Different Mechanisms of Ca2+ Transport in NMDA and Ca2+-permeable AMPA Glutamate Receptor Channels

The channel of the glutamate N-methyl-d-aspartate receptor (NMDAR) transports Ca2+ approximately four times more efficiently than that of Ca2+-permeable α-amino-3-hydroxy-5-methyl-4-isoxazolepropionate receptors (AMPAR). To investigate the basis of this difference in these glutamate receptors (GluRs), we measured the ratio of Cs+ efflux and Ca2+ influx in recombinant NMDAR and Ca2+-permeable AMPAR channels expressed in human embryonic kidney 293 (HEK 293) cells over a wide voltage range. At any one potential, this biionic flux ratio was measured by quantifying the total charge and the charge carried by Ca2+ using whole-cell currents and fluorometric techniques (dye overload) with Cs+ internally and Ca2+ externally (1.8 or 10 mM) as the only permeant ions. In AMPAR channels, composed of either GluR-A(Q) or GluR-B(Q) subunits, the biionic flux ratio had a biionic flux-ratio exponent of 1, consistent with the prediction of the Goldman-Hodgkin-Katz current equation. In contrast, for NMDAR channels composed of NR1 and NR2A subunits, the biionic flux-ratio exponent was ∼2, indicating a deviation from Goldman-Hodgkin-Katz. Consistent with these results, in NMDAR channels under biionic conditions with high external Ca2+ and Cs+ as the reference ions, Ca2+ permeability (PCa/PCs) was concentration dependent, being highest around physiological concentrations (1–1.8 mM; PCa/PCs ≈ 6.1) and reduced at both higher (110 mM; PCa/PCs ≈ 2.6) and lower (0.18 mM; PCa/PCs ≈ 2.2) concentrations. PCa/PCs in AMPAR channels was not concentration dependent, being around 1.65 in 0.3–110 mM Ca2+. In AMPAR and NMDAR channels, the Q/R/N site is a critical determinant of Ca2+ permeability. However, mutant AMPAR channels, which had an asparagine substituted at the Q/R site, also showed a biionic flux-ratio exponent of 1 and concentration-independent permeability ratios, indicating that the difference in Ca2+ transport is not due to the amino acid residue located at the Q/R/N site. We suggest that the difference in Ca2+ transport properties between the glutamate receptor subtypes reflects that the pore of NMDAR channels has multiple sites for Ca2+, whereas that of AMPAR channels only a single site

Shack-Hartmann wave front measurements in cortical tissue for deconvolution of large three-dimensional mosaic transmitted light brightfield micrographs

We present a novel approach for deconvolution of 3D image stacks of cortical tissue taken by mosaic/optical-sectioning technology, using a transmitted light brightfield microscope. Mosaic/optical-sectioning offers the possibility of imaging large volumes (e.g. from cortical sections) on a millimetre scale at sub-micrometre resolution. However, a blurred contribution from out-of-focus light results in an image quality that usually prohibits 3D quantitative analysis. Such quantitative analysis is only possible after deblurring by deconvolution. The resulting image quality is strongly dependent on how accurate the point spread function used for deconvolution resembles the properties of the imaging system. Since direct measurement of the true point spread function is laborious and modelled point spread functions usually deviate from measured ones, we present a method of optimizing the microscope until it meets almost ideal imaging conditions. These conditions are validated by measuring the aberration function of the microscope and tissue using a Shack-Hartmann sensor. The analysis shows that cortical tissue from rat brains embedded in Mowiol and imaged by an oil-immersion objective can be regarded as having a homogeneous index of refraction. In addition, the amount of spherical aberration that is caused by the optics or the specimen is relatively low. Consequently the image formation is simplified to refraction between the embedding and immersion medium and to 3D diffraction at the finite entrance pupil of the objective. The resulting model point spread function is applied to the image stacks by linear or iterative deconvolution algorithms. For the presented dataset of large 3D images the linear approach proves to be superior. The linear deconvolution yields a significant improvement in signal-to-noise ratio and resolution. This novel approach allows a quantitative analysis of the cortical image stacks such as the reconstruction of biocytin-stained neuronal dendrites and axons

Exact ground state of finite Bose-Einstein condensates on a ring

The exact ground state of the many-body Schr\"odinger equation for $N$ bosons on a one-dimensional ring interacting via pairwise $\delta$-function interaction is presented for up to fifty particles. The solutions are obtained by solving Lieb and Liniger's system of coupled transcendental equations for finite $N$. The ground state energies for repulsive and attractive interaction are shown to be smoothly connected at the point of zero interaction strength, implying that the \emph{Bethe-ansatz} can be used also for attractive interaction for all cases studied. For repulsive interaction the exact energies are compared to (i) Lieb and Liniger's thermodynamic limit solution and (ii) the Tonks-Girardeau gas limit. It is found that the energy of the thermodynamic limit solution can differ substantially from that of the exact solution for finite $N$ when the interaction is weak or when $N$ is small. A simple relation between the Tonks-Girardeau gas limit and the solution for finite interaction strength is revealed. For attractive interaction we find that the true ground state energy is given to a good approximation by the energy of the system of $N$ attractive bosons on an infinite line, provided the interaction is stronger than the critical interaction strength of mean-field theory.Comment: 28 pages, 11 figure

Optimal time-dependent lattice models for nonequilibrium dynamics

Lattice models are abundant in theoretical and condensed-matter physics. Generally, lattice models contain time-independent hopping and interaction parameters that are derived from the Wannier functions of the noninteracting problem. Here, we present a new concept based on time-dependent Wannier functions and the variational principle that leads to optimal time-dependent lattice models. As an application, we use the Bose-Hubbard model with time-dependent Wannier functions to study a quench scenario involving higher bands. We find a separation of times scales in the dynamics and show that under some circumstances the multi-band nonequilibrium dynamics of a quantum system can be obtained essentially at the cost of a single-band model.Comment: 14 pages, 3 figure

Mean first-passage times for an ac-driven magnetic moment of a nanoparticle

The two-dimensional backward Fokker-Planck equation is used to calculate the mean first-passage times (MFPTs) of the magnetic moment of a nanoparticle driven by a rotating magnetic field. It is shown that a magnetic field that is rapidly rotating in the plane {\it perpendicular} to the easy axis of the nanoparticle governs the MFPTs just in the same way as a static magnetic field that is applied {\it along} the easy axis. Within this framework, the features of the magnetic relaxation and net magnetization of systems composed of ferromagnetic nanoparticles arising from the action of the rotating field are revealed.Comment: 7 pages, 1 figur

Rapidly driven nanoparticles: Mean first-passage times and relaxation of the magnetic moment

We present an analytical method of calculating the mean first-passage times (MFPTs) for the magnetic moment of a uniaxial nanoparticle which is driven by a rapidly rotating, circularly polarized magnetic field and interacts with a heat bath. The method is based on the solution of the equation for the MFPT derived from the two-dimensional backward Fokker-Planck equation in the rotating frame. We solve these equations in the high-frequency limit and perform precise, numerical simulations which verify the analytical findings. The results are used for the description of the rates of escape from the metastable domains which in turn determine the magnetic relaxation dynamics. A main finding is that the presence of a rotating field can cause a drastic decrease of the relaxation time and a strong magnetization of the nanoparticle system. The resulting stationary magnetization along the direction of the easy axis is compared with the mean magnetization following from the stationary solution of the Fokker-Planck equation.Comment: 24 pages, 4 figure

The impact of neuron morphology on cortical network architecture

The neurons in the cerebral cortex are not randomly interconnected. This specificity in wiring can result from synapse formation mechanisms that connect neurons, depending on their electrical activity and genetically defined identity. Here, we report that the morphological properties of the neurons provide an additional prominent source by which wiring specificity emerges in cortical networks. This morphologically determined wiring specificity reflects similarities between the neurons’ axo-dendritic projections patterns, the packing density, and the cellular diversity of the neuropil. The higher these three factors are, the more recurrent is the topology of the network. Conversely, the lower these factors are, the more feedforward is the network’s topology. These principles predict the empirically observed occurrences of clusters of synapses, cell type-specific connectivity patterns, and nonrandom network motifs. Thus, we demonstrate that wiring specificity emerges in the cerebral cortex at subcellular, cellular, and network scales from the specific morphological properties of its neuronal constituents

Correlation entropy of synaptic input-output dynamics

The responses of synapses in the neocortex show highly stochastic and nonlinear behavior. The microscopic dynamics underlying this behavior, and its computational consequences during natural patterns of synaptic input, are not explained by conventional macroscopic models of deterministic ensemble mean dynamics. Here, we introduce the correlation entropy of the synaptic input-output map as a measure of synaptic reliability which explicitly includes the microscopic dynamics. Applying this to experimental data, we find that cortical synapses show a low-dimensional chaos driven by the natural input pattern.Comment: 7 pages, 6 Figures (7 figure files

Bose-Hubbard model with occupation dependent parameters

We study the ground-state properties of ultracold bosons in an optical lattice in the regime of strong interactions. The system is described by a non-standard Bose-Hubbard model with both occupation-dependent tunneling and on-site interaction. We find that for sufficiently strong coupling the system features a phase-transition from a Mott insulator with one particle per site to a superfluid of spatially extended particle pairs living on top of the Mott background -- instead of the usual transition to a superfluid of single particles/holes. Increasing the interaction further, a superfluid of particle pairs localized on a single site (rather than being extended) on top of the Mott background appears. This happens at the same interaction strength where the Mott-insulator phase with 2 particles per site is destroyed completely by particle-hole fluctuations for arbitrarily small tunneling. In another regime, characterized by weak interaction, but high occupation numbers, we observe a dynamical instability in the superfluid excitation spectrum. The new ground state is a superfluid, forming a 2D slab, localized along one spatial direction that is spontaneously chosen.Comment: 16 pages, 4 figure

Dynamics of cold bosons in optical lattices: Effects of higher Bloch bands

The extended effective multiorbital Bose-Hubbard-type Hamiltonian which takes into account higher Bloch bands, is discussed for boson systems in optical lattices, with emphasis on dynamical properties, in relation with current experiments. It is shown that the renormalization of Hamiltonian parameters depends on the dimension of the problem studied. Therefore, mean field phase diagrams do not scale with the coordination number of the lattice. The effect of Hamiltonian parameters renormalization on the dynamics in reduced one-dimensional optical lattice potential is analyzed. We study both the quasi-adiabatic quench through the superfluid-Mott insulator transition and the absorption spectroscopy, that is energy absorption rate when the lattice depth is periodically modulated.Comment: 23 corrected interesting pages, no Higgs boson insid