Dendritic spike induction of postsynaptic cerebellar LTP

The architecture of parallel fiber (PF) axons contacting cerebellar Purkinje neurons (PNs) retains spatial information over long distances. PF synapses can trigger local dendritic calcium spikes, but whether and how this calcium signal leads to plastic changes that decode the PF input organization is unknown. By combining voltage and calcium imaging, we show that PF-elicited calcium signals, mediated by voltage-gated calcium channels, increase non-linearly during high-frequency bursts of electrically constant calcium spikes because they locally and transiently saturate the endogenous buffer. We demonstrate that these non-linear calcium signals, independently of NMDA or metabotropic glutamate receptor activation, can induce PF long-term potentiation (LTP). Two-photon imaging in coronal slices revealed that calcium signals inducing LTP can be observed by stimulating either the PF or the ascending fiber pathway. We propose that local dendritic calcium spikes, evoked by synaptic potentials, provide a unique mechanism to spatially decode PF signals into cerebellar circuitry changes

Accurate multi-boson long-time dynamics in triple-well periodic traps

To solve the many-boson Schr\"odinger equation we utilize the Multiconfigurational time-dependent Hartree method for bosons (MCTDHB). To be able to attack larger systems and/or to propagate the solution for longer times, we implement a parallel version of the MCTDHB method thereby realizing the recently proposed [Streltsov {\it et al.} arXiv:0910.2577v1] novel idea how to construct efficiently the result of the action of the Hamiltonian on a bosonic state vector. We study the real-space dynamics of repulsive bosonic systems made of N=12, 51 and 3003 bosons in triple-well periodic potentials. The ground state of this system is three-fold fragmented. By suddenly strongly distorting the trap potential, the system performs complex many-body quantum dynamics. At long times it reveals a tendency to an oscillatory behavior around a threefold fragmented state. These oscillations are strongly suppressed and damped by quantum depletions. In spite of the richness of the observed dynamics, the three time-adaptive orbitals of MCTDHB(M=3) are capable to describe the many-boson quantum dynamics of the system for short and intermediate times. For longer times, however, more self-consistent time-adaptive orbitals are needed to correctly describe the non-equilibrium many-body physics. The convergence of the MCTDHB($M$) method with the number $M$ of self-consistent time-dependent orbitals used is demonstrated.Comment: 37 pages, 7 figure

Delta-subunit-containing GABAA-receptors mediate tonic inhibition in paracapsular cells of the mouse amygdala

The intercalated paracapsular cells (pcs) are small GABAergic interneurons that form densely populated clusters surrounding the basolateral (BLA) complex of the amygdala. Their main task in the amygdala circuitry appears to be the control of information flow, as they act as an inhibitory interface between input and output nuclei. Modulation of their activity is thus thought to affect amygdala output and the generation of fear and anxiety. Recent evidence indicates that pcs express benzodiazepine (BZ)-sensitive GABA(A) receptor (GABA(A)R) variants containing the α2- and α3-subunit for transmission of post-synaptic currents, yet little is known about the expression of extrasynaptic GABA(A)Rs, mediating tonic inhibition and regulating neuronal excitability. Here, we show that pcs from the lateral and medial intercalated cell cluster (l- and mITC, respectively) express a tonic GABAergic conductance that could be significantly increased in a concentration-dependent manner by the δ-preferring GABA(A)R agonist THIP (0.5–10 μM), but not by the BZ diazepam (1 μM). The neurosteroid THDOC (300 nM) also increased tonic currents in pcs significantly, but only in the presence of additional GABA (5 μM). Immunohistochemical stainings revealed that both the δ-GABA(A)R and the α4-GABA(A)R subunit are expressed throughout all ITCs, while no staining for the α5-GABA(A)R subunit could be detected. Moreover, 1 μM THIP dampened excitability in pcs most likely by increasing shunting inhibition. In line with this, THIP significantly decreased lITC-generated inhibition in target cells residing in the BLA nucleus by 30%. Taken together these results demonstrate for the first time that pcs express a tonic inhibitory conductance mediated most likely by α4/δ-containing GABA(A)Rs. This data also suggest that δ-GABA(A)R targeting compounds might possibly interfere with pcs-related neuronal processes such as fear extinction

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