonstrated neuroprotective effects on inhibiting glutamate-induced neurotoxicity, the efficiency of stigmasterol is limited due to its poor water solubility. We conjugated stigmasterol to soluble soybean polysaccharides with chitosan nanoparticles to overcome the limitations. We found that the encapsulated stigmasterol increased water solubility and enhanced the protective effect on attenuating the Cdk5/p35/p25 signaling pathway compared with free stigmasterol. CONCLUSION: Our findings illustrate the neuroprotective effect and the improved utility of stigmasterol in inhibiting glutamate-induced neurotoxicity.

Changes in the prefrontal cortex after the hippocampus was injected with Aß25-35 via the P35/P25-CDK5-Tau hyperphosphorylation signaling pathway.

Alzheimer's disease (AD) is one of the common neurodegenerative illnesses in aging populations around the world. Recently, psychiatric symptoms are becoming increasingly important in recognizing the manifestations of AD in addition to cognitive impairment. Some studies suggest that the prefrontal cortex (PFC) is closely related to apathy/depression, and a network may exist between the CA1 of hippocampus and PFC. However, whether the injection of Aß2535 into hippocampi may result in PFC abnormalities in AD model rats is unclear. In this study, it was investigated the changes in the PFCs after the hippocampal injection via the P35/P25 - Cyclin-dependent kinase5 (CDK5) - Tau hyperphosphorylation signaling pathway. Our results demonstrated that rats injected with Aß25-35 showed decreased learning and memory ability, and increased depression-like behaviors compared with uninjected controls and saline-injected shams. P35/P25, CDK5, Tau[pS199], and Tau[pS202] are significantly elevated in the PFCs and hippocampi after Aß25-35 was injected into the hippocampi. Furthermore, P35/P25-CDK5 complexes were detected in vivo by immunofluorescence and co-immunoprecipitation. Therefore, the relative expression of proteins associated with the P35/P25-CDK5 pathway showed the same changes in the hippocampi and PFCs after Aß25-35 injection. These findings demonstrate a potential mechanism for prefrontal-mediated cognitive impairment and the psychiatric symptoms of AD.

[Effect of electroacupuncture on the P35/P25-cyclin-dependent kinase 5-Tau pathway in hippocampus of rats with Alzheimer's disease].

OBJECTIVE: To investigate the effect of electroacupuncture on the P35/P25-cyclin-dependent kinase 5 (CDK5)-Tau pathway in rats with Alzheimer's disease (AD), as well as the mechanism of electroacupuncture in the prevention and treatment of AD. METHODS: Sprague-Dawley rats were randomly divided into control group, sham-operation group, model group, and electroacupuncture treatment group, with 12 rats in each group. A rat model of AD was established by injection of Aß25-35 into the bilateral hippocampus. The rats in the electroacupuncture treatment group were given electroacupuncture at "Baihui" (GV20) and "Shenshu" (BL23) once a day, 15 min each time, for 10 days. Morris water maze was used to evaluate learning and memory abilities, immunohistochemistry was used to measure the distribution and expression of P35/P25, CDK5, and Tau5 in the hippocampus, and Western blot was used to measure the expression of the above mentioned proteins, phosphory-lated Tau(Ser199, Ser202). RESULTS: In the visual platform test, there were no significant differences in escape latency and search path between groups (P>0.05). In the hidden platform test, there were no significant differences in escape latency and search path between the control group and the sham-operation group (P>0.05); the model group had significantly longer escape latency and search path than the control group and the sham-operation group (P<0.05). Compared with the model group, the electroacupuncture treatment group had significantly shorter escape latency and search path (P<0.05). In the spatial exploration test, there was no significant difference in the number of platform crossings between the control group and the sham-operation group (P<0.05). The model group had a significantly lower number of platform crossings than the control group and the sham-operation group (P<0.01, P<0.05). The electroacupuncture treatment group had a significantly higher number of platform crossings than the model group (P<0.05). Compared with the control group and the sham-operation group, the model group had significant increases in the protein expression of P35/P25 and CDK5 (P<0.001), and the electroacupuncture treatment group had significant reductions compared with the model group (P<0.001). There was no significant difference in the protein expression of Tau5 between groups (P>0.05). The model group had significantly higher protein expression of phosphorylated Tau(Ser199, Ser202) in the hippocampus than the control group and the sham-operation group (P<0.01, P<0.05). The electroacupuncture treatment group had significantly lower protein expression of phosphorylated Tau(Ser199，Ser202) than the model group (P<0.05, P<0.01). CONCLUSION: Electroacupuncture may delay the progression of AD by affecting the expression of proteins involved in the P35/P25-CDK5-Tau pathway in the hippocampus of rats.

Spectral shift functions and Dirichlet-to-Neumann maps.

The spectral shift function of a pair of self-adjoint operators is expressed via an abstract operator-valued Titchmarsh-Weyl m-function. This general result is applied to different self-adjoint realizations of second-order elliptic partial differential operators on smooth domains with compact boundaries and Schrödinger operators with compactly supported potentials. In these applications the spectral shift function is determined in an explicit form with the help of (energy parameter dependent) Dirichlet-to-Neumann maps.

Lead exposure and tau hyperphosphorylation: An in vitro study.

The presence of fibrillary lesions, which are mainly composed of the microtubule associated protein tau (MAPT) in neurons, has gained immense recognition due to their presence in numerous neurodegenerative diseases, including Alzheimer's disease (AD). Dysregulation of tau is related with its altered site-specific phosphorylation which is followed by tau polymerization, neuronal dysfunction and death. Previous reports by us suggest that molecular alterations favor abundant tau phosphorylation and immunoreactivity in the frontal cortex of aged primates and rodents with past exposure to lead (Pb). Here we report the involvement of Pb-induced alterations in tau and hyperphosphorylation of tau in differentiated Human Neuroblastoma SH-SY5Y cells exposed to a series of Pb concentrations (5-100µM) for 48h. These cells were analyzed for the protein expression of total tau, site-specific tau hyperphosphorylation, cyclin dependent kinase 5 (CDK5) and p35/p25 at selected time points (24-144h), after Pb exposure had ceased. Western blot analysis revealed aberrant tau levels as well as site-specific tau hyperphosphorylation accompanied by elevated CDK5 levels and altered protein ratio of p35/p25 particularly at 72 and 144h. These changes provide additional evidence that neurodegenerative events are subject to environmental influences.

Antiallodynic Effects of Electroacupuncture Combined with MK-801 Treatment through the Regulation of p35/p25 in Experimental Diabetic Neuropathy.

The anti-allodynic effect of NMDA receptor antagonist and acupuncture treatments were explored through spinal p35 regulation of diabetic neuropathic rat. We evaluated the change over time of p35/p25 protein levels in the spinal cord compared with behavioral responses to thermal and mechanical stimulation in streptozotocin (STZ)-induced diabetic rats. Additionally, we studied p35 expression when electroacupuncture (EA) and a sub-effective dose of NMDA (N-methyl-D-aspartate) receptor antagonist (MK-801) were used to treat hyperalgesia in the diabetic neuropathic pain (DNP). Thermal paw withdrawal latency (PWL) and mechanical paw withdrawal threshold (PWT) were significantly decreased in the early stage of diabetes in rats. p35 expression after STZ injection gradually decreased from 1 week to 4 weeks compared to normal controls. p25 expression in 4-week diabetic rats was significantly higher than that of 2-week diabetic rats, and thermal PWL in 4-week diabetic rats showed delayed responses to painful thermal stimulation compared with those at 2 weeks. EA applied to the SP-9 point (2 Hz frequency) significantly prevented the thermal and mechanical hyperalgesia in the DNP rat. Additionally, EA combined with MK-801 prolonged anti-hyperalgesia, increased p35 expression, and decreased the cleavage of p35 to p25 during diabetic neuropathic pain. In this study we show EA combined with a sub-effective dose of MK-801 treatment in DNP induced by STZ that is related to p35/p25 expression in spinal cord.