TREK-1 and Best1 channels mediate fast and slow glutamate release in astrocytes upon GPCR activation.

Astrocytes release glutamate upon activation of various GPCRs to exert important roles in synaptic functions. However, the molecular mechanism of release has been controversial. Here, we report two kinetically distinct modes of nonvesicular, channel-mediated glutamate release. The fast mode requires activation of G(αi), dissociation of G(ßγ), and subsequent opening of glutamate-permeable, two-pore domain potassium channel TREK-1 through direct interaction between G(ßγ) and N terminus of TREK-1. The slow mode is Ca(2+) dependent and requires G(αq) activation and opening of glutamate-permeable, Ca(2+)-activated anion channel Best1. Ultrastructural analyses demonstrate that TREK-1 is preferentially localized at cell body and processes, whereas Best1 is mostly found in microdomains of astrocytes near synapses. Diffusion modeling predicts that the fast mode can target neuronal mGluR with peak glutamate concentration of 100 µM, whereas slow mode targets neuronal NMDA receptors at around 1 µM. Our results reveal two distinct sources of astrocytic glutamate that can differentially influence neighboring neurons.

Entropy formula of N-body system.

We prove a proposition that the entropy of the system composed of finite N molecules of ideal gas is the q-entropy or Havrda-Charvát-Tsallis entropy, which is also known as Tsallis entropy, with the entropic index [Formula: see text] in D-dimensional space. The indispensable infinity assumption used by Boltzmann and others in their derivation of entropy formulae is not involved in our derivation, therefore our derived formula is exact. The analogy of the N-body system brings us to obtain the entropic index of a combined system [Formula: see text] formed from subsystems having different entropic indexes [Formula: see text] and [Formula: see text] as [Formula: see text]. It is possible to use the number N for the physical measure of deviation from Boltzmann entropy.

Ultrasonic Neuromodulation via Astrocytic TRPA1.

Low-intensity, low-frequency ultrasound (LILFU) is the next-generation, non-invasive brain stimulation technology for treating various neurological and psychiatric disorders. However, the underlying cellular and molecular mechanism of LILFU-induced neuromodulation has remained unknown. Here, we report that LILFU-induced neuromodulation is initiated by opening of TRPA1 channels in astrocytes. The Ca2+ entry through TRPA1 causes a release of gliotransmitters including glutamate through Best1 channels in astrocytes. The released glutamate activates NMDA receptors in neighboring neurons to elicit action potential firing. Our results reveal an unprecedented mechanism of LILFU-induced neuromodulation, involving TRPA1 as a unique sensor for LILFU and glutamate-releasing Best1 as a mediator of glia-neuron interaction. These discoveries should prove to be useful for optimization of human brain stimulation and ultrasonogenetic manipulations of TRPA1.

Univariate polynomial equation providing on-lattice higher-order models of thermal lattice Boltzmann theory.

A univariate polynomial equation is presented. It provides on-lattice higher-order models of the thermal lattice Boltzmann equation. The models can be accurate up to any required level and can be applied to regular lattices, which allow efficient and accurate approximate solutions of the Boltzmann equation. We derive models approaching the complete Galilean invariant and providing accuracy of the fourth-order moment and beyond. We simulate one-dimensional thermal shock tube problems to illustrate the accuracy of our models. Moreover, we show the remarkably enhanced stability obtained by our models and our discretized equilibrium distributions.

Multidimensional on-lattice higher-order models in the thermal lattice Boltzmann theory.

We present a set of uniform polynomial equations that provides multidimensional on-lattice higher-order models of the lattice Boltzmann theory while keeping compact the number of discrete velocities. As examples, we explicitly derive one-, two-, and three-dimensional on-lattice models applicable to describing thermal compressible flows of the accuracy levels of the Navier-Stokes equations with smaller numbers of discrete velocities in comparison to the existing models. We demonstrate the accuracy and stability of the one-, two-, and three-dimensional models by using the Riemann problem.

Thermal lattice Boltzmann method based on a theoretically simple derivation of the Taylor expansion.

We propose an approach to derive the thermal lattice Boltzmann method that is based on the Taylor expansion in variables of temperature as well as velocity and a direct calculation upon the Gaussian quadrature based hypothesis. This enables us to overcome the isothermal limitation and the low-order accuracy simultaneously. A systematic framework is explained for constructing numerically stable lattice Boltzmann models. The stability of this one-dimensional lattice Boltzmann model is demonstrated with a shock tube simulation.

Robust thermal boundary conditions applicable to a wall along which temperature varies in lattice-gas cellular automata.

We show that the heat exchange between fluid particles and boundary walls can be achieved by controlling the velocity change rate following the particles' collision with a wall in discrete kinetic theory, such as the lattice-gas cellular automata and the lattice Boltzmann method. We derive a relation between the velocity change rate and temperature so that we can control the velocity change rate according to a given temperature boundary condition. This relation enables us to deal with the thermal boundary whose temperature varies along a wall in contrast to the previous works of the lattice-gas cellular automata. In addition, we present simulation results to compare our method to the existing and give an example in a microchannel with a high temperature gradient boundary condition by the lattice-gas cellular automata.