Altered Kv2.1 functioning promotes increased excitability in hippocampal neurons of an Alzheimer's disease mouse model.

Altered neuronal excitability is emerging as an important feature in Alzheimer's disease (AD). Kv2.1 potassium channels are important modulators of neuronal excitability and synaptic activity. We investigated Kv2.1 currents and its relation to the intrinsic synaptic activity of hippocampal neurons from 3xTg-AD (triple transgenic mouse model of Alzheimer's disease) mice, a widely employed preclinical AD model. Synaptic activity was also investigated by analyzing spontaneous [Ca(2+)]i spikes. Compared with wild-type (Non-Tg (non-transgenic mouse model)) cultures, 3xTg-AD neurons showed enhanced spike frequency and decreased intensity. Compared with Non-Tg cultures, 3xTg-AD hippocampal neurons revealed reduced Kv2.1-dependent Ik current densities as well as normalized conductances. 3xTg-AD cultures also exhibited an overall decrease in the number of functional Kv2.1 channels. Immunofluorescence assay revealed an increase in Kv2.1 channel oligomerization, a condition associated with blockade of channel function. In Non-Tg neurons, pharmacological blockade of Kv2.1 channels reproduced the altered pattern found in the 3xTg-AD cultures. Moreover, compared with untreated sister cultures, pharmacological inhibition of Kv2.1 in 3xTg-AD neurons did not produce any significant modification in Ik current densities. Reactive oxygen species (ROS) promote Kv2.1 oligomerization, thereby acting as negative modulator of the channel activity. Glutamate receptor activation produced higher ROS levels in hippocampal 3xTg-AD cultures compared with Non-Tg neurons. Antioxidant treatment with N-Acetyl-Cysteine was found to rescue Kv2.1-dependent currents and decreased spontaneous hyperexcitability in 3xTg-AD neurons. Analogous results regarding spontaneous synaptic activity were observed in neuronal cultures treated with the antioxidant 6-hydroxy-2,5,7,8-tetramethylchroman-2-carboxylic acid (Trolox). Our study indicates that AD-related mutations may promote enhanced ROS generation, oxidative-dependent oligomerization, and loss of function of Kv2.1 channels. These processes can be part on the increased neuronal excitability of these neurons. These steps may set a deleterious vicious circle that eventually helps to promote excitotoxic damage found in the AD brain

Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum

Motivated by a problem in climate dynamics, we investigate the solution of a Bessel-like process with negative constant drift, described by a Fokker-Planck equation with a potential V(x) = - [b \ln(x) + a\, x], for b>0 and a<0. The problem belongs to a family of Fokker-Planck equations with logarithmic potentials closely related to the Bessel process, that has been extensively studied for its applications in physics, biology and finance. The Bessel-like process we consider can be solved by seeking solutions through an expansion into a complete set of eigenfunctions. The associated imaginary-time Schroedinger equation exhibits a mix of discrete and continuous eigenvalue spectra, corresponding to the quantum Coulomb potential describing the bound states of the hydrogen atom. We present a technique to evaluate the normalization factor of the continuous spectrum of eigenfunctions that relies solely upon their asymptotic behavior. We demonstrate the technique by solving the Brownian motion problem and the Bessel process both with a negative constant drift. We conclude with a comparison with other analytical methods and with numerical solutions.Comment: 21 pages, 8 figure